TSTP Solution File: SWV487+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV487+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 15:17:47 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV487+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 03:57:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(int_leq_type, type, (
% 0.19/0.43 int_leq: ( $i * $i ) > $o)).
% 0.19/0.43 tff(tptp_fun_J_1_type, type, (
% 0.19/0.43 tptp_fun_J_1: $i)).
% 0.19/0.43 tff(real_zero_type, type, (
% 0.19/0.43 real_zero: $i)).
% 0.19/0.43 tff(a_type, type, (
% 0.19/0.43 a: ( $i * $i ) > $i)).
% 0.19/0.43 tff(plus_type, type, (
% 0.19/0.43 plus: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_K_0_type, type, (
% 0.19/0.43 tptp_fun_K_0: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_I_2_type, type, (
% 0.19/0.43 tptp_fun_I_2: $i)).
% 0.19/0.43 tff(int_less_type, type, (
% 0.19/0.43 int_less: ( $i * $i ) > $o)).
% 0.19/0.43 tff(int_zero_type, type, (
% 0.19/0.43 int_zero: $i)).
% 0.19/0.43 tff(n_type, type, (
% 0.19/0.43 n: $i)).
% 0.19/0.43 tff(int_one_type, type, (
% 0.19/0.43 int_one: $i)).
% 0.19/0.43 tff(lu_type, type, (
% 0.19/0.43 lu: ( $i * $i ) > $i)).
% 0.19/0.43 tff(1,plain,
% 0.19/0.43 (^[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))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 (^[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))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(4,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (^[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)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 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')).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 (![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.43 tff(11,plain,(
% 0.19/0.43 ![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)))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[10])).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 ((~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 ((~![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)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))) | ((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 ((~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)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 ((~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))) <=> (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 ((~![I: $i, J: $i] : (((int_leq(int_one, J) & int_less(J, I)) & int_leq(I, n)) => (a(I, J) = real_zero))) <=> (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(25,axiom,(~![I: $i, J: $i] : (((int_leq(int_one, J) & int_less(J, I)) & int_leq(I, n)) => (a(I, J) = real_zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ut')).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[31, 23])).
% 0.19/0.44 tff(33,plain,(
% 0.19/0.44 ~((~(int_leq(int_one, J!1) & int_less(J!1, I!2) & int_leq(I!2, n))) | (a(I!2, J!1) = real_zero))),
% 0.19/0.44 inference(skolemize,[status(sab)],[32])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (int_leq(int_one, J!1) & int_less(J!1, I!2) & int_leq(I!2, n)),
% 0.19/0.44 inference(or_elim,[status(thm)],[33])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 (int_less(J!1, I!2)),
% 0.19/0.44 inference(and_elim,[status(thm)],[34])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 ((~((~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)))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 ((~((~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)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (~((~(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))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[37, 22])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (((~(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)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = a(I!2, J!1)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 ((a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero) <=> (a(I!2, J!1) = real_zero)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 ((a(I!2, J!1) = real_zero) <=> (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero)),
% 0.19/0.44 inference(symmetry,[status(thm)],[42])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 ((~(a(I!2, J!1) = real_zero)) <=> (~(a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 (~(a(I!2, J!1) = real_zero)),
% 0.19/0.44 inference(or_elim,[status(thm)],[33])).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 (~(a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 (I!2 = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.19/0.44 inference(symmetry,[status(thm)],[40])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 (((~![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))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 ((~((~((~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)))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 (((~![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))))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.44 tff(51,plain,
% 0.19/0.44 (((~![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))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[50, 48])).
% 0.19/0.44 tff(52,plain,
% 0.19/0.44 ((~![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)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 ((~![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)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (~((~((~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))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[53, 13])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (((~((~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))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 ((~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)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (^[I: $i] : refl((int_less(int_zero, I) <=> int_leq(int_one, I)) <=> (int_less(int_zero, I) <=> int_leq(int_one, I)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(60,axiom,(![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','one_successor_of_zero')).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.45 tff(62,plain,(
% 0.19/0.45 ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.45 inference(skolemize,[status(sab)],[61])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, J!1) <=> int_leq(int_one, J!1))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 (int_less(int_zero, J!1) <=> int_leq(int_one, J!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 (int_leq(int_one, J!1)),
% 0.19/0.45 inference(and_elim,[status(thm)],[34])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1) | (~int_leq(int_one, J!1))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 (int_less(int_zero, J!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 (![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J))) <=> ![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 (^[I: $i, J: $i, K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_less(I, J) & int_less(J, K)) <=> (~((~int_less(J, K)) | (~int_less(I, J))))), ((~(int_less(I, J) & int_less(J, K))) <=> (~(~((~int_less(J, K)) | (~int_less(I, J))))))), rewrite((~(~((~int_less(J, K)) | (~int_less(I, J))))) <=> ((~int_less(J, K)) | (~int_less(I, J)))), ((~(int_less(I, J) & int_less(J, K))) <=> ((~int_less(J, K)) | (~int_less(I, J))))), (((~(int_less(I, J) & int_less(J, K))) | int_less(I, K)) <=> (((~int_less(J, K)) | (~int_less(I, J))) | int_less(I, K)))), rewrite((((~int_less(J, K)) | (~int_less(I, J))) | int_less(I, K)) <=> (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))), (((~(int_less(I, J) & int_less(J, K))) | int_less(I, K)) <=> (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 (![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K)) <=> ![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 (![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K)) <=> ![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 (^[I: $i, J: $i, K: $i] : rewrite(((int_less(I, J) & int_less(J, K)) => int_less(I, K)) <=> ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 (![I: $i, J: $i, K: $i] : ((int_less(I, J) & int_less(J, K)) => int_less(I, K)) <=> ![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.45 tff(76,axiom,(![I: $i, J: $i, K: $i] : ((int_less(I, J) & int_less(J, K)) => int_less(I, K))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','int_less_transitive')).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 (![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 (![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.19/0.45 tff(79,plain,(
% 0.19/0.45 ![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K))),
% 0.19/0.45 inference(skolemize,[status(sab)],[78])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 (![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 (![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | ((~int_less(int_zero, J!1)) | (~int_less(J!1, I!2)) | int_less(int_zero, I!2))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(int_zero, J!1)) | (~int_less(J!1, I!2)) | int_less(int_zero, I!2))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 ((int_less(int_zero, I!2) | (~int_less(J!1, I!2)) | (~int_less(int_zero, J!1))) <=> ((~int_less(int_zero, J!1)) | (~int_less(J!1, I!2)) | int_less(int_zero, I!2))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(int_zero, I!2) | (~int_less(J!1, I!2)) | (~int_less(int_zero, J!1)))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | ((~int_less(int_zero, J!1)) | (~int_less(J!1, I!2)) | int_less(int_zero, I!2)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.45 tff(85,plain,
% 0.19/0.45 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(int_zero, I!2) | (~int_less(J!1, I!2)) | (~int_less(int_zero, J!1)))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(int_zero, J!1)) | (~int_less(J!1, I!2)) | int_less(int_zero, I!2))),
% 0.19/0.45 inference(transitivity,[status(thm)],[84, 82])).
% 0.19/0.45 tff(86,plain,
% 0.19/0.45 ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(int_zero, I!2) | (~int_less(J!1, I!2)) | (~int_less(int_zero, J!1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(87,plain,
% 0.19/0.45 ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(int_zero, J!1)) | (~int_less(J!1, I!2)) | int_less(int_zero, I!2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 (int_less(int_zero, I!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[87, 81, 35, 69])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 ((~((~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)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(90,plain,
% 0.19/0.45 ((~((~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)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 (~((~(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))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[90, 56])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 (((~(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)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 (^[I: $i, J: $i] : refl((plus(I, J) = plus(J, I)) <=> (plus(I, J) = plus(J, I)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(95,plain,
% 0.19/0.45 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.45 tff(96,plain,
% 0.19/0.45 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(97,axiom,(![I: $i, J: $i] : (plus(I, J) = plus(J, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_commutative')).
% 0.19/0.45 tff(98,plain,
% 0.19/0.45 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.45 tff(99,plain,(
% 0.19/0.45 ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.45 inference(skolemize,[status(sab)],[98])).
% 0.19/0.45 tff(100,plain,
% 0.19/0.45 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.19/0.45 tff(101,plain,
% 0.19/0.45 ((~![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))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(102,plain,
% 0.19/0.45 (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = plus(tptp_fun_K_0(I!2, int_zero), int_zero)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.45 tff(103,plain,
% 0.19/0.45 (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = plus(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.19/0.45 inference(symmetry,[status(thm)],[102])).
% 0.19/0.45 tff(104,plain,
% 0.19/0.45 (^[I: $i] : refl((plus(I, int_zero) = I) <=> (plus(I, int_zero) = I))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(105,plain,
% 0.19/0.45 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.45 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.45 tff(106,plain,
% 0.19/0.45 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(107,axiom,(![I: $i] : (plus(I, int_zero) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_zero')).
% 0.19/0.45 tff(108,plain,
% 0.19/0.45 (![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.45 tff(109,plain,(
% 0.19/0.45 ![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.45 inference(skolemize,[status(sab)],[108])).
% 0.19/0.45 tff(110,plain,
% 0.19/0.45 (![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.19/0.45 tff(111,plain,
% 0.19/0.45 ((~![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))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(112,plain,
% 0.19/0.45 (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = tptp_fun_K_0(I!2, int_zero)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.45 tff(113,plain,
% 0.19/0.45 (tptp_fun_K_0(I!2, int_zero) = plus(tptp_fun_K_0(I!2, int_zero), int_zero)),
% 0.19/0.45 inference(symmetry,[status(thm)],[112])).
% 0.19/0.45 tff(114,plain,
% 0.19/0.45 (tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[113, 103, 93, 47])).
% 0.19/0.45 tff(115,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(116,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.45 tff(117,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(118,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(119,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.45 tff(120,axiom,(![I: $i, J: $i] : (int_leq(I, J) <=> (int_less(I, J) | (I = J)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','int_leq')).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.19/0.45 tff(123,plain,(
% 0.19/0.45 ![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[122])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(J!1, n) <=> ((J!1 = n) | int_less(J!1, n)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(126,plain,
% 0.19/0.45 (int_leq(J!1, n) <=> ((J!1 = n) | int_less(J!1, n))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.19/0.45 tff(127,assumption,(~int_leq(J!1, n)), introduced(assumption)).
% 0.19/0.45 tff(128,plain,
% 0.19/0.45 ((~(int_leq(J!1, n) <=> ((J!1 = n) | int_less(J!1, n)))) | int_leq(J!1, n) | (~((J!1 = n) | int_less(J!1, n)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(129,plain,
% 0.19/0.45 ((~(int_leq(J!1, n) <=> ((J!1 = n) | int_less(J!1, n)))) | (~((J!1 = n) | int_less(J!1, n)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.19/0.45 tff(130,plain,
% 0.19/0.45 (~((J!1 = n) | int_less(J!1, n))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[129, 126])).
% 0.19/0.45 tff(131,plain,
% 0.19/0.45 (((J!1 = n) | int_less(J!1, n)) | (~int_less(J!1, n))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(132,plain,
% 0.19/0.45 (~int_less(J!1, n)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.19/0.45 tff(133,plain,
% 0.19/0.45 ((n = I!2) <=> (I!2 = n)),
% 0.19/0.45 inference(commutativity,[status(thm)],[])).
% 0.19/0.45 tff(134,plain,
% 0.19/0.45 ((~(n = I!2)) <=> (~(I!2 = n))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[133])).
% 0.19/0.45 tff(135,plain,
% 0.19/0.45 (^[I: $i, J: $i] : refl((int_leq(J, I) | int_less(I, J)) <=> (int_leq(J, I) | int_less(I, J)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(136,plain,
% 0.19/0.45 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[135])).
% 0.19/0.45 tff(137,plain,
% 0.19/0.45 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(138,plain,
% 0.19/0.45 (^[I: $i, J: $i] : rewrite((int_less(I, J) | int_leq(J, I)) <=> (int_leq(J, I) | int_less(I, J)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 (![I: $i, J: $i] : (int_less(I, J) | int_leq(J, I)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[138])).
% 0.19/0.46 tff(140,axiom,(![I: $i, J: $i] : (int_less(I, J) | int_leq(J, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','int_less_total')).
% 0.19/0.46 tff(141,plain,
% 0.19/0.46 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.46 tff(142,plain,
% 0.19/0.46 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.19/0.46 tff(143,plain,(
% 0.19/0.46 ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.19/0.46 inference(skolemize,[status(sab)],[142])).
% 0.19/0.46 tff(144,plain,
% 0.19/0.46 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 (((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | (int_leq(J!1, n) | int_less(n, J!1))) <=> ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | int_leq(J!1, n) | int_less(n, J!1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(146,plain,
% 0.19/0.46 ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | (int_leq(J!1, n) | int_less(n, J!1))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(147,plain,
% 0.19/0.46 ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | int_leq(J!1, n) | int_less(n, J!1)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.46 tff(148,plain,
% 0.19/0.46 (int_less(n, J!1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[147, 144, 127])).
% 0.19/0.46 tff(149,plain,
% 0.19/0.46 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | ((~int_less(J!1, I!2)) | (~int_less(n, J!1)) | int_less(n, I!2))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(J!1, I!2)) | (~int_less(n, J!1)) | int_less(n, I!2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(150,plain,
% 0.19/0.46 ((int_less(n, I!2) | (~int_less(J!1, I!2)) | (~int_less(n, J!1))) <=> ((~int_less(J!1, I!2)) | (~int_less(n, J!1)) | int_less(n, I!2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(151,plain,
% 0.19/0.46 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(n, I!2) | (~int_less(J!1, I!2)) | (~int_less(n, J!1)))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | ((~int_less(J!1, I!2)) | (~int_less(n, J!1)) | int_less(n, I!2)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[150])).
% 0.19/0.46 tff(152,plain,
% 0.19/0.46 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(n, I!2) | (~int_less(J!1, I!2)) | (~int_less(n, J!1)))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(J!1, I!2)) | (~int_less(n, J!1)) | int_less(n, I!2))),
% 0.19/0.46 inference(transitivity,[status(thm)],[151, 149])).
% 0.19/0.46 tff(153,plain,
% 0.19/0.46 ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(n, I!2) | (~int_less(J!1, I!2)) | (~int_less(n, J!1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(154,plain,
% 0.19/0.46 ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(J!1, I!2)) | (~int_less(n, J!1)) | int_less(n, I!2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.46 tff(155,plain,
% 0.19/0.46 (int_less(n, I!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[154, 81, 35, 148])).
% 0.19/0.46 tff(156,plain,
% 0.19/0.46 (^[I: $i, J: $i] : refl(((~(I = J)) | (~int_less(I, J))) <=> ((~(I = J)) | (~int_less(I, J))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(157,plain,
% 0.19/0.46 (![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J))) <=> ![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[156])).
% 0.19/0.46 tff(158,plain,
% 0.19/0.46 (![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J))) <=> ![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(159,plain,
% 0.19/0.46 (^[I: $i, J: $i] : rewrite((int_less(I, J) => (~(I = J))) <=> ((~(I = J)) | (~int_less(I, J))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(160,plain,
% 0.19/0.46 (![I: $i, J: $i] : (int_less(I, J) => (~(I = J))) <=> ![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[159])).
% 0.19/0.46 tff(161,axiom,(![I: $i, J: $i] : (int_less(I, J) => (~(I = J)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','int_less_irreflexive')).
% 0.19/0.46 tff(162,plain,
% 0.19/0.46 (![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.46 tff(163,plain,
% 0.19/0.46 (![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.19/0.46 tff(164,plain,(
% 0.19/0.46 ![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[163])).
% 0.19/0.46 tff(165,plain,
% 0.19/0.46 (![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.19/0.46 tff(166,plain,
% 0.19/0.46 (((~![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J)))) | ((~(n = I!2)) | (~int_less(n, I!2)))) <=> ((~![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J)))) | (~(n = I!2)) | (~int_less(n, I!2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(167,plain,
% 0.19/0.46 ((~![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J)))) | ((~(n = I!2)) | (~int_less(n, I!2)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 ((~![I: $i, J: $i] : ((~(I = J)) | (~int_less(I, J)))) | (~(n = I!2)) | (~int_less(n, I!2))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.19/0.46 tff(169,plain,
% 0.19/0.46 (~(n = I!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[168, 165, 155])).
% 0.19/0.46 tff(170,plain,
% 0.19/0.46 (~(I!2 = n)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[169, 134])).
% 0.19/0.46 tff(171,plain,
% 0.19/0.46 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(I!2, n) <=> ((I!2 = n) | int_less(I!2, n)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(172,plain,
% 0.19/0.46 (int_leq(I!2, n) <=> ((I!2 = n) | int_less(I!2, n))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[171, 124])).
% 0.19/0.46 tff(173,plain,
% 0.19/0.46 (int_leq(I!2, n)),
% 0.19/0.46 inference(and_elim,[status(thm)],[34])).
% 0.19/0.46 tff(174,plain,
% 0.19/0.46 ((~(int_leq(I!2, n) <=> ((I!2 = n) | int_less(I!2, n)))) | (~int_leq(I!2, n)) | ((I!2 = n) | int_less(I!2, n))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(175,plain,
% 0.19/0.46 ((~(int_leq(I!2, n) <=> ((I!2 = n) | int_less(I!2, n)))) | ((I!2 = n) | int_less(I!2, n))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.19/0.46 tff(176,plain,
% 0.19/0.46 ((I!2 = n) | int_less(I!2, n)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[175, 172])).
% 0.19/0.46 tff(177,plain,
% 0.19/0.46 ((~((I!2 = n) | int_less(I!2, n))) | (I!2 = n) | int_less(I!2, n)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(178,plain,
% 0.19/0.46 ((I!2 = n) | int_less(I!2, n)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.19/0.46 tff(179,plain,
% 0.19/0.46 (int_less(I!2, n)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[178, 170])).
% 0.19/0.46 tff(180,plain,
% 0.19/0.46 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | ((~int_less(I!2, n)) | (~int_less(J!1, I!2)) | int_less(J!1, n))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(I!2, n)) | (~int_less(J!1, I!2)) | int_less(J!1, n))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(181,plain,
% 0.19/0.46 ((int_less(J!1, n) | (~int_less(I!2, n)) | (~int_less(J!1, I!2))) <=> ((~int_less(I!2, n)) | (~int_less(J!1, I!2)) | int_less(J!1, n))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(182,plain,
% 0.19/0.46 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(J!1, n) | (~int_less(I!2, n)) | (~int_less(J!1, I!2)))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | ((~int_less(I!2, n)) | (~int_less(J!1, I!2)) | int_less(J!1, n)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[181])).
% 0.19/0.46 tff(183,plain,
% 0.19/0.46 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(J!1, n) | (~int_less(I!2, n)) | (~int_less(J!1, I!2)))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(I!2, n)) | (~int_less(J!1, I!2)) | int_less(J!1, n))),
% 0.19/0.46 inference(transitivity,[status(thm)],[182, 180])).
% 0.19/0.46 tff(184,plain,
% 0.19/0.46 ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(J!1, n) | (~int_less(I!2, n)) | (~int_less(J!1, I!2)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(185,plain,
% 0.19/0.46 ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(I!2, n)) | (~int_less(J!1, I!2)) | int_less(J!1, n)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.19/0.46 tff(186,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[185, 81, 35, 179, 132])).
% 0.19/0.46 tff(187,plain,(int_leq(J!1, n)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(188,plain,
% 0.19/0.46 (tptp_fun_K_0(I!2, int_zero) = I!2),
% 0.19/0.46 inference(transitivity,[status(thm)],[113, 103, 93])).
% 0.19/0.46 tff(189,plain,
% 0.19/0.46 (int_leq(tptp_fun_K_0(I!2, int_zero), n) <=> int_leq(I!2, n)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[188])).
% 0.19/0.46 tff(190,plain,
% 0.19/0.46 (int_leq(I!2, n) <=> int_leq(tptp_fun_K_0(I!2, int_zero), n)),
% 0.19/0.46 inference(symmetry,[status(thm)],[189])).
% 0.19/0.46 tff(191,plain,
% 0.19/0.46 (int_leq(tptp_fun_K_0(I!2, int_zero), n)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[173, 190])).
% 0.19/0.46 tff(192,plain,
% 0.19/0.46 ((~![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)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(193,plain,
% 0.19/0.46 (int_less(int_zero, tptp_fun_K_0(I!2, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[192, 63])).
% 0.19/0.46 tff(194,plain,
% 0.19/0.46 (((~(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))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(195,plain,
% 0.19/0.46 (int_less(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[194, 91])).
% 0.19/0.46 tff(196,plain,
% 0.19/0.46 ((~(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))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(197,plain,
% 0.19/0.46 ((~(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))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.19/0.46 tff(198,plain,
% 0.19/0.46 (int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[197, 193])).
% 0.19/0.46 tff(199,plain,
% 0.19/0.46 (^[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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(200,plain,
% 0.19/0.46 (![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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[199])).
% 0.19/0.46 tff(201,plain,
% 0.19/0.46 (^[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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(202,plain,
% 0.19/0.46 (![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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[201])).
% 0.19/0.46 tff(203,plain,
% 0.19/0.46 (![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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[202, 200])).
% 0.19/0.46 tff(204,plain,
% 0.19/0.46 (^[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(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_zero, C) & (J = plus(I, C))) <=> (~((~int_leq(int_zero, C)) | (~(J = plus(I, C)))))), ((~(int_leq(int_zero, C) & (J = plus(I, C)))) <=> (~(~((~int_leq(int_zero, C)) | (~(J = plus(I, C)))))))), rewrite((~(~((~int_leq(int_zero, C)) | (~(J = plus(I, C)))))) <=> ((~int_leq(int_zero, C)) | (~(J = plus(I, C))))), ((~(int_leq(int_zero, C) & (J = plus(I, C)))) <=> ((~int_leq(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)) = lu(K, plus(K, C)))) <=> (((~int_leq(int_one, K)) | (~int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))) <=> ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))), (((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))) <=> ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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)) = lu(K, plus(K, C)))) <=> ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))) <=> (((~int_leq(int_zero, C)) | (~(J = plus(I, C)))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), rewrite((((~int_leq(int_zero, C)) | (~(J = plus(I, C)))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))) <=> ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))) <=> ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))), (![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))) <=> ![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))) <=> (![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)))) & ![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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)))) & ![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))) <=> (~((~![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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> (((~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ((~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(205,plain,
% 0.19/0.47 (![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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ![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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[204])).
% 0.19/0.47 tff(206,plain,
% 0.19/0.47 (![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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ![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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(207,plain,
% 0.19/0.47 (^[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)))), 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))) & ![C: $i] : ((int_leq(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = lu(K, plus(K, C)))))) <=> (![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_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))), (((((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))) & ![C: $i] : ((int_leq(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ((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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))))), 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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ((~(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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))), (((((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))) & ![C: $i] : ((int_leq(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ((~(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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(208,plain,
% 0.19/0.47 (![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))) & ![C: $i] : ((int_leq(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ![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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[207])).
% 0.19/0.47 tff(209,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))) & ![C: $i] : ((int_leq(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = lu(K, plus(K, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qiu')).
% 0.19/0.47 tff(210,plain,
% 0.19/0.47 (![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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 (![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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[210, 206])).
% 0.19/0.47 tff(212,plain,(
% 0.19/0.47 ![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))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[211])).
% 0.19/0.47 tff(213,plain,
% 0.19/0.47 (![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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[212, 205])).
% 0.19/0.47 tff(214,plain,
% 0.19/0.47 (![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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[213, 203])).
% 0.19/0.47 tff(215,plain,
% 0.19/0.47 (((~![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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), 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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), 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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(216,plain,
% 0.19/0.47 (((~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))) <=> ((~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), 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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(217,plain,
% 0.19/0.47 ((~((~![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_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(218,plain,
% 0.19/0.47 (((~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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)) | (~((~![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_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[217])).
% 0.19/0.48 tff(219,plain,
% 0.19/0.48 (((~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))) <=> ((~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), 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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[218, 216])).
% 0.19/0.48 tff(220,plain,
% 0.19/0.48 (((~![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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), 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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[219])).
% 0.19/0.48 tff(221,plain,
% 0.19/0.48 (((~![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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), 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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[220, 215])).
% 0.19/0.48 tff(222,plain,
% 0.19/0.48 ((~![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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(223,plain,
% 0.19/0.48 ((~![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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), 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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.19/0.48 tff(224,plain,
% 0.19/0.48 ((~int_leq(J!1, n)) | (~int_leq(tptp_fun_K_0(I!2, int_zero), 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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[223, 214, 66, 198])).
% 0.19/0.48 tff(225,plain,
% 0.19/0.48 ((~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))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[224, 191])).
% 0.19/0.48 tff(226,plain,
% 0.19/0.48 (~((~![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_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[225, 187])).
% 0.19/0.48 tff(227,plain,
% 0.19/0.48 (((~![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_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~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))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(228,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.19/0.48 tff(229,plain,
% 0.19/0.48 (((~(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))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(230,plain,
% 0.19/0.48 (int_less(int_zero, tptp_fun_K_0(I!2, J!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[229, 38])).
% 0.19/0.48 tff(231,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(232,plain,
% 0.19/0.48 (((~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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(233,plain,
% 0.19/0.48 (((~![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))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[232])).
% 0.19/0.48 tff(234,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[233, 231])).
% 0.19/0.48 tff(235,plain,
% 0.19/0.48 ((~![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))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(236,plain,
% 0.19/0.48 ((~![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))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.19/0.48 tff(237,plain,
% 0.19/0.48 (![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))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[236, 230, 228, 114])).
% 0.19/0.48 tff(238,plain,
% 0.19/0.48 (((~![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))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(239,plain,
% 0.19/0.48 ((~![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))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(240,plain,
% 0.19/0.48 ((~![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)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.19/0.48 tff(241,plain,
% 0.19/0.48 ((~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[240, 66, 237])).
% 0.19/0.48 tff(242,plain,
% 0.19/0.48 (~int_leq(J!1, J!1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[241, 46])).
% 0.19/0.48 tff(243,plain,
% 0.19/0.48 (((~![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))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(244,plain,
% 0.19/0.48 ((int_leq(J!1, J!1) <=> $true) <=> int_leq(J!1, J!1)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(245,plain,
% 0.19/0.49 (($true | int_less(J!1, J!1)) <=> $true),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(246,plain,
% 0.19/0.49 ((J!1 = J!1) <=> $true),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(247,plain,
% 0.19/0.49 (((J!1 = J!1) | int_less(J!1, J!1)) <=> ($true | int_less(J!1, J!1))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[246])).
% 0.19/0.49 tff(248,plain,
% 0.19/0.49 (((J!1 = J!1) | int_less(J!1, J!1)) <=> $true),
% 0.19/0.49 inference(transitivity,[status(thm)],[247, 245])).
% 0.19/0.49 tff(249,plain,
% 0.19/0.49 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> (int_leq(J!1, J!1) <=> $true)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[248])).
% 0.19/0.49 tff(250,plain,
% 0.19/0.49 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> int_leq(J!1, J!1)),
% 0.19/0.49 inference(transitivity,[status(thm)],[249, 244])).
% 0.19/0.49 tff(251,plain,
% 0.19/0.49 (((~![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))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.49 tff(252,plain,
% 0.19/0.49 (((~![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))),
% 0.19/0.49 inference(transitivity,[status(thm)],[251, 243])).
% 0.19/0.49 tff(253,plain,
% 0.19/0.49 ((~![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)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(254,plain,
% 0.19/0.49 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.19/0.49 tff(255,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[254, 124, 242])).
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------