TSTP Solution File: SWV489+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV489+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 0.19s 0.49s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV489+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 04:01:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 tff(int_leq_type, type, (
% 0.19/0.49 int_leq: ( $i * $i ) > $o)).
% 0.19/0.49 tff(tptp_fun_J_1_type, type, (
% 0.19/0.49 tptp_fun_J_1: $i)).
% 0.19/0.49 tff(real_zero_type, type, (
% 0.19/0.49 real_zero: $i)).
% 0.19/0.49 tff(a_type, type, (
% 0.19/0.49 a: ( $i * $i ) > $i)).
% 0.19/0.49 tff(plus_type, type, (
% 0.19/0.49 plus: ( $i * $i ) > $i)).
% 0.19/0.49 tff(tptp_fun_K_0_type, type, (
% 0.19/0.49 tptp_fun_K_0: ( $i * $i ) > $i)).
% 0.19/0.49 tff(tptp_fun_I_2_type, type, (
% 0.19/0.49 tptp_fun_I_2: $i)).
% 0.19/0.49 tff(int_less_type, type, (
% 0.19/0.49 int_less: ( $i * $i ) > $o)).
% 0.19/0.49 tff(int_zero_type, type, (
% 0.19/0.49 int_zero: $i)).
% 0.19/0.49 tff(int_one_type, type, (
% 0.19/0.49 int_one: $i)).
% 0.19/0.49 tff(n_type, type, (
% 0.19/0.49 n: $i)).
% 0.19/0.49 tff(real_one_type, type, (
% 0.19/0.49 real_one: $i)).
% 0.19/0.49 tff(1,plain,
% 0.19/0.49 (^[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))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(2,plain,
% 0.19/0.49 (![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)))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.49 tff(3,plain,
% 0.19/0.49 (^[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))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(4,plain,
% 0.19/0.49 (![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)))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.49 tff(5,plain,
% 0.19/0.49 (![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)))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.49 tff(6,plain,
% 0.19/0.49 (^[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)))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(7,plain,
% 0.19/0.49 (![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)))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.49 tff(8,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(9,axiom,(![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_and_inverse')).
% 0.19/0.49 tff(10,plain,
% 0.19/0.49 (![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.49 tff(11,plain,(
% 0.19/0.49 ![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)))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[10])).
% 0.19/0.49 tff(12,plain,
% 0.19/0.49 (![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)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.49 tff(13,plain,
% 0.19/0.49 (![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)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.49 tff(14,plain,
% 0.19/0.49 (((~![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) | ![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)))))))))) <=> ((~![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) | ![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))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(15,plain,
% 0.19/0.49 ((~((~((~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) | ![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)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(16,plain,
% 0.19/0.50 (((~![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) | ![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))))))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.50 tff(17,plain,
% 0.19/0.50 (((~![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) | ![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))))))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.50 tff(18,plain,
% 0.19/0.50 ((~![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)))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(19,plain,
% 0.19/0.50 ((~![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) | ![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)))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 (~((~(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))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.19/0.50 tff(21,plain,
% 0.19/0.50 (((~(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)))))))) | ((~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))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(22,plain,
% 0.19/0.50 ((~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)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.50 tff(23,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(24,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.50 tff(25,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(26,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(27,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.50 tff(28,axiom,(![I: $i, J: $i] : (int_leq(I, J) <=> (int_less(I, J) | (I = J)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','int_leq')).
% 0.19/0.50 tff(29,plain,
% 0.19/0.50 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.50 tff(31,plain,(
% 0.19/0.50 ![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[30])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 ((~![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)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(34,plain,
% 0.19/0.50 (int_leq(J!1, I!2) <=> ((J!1 = I!2) | int_less(J!1, I!2))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.50 tff(35,assumption,((~((~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] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1)))))), introduced(assumption)).
% 0.19/0.50 tff(36,plain,
% 0.19/0.50 (((~![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] : ((~int_less(int_zero, K)) | (~(plus(I!2, 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(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] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(37,plain,
% 0.19/0.50 ((~((~((~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)) | (~((~(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] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1)))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(38,plain,
% 0.19/0.50 (((~![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)) | (~((~(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] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.50 tff(39,plain,
% 0.19/0.50 (((~![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)) | (~((~(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] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[38, 36])).
% 0.19/0.50 tff(40,plain,
% 0.19/0.50 ((~![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)))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(41,plain,
% 0.19/0.50 ((~![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: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1)))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.50 tff(42,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[41, 13, 35])).
% 0.19/0.50 tff(43,plain,(~((~((~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] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(44,plain,
% 0.19/0.50 (((~((~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] : ((~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))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(45,plain,
% 0.19/0.50 ((~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)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.50 tff(46,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)).
% 0.19/0.50 tff(47,plain,
% 0.19/0.50 (((~(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)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(48,plain,
% 0.19/0.50 (plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.50 tff(49,plain,
% 0.19/0.50 (J!1 = plus(I!2, tptp_fun_K_0(J!1, I!2))),
% 0.19/0.50 inference(symmetry,[status(thm)],[48])).
% 0.19/0.50 tff(50,plain,
% 0.19/0.50 (((~![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))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(51,plain,
% 0.19/0.50 ((~((~((~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)))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(52,plain,
% 0.19/0.50 (((~![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))))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.50 tff(53,plain,
% 0.19/0.50 (((~![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))))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.50 tff(54,plain,
% 0.19/0.50 ((~![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)))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(55,plain,
% 0.19/0.51 ((~![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)))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.51 tff(56,plain,
% 0.19/0.51 (~((~((~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))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[55, 13])).
% 0.19/0.51 tff(57,plain,
% 0.19/0.51 (((~((~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))))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(58,plain,
% 0.19/0.51 ((~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)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.51 tff(59,plain,
% 0.19/0.51 (^[I: $i] : refl((int_less(int_zero, I) <=> int_leq(int_one, I)) <=> (int_less(int_zero, I) <=> int_leq(int_one, I)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(60,plain,
% 0.19/0.51 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.51 tff(61,plain,
% 0.19/0.51 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(62,axiom,(![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','one_successor_of_zero')).
% 0.19/0.51 tff(63,plain,
% 0.19/0.51 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.51 tff(64,plain,(
% 0.19/0.51 ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.51 inference(skolemize,[status(sab)],[63])).
% 0.19/0.51 tff(65,plain,
% 0.19/0.51 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.19/0.51 tff(66,plain,
% 0.19/0.51 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, J!1) <=> int_leq(int_one, J!1))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(67,plain,
% 0.19/0.51 (int_less(int_zero, J!1) <=> int_leq(int_one, J!1)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.51 tff(68,plain,
% 0.19/0.51 ((~![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: $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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(69,plain,
% 0.19/0.51 ((~![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: $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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(70,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))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d')).
% 0.19/0.51 tff(71,plain,
% 0.19/0.51 (~![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.51 tff(72,plain,
% 0.19/0.51 (~![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[71, 68])).
% 0.19/0.51 tff(73,plain,
% 0.19/0.51 (~![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.19/0.51 tff(74,plain,
% 0.19/0.51 (~![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[73, 68])).
% 0.19/0.51 tff(75,plain,
% 0.19/0.51 (~![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[74, 68])).
% 0.19/0.51 tff(76,plain,
% 0.19/0.51 (~![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.19/0.51 tff(77,plain,
% 0.19/0.51 (~![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[76, 68])).
% 0.19/0.51 tff(78,plain,(
% 0.19/0.51 ~((~(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))),
% 0.19/0.51 inference(skolemize,[status(sab)],[77])).
% 0.19/0.51 tff(79,plain,
% 0.19/0.51 (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))),
% 0.19/0.51 inference(or_elim,[status(thm)],[78])).
% 0.19/0.51 tff(80,plain,
% 0.19/0.51 (int_leq(int_one, J!1)),
% 0.19/0.51 inference(and_elim,[status(thm)],[79])).
% 0.19/0.51 tff(81,plain,
% 0.19/0.51 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1) | (~int_leq(int_one, J!1))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(82,plain,
% 0.19/0.51 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.51 tff(83,plain,
% 0.19/0.51 (int_less(int_zero, J!1)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[82, 67])).
% 0.19/0.51 tff(84,plain,
% 0.19/0.51 ((~((~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)))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(85,plain,
% 0.19/0.51 ((~((~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)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.51 tff(86,plain,
% 0.19/0.51 (~((~(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))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[85, 58])).
% 0.19/0.51 tff(87,plain,
% 0.19/0.51 (((~(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)),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(88,plain,
% 0.19/0.51 (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.51 tff(89,plain,
% 0.19/0.51 (^[I: $i, J: $i] : refl((plus(I, J) = plus(J, I)) <=> (plus(I, J) = plus(J, I)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(90,plain,
% 0.19/0.51 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.51 tff(91,plain,
% 0.19/0.51 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(92,axiom,(![I: $i, J: $i] : (plus(I, J) = plus(J, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_commutative')).
% 0.19/0.51 tff(93,plain,
% 0.19/0.51 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.51 tff(94,plain,(
% 0.19/0.51 ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.51 inference(skolemize,[status(sab)],[93])).
% 0.19/0.51 tff(95,plain,
% 0.19/0.51 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.19/0.51 tff(96,plain,
% 0.19/0.51 ((~![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))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(97,plain,
% 0.19/0.51 (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = plus(tptp_fun_K_0(J!1, int_zero), int_zero)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.19/0.51 tff(98,plain,
% 0.19/0.51 (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = plus(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.19/0.51 inference(symmetry,[status(thm)],[97])).
% 0.19/0.51 tff(99,plain,
% 0.19/0.51 (^[I: $i] : refl((plus(I, int_zero) = I) <=> (plus(I, int_zero) = I))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(100,plain,
% 0.19/0.51 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.51 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.51 tff(101,plain,
% 0.19/0.51 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(102,axiom,(![I: $i] : (plus(I, int_zero) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_zero')).
% 0.19/0.51 tff(103,plain,
% 0.19/0.51 (![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.51 tff(104,plain,(
% 0.19/0.51 ![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.51 inference(skolemize,[status(sab)],[103])).
% 0.19/0.51 tff(105,plain,
% 0.19/0.51 (![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.19/0.51 tff(106,plain,
% 0.19/0.51 ((~![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))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(107,plain,
% 0.19/0.51 (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = tptp_fun_K_0(J!1, int_zero)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.19/0.51 tff(108,plain,
% 0.19/0.51 (tptp_fun_K_0(J!1, int_zero) = plus(tptp_fun_K_0(J!1, int_zero), int_zero)),
% 0.19/0.51 inference(symmetry,[status(thm)],[107])).
% 0.19/0.51 tff(109,plain,
% 0.19/0.51 (tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2))),
% 0.19/0.51 inference(transitivity,[status(thm)],[108, 98, 88, 49])).
% 0.19/0.51 tff(110,plain,
% 0.19/0.51 (((~(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))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(111,plain,
% 0.19/0.51 (int_less(int_zero, tptp_fun_K_0(J!1, I!2))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[110, 46])).
% 0.19/0.51 tff(112,plain,
% 0.19/0.51 (tptp_fun_K_0(J!1, int_zero) = J!1),
% 0.19/0.51 inference(transitivity,[status(thm)],[108, 98, 88])).
% 0.19/0.51 tff(113,plain,
% 0.19/0.51 (int_leq(tptp_fun_K_0(J!1, int_zero), n) <=> int_leq(J!1, n)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.51 tff(114,plain,
% 0.19/0.51 (int_leq(J!1, n) <=> int_leq(tptp_fun_K_0(J!1, int_zero), n)),
% 0.19/0.51 inference(symmetry,[status(thm)],[113])).
% 0.19/0.51 tff(115,plain,
% 0.19/0.51 (int_leq(J!1, n)),
% 0.19/0.51 inference(and_elim,[status(thm)],[79])).
% 0.19/0.51 tff(116,plain,
% 0.19/0.51 (int_leq(tptp_fun_K_0(J!1, int_zero), n)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.51 tff(117,plain,
% 0.19/0.51 ((~![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)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(118,plain,
% 0.19/0.51 (int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[117, 65])).
% 0.19/0.51 tff(119,plain,
% 0.19/0.51 (((~(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))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(120,plain,
% 0.19/0.51 (int_less(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[119, 86])).
% 0.19/0.51 tff(121,plain,
% 0.19/0.51 ((~(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))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(122,plain,
% 0.19/0.51 ((~(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))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.51 tff(123,plain,
% 0.19/0.51 (int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[122, 118])).
% 0.19/0.51 tff(124,plain,
% 0.19/0.51 (int_leq(I!2, n)),
% 0.19/0.51 inference(and_elim,[status(thm)],[79])).
% 0.19/0.51 tff(125,plain,
% 0.19/0.51 (int_leq(int_one, I!2)),
% 0.19/0.51 inference(and_elim,[status(thm)],[79])).
% 0.19/0.51 tff(126,plain,
% 0.19/0.51 (^[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)))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(127,plain,
% 0.19/0.51 (![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)))))))) <=> ![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))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.51 tff(128,plain,
% 0.19/0.51 (^[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)))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(129,plain,
% 0.19/0.51 (![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)))))))) <=> ![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))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.51 tff(130,plain,
% 0.19/0.51 (![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)))))))) <=> ![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))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[129, 127])).
% 0.19/0.51 tff(131,plain,
% 0.19/0.51 (^[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(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))))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(132,plain,
% 0.19/0.52 (![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] : ((~(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))))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[131])).
% 0.19/0.52 tff(133,plain,
% 0.19/0.52 (![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] : ((~(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)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(134,plain,
% 0.19/0.52 (^[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)))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(135,plain,
% 0.19/0.52 (![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] : ((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)))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[134])).
% 0.19/0.52 tff(136,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/sandbox2/benchmark/theBenchmark.p','qii')).
% 0.19/0.52 tff(137,plain,
% 0.19/0.52 (![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] : ((~(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)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.52 tff(138,plain,
% 0.19/0.52 (![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] : ((~(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)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.19/0.52 tff(139,plain,(
% 0.19/0.52 ![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] : ((~(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)))))),
% 0.19/0.52 inference(skolemize,[status(sab)],[138])).
% 0.19/0.52 tff(140,plain,
% 0.19/0.52 (![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))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.19/0.52 tff(141,plain,
% 0.19/0.52 (![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))))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[140, 130])).
% 0.19/0.53 tff(142,plain,
% 0.19/0.53 (((~![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))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(143,plain,
% 0.19/0.53 (((~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))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(144,plain,
% 0.19/0.53 ((~((~![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)))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(145,plain,
% 0.19/0.53 (((~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))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[144])).
% 0.19/0.53 tff(146,plain,
% 0.19/0.53 (((~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))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[145, 143])).
% 0.19/0.53 tff(147,plain,
% 0.19/0.53 (((~![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)))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[146])).
% 0.19/0.53 tff(148,plain,
% 0.19/0.53 (((~![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))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[147, 142])).
% 0.19/0.53 tff(149,plain,
% 0.19/0.53 ((~![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))))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(150,plain,
% 0.19/0.53 ((~![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)))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.53 tff(151,plain,
% 0.19/0.53 ((~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)))))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[150, 141, 125, 124, 123])).
% 0.19/0.53 tff(152,plain,
% 0.19/0.53 (~((~![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(unit_resolution,[status(thm)],[151, 116])).
% 0.45/0.54 tff(153,plain,
% 0.45/0.54 (((~![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))))),
% 0.45/0.54 inference(tautology,[status(thm)],[])).
% 0.45/0.54 tff(154,plain,
% 0.45/0.54 (![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)],[153, 152])).
% 0.45/0.55 tff(155,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(156,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(157,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)],[156])).
% 0.45/0.55 tff(158,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)],[157, 155])).
% 0.45/0.55 tff(159,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(160,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)],[159, 158])).
% 0.45/0.55 tff(161,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)],[160, 154, 111, 109])).
% 0.45/0.55 tff(162,assumption,(~int_leq(I!2, I!2)), introduced(assumption)).
% 0.45/0.55 tff(163,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(164,plain,
% 0.45/0.55 ((int_leq(I!2, I!2) <=> $true) <=> int_leq(I!2, I!2)),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(165,plain,
% 0.45/0.55 (($true | int_less(I!2, I!2)) <=> $true),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(166,plain,
% 0.45/0.55 ((I!2 = I!2) <=> $true),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(167,plain,
% 0.45/0.55 (((I!2 = I!2) | int_less(I!2, I!2)) <=> ($true | int_less(I!2, I!2))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[166])).
% 0.45/0.55 tff(168,plain,
% 0.45/0.55 (((I!2 = I!2) | int_less(I!2, I!2)) <=> $true),
% 0.45/0.55 inference(transitivity,[status(thm)],[167, 165])).
% 0.45/0.55 tff(169,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)],[168])).
% 0.45/0.55 tff(170,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)],[169, 164])).
% 0.45/0.55 tff(171,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)],[170])).
% 0.45/0.55 tff(172,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)],[171, 163])).
% 0.45/0.55 tff(173,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(174,plain,
% 0.45/0.55 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.45/0.55 tff(175,plain,
% 0.45/0.55 ($false),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[174, 32, 162])).
% 0.45/0.55 tff(176,plain,(int_leq(I!2, I!2)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.55 tff(177,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(178,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(179,plain,
% 0.45/0.55 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.45/0.55 tff(180,plain,
% 0.45/0.55 (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[179, 125, 176, 161])).
% 0.45/0.55 tff(181,plain,
% 0.45/0.55 (a(I!2, J!1) = a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2)))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[49])).
% 0.45/0.55 tff(182,plain,
% 0.45/0.55 (a(I!2, J!1) = real_zero),
% 0.45/0.55 inference(transitivity,[status(thm)],[181, 180])).
% 0.45/0.55 tff(183,plain,
% 0.45/0.55 (~(a(I!2, J!1) = real_zero)),
% 0.45/0.55 inference(or_elim,[status(thm)],[78])).
% 0.45/0.55 tff(184,plain,
% 0.45/0.55 ($false),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.45/0.55 tff(185,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)))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.55 tff(186,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)) | (~((~(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)],[])).
% 0.45/0.55 tff(187,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))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.45/0.55 tff(188,plain,
% 0.45/0.55 (~int_less(I!2, J!1)),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[187, 45])).
% 0.45/0.55 tff(189,assumption,(~int_leq(J!1, I!2)), introduced(assumption)).
% 0.45/0.55 tff(190,plain,
% 0.45/0.55 (^[I: $i, J: $i] : refl((int_leq(J, I) | int_less(I, J)) <=> (int_leq(J, I) | int_less(I, J)))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(191,plain,
% 0.45/0.55 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[190])).
% 0.45/0.55 tff(192,plain,
% 0.45/0.55 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(193,plain,
% 0.45/0.55 (^[I: $i, J: $i] : rewrite((int_less(I, J) | int_leq(J, I)) <=> (int_leq(J, I) | int_less(I, J)))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(194,plain,
% 0.45/0.55 (![I: $i, J: $i] : (int_less(I, J) | int_leq(J, I)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[193])).
% 0.45/0.55 tff(195,axiom,(![I: $i, J: $i] : (int_less(I, J) | int_leq(J, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','int_less_total')).
% 0.45/0.55 tff(196,plain,
% 0.45/0.55 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.45/0.55 tff(197,plain,
% 0.45/0.55 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.45/0.55 tff(198,plain,(
% 0.45/0.55 ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.55 inference(skolemize,[status(sab)],[197])).
% 0.45/0.55 tff(199,plain,
% 0.45/0.55 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.45/0.55 tff(200,plain,
% 0.45/0.55 (((~![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))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(201,plain,
% 0.45/0.55 ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | (int_leq(J!1, I!2) | int_less(I!2, J!1))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(202,plain,
% 0.45/0.55 ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | int_leq(J!1, I!2) | int_less(I!2, J!1)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.45/0.55 tff(203,plain,
% 0.45/0.55 ($false),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[202, 199, 189, 188])).
% 0.45/0.55 tff(204,plain,(int_leq(J!1, I!2)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.55 tff(205,plain,
% 0.45/0.55 ((~(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))),
% 0.45/0.55 inference(tautology,[status(thm)],[])).
% 0.45/0.55 tff(206,plain,
% 0.45/0.55 ((~(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))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.45/0.55 tff(207,plain,
% 0.45/0.55 ((J!1 = I!2) | int_less(J!1, I!2)),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[206, 34])).
% 0.45/0.55 tff(208,plain,
% 0.45/0.55 ((J!1 = I!2) <=> (I!2 = J!1)),
% 0.45/0.55 inference(commutativity,[status(thm)],[])).
% 0.45/0.55 tff(209,plain,
% 0.45/0.55 ((I!2 = J!1) <=> (J!1 = I!2)),
% 0.45/0.55 inference(symmetry,[status(thm)],[208])).
% 0.45/0.55 tff(210,plain,
% 0.45/0.55 ((~(I!2 = J!1)) <=> (~(J!1 = I!2))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[209])).
% 0.45/0.55 tff(211,plain,
% 0.45/0.55 (~(I!2 = J!1)),
% 0.45/0.55 inference(and_elim,[status(thm)],[79])).
% 0.45/0.55 tff(212,plain,
% 0.45/0.55 (~(J!1 = I!2)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.45/0.55 tff(213,plain,
% 0.45/0.55 ((~((J!1 = I!2) | int_less(J!1, I!2))) | (J!1 = I!2) | int_less(J!1, I!2)),
% 0.45/0.55 inference(tautology,[status(thm)],[])).
% 0.45/0.55 tff(214,plain,
% 0.45/0.55 (int_less(J!1, I!2)),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[213, 212, 207])).
% 0.45/0.55 tff(215,plain,
% 0.45/0.55 ((~((~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)))))),
% 0.45/0.55 inference(tautology,[status(thm)],[])).
% 0.45/0.55 tff(216,plain,
% 0.45/0.55 ((~((~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)))))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.45/0.55 tff(217,plain,
% 0.45/0.55 (~((~(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))))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[216, 22])).
% 0.45/0.55 tff(218,plain,
% 0.45/0.55 (((~(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)),
% 0.45/0.55 inference(tautology,[status(thm)],[])).
% 0.45/0.55 tff(219,plain,
% 0.45/0.55 (plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.45/0.55 tff(220,plain,
% 0.45/0.55 (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = a(I!2, J!1)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[219])).
% 0.45/0.55 tff(221,plain,
% 0.45/0.55 ((a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero) <=> (a(I!2, J!1) = real_zero)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[220])).
% 0.45/0.55 tff(222,plain,
% 0.45/0.55 ((a(I!2, J!1) = real_zero) <=> (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero)),
% 0.45/0.55 inference(symmetry,[status(thm)],[221])).
% 0.45/0.55 tff(223,plain,
% 0.45/0.55 ((~(a(I!2, J!1) = real_zero)) <=> (~(a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[222])).
% 0.45/0.55 tff(224,plain,
% 0.45/0.55 (~(a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[183, 223])).
% 0.45/0.55 tff(225,plain,
% 0.45/0.55 (I!2 = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.45/0.55 inference(symmetry,[status(thm)],[219])).
% 0.45/0.55 tff(226,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(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))))))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(227,plain,
% 0.45/0.55 ((~((~((~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)))))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(228,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(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))))))))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[227])).
% 0.45/0.55 tff(229,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(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))))))))),
% 0.45/0.55 inference(transitivity,[status(thm)],[228, 226])).
% 0.45/0.55 tff(230,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(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)))))))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(231,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(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)],[230, 229])).
% 0.45/0.56 tff(232,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)],[231, 13])).
% 0.45/0.56 tff(233,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(234,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)],[233, 232])).
% 0.45/0.56 tff(235,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(236,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)],[235, 65])).
% 0.45/0.56 tff(237,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(238,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)],[237, 125])).
% 0.45/0.56 tff(239,plain,
% 0.45/0.56 (int_less(int_zero, I!2)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[238, 236])).
% 0.45/0.56 tff(240,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(241,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)],[240, 239])).
% 0.45/0.56 tff(242,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)],[241, 234])).
% 0.45/0.56 tff(243,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(244,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)],[243, 242])).
% 0.45/0.56 tff(245,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(246,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)],[245, 95])).
% 0.45/0.56 tff(247,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)],[246])).
% 0.45/0.56 tff(248,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(249,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)],[248, 105])).
% 0.45/0.56 tff(250,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)],[249])).
% 0.45/0.56 tff(251,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)],[250, 247, 244, 225])).
% 0.45/0.56 tff(252,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(253,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)],[252, 217])).
% 0.45/0.56 tff(254,plain,
% 0.45/0.56 (tptp_fun_K_0(I!2, int_zero) = I!2),
% 0.45/0.56 inference(transitivity,[status(thm)],[250, 247, 244])).
% 0.45/0.56 tff(255,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)],[254])).
% 0.45/0.56 tff(256,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)],[255])).
% 0.45/0.56 tff(257,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)],[124, 256])).
% 0.45/0.56 tff(258,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(259,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)],[258, 65])).
% 0.45/0.56 tff(260,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(261,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)],[260, 242])).
% 0.45/0.56 tff(262,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(263,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)],[262, 261])).
% 0.45/0.56 tff(264,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)],[263, 259])).
% 0.45/0.56 tff(265,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)))))))))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(266,plain,
% 0.45/0.56 (((~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)))))))))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(267,plain,
% 0.45/0.56 ((~((~![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))))))))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(268,plain,
% 0.45/0.56 (((~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)))))))))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[267])).
% 0.47/0.56 tff(269,plain,
% 0.47/0.56 (((~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)))))))))),
% 0.47/0.56 inference(transitivity,[status(thm)],[268, 266])).
% 0.47/0.56 tff(270,plain,
% 0.47/0.56 (((~![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, 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))))))))))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[269])).
% 0.47/0.56 tff(271,plain,
% 0.47/0.56 (((~![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, 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)))))))))),
% 0.47/0.56 inference(transitivity,[status(thm)],[270, 265])).
% 0.47/0.56 tff(272,plain,
% 0.47/0.56 ((~![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, 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)))))))))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(273,plain,
% 0.47/0.56 ((~![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))))))))),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.47/0.57 tff(274,plain,
% 0.47/0.57 ((~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))))))))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[273, 141, 80, 115, 264])).
% 0.47/0.57 tff(275,plain,
% 0.47/0.57 (~((~![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)))))))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[274, 257])).
% 0.47/0.57 tff(276,plain,
% 0.47/0.57 (((~![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))))),
% 0.47/0.57 inference(tautology,[status(thm)],[])).
% 0.47/0.57 tff(277,plain,
% 0.47/0.57 (![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))))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[276, 275])).
% 0.47/0.57 tff(278,plain,
% 0.47/0.57 (((~![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)))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(279,plain,
% 0.47/0.57 (((~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)))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(280,plain,
% 0.47/0.57 (((~![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] : ((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))))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[279])).
% 0.47/0.57 tff(281,plain,
% 0.47/0.57 (((~![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] : ((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)))),
% 0.47/0.57 inference(transitivity,[status(thm)],[280, 278])).
% 0.47/0.57 tff(282,plain,
% 0.47/0.57 ((~![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] : ((a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(283,plain,
% 0.47/0.57 ((~![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))),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.47/0.57 tff(284,plain,
% 0.47/0.57 (![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))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[283, 277, 253, 251])).
% 0.47/0.57 tff(285,plain,
% 0.47/0.57 (((~![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))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(286,plain,
% 0.47/0.57 ((~![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))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(287,plain,
% 0.47/0.57 ((~![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)),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.47/0.57 tff(288,plain,
% 0.47/0.57 ((~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero)),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[287, 80, 284])).
% 0.47/0.57 tff(289,plain,
% 0.47/0.57 (~int_leq(J!1, J!1)),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[288, 224])).
% 0.47/0.57 tff(290,plain,
% 0.47/0.57 (((~![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))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(291,plain,
% 0.47/0.57 ((int_leq(J!1, J!1) <=> $true) <=> int_leq(J!1, J!1)),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(292,plain,
% 0.47/0.57 (($true | int_less(J!1, J!1)) <=> $true),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(293,plain,
% 0.47/0.57 ((J!1 = J!1) <=> $true),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(294,plain,
% 0.47/0.57 (((J!1 = J!1) | int_less(J!1, J!1)) <=> ($true | int_less(J!1, J!1))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[293])).
% 0.47/0.57 tff(295,plain,
% 0.47/0.57 (((J!1 = J!1) | int_less(J!1, J!1)) <=> $true),
% 0.47/0.57 inference(transitivity,[status(thm)],[294, 292])).
% 0.47/0.57 tff(296,plain,
% 0.47/0.57 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> (int_leq(J!1, J!1) <=> $true)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[295])).
% 0.47/0.57 tff(297,plain,
% 0.47/0.57 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> int_leq(J!1, J!1)),
% 0.47/0.57 inference(transitivity,[status(thm)],[296, 291])).
% 0.47/0.57 tff(298,plain,
% 0.47/0.57 (((~![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))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[297])).
% 0.47/0.57 tff(299,plain,
% 0.47/0.57 (((~![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))),
% 0.47/0.57 inference(transitivity,[status(thm)],[298, 290])).
% 0.47/0.57 tff(300,plain,
% 0.47/0.57 ((~![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)))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(301,plain,
% 0.47/0.57 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1)),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.47/0.57 tff(302,plain,
% 0.47/0.57 ($false),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[301, 32, 289])).
% 0.47/0.57 % SZS output end Proof
%------------------------------------------------------------------------------