TSTP Solution File: SWV490+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV490+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:17:48 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV490+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 04:02:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 tff(real_one_type, type, (
% 0.20/0.50 real_one: $i)).
% 0.20/0.50 tff(real_zero_type, type, (
% 0.20/0.50 real_zero: $i)).
% 0.20/0.50 tff(a_type, type, (
% 0.20/0.50 a: ( $i * $i ) > $i)).
% 0.20/0.50 tff(tptp_fun_J_1_type, type, (
% 0.20/0.50 tptp_fun_J_1: $i)).
% 0.20/0.50 tff(int_leq_type, type, (
% 0.20/0.50 int_leq: ( $i * $i ) > $o)).
% 0.20/0.50 tff(int_less_type, type, (
% 0.20/0.50 int_less: ( $i * $i ) > $o)).
% 0.20/0.50 tff(int_one_type, type, (
% 0.20/0.50 int_one: $i)).
% 0.20/0.50 tff(tptp_fun_I_2_type, type, (
% 0.20/0.50 tptp_fun_I_2: $i)).
% 0.20/0.50 tff(plus_type, type, (
% 0.20/0.50 plus: ( $i * $i ) > $i)).
% 0.20/0.50 tff(int_zero_type, type, (
% 0.20/0.50 int_zero: $i)).
% 0.20/0.50 tff(n_type, type, (
% 0.20/0.50 n: $i)).
% 0.20/0.50 tff(tptp_fun_K_0_type, type, (
% 0.20/0.50 tptp_fun_K_0: ( $i * $i ) > $i)).
% 0.20/0.50 tff(1,assumption,(~int_leq(J!1, J!1)), introduced(assumption)).
% 0.20/0.50 tff(2,plain,
% 0.20/0.50 (^[I: $i, J: $i] : refl((int_leq(I, J) <=> ((I = J) | int_less(I, J))) <=> (int_leq(I, J) <=> ((I = J) | int_less(I, J))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(3,plain,
% 0.20/0.50 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J))) <=> ![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.50 tff(4,plain,
% 0.20/0.50 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J))) <=> ![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(5,plain,
% 0.20/0.50 (^[I: $i, J: $i] : rewrite((int_leq(I, J) <=> (int_less(I, J) | (I = J))) <=> (int_leq(I, J) <=> ((I = J) | int_less(I, J))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(6,plain,
% 0.20/0.50 (![I: $i, J: $i] : (int_leq(I, J) <=> (int_less(I, J) | (I = J))) <=> ![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.50 tff(7,axiom,(![I: $i, J: $i] : (int_leq(I, J) <=> (int_less(I, J) | (I = J)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','int_leq')).
% 0.20/0.50 tff(8,plain,
% 0.20/0.50 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.50 tff(9,plain,
% 0.20/0.50 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.50 tff(10,plain,(
% 0.20/0.50 ![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[9])).
% 0.20/0.50 tff(11,plain,
% 0.20/0.50 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.50 tff(12,plain,
% 0.20/0.50 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1)) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(13,plain,
% 0.20/0.50 ((int_leq(J!1, J!1) <=> $true) <=> int_leq(J!1, J!1)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(14,plain,
% 0.20/0.50 (($true | int_less(J!1, J!1)) <=> $true),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(15,plain,
% 0.20/0.50 ((J!1 = J!1) <=> $true),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(16,plain,
% 0.20/0.50 (((J!1 = J!1) | int_less(J!1, J!1)) <=> ($true | int_less(J!1, J!1))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[15])).
% 0.20/0.50 tff(17,plain,
% 0.20/0.50 (((J!1 = J!1) | int_less(J!1, J!1)) <=> $true),
% 0.20/0.50 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.50 tff(18,plain,
% 0.20/0.50 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> (int_leq(J!1, J!1) <=> $true)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.50 tff(19,plain,
% 0.20/0.50 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> int_leq(J!1, J!1)),
% 0.20/0.50 inference(transitivity,[status(thm)],[18, 13])).
% 0.20/0.50 tff(20,plain,
% 0.20/0.50 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1)))) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.50 tff(21,plain,
% 0.20/0.50 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1)))) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1))),
% 0.20/0.50 inference(transitivity,[status(thm)],[20, 12])).
% 0.20/0.50 tff(22,plain,
% 0.20/0.50 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.50 tff(24,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[23, 11, 1])).
% 0.20/0.50 tff(25,plain,(int_leq(J!1, J!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(26,plain,
% 0.20/0.50 ((~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))) <=> (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 ((~![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => (((~(I = J)) => (a(I, J) = real_zero)) & ((I = J) => (~(a(I, J) = real_zero)))))) <=> (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(28,axiom,(~![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => (((~(I = J)) => (a(I, J) = real_zero)) & ((I = J) => (~(a(I, J) = real_zero)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','di')).
% 0.20/0.50 tff(29,plain,
% 0.20/0.50 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.50 tff(30,plain,
% 0.20/0.50 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.20/0.50 tff(33,plain,
% 0.20/0.50 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.20/0.50 tff(34,plain,
% 0.20/0.50 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.20/0.50 tff(36,plain,(
% 0.20/0.50 ~((~(int_leq(int_one, I!2) & int_leq(I!2, n) & int_leq(int_one, J!1) & int_leq(J!1, n))) | (((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero)))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[35])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 (int_leq(int_one, I!2) & int_leq(I!2, n) & int_leq(int_one, J!1) & int_leq(J!1, n)),
% 0.20/0.50 inference(or_elim,[status(thm)],[36])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 (int_leq(J!1, n)),
% 0.20/0.50 inference(and_elim,[status(thm)],[37])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 (int_leq(int_one, J!1)),
% 0.20/0.50 inference(and_elim,[status(thm)],[37])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 (int_leq(I!2, n)),
% 0.20/0.50 inference(and_elim,[status(thm)],[37])).
% 0.20/0.50 tff(41,plain,
% 0.20/0.50 (int_leq(int_one, I!2)),
% 0.20/0.50 inference(and_elim,[status(thm)],[37])).
% 0.20/0.50 tff(42,plain,
% 0.20/0.50 (^[I: $i, J: $i] : refl(((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(43,plain,
% 0.20/0.50 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 (^[I: $i, J: $i] : rewrite(((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(45,plain,
% 0.20/0.50 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.50 tff(46,plain,
% 0.20/0.50 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[45, 43])).
% 0.20/0.50 tff(47,plain,
% 0.20/0.50 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) <=> (~((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))))), ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) <=> (~(~((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))))))), rewrite((~(~((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)))), ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))))), trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_less(int_zero, C) & (I = plus(J, C))) <=> (~((~int_less(int_zero, C)) | (~(I = plus(J, C)))))), ((~(int_less(int_zero, C) & (I = plus(J, C)))) <=> (~(~((~int_less(int_zero, C)) | (~(I = plus(J, C)))))))), rewrite((~(~((~int_less(int_zero, C)) | (~(I = plus(J, C)))))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C))))), ((~(int_less(int_zero, C) & (I = plus(J, C)))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C)))))), quant_intro(proof_bind(^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, K) & int_leq(K, J)) <=> (~((~int_leq(int_one, K)) | (~int_leq(K, J))))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> (~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))))), rewrite((~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J)))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero)) <=> (((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(plus(K, C), K) = real_zero)))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(plus(K, C), K) = real_zero)) <=> ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero)) <=> ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero)) <=> ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) <=> (((~int_less(int_zero, C)) | (~(I = plus(J, C)))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), rewrite((((~int_less(int_zero, C)) | (~(I = plus(J, C)))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))))), (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) <=> ![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), quant_intro(proof_bind(^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, K) & int_leq(K, J)) <=> (~((~int_leq(int_one, K)) | (~int_leq(K, J))))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> (~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))))), rewrite((~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J)))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) <=> (((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(K, K) = real_one)))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(K, K) = real_one)) <=> ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) <=> ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) <=> ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_less(int_zero, C) & (J = plus(I, C))) <=> (~((~int_less(int_zero, C)) | (~(J = plus(I, C)))))), ((~(int_less(int_zero, C) & (J = plus(I, C)))) <=> (~(~((~int_less(int_zero, C)) | (~(J = plus(I, C)))))))), rewrite((~(~((~int_less(int_zero, C)) | (~(J = plus(I, C)))))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C))))), ((~(int_less(int_zero, C) & (J = plus(I, C)))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C)))))), quant_intro(proof_bind(^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, K) & int_leq(K, I)) <=> (~((~int_leq(int_one, K)) | (~int_leq(K, I))))), ((~(int_leq(int_one, K) & int_leq(K, I))) <=> (~(~((~int_leq(int_one, K)) | (~int_leq(K, I))))))), rewrite((~(~((~int_leq(int_one, K)) | (~int_leq(K, I))))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, I)))), ((~(int_leq(int_one, K) & int_leq(K, I))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> (((~int_leq(int_one, K)) | (~int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))), (((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> (((~int_less(int_zero, C)) | (~(J = plus(I, C)))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), rewrite((((~int_less(int_zero, C)) | (~(J = plus(I, C)))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))), (![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> ![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))) <=> (![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) & ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J))) & ![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))), rewrite((![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) & ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J))) & ![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))), ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))), (((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> (((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))), rewrite((((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))), (((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(48,plain,
% 0.20/0.51 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.51 tff(49,plain,
% 0.20/0.51 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(50,plain,
% 0.20/0.51 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite(((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) <=> (int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J))), ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) <=> ((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J)) & int_leq(J, n)))), rewrite(((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J)) & int_leq(J, n)) <=> (int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))), ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) <=> (int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)))), trans(monotonicity(rewrite((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[K: $i] : rewrite(((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)) <=> ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), (![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)) <=> ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), (((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))) <=> ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))), rewrite(((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), (((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))) <=> ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), (![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))) <=> ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))), (((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))) <=> ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one))) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), rewrite(((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one))) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))), (((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), (((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))))) <=> ((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) => (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))))), rewrite(((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) => (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), (((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))))) <=> ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(51,plain,
% 0.20/0.51 (![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))))) <=> ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.51 tff(52,axiom,(![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qii')).
% 0.20/0.51 tff(53,plain,
% 0.20/0.51 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.51 tff(54,plain,
% 0.20/0.51 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.51 tff(55,plain,(
% 0.20/0.51 ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[54])).
% 0.20/0.51 tff(56,plain,
% 0.20/0.51 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.51 tff(57,plain,
% 0.20/0.51 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.20/0.51 tff(58,plain,
% 0.20/0.51 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(59,plain,
% 0.20/0.52 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))) <=> ((~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.43/0.52 inference(rewrite,[status(thm)],[])).
% 0.43/0.52 tff(60,plain,
% 0.43/0.52 ((~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))),
% 0.43/0.52 inference(rewrite,[status(thm)],[])).
% 0.43/0.52 tff(61,plain,
% 0.43/0.52 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))) <=> ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.43/0.52 inference(monotonicity,[status(thm)],[60])).
% 0.43/0.52 tff(62,plain,
% 0.43/0.52 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))) <=> ((~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.43/0.52 inference(transitivity,[status(thm)],[61, 59])).
% 0.43/0.52 tff(63,plain,
% 0.43/0.52 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))))),
% 0.43/0.52 inference(monotonicity,[status(thm)],[62])).
% 0.43/0.52 tff(64,plain,
% 0.43/0.52 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.43/0.52 inference(transitivity,[status(thm)],[63, 58])).
% 0.43/0.52 tff(65,plain,
% 0.43/0.52 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.43/0.52 inference(quant_inst,[status(thm)],[])).
% 0.43/0.52 tff(66,plain,
% 0.43/0.52 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))),
% 0.43/0.52 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.43/0.52 tff(67,plain,
% 0.43/0.52 (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))),
% 0.43/0.52 inference(unit_resolution,[status(thm)],[66, 57, 41, 40, 39, 38])).
% 0.43/0.52 tff(68,plain,
% 0.43/0.52 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))) | ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))),
% 0.43/0.52 inference(tautology,[status(thm)],[])).
% 0.43/0.52 tff(69,plain,
% 0.43/0.52 (![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))),
% 0.43/0.52 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.43/0.52 tff(70,plain,
% 0.43/0.52 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | ((~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1)))) <=> ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1)))),
% 0.43/0.52 inference(rewrite,[status(thm)],[])).
% 0.43/0.52 tff(71,plain,
% 0.43/0.52 (((a(J!1, J!1) = real_one) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1))) <=> ((~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1)))),
% 0.43/0.52 inference(rewrite,[status(thm)],[])).
% 0.43/0.52 tff(72,plain,
% 0.43/0.52 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | ((a(J!1, J!1) = real_one) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)))) <=> ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | ((~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1))))),
% 0.43/0.52 inference(monotonicity,[status(thm)],[71])).
% 0.43/0.52 tff(73,plain,
% 0.43/0.52 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | ((a(J!1, J!1) = real_one) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)))) <=> ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1)))),
% 0.43/0.52 inference(transitivity,[status(thm)],[72, 70])).
% 0.43/0.52 tff(74,plain,
% 0.43/0.52 ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | ((a(J!1, J!1) = real_one) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)))),
% 0.43/0.52 inference(quant_inst,[status(thm)],[])).
% 0.43/0.52 tff(75,plain,
% 0.43/0.52 ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1))),
% 0.43/0.52 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.43/0.52 tff(76,plain,
% 0.43/0.52 ((a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1))),
% 0.43/0.52 inference(unit_resolution,[status(thm)],[75, 39, 69])).
% 0.43/0.52 tff(77,plain,
% 0.43/0.52 (a(J!1, J!1) = real_one),
% 0.43/0.52 inference(unit_resolution,[status(thm)],[76, 25])).
% 0.43/0.52 tff(78,plain,
% 0.43/0.52 (^[I: $i, J: $i] : refl((~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))))))),
% 0.43/0.52 inference(bind,[status(th)],[])).
% 0.43/0.52 tff(79,plain,
% 0.43/0.52 (![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))))) <=> ![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))),
% 0.43/0.53 inference(quant_intro,[status(thm)],[78])).
% 0.43/0.53 tff(80,plain,
% 0.43/0.53 (^[I: $i, J: $i] : rewrite((~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))))))),
% 0.43/0.53 inference(bind,[status(th)],[])).
% 0.43/0.53 tff(81,plain,
% 0.43/0.53 (![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))))) <=> ![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))),
% 0.43/0.53 inference(quant_intro,[status(thm)],[80])).
% 0.43/0.53 tff(82,plain,
% 0.43/0.53 (![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))))) <=> ![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))),
% 0.43/0.53 inference(transitivity,[status(thm)],[81, 79])).
% 0.43/0.53 tff(83,plain,
% 0.43/0.53 (^[I: $i, J: $i] : trans(monotonicity(rewrite(((~int_less(I, J)) | ((plus(I, tptp_fun_K_0(J, I)) = J) & int_less(int_zero, tptp_fun_K_0(J, I)))) <=> ((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))), rewrite((int_less(I, J) | ![K: $i] : (~((plus(I, K) = J) & int_less(int_zero, K)))) <=> (int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))), ((((~int_less(I, J)) | ((plus(I, tptp_fun_K_0(J, I)) = J) & int_less(int_zero, tptp_fun_K_0(J, I)))) & (int_less(I, J) | ![K: $i] : (~((plus(I, K) = J) & int_less(int_zero, K))))) <=> (((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I)))))) & (int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))))), rewrite((((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I)))))) & (int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))) <=> (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))), ((((~int_less(I, J)) | ((plus(I, tptp_fun_K_0(J, I)) = J) & int_less(int_zero, tptp_fun_K_0(J, I)))) & (int_less(I, J) | ![K: $i] : (~((plus(I, K) = J) & int_less(int_zero, K))))) <=> (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))))),
% 0.43/0.53 inference(bind,[status(th)],[])).
% 0.43/0.53 tff(84,plain,
% 0.43/0.53 (![I: $i, J: $i] : (((~int_less(I, J)) | ((plus(I, tptp_fun_K_0(J, I)) = J) & int_less(int_zero, tptp_fun_K_0(J, I)))) & (int_less(I, J) | ![K: $i] : (~((plus(I, K) = J) & int_less(int_zero, K))))) <=> ![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))),
% 0.43/0.53 inference(quant_intro,[status(thm)],[83])).
% 0.43/0.53 tff(85,plain,
% 0.43/0.53 (![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K))) <=> ![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(86,axiom,(![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus_and_inverse')).
% 0.43/0.53 tff(87,plain,
% 0.43/0.53 (![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.43/0.53 tff(88,plain,(
% 0.43/0.53 ![I: $i, J: $i] : (((~int_less(I, J)) | ((plus(I, tptp_fun_K_0(J, I)) = J) & int_less(int_zero, tptp_fun_K_0(J, I)))) & (int_less(I, J) | ![K: $i] : (~((plus(I, K) = J) & int_less(int_zero, K)))))),
% 0.43/0.53 inference(skolemize,[status(sab)],[87])).
% 0.43/0.53 tff(89,plain,
% 0.43/0.53 (![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.43/0.53 tff(90,plain,
% 0.43/0.53 (![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.43/0.53 tff(91,plain,
% 0.43/0.53 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(92,plain,
% 0.43/0.53 ((~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(93,plain,
% 0.43/0.53 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))))),
% 0.43/0.53 inference(monotonicity,[status(thm)],[92])).
% 0.43/0.53 tff(94,plain,
% 0.43/0.53 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))))),
% 0.43/0.53 inference(transitivity,[status(thm)],[93, 91])).
% 0.43/0.53 tff(95,plain,
% 0.43/0.53 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K)))))))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(96,plain,
% 0.43/0.53 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.43/0.53 tff(97,plain,
% 0.43/0.53 (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[96, 90])).
% 0.43/0.53 tff(98,plain,
% 0.43/0.53 (((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))) | ((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))),
% 0.43/0.53 inference(tautology,[status(thm)],[])).
% 0.43/0.53 tff(99,plain,
% 0.43/0.53 ((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1)))))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.43/0.53 tff(100,plain,
% 0.43/0.53 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(J!1, I!2) <=> ((J!1 = I!2) | int_less(J!1, I!2)))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(101,plain,
% 0.43/0.53 (int_leq(J!1, I!2) <=> ((J!1 = I!2) | int_less(J!1, I!2))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[100, 11])).
% 0.43/0.53 tff(102,assumption,(~(a(I!2, J!1) = real_zero)), introduced(assumption)).
% 0.43/0.53 tff(103,assumption,(~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))), introduced(assumption)).
% 0.43/0.53 tff(104,plain,
% 0.43/0.53 (((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2)))) | (plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)),
% 0.43/0.53 inference(tautology,[status(thm)],[])).
% 0.43/0.53 tff(105,plain,
% 0.43/0.53 (plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.43/0.53 tff(106,plain,
% 0.43/0.53 (J!1 = plus(I!2, tptp_fun_K_0(J!1, I!2))),
% 0.43/0.53 inference(symmetry,[status(thm)],[105])).
% 0.43/0.53 tff(107,plain,
% 0.43/0.53 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1))))))))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(108,plain,
% 0.43/0.53 ((~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~(plus(int_zero, K) = J!1)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1)))))))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(109,plain,
% 0.43/0.53 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~(plus(int_zero, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1))))))))),
% 0.43/0.53 inference(monotonicity,[status(thm)],[108])).
% 0.43/0.53 tff(110,plain,
% 0.43/0.53 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~(plus(int_zero, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1))))))))),
% 0.43/0.53 inference(transitivity,[status(thm)],[109, 107])).
% 0.43/0.53 tff(111,plain,
% 0.43/0.53 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~(plus(int_zero, K) = J!1)) | (~int_less(int_zero, K)))))))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(112,plain,
% 0.43/0.53 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1)))))))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.43/0.53 tff(113,plain,
% 0.43/0.53 (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1))))))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[112, 90])).
% 0.43/0.53 tff(114,plain,
% 0.43/0.53 (((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1)))))) | ((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))),
% 0.43/0.53 inference(tautology,[status(thm)],[])).
% 0.43/0.53 tff(115,plain,
% 0.43/0.53 ((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero)))))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.43/0.53 tff(116,plain,
% 0.43/0.53 (^[I: $i] : refl((int_less(int_zero, I) <=> int_leq(int_one, I)) <=> (int_less(int_zero, I) <=> int_leq(int_one, I)))),
% 0.43/0.53 inference(bind,[status(th)],[])).
% 0.43/0.53 tff(117,plain,
% 0.43/0.53 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.43/0.53 inference(quant_intro,[status(thm)],[116])).
% 0.43/0.53 tff(118,plain,
% 0.43/0.53 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(119,axiom,(![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','one_successor_of_zero')).
% 0.43/0.53 tff(120,plain,
% 0.43/0.53 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.43/0.53 tff(121,plain,(
% 0.43/0.53 ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.43/0.53 inference(skolemize,[status(sab)],[120])).
% 0.43/0.53 tff(122,plain,
% 0.43/0.53 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.43/0.53 tff(123,plain,
% 0.43/0.53 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, J!1) <=> int_leq(int_one, J!1))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(124,plain,
% 0.43/0.53 (int_less(int_zero, J!1) <=> int_leq(int_one, J!1)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.43/0.53 tff(125,plain,
% 0.43/0.53 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1) | (~int_leq(int_one, J!1))),
% 0.43/0.53 inference(tautology,[status(thm)],[])).
% 0.43/0.53 tff(126,plain,
% 0.43/0.53 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[125, 39])).
% 0.43/0.53 tff(127,plain,
% 0.43/0.53 (int_less(int_zero, J!1)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[126, 124])).
% 0.43/0.53 tff(128,plain,
% 0.43/0.53 ((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero)))))),
% 0.43/0.53 inference(tautology,[status(thm)],[])).
% 0.43/0.53 tff(129,plain,
% 0.43/0.53 ((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero)))))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.43/0.53 tff(130,plain,
% 0.43/0.53 (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[129, 115])).
% 0.43/0.53 tff(131,plain,
% 0.43/0.54 (((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero)))) | (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)),
% 0.43/0.54 inference(tautology,[status(thm)],[])).
% 0.43/0.54 tff(132,plain,
% 0.43/0.54 (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.43/0.54 tff(133,plain,
% 0.43/0.54 (^[I: $i, J: $i] : refl((plus(I, J) = plus(J, I)) <=> (plus(I, J) = plus(J, I)))),
% 0.43/0.54 inference(bind,[status(th)],[])).
% 0.43/0.54 tff(134,plain,
% 0.43/0.54 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.43/0.54 inference(quant_intro,[status(thm)],[133])).
% 0.43/0.54 tff(135,plain,
% 0.43/0.54 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(136,axiom,(![I: $i, J: $i] : (plus(I, J) = plus(J, I))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus_commutative')).
% 0.43/0.54 tff(137,plain,
% 0.43/0.54 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.43/0.54 tff(138,plain,(
% 0.43/0.54 ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.43/0.54 inference(skolemize,[status(sab)],[137])).
% 0.43/0.54 tff(139,plain,
% 0.43/0.54 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.43/0.54 tff(140,plain,
% 0.43/0.54 ((~![I: $i, J: $i] : (plus(I, J) = plus(J, I))) | (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = plus(tptp_fun_K_0(J!1, int_zero), int_zero))),
% 0.43/0.54 inference(quant_inst,[status(thm)],[])).
% 0.43/0.54 tff(141,plain,
% 0.43/0.54 (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = plus(tptp_fun_K_0(J!1, int_zero), int_zero)),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.43/0.54 tff(142,plain,
% 0.43/0.54 (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = plus(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.43/0.54 inference(symmetry,[status(thm)],[141])).
% 0.43/0.54 tff(143,plain,
% 0.43/0.54 (^[I: $i] : refl((plus(I, int_zero) = I) <=> (plus(I, int_zero) = I))),
% 0.43/0.54 inference(bind,[status(th)],[])).
% 0.43/0.54 tff(144,plain,
% 0.43/0.54 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.43/0.54 inference(quant_intro,[status(thm)],[143])).
% 0.43/0.54 tff(145,plain,
% 0.43/0.54 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(146,axiom,(![I: $i] : (plus(I, int_zero) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus_zero')).
% 0.43/0.54 tff(147,plain,
% 0.43/0.54 (![I: $i] : (plus(I, int_zero) = I)),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.43/0.54 tff(148,plain,(
% 0.43/0.54 ![I: $i] : (plus(I, int_zero) = I)),
% 0.43/0.54 inference(skolemize,[status(sab)],[147])).
% 0.43/0.54 tff(149,plain,
% 0.43/0.54 (![I: $i] : (plus(I, int_zero) = I)),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.43/0.54 tff(150,plain,
% 0.43/0.54 ((~![I: $i] : (plus(I, int_zero) = I)) | (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = tptp_fun_K_0(J!1, int_zero))),
% 0.43/0.54 inference(quant_inst,[status(thm)],[])).
% 0.43/0.54 tff(151,plain,
% 0.43/0.54 (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = tptp_fun_K_0(J!1, int_zero)),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.43/0.54 tff(152,plain,
% 0.43/0.54 (tptp_fun_K_0(J!1, int_zero) = plus(tptp_fun_K_0(J!1, int_zero), int_zero)),
% 0.43/0.54 inference(symmetry,[status(thm)],[151])).
% 0.43/0.54 tff(153,plain,
% 0.43/0.54 (tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2))),
% 0.43/0.54 inference(transitivity,[status(thm)],[152, 142, 132, 106])).
% 0.43/0.54 tff(154,plain,
% 0.43/0.54 (((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2)))) | int_less(int_zero, tptp_fun_K_0(J!1, I!2))),
% 0.43/0.54 inference(tautology,[status(thm)],[])).
% 0.43/0.54 tff(155,plain,
% 0.43/0.54 (int_less(int_zero, tptp_fun_K_0(J!1, I!2))),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[154, 103])).
% 0.43/0.54 tff(156,plain,
% 0.43/0.54 (tptp_fun_K_0(J!1, int_zero) = J!1),
% 0.43/0.54 inference(transitivity,[status(thm)],[152, 142, 132])).
% 0.43/0.54 tff(157,plain,
% 0.43/0.54 (int_leq(tptp_fun_K_0(J!1, int_zero), n) <=> int_leq(J!1, n)),
% 0.43/0.54 inference(monotonicity,[status(thm)],[156])).
% 0.43/0.54 tff(158,plain,
% 0.43/0.54 (int_leq(J!1, n) <=> int_leq(tptp_fun_K_0(J!1, int_zero), n)),
% 0.43/0.54 inference(symmetry,[status(thm)],[157])).
% 0.43/0.54 tff(159,plain,
% 0.43/0.54 (int_leq(tptp_fun_K_0(J!1, int_zero), n)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[38, 158])).
% 0.45/0.54 tff(160,plain,
% 0.45/0.54 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero)))),
% 0.45/0.54 inference(quant_inst,[status(thm)],[])).
% 0.45/0.54 tff(161,plain,
% 0.45/0.54 (int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[160, 122])).
% 0.45/0.54 tff(162,plain,
% 0.45/0.54 (((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero)))) | int_less(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.45/0.54 inference(tautology,[status(thm)],[])).
% 0.45/0.54 tff(163,plain,
% 0.45/0.54 (int_less(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[162, 130])).
% 0.45/0.54 tff(164,plain,
% 0.45/0.54 ((~(int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero)))) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.45/0.54 inference(tautology,[status(thm)],[])).
% 0.45/0.54 tff(165,plain,
% 0.45/0.54 ((~(int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero)))) | int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.45/0.54 tff(166,plain,
% 0.45/0.54 (int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[165, 161])).
% 0.45/0.54 tff(167,plain,
% 0.45/0.54 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(168,plain,
% 0.45/0.54 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))) <=> ((~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(169,plain,
% 0.45/0.54 ((~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))) <=> (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(170,plain,
% 0.45/0.54 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))) <=> ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.45/0.54 inference(monotonicity,[status(thm)],[169])).
% 0.45/0.54 tff(171,plain,
% 0.45/0.54 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))) <=> ((~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.45/0.54 inference(transitivity,[status(thm)],[170, 168])).
% 0.45/0.54 tff(172,plain,
% 0.45/0.54 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))))),
% 0.45/0.54 inference(monotonicity,[status(thm)],[171])).
% 0.45/0.54 tff(173,plain,
% 0.45/0.54 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.45/0.54 inference(transitivity,[status(thm)],[172, 167])).
% 0.45/0.54 tff(174,plain,
% 0.45/0.54 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.45/0.54 inference(quant_inst,[status(thm)],[])).
% 0.45/0.54 tff(175,plain,
% 0.45/0.54 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(I!2, n)) | (~int_leq(int_one, I!2)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.45/0.54 tff(176,plain,
% 0.45/0.54 ((~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[175, 57, 41, 40, 166])).
% 0.45/0.55 tff(177,plain,
% 0.45/0.55 (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[176, 159])).
% 0.45/0.55 tff(178,plain,
% 0.45/0.55 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))) | ![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))),
% 0.45/0.55 inference(tautology,[status(thm)],[])).
% 0.45/0.55 tff(179,plain,
% 0.45/0.55 (![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.45/0.55 tff(180,plain,
% 0.45/0.55 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero)))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero)))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(181,plain,
% 0.45/0.55 (((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))) <=> ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero)))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(182,plain,
% 0.45/0.55 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[181])).
% 0.45/0.55 tff(183,plain,
% 0.45/0.55 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero)))),
% 0.45/0.55 inference(transitivity,[status(thm)],[182, 180])).
% 0.45/0.55 tff(184,plain,
% 0.45/0.55 ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(185,plain,
% 0.45/0.55 ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.45/0.55 tff(186,plain,
% 0.45/0.55 (![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[185, 179, 155, 153])).
% 0.45/0.55 tff(187,assumption,(~int_leq(I!2, I!2)), introduced(assumption)).
% 0.45/0.55 tff(188,plain,
% 0.45/0.55 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2)) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(189,plain,
% 0.45/0.55 ((int_leq(I!2, I!2) <=> $true) <=> int_leq(I!2, I!2)),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(190,plain,
% 0.45/0.55 (($true | int_less(I!2, I!2)) <=> $true),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(191,plain,
% 0.45/0.55 ((I!2 = I!2) <=> $true),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(192,plain,
% 0.45/0.55 (((I!2 = I!2) | int_less(I!2, I!2)) <=> ($true | int_less(I!2, I!2))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[191])).
% 0.45/0.55 tff(193,plain,
% 0.45/0.55 (((I!2 = I!2) | int_less(I!2, I!2)) <=> $true),
% 0.45/0.55 inference(transitivity,[status(thm)],[192, 190])).
% 0.45/0.55 tff(194,plain,
% 0.45/0.55 ((int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2))) <=> (int_leq(I!2, I!2) <=> $true)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[193])).
% 0.45/0.55 tff(195,plain,
% 0.45/0.55 ((int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2))) <=> int_leq(I!2, I!2)),
% 0.45/0.55 inference(transitivity,[status(thm)],[194, 189])).
% 0.45/0.55 tff(196,plain,
% 0.45/0.55 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2)))) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[195])).
% 0.45/0.55 tff(197,plain,
% 0.45/0.55 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2)))) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2))),
% 0.45/0.55 inference(transitivity,[status(thm)],[196, 188])).
% 0.45/0.55 tff(198,plain,
% 0.45/0.55 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2)))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(199,plain,
% 0.45/0.55 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.45/0.55 tff(200,plain,
% 0.45/0.55 ($false),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[199, 11, 187])).
% 0.45/0.55 tff(201,plain,(int_leq(I!2, I!2)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.55 tff(202,plain,
% 0.45/0.55 (((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero))) <=> ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(203,plain,
% 0.45/0.55 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(204,plain,
% 0.45/0.55 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.45/0.55 tff(205,plain,
% 0.45/0.55 (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[204, 41, 201, 186])).
% 0.45/0.55 tff(206,plain,
% 0.45/0.55 (a(I!2, J!1) = a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2)))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[106])).
% 0.45/0.55 tff(207,plain,
% 0.45/0.55 (a(I!2, J!1) = real_zero),
% 0.45/0.55 inference(transitivity,[status(thm)],[206, 205])).
% 0.45/0.55 tff(208,plain,
% 0.45/0.55 ($false),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[102, 207])).
% 0.45/0.55 tff(209,plain,(((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2)))) | (a(I!2, J!1) = real_zero)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.55 tff(210,plain,
% 0.45/0.55 ((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2)))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[209, 102])).
% 0.45/0.55 tff(211,assumption,((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2)))))))), introduced(assumption)).
% 0.45/0.55 tff(212,plain,
% 0.45/0.55 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2)))))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(213,plain,
% 0.45/0.55 ((~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K))))))) <=> (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2)))))))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(214,plain,
% 0.45/0.55 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))))))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[213])).
% 0.45/0.55 tff(215,plain,
% 0.45/0.55 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))))))),
% 0.45/0.55 inference(transitivity,[status(thm)],[214, 212])).
% 0.45/0.55 tff(216,plain,
% 0.45/0.55 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K)))))))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(217,plain,
% 0.45/0.55 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2)))))))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.45/0.55 tff(218,plain,
% 0.45/0.55 ($false),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[217, 90, 211])).
% 0.45/0.55 tff(219,plain,(~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.55 tff(220,plain,
% 0.45/0.55 (((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2)))))))) | ((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))),
% 0.45/0.55 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(221,plain,
% 0.45/0.56 ((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2)))))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.45/0.56 tff(222,plain,
% 0.45/0.56 ((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2)))))),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(223,plain,
% 0.45/0.56 ((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2)))))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.45/0.56 tff(224,plain,
% 0.45/0.56 (~int_less(I!2, J!1)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[223, 210])).
% 0.45/0.56 tff(225,assumption,(~int_less(I!2, J!1)), introduced(assumption)).
% 0.45/0.56 tff(226,assumption,(~int_leq(J!1, I!2)), introduced(assumption)).
% 0.45/0.56 tff(227,plain,
% 0.45/0.56 (^[I: $i, J: $i] : refl((int_leq(J, I) | int_less(I, J)) <=> (int_leq(J, I) | int_less(I, J)))),
% 0.45/0.56 inference(bind,[status(th)],[])).
% 0.45/0.56 tff(228,plain,
% 0.45/0.56 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.56 inference(quant_intro,[status(thm)],[227])).
% 0.45/0.56 tff(229,plain,
% 0.45/0.56 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(230,plain,
% 0.45/0.56 (^[I: $i, J: $i] : rewrite((int_less(I, J) | int_leq(J, I)) <=> (int_leq(J, I) | int_less(I, J)))),
% 0.45/0.56 inference(bind,[status(th)],[])).
% 0.45/0.56 tff(231,plain,
% 0.45/0.56 (![I: $i, J: $i] : (int_less(I, J) | int_leq(J, I)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.56 inference(quant_intro,[status(thm)],[230])).
% 0.45/0.56 tff(232,axiom,(![I: $i, J: $i] : (int_less(I, J) | int_leq(J, I))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','int_less_total')).
% 0.45/0.56 tff(233,plain,
% 0.45/0.56 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.45/0.56 tff(234,plain,
% 0.45/0.56 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[233, 229])).
% 0.45/0.56 tff(235,plain,(
% 0.45/0.56 ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.56 inference(skolemize,[status(sab)],[234])).
% 0.45/0.56 tff(236,plain,
% 0.45/0.56 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[235, 228])).
% 0.45/0.56 tff(237,plain,
% 0.45/0.56 (((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | (int_leq(J!1, I!2) | int_less(I!2, J!1))) <=> ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | int_leq(J!1, I!2) | int_less(I!2, J!1))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(238,plain,
% 0.45/0.56 ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | (int_leq(J!1, I!2) | int_less(I!2, J!1))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(239,plain,
% 0.45/0.56 ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | int_leq(J!1, I!2) | int_less(I!2, J!1)),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.45/0.56 tff(240,plain,
% 0.45/0.56 ($false),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[239, 236, 226, 225])).
% 0.45/0.56 tff(241,plain,(int_leq(J!1, I!2) | int_less(I!2, J!1)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.56 tff(242,plain,
% 0.45/0.56 (int_leq(J!1, I!2)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[241, 224])).
% 0.45/0.56 tff(243,plain,
% 0.45/0.56 ((~(int_leq(J!1, I!2) <=> ((J!1 = I!2) | int_less(J!1, I!2)))) | (~int_leq(J!1, I!2)) | ((J!1 = I!2) | int_less(J!1, I!2))),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(244,plain,
% 0.45/0.56 ((~(int_leq(J!1, I!2) <=> ((J!1 = I!2) | int_less(J!1, I!2)))) | ((J!1 = I!2) | int_less(J!1, I!2))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.45/0.56 tff(245,plain,
% 0.45/0.56 ((J!1 = I!2) | int_less(J!1, I!2)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[244, 101])).
% 0.45/0.56 tff(246,plain,
% 0.45/0.56 ((J!1 = I!2) <=> (I!2 = J!1)),
% 0.45/0.56 inference(commutativity,[status(thm)],[])).
% 0.45/0.56 tff(247,plain,
% 0.45/0.56 ((I!2 = J!1) <=> (J!1 = I!2)),
% 0.45/0.56 inference(symmetry,[status(thm)],[246])).
% 0.45/0.56 tff(248,plain,
% 0.45/0.56 ((~(I!2 = J!1)) <=> (~(J!1 = I!2))),
% 0.45/0.56 inference(monotonicity,[status(thm)],[247])).
% 0.45/0.56 tff(249,plain,
% 0.45/0.56 (((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))) | (a(I!2, J!1) = real_zero)),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(250,plain,
% 0.45/0.56 ((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[249, 102])).
% 0.45/0.56 tff(251,plain,
% 0.45/0.56 ((~(~((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))))))) <=> ((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero)))))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(252,plain,
% 0.45/0.56 ((((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero)))) <=> (~((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))))))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(253,plain,
% 0.45/0.56 ((~(((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))))) <=> (~(~((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero)))))))),
% 0.45/0.56 inference(monotonicity,[status(thm)],[252])).
% 0.45/0.56 tff(254,plain,
% 0.45/0.56 ((~(((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))))) <=> ((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero)))))),
% 0.45/0.56 inference(transitivity,[status(thm)],[253, 251])).
% 0.45/0.56 tff(255,plain,
% 0.45/0.56 (~(((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))))),
% 0.45/0.56 inference(or_elim,[status(thm)],[36])).
% 0.45/0.56 tff(256,plain,
% 0.45/0.56 ((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.45/0.56 tff(257,plain,
% 0.45/0.56 (~((I!2 = J!1) | (a(I!2, J!1) = real_zero))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[256, 250])).
% 0.45/0.56 tff(258,plain,
% 0.45/0.56 (((I!2 = J!1) | (a(I!2, J!1) = real_zero)) | (~(I!2 = J!1))),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(259,plain,
% 0.45/0.56 (~(I!2 = J!1)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.45/0.56 tff(260,plain,
% 0.45/0.56 (~(J!1 = I!2)),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[259, 248])).
% 0.45/0.56 tff(261,plain,
% 0.45/0.56 ((~((J!1 = I!2) | int_less(J!1, I!2))) | (J!1 = I!2) | int_less(J!1, I!2)),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(262,plain,
% 0.45/0.56 (int_less(J!1, I!2)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[261, 260, 245])).
% 0.45/0.56 tff(263,plain,
% 0.45/0.56 ((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1)))))),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(264,plain,
% 0.45/0.56 ((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1)))))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.45/0.56 tff(265,plain,
% 0.45/0.56 (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[264, 99])).
% 0.45/0.56 tff(266,plain,
% 0.45/0.56 (((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1)))) | (plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(267,plain,
% 0.45/0.56 (plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[266, 265])).
% 0.45/0.56 tff(268,plain,
% 0.45/0.56 (I!2 = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.45/0.56 inference(symmetry,[status(thm)],[267])).
% 0.45/0.56 tff(269,plain,
% 0.45/0.56 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2))))))))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(270,plain,
% 0.45/0.56 ((~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~(plus(int_zero, K) = I!2)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2)))))))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(271,plain,
% 0.45/0.56 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~(plus(int_zero, K) = I!2)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2))))))))),
% 0.45/0.56 inference(monotonicity,[status(thm)],[270])).
% 0.45/0.56 tff(272,plain,
% 0.45/0.56 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~(plus(int_zero, K) = I!2)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2))))))))),
% 0.45/0.56 inference(transitivity,[status(thm)],[271, 269])).
% 0.45/0.56 tff(273,plain,
% 0.45/0.56 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~(plus(int_zero, K) = I!2)) | (~int_less(int_zero, K)))))))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(274,plain,
% 0.45/0.56 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2)))))))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.45/0.56 tff(275,plain,
% 0.45/0.56 (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2))))))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[274, 90])).
% 0.45/0.56 tff(276,plain,
% 0.45/0.56 (((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2)))))) | ((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(277,plain,
% 0.45/0.56 ((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero)))))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[276, 275])).
% 0.45/0.56 tff(278,plain,
% 0.45/0.56 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, I!2) <=> int_leq(int_one, I!2))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(279,plain,
% 0.45/0.56 (int_less(int_zero, I!2) <=> int_leq(int_one, I!2)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[278, 122])).
% 0.45/0.56 tff(280,plain,
% 0.45/0.56 ((~(int_less(int_zero, I!2) <=> int_leq(int_one, I!2))) | int_less(int_zero, I!2) | (~int_leq(int_one, I!2))),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(281,plain,
% 0.45/0.56 ((~(int_less(int_zero, I!2) <=> int_leq(int_one, I!2))) | int_less(int_zero, I!2)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[280, 41])).
% 0.45/0.56 tff(282,plain,
% 0.45/0.56 (int_less(int_zero, I!2)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[281, 279])).
% 0.45/0.56 tff(283,plain,
% 0.45/0.56 ((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero)))))),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(284,plain,
% 0.45/0.56 ((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero)))))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.45/0.56 tff(285,plain,
% 0.45/0.56 (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[284, 277])).
% 0.45/0.56 tff(286,plain,
% 0.45/0.56 (((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero)))) | (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(287,plain,
% 0.45/0.56 (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[286, 285])).
% 0.45/0.56 tff(288,plain,
% 0.45/0.56 ((~![I: $i, J: $i] : (plus(I, J) = plus(J, I))) | (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = plus(tptp_fun_K_0(I!2, int_zero), int_zero))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(289,plain,
% 0.45/0.56 (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = plus(tptp_fun_K_0(I!2, int_zero), int_zero)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[288, 139])).
% 0.45/0.56 tff(290,plain,
% 0.45/0.56 (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = plus(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.45/0.56 inference(symmetry,[status(thm)],[289])).
% 0.45/0.56 tff(291,plain,
% 0.45/0.56 ((~![I: $i] : (plus(I, int_zero) = I)) | (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = tptp_fun_K_0(I!2, int_zero))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(292,plain,
% 0.45/0.56 (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = tptp_fun_K_0(I!2, int_zero)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[291, 149])).
% 0.45/0.56 tff(293,plain,
% 0.45/0.56 (tptp_fun_K_0(I!2, int_zero) = plus(tptp_fun_K_0(I!2, int_zero), int_zero)),
% 0.45/0.56 inference(symmetry,[status(thm)],[292])).
% 0.45/0.56 tff(294,plain,
% 0.45/0.56 (tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.45/0.56 inference(transitivity,[status(thm)],[293, 290, 287, 268])).
% 0.45/0.56 tff(295,plain,
% 0.45/0.56 (((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1)))) | int_less(int_zero, tptp_fun_K_0(I!2, J!1))),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(296,plain,
% 0.45/0.56 (int_less(int_zero, tptp_fun_K_0(I!2, J!1))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[295, 265])).
% 0.45/0.56 tff(297,plain,
% 0.45/0.56 (tptp_fun_K_0(I!2, int_zero) = I!2),
% 0.45/0.56 inference(transitivity,[status(thm)],[293, 290, 287])).
% 0.45/0.56 tff(298,plain,
% 0.45/0.56 (int_leq(tptp_fun_K_0(I!2, int_zero), n) <=> int_leq(I!2, n)),
% 0.45/0.56 inference(monotonicity,[status(thm)],[297])).
% 0.45/0.56 tff(299,plain,
% 0.45/0.56 (int_leq(I!2, n) <=> int_leq(tptp_fun_K_0(I!2, int_zero), n)),
% 0.45/0.56 inference(symmetry,[status(thm)],[298])).
% 0.45/0.56 tff(300,plain,
% 0.45/0.56 (int_leq(tptp_fun_K_0(I!2, int_zero), n)),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[40, 299])).
% 0.45/0.56 tff(301,plain,
% 0.45/0.56 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, tptp_fun_K_0(I!2, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(I!2, int_zero)))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(302,plain,
% 0.45/0.56 (int_less(int_zero, tptp_fun_K_0(I!2, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[301, 122])).
% 0.45/0.56 tff(303,plain,
% 0.45/0.56 (((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero)))) | int_less(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(304,plain,
% 0.45/0.56 (int_less(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[303, 285])).
% 0.45/0.56 tff(305,plain,
% 0.45/0.56 ((~(int_less(int_zero, tptp_fun_K_0(I!2, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(I!2, int_zero)))) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(306,plain,
% 0.45/0.56 ((~(int_less(int_zero, tptp_fun_K_0(I!2, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(I!2, int_zero)))) | int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[305, 304])).
% 0.45/0.56 tff(307,plain,
% 0.45/0.56 (int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[306, 302])).
% 0.45/0.56 tff(308,plain,
% 0.45/0.56 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.45/0.57 inference(rewrite,[status(thm)],[])).
% 0.45/0.57 tff(309,plain,
% 0.45/0.57 (((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))) <=> ((~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.45/0.57 inference(rewrite,[status(thm)],[])).
% 0.45/0.57 tff(310,plain,
% 0.45/0.57 ((~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))) <=> (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))),
% 0.45/0.57 inference(rewrite,[status(thm)],[])).
% 0.45/0.57 tff(311,plain,
% 0.45/0.57 (((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))) <=> ((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.45/0.57 inference(monotonicity,[status(thm)],[310])).
% 0.45/0.57 tff(312,plain,
% 0.45/0.57 (((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))) <=> ((~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.45/0.57 inference(transitivity,[status(thm)],[311, 309])).
% 0.45/0.57 tff(313,plain,
% 0.45/0.57 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))))),
% 0.45/0.57 inference(monotonicity,[status(thm)],[312])).
% 0.45/0.57 tff(314,plain,
% 0.45/0.57 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.45/0.57 inference(transitivity,[status(thm)],[313, 308])).
% 0.45/0.57 tff(315,plain,
% 0.45/0.57 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.45/0.57 inference(quant_inst,[status(thm)],[])).
% 0.45/0.57 tff(316,plain,
% 0.45/0.57 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))),
% 0.45/0.57 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.45/0.57 tff(317,plain,
% 0.45/0.57 ((~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))),
% 0.45/0.57 inference(unit_resolution,[status(thm)],[316, 57, 39, 38, 307])).
% 0.45/0.57 tff(318,plain,
% 0.45/0.57 (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))),
% 0.45/0.57 inference(unit_resolution,[status(thm)],[317, 300])).
% 0.45/0.57 tff(319,plain,
% 0.45/0.57 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))) | ![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))),
% 0.45/0.57 inference(tautology,[status(thm)],[])).
% 0.45/0.57 tff(320,plain,
% 0.45/0.57 (![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))),
% 0.45/0.57 inference(unit_resolution,[status(thm)],[319, 318])).
% 0.45/0.57 tff(321,plain,
% 0.45/0.57 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero)))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero)))),
% 0.45/0.57 inference(rewrite,[status(thm)],[])).
% 0.45/0.57 tff(322,plain,
% 0.45/0.57 (((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) <=> ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero)))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(323,plain,
% 0.45/0.58 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))))),
% 0.45/0.58 inference(monotonicity,[status(thm)],[322])).
% 0.45/0.58 tff(324,plain,
% 0.45/0.58 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero)))),
% 0.45/0.58 inference(transitivity,[status(thm)],[323, 321])).
% 0.45/0.58 tff(325,plain,
% 0.45/0.58 ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))),
% 0.45/0.58 inference(quant_inst,[status(thm)],[])).
% 0.45/0.58 tff(326,plain,
% 0.45/0.58 ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))),
% 0.45/0.58 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.45/0.58 tff(327,plain,
% 0.45/0.58 (![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))),
% 0.45/0.58 inference(unit_resolution,[status(thm)],[326, 320, 296, 294])).
% 0.45/0.58 tff(328,plain,
% 0.45/0.58 (((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))) | ((~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero))) <=> ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(329,plain,
% 0.45/0.58 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))) | ((~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero))),
% 0.45/0.58 inference(quant_inst,[status(thm)],[])).
% 0.45/0.58 tff(330,plain,
% 0.45/0.58 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero)),
% 0.45/0.58 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.45/0.58 tff(331,plain,
% 0.45/0.58 (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero),
% 0.45/0.58 inference(unit_resolution,[status(thm)],[330, 39, 25, 327])).
% 0.45/0.58 tff(332,plain,
% 0.45/0.58 (a(I!2, J!1) = a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1)),
% 0.45/0.58 inference(monotonicity,[status(thm)],[268])).
% 0.45/0.58 tff(333,plain,
% 0.45/0.58 (a(I!2, J!1) = real_zero),
% 0.45/0.58 inference(transitivity,[status(thm)],[332, 331])).
% 0.45/0.58 tff(334,plain,
% 0.45/0.58 ($false),
% 0.45/0.58 inference(unit_resolution,[status(thm)],[102, 333])).
% 0.45/0.58 tff(335,plain,(a(I!2, J!1) = real_zero), inference(lemma,lemma(discharge,[]))).
% 0.45/0.58 tff(336,plain,
% 0.45/0.58 (((I!2 = J!1) | (a(I!2, J!1) = real_zero)) | (~(a(I!2, J!1) = real_zero))),
% 0.45/0.58 inference(tautology,[status(thm)],[])).
% 0.45/0.58 tff(337,plain,
% 0.45/0.58 ((I!2 = J!1) | (a(I!2, J!1) = real_zero)),
% 0.45/0.58 inference(unit_resolution,[status(thm)],[336, 335])).
% 0.45/0.58 tff(338,plain,
% 0.45/0.58 (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero)))),
% 0.45/0.58 inference(unit_resolution,[status(thm)],[256, 337])).
% 0.45/0.58 tff(339,plain,
% 0.45/0.58 (((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))) | (I!2 = J!1)),
% 0.45/0.58 inference(tautology,[status(thm)],[])).
% 0.45/0.58 tff(340,plain,
% 0.45/0.58 (I!2 = J!1),
% 0.45/0.58 inference(unit_resolution,[status(thm)],[339, 338])).
% 0.45/0.58 tff(341,plain,
% 0.45/0.58 (a(I!2, J!1) = a(J!1, J!1)),
% 0.45/0.58 inference(monotonicity,[status(thm)],[340])).
% 0.45/0.58 tff(342,plain,
% 0.45/0.58 (real_zero = a(I!2, J!1)),
% 0.45/0.58 inference(symmetry,[status(thm)],[335])).
% 0.45/0.58 tff(343,plain,
% 0.45/0.58 (real_zero = real_one),
% 0.45/0.58 inference(transitivity,[status(thm)],[342, 341, 77])).
% 0.45/0.58 tff(344,plain,
% 0.45/0.58 ((~(real_zero = real_one)) <=> (~(real_zero = real_one))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(345,axiom,(~(real_zero = real_one)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','real_constants')).
% 0.45/0.58 tff(346,plain,
% 0.45/0.58 (~(real_zero = real_one)),
% 0.45/0.58 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.45/0.58 tff(347,plain,
% 0.45/0.58 ($false),
% 0.45/0.58 inference(unit_resolution,[status(thm)],[346, 343])).
% 0.45/0.58 % SZS output end Proof
%------------------------------------------------------------------------------