%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV486+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:34:09 AM UTC 2025
% Result : Theorem 0.19s 0.51s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV486+2 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:52:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 % SZS output start Proof
% 0.19/0.51 tff(int_leq_type, type, (
% 0.19/0.51 int_leq: ( $i * $i ) > $o)).
% 0.19/0.51 tff(tptp_fun_I_2_type, type, (
% 0.19/0.51 tptp_fun_I_2: $i)).
% 0.19/0.51 tff(real_zero_type, type, (
% 0.19/0.51 real_zero: $i)).
% 0.19/0.51 tff(a_type, type, (
% 0.19/0.51 a: ( $i * $i ) > $i)).
% 0.19/0.51 tff(plus_type, type, (
% 0.19/0.51 plus: ( $i * $i ) > $i)).
% 0.19/0.51 tff(tptp_fun_K_0_type, type, (
% 0.19/0.51 tptp_fun_K_0: ( $i * $i ) > $i)).
% 0.19/0.51 tff(tptp_fun_J_1_type, type, (
% 0.19/0.51 tptp_fun_J_1: $i)).
% 0.19/0.51 tff(int_less_type, type, (
% 0.19/0.51 int_less: ( $i * $i ) > $o)).
% 0.19/0.51 tff(int_zero_type, type, (
% 0.19/0.51 int_zero: $i)).
% 0.19/0.51 tff(n_type, type, (
% 0.19/0.51 n: $i)).
% 0.19/0.51 tff(int_one_type, type, (
% 0.19/0.51 int_one: $i)).
% 0.19/0.51 tff(lu_type, type, (
% 0.19/0.51 lu: ( $i * $i ) > $i)).
% 0.19/0.51 tff(real_one_type, type, (
% 0.19/0.51 real_one: $i)).
% 0.19/0.51 tff(1,plain,
% 0.19/0.51 (^[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))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(2,plain,
% 0.19/0.51 (![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))))) <=> ![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)))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.51 tff(3,plain,
% 0.19/0.51 (^[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))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(4,plain,
% 0.19/0.51 (![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))))) <=> ![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)))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.51 tff(5,plain,
% 0.19/0.51 (![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K))))))) <=> ![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)))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.51 tff(6,plain,
% 0.19/0.51 (^[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)))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(7,plain,
% 0.19/0.51 (![I: $i, J: $i] : (((~int_less(I, J)) | ((plus(I, tptp_fun_K_0(J, I)) = J) & int_less(int_zero, tptp_fun_K_0(J, I)))) & (int_less(I, J) | ![K: $i] : (~((plus(I, K) = J) & int_less(int_zero, K))))) <=> ![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)))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.51 tff(8,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 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/sandbox/benchmark/theBenchmark.p','plus_and_inverse')).
% 0.19/0.51 tff(10,plain,
% 0.19/0.51 (![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.51 tff(11,plain,(
% 0.19/0.51 ![I: $i, J: $i] : (((~int_less(I, J)) | ((plus(I, tptp_fun_K_0(J, I)) = J) & int_less(int_zero, tptp_fun_K_0(J, I)))) & (int_less(I, J) | ![K: $i] : (~((plus(I, K) = J) & int_less(int_zero, K)))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[10])).
% 0.19/0.51 tff(12,plain,
% 0.19/0.51 (![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.51 tff(13,plain,
% 0.19/0.51 (![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.51 tff(14,plain,
% 0.19/0.51 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(15,plain,
% 0.19/0.51 ((~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1)))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(16,plain,
% 0.19/0.51 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.51 tff(17,plain,
% 0.19/0.51 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.51 tff(18,plain,
% 0.19/0.51 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K)))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(19,plain,
% 0.19/0.51 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1)))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.51 tff(20,plain,
% 0.19/0.51 (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.19/0.51 tff(21,plain,
% 0.19/0.51 (((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1)))))) | ((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(22,plain,
% 0.19/0.51 ((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.51 tff(23,plain,
% 0.19/0.51 ((~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero))) <=> (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(24,plain,
% 0.19/0.52 ((~![I: $i, J: $i] : (((int_leq(int_one, I) & int_less(I, J)) & int_leq(J, n)) => (a(I, J) = real_zero))) <=> (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(25,axiom,(~![I: $i, J: $i] : (((int_leq(int_one, I) & int_less(I, J)) & int_leq(J, n)) => (a(I, J) = real_zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lt')).
% 0.19/0.52 tff(26,plain,
% 0.19/0.52 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.52 tff(27,plain,
% 0.19/0.52 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.19/0.52 tff(28,plain,
% 0.19/0.52 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.52 tff(29,plain,
% 0.19/0.52 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.19/0.52 tff(30,plain,(
% 0.19/0.52 ~((~(int_leq(int_one, I!2) & int_less(I!2, J!1) & int_leq(J!1, n))) | (a(I!2, J!1) = real_zero))),
% 0.19/0.52 inference(skolemize,[status(sab)],[29])).
% 0.19/0.52 tff(31,plain,
% 0.19/0.52 (int_leq(int_one, I!2) & int_less(I!2, J!1) & int_leq(J!1, n)),
% 0.19/0.52 inference(or_elim,[status(thm)],[30])).
% 0.19/0.52 tff(32,plain,
% 0.19/0.52 (int_less(I!2, J!1)),
% 0.19/0.52 inference(and_elim,[status(thm)],[31])).
% 0.19/0.52 tff(33,plain,
% 0.19/0.52 ((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(34,plain,
% 0.19/0.52 ((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.52 tff(35,plain,
% 0.19/0.52 (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[34, 22])).
% 0.19/0.52 tff(36,plain,
% 0.19/0.52 (((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))) | (plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(37,plain,
% 0.19/0.52 (plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.52 tff(38,plain,
% 0.19/0.52 (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = a(I!2, J!1)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.52 tff(39,plain,
% 0.19/0.52 ((a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero) <=> (a(I!2, J!1) = real_zero)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.52 tff(40,plain,
% 0.19/0.52 ((a(I!2, J!1) = real_zero) <=> (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero)),
% 0.19/0.52 inference(symmetry,[status(thm)],[39])).
% 0.19/0.52 tff(41,plain,
% 0.19/0.52 ((~(a(I!2, J!1) = real_zero)) <=> (~(a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.52 tff(42,plain,
% 0.19/0.52 (~(a(I!2, J!1) = real_zero)),
% 0.19/0.52 inference(or_elim,[status(thm)],[30])).
% 0.19/0.52 tff(43,plain,
% 0.19/0.52 (~(a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.52 tff(44,plain,
% 0.19/0.52 (J!1 = plus(I!2, tptp_fun_K_0(J!1, I!2))),
% 0.19/0.52 inference(symmetry,[status(thm)],[37])).
% 0.19/0.52 tff(45,plain,
% 0.19/0.52 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(46,plain,
% 0.19/0.52 ((~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~(plus(int_zero, K) = J!1)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1)))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(47,plain,
% 0.19/0.52 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~(plus(int_zero, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1))))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.52 tff(48,plain,
% 0.19/0.52 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~(plus(int_zero, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.52 tff(49,plain,
% 0.19/0.52 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~(plus(int_zero, K) = J!1)) | (~int_less(int_zero, K)))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(50,plain,
% 0.19/0.52 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1)))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.52 tff(51,plain,
% 0.19/0.52 (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[50, 13])).
% 0.19/0.52 tff(52,plain,
% 0.19/0.52 (((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1)))))) | ((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(53,plain,
% 0.19/0.52 ((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.52 tff(54,plain,
% 0.19/0.52 (^[I: $i] : refl((int_less(int_zero, I) <=> int_leq(int_one, I)) <=> (int_less(int_zero, I) <=> int_leq(int_one, I)))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(55,plain,
% 0.19/0.52 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.52 tff(56,plain,
% 0.19/0.52 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(57,axiom,(![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','one_successor_of_zero')).
% 0.19/0.52 tff(58,plain,
% 0.19/0.52 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.52 tff(59,plain,(
% 0.19/0.52 ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.52 inference(skolemize,[status(sab)],[58])).
% 0.19/0.52 tff(60,plain,
% 0.19/0.52 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.52 tff(61,plain,
% 0.19/0.52 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, I!2) <=> int_leq(int_one, I!2))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(62,plain,
% 0.19/0.52 (int_less(int_zero, I!2) <=> int_leq(int_one, I!2)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.19/0.52 tff(63,plain,
% 0.19/0.52 (int_leq(int_one, I!2)),
% 0.19/0.52 inference(and_elim,[status(thm)],[31])).
% 0.19/0.52 tff(64,plain,
% 0.19/0.52 ((~(int_less(int_zero, I!2) <=> int_leq(int_one, I!2))) | int_less(int_zero, I!2) | (~int_leq(int_one, I!2))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(65,plain,
% 0.19/0.52 ((~(int_less(int_zero, I!2) <=> int_leq(int_one, I!2))) | int_less(int_zero, I!2)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.52 tff(66,plain,
% 0.19/0.52 (int_less(int_zero, I!2)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[65, 62])).
% 0.19/0.52 tff(67,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(68,plain,
% 0.19/0.52 (^[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)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(69,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.52 tff(70,plain,
% 0.19/0.52 (![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))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(71,plain,
% 0.19/0.52 (^[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)))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(72,plain,
% 0.19/0.52 (![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))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.52 tff(73,axiom,(![I: $i, J: $i, K: $i] : ((int_less(I, J) & int_less(J, K)) => int_less(I, K))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','int_less_transitive')).
% 0.19/0.52 tff(74,plain,
% 0.19/0.52 (![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.52 tff(75,plain,
% 0.19/0.52 (![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.19/0.52 tff(76,plain,(
% 0.19/0.52 ![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K))),
% 0.19/0.52 inference(skolemize,[status(sab)],[75])).
% 0.19/0.52 tff(77,plain,
% 0.19/0.52 (![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.19/0.52 tff(78,plain,
% 0.19/0.52 (![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.19/0.52 tff(79,plain,
% 0.19/0.52 (((~![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(I!2, J!1)) | 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, I!2)) | (~int_less(I!2, J!1)) | int_less(int_zero, J!1))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(80,plain,
% 0.19/0.52 ((int_less(int_zero, J!1) | (~int_less(I!2, J!1)) | (~int_less(int_zero, I!2))) <=> ((~int_less(int_zero, I!2)) | (~int_less(I!2, J!1)) | int_less(int_zero, J!1))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(81,plain,
% 0.19/0.52 (((~![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(I!2, J!1)) | (~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, I!2)) | (~int_less(I!2, J!1)) | int_less(int_zero, J!1)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[80])).
% 0.19/0.52 tff(82,plain,
% 0.19/0.52 (((~![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(I!2, J!1)) | (~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, I!2)) | (~int_less(I!2, J!1)) | int_less(int_zero, J!1))),
% 0.19/0.52 inference(transitivity,[status(thm)],[81, 79])).
% 0.19/0.52 tff(83,plain,
% 0.19/0.52 ((~![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(I!2, J!1)) | (~int_less(int_zero, I!2)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(84,plain,
% 0.19/0.52 ((~![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(I!2, J!1)) | int_less(int_zero, J!1)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.52 tff(85,plain,
% 0.19/0.52 (int_less(int_zero, J!1)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[84, 78, 32, 66])).
% 0.19/0.52 tff(86,plain,
% 0.19/0.52 ((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(87,plain,
% 0.19/0.52 ((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.52 tff(88,plain,
% 0.19/0.52 (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[87, 53])).
% 0.19/0.52 tff(89,plain,
% 0.19/0.52 (((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1))) | (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(90,plain,
% 0.19/0.52 (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.19/0.52 tff(91,plain,
% 0.19/0.52 (^[I: $i, J: $i] : refl((plus(I, J) = plus(J, I)) <=> (plus(I, J) = plus(J, I)))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(92,plain,
% 0.19/0.52 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.52 tff(93,plain,
% 0.19/0.52 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(94,axiom,(![I: $i, J: $i] : (plus(I, J) = plus(J, I))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus_commutative')).
% 0.19/0.52 tff(95,plain,
% 0.19/0.52 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.52 tff(96,plain,(
% 0.19/0.52 ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.52 inference(skolemize,[status(sab)],[95])).
% 0.19/0.52 tff(97,plain,
% 0.19/0.52 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.52 tff(98,plain,
% 0.19/0.52 ((~![I: $i, J: $i] : (plus(I, J) = plus(J, I))) | (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = plus(tptp_fun_K_0(J!1, int_zero), int_zero))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(99,plain,
% 0.19/0.52 (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = plus(tptp_fun_K_0(J!1, int_zero), int_zero)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.52 tff(100,plain,
% 0.19/0.52 (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = plus(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.19/0.52 inference(symmetry,[status(thm)],[99])).
% 0.19/0.52 tff(101,plain,
% 0.19/0.52 (^[I: $i] : refl((plus(I, int_zero) = I) <=> (plus(I, int_zero) = I))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(102,plain,
% 0.19/0.52 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.52 inference(quant_intro,[status(thm)],[101])).
% 0.19/0.52 tff(103,plain,
% 0.19/0.52 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(104,axiom,(![I: $i] : (plus(I, int_zero) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus_zero')).
% 0.19/0.52 tff(105,plain,
% 0.19/0.52 (![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.52 tff(106,plain,(
% 0.19/0.52 ![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.52 inference(skolemize,[status(sab)],[105])).
% 0.19/0.52 tff(107,plain,
% 0.19/0.52 (![I: $i] : (plus(I, int_zero) = I)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.19/0.52 tff(108,plain,
% 0.19/0.52 ((~![I: $i] : (plus(I, int_zero) = I)) | (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = tptp_fun_K_0(J!1, int_zero))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(109,plain,
% 0.19/0.52 (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = tptp_fun_K_0(J!1, int_zero)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.52 tff(110,plain,
% 0.19/0.52 (tptp_fun_K_0(J!1, int_zero) = plus(tptp_fun_K_0(J!1, int_zero), int_zero)),
% 0.19/0.52 inference(symmetry,[status(thm)],[109])).
% 0.19/0.52 tff(111,plain,
% 0.19/0.52 (tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2))),
% 0.19/0.52 inference(transitivity,[status(thm)],[110, 100, 90, 44])).
% 0.19/0.52 tff(112,plain,
% 0.19/0.52 (^[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))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(113,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.52 tff(114,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(115,plain,
% 0.19/0.52 (^[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))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(116,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.52 tff(117,axiom,(![I: $i, J: $i] : (int_leq(I, J) <=> (int_less(I, J) | (I = J)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','int_leq')).
% 0.19/0.52 tff(118,plain,
% 0.19/0.52 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.52 tff(119,plain,
% 0.19/0.52 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.19/0.52 tff(120,plain,(
% 0.19/0.52 ![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.19/0.52 inference(skolemize,[status(sab)],[119])).
% 0.19/0.52 tff(121,plain,
% 0.19/0.52 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.19/0.52 tff(122,plain,
% 0.19/0.52 ((~![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)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(123,plain,
% 0.19/0.52 (int_leq(I!2, n) <=> ((I!2 = n) | int_less(I!2, n))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.19/0.52 tff(124,assumption,(~int_less(I!2, n)), introduced(assumption)).
% 0.19/0.52 tff(125,plain,
% 0.19/0.52 ((plus(I!2, tptp_fun_K_0(J!1, I!2)) = n) <=> (J!1 = n)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.52 tff(126,plain,
% 0.19/0.52 ((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = n)) <=> (~(J!1 = n))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.52 tff(127,plain,
% 0.19/0.52 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, I!2))) | (~(plus(I!2, tptp_fun_K_0(n, I!2)) = n)))))) | (~(int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, I!2))) | (~(plus(I!2, tptp_fun_K_0(n, I!2)) = n)))))) | (~(int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(128,plain,
% 0.19/0.52 ((~((~((~int_less(I!2, n)) | (~((~(plus(I!2, tptp_fun_K_0(n, I!2)) = n)) | (~int_less(int_zero, tptp_fun_K_0(n, I!2))))))) | (~(int_less(I!2, n) | ![K: $i] : ((~(plus(I!2, K) = n)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(I!2, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, I!2))) | (~(plus(I!2, tptp_fun_K_0(n, I!2)) = n)))))) | (~(int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n)))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(129,plain,
% 0.19/0.52 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, n)) | (~((~(plus(I!2, tptp_fun_K_0(n, I!2)) = n)) | (~int_less(int_zero, tptp_fun_K_0(n, I!2))))))) | (~(int_less(I!2, n) | ![K: $i] : ((~(plus(I!2, K) = n)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, I!2))) | (~(plus(I!2, tptp_fun_K_0(n, I!2)) = n)))))) | (~(int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.53 tff(130,plain,
% 0.19/0.53 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, n)) | (~((~(plus(I!2, tptp_fun_K_0(n, I!2)) = n)) | (~int_less(int_zero, tptp_fun_K_0(n, I!2))))))) | (~(int_less(I!2, n) | ![K: $i] : ((~(plus(I!2, K) = n)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, I!2))) | (~(plus(I!2, tptp_fun_K_0(n, I!2)) = n)))))) | (~(int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[129, 127])).
% 0.19/0.53 tff(131,plain,
% 0.19/0.53 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, n)) | (~((~(plus(I!2, tptp_fun_K_0(n, I!2)) = n)) | (~int_less(int_zero, tptp_fun_K_0(n, I!2))))))) | (~(int_less(I!2, n) | ![K: $i] : ((~(plus(I!2, K) = n)) | (~int_less(int_zero, K)))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(132,plain,
% 0.19/0.53 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, I!2))) | (~(plus(I!2, tptp_fun_K_0(n, I!2)) = n)))))) | (~(int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n)))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.53 tff(133,plain,
% 0.19/0.53 (~((~((~int_less(I!2, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, I!2))) | (~(plus(I!2, tptp_fun_K_0(n, I!2)) = n)))))) | (~(int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n))))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[132, 13])).
% 0.19/0.53 tff(134,plain,
% 0.19/0.53 (((~((~int_less(I!2, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, I!2))) | (~(plus(I!2, tptp_fun_K_0(n, I!2)) = n)))))) | (~(int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n)))))) | (int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(135,plain,
% 0.19/0.53 (int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.53 tff(136,plain,
% 0.19/0.53 ((~(int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n))))) | int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(137,plain,
% 0.19/0.53 ((~(int_less(I!2, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n))))) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[136, 124])).
% 0.19/0.53 tff(138,plain,
% 0.19/0.53 (![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[137, 135])).
% 0.19/0.53 tff(139,plain,
% 0.19/0.53 (((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))) | int_less(int_zero, tptp_fun_K_0(J!1, I!2))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(140,plain,
% 0.19/0.53 (int_less(int_zero, tptp_fun_K_0(J!1, I!2))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[139, 35])).
% 0.19/0.53 tff(141,plain,
% 0.19/0.53 (((~![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n)))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = n)))) <=> ((~![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n)))) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = n)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(142,plain,
% 0.19/0.53 ((~![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n)))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = n)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(143,plain,
% 0.19/0.53 ((~![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = n)))) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = n))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.53 tff(144,plain,
% 0.19/0.53 (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = n)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[143, 140, 138])).
% 0.19/0.53 tff(145,plain,
% 0.19/0.53 (~(J!1 = n)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[144, 126])).
% 0.19/0.53 tff(146,plain,
% 0.19/0.53 ((~![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)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(147,plain,
% 0.19/0.53 (int_leq(J!1, n) <=> ((J!1 = n) | int_less(J!1, n))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[146, 121])).
% 0.19/0.53 tff(148,plain,
% 0.19/0.53 (int_leq(J!1, n)),
% 0.19/0.53 inference(and_elim,[status(thm)],[31])).
% 0.19/0.53 tff(149,plain,
% 0.19/0.53 ((~(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))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(150,plain,
% 0.19/0.53 ((~(int_leq(J!1, n) <=> ((J!1 = n) | int_less(J!1, n)))) | ((J!1 = n) | int_less(J!1, n))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.19/0.53 tff(151,plain,
% 0.19/0.53 ((J!1 = n) | int_less(J!1, n)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[150, 147])).
% 0.19/0.53 tff(152,plain,
% 0.19/0.53 ((~((J!1 = n) | int_less(J!1, n))) | (J!1 = n) | int_less(J!1, n)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(153,plain,
% 0.19/0.53 ((J!1 = n) | int_less(J!1, n)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.19/0.53 tff(154,plain,
% 0.19/0.53 (int_less(J!1, n)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[153, 145])).
% 0.19/0.53 tff(155,plain,
% 0.19/0.53 (((~![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, J!1)) | int_less(I!2, n))) <=> ((~![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, J!1)) | int_less(I!2, n))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(156,plain,
% 0.19/0.53 ((int_less(I!2, n) | (~int_less(J!1, n)) | (~int_less(I!2, J!1))) <=> ((~int_less(J!1, n)) | (~int_less(I!2, J!1)) | int_less(I!2, n))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(157,plain,
% 0.19/0.53 (((~![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, n)) | (~int_less(I!2, J!1)))) <=> ((~![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, J!1)) | int_less(I!2, n)))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[156])).
% 0.19/0.53 tff(158,plain,
% 0.19/0.53 (((~![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, n)) | (~int_less(I!2, J!1)))) <=> ((~![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, J!1)) | int_less(I!2, n))),
% 0.19/0.53 inference(transitivity,[status(thm)],[157, 155])).
% 0.19/0.53 tff(159,plain,
% 0.19/0.53 ((~![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, n)) | (~int_less(I!2, J!1)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(160,plain,
% 0.19/0.53 ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(J!1, n)) | (~int_less(I!2, J!1)) | int_less(I!2, n)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.53 tff(161,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[160, 78, 32, 154, 124])).
% 0.19/0.53 tff(162,plain,(int_less(I!2, n)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(163,plain,
% 0.19/0.53 (((I!2 = n) | int_less(I!2, n)) | (~int_less(I!2, n))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(164,plain,
% 0.19/0.53 ((I!2 = n) | int_less(I!2, n)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.19/0.53 tff(165,plain,
% 0.19/0.53 ((~(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)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(166,plain,
% 0.19/0.53 ((~(int_leq(I!2, n) <=> ((I!2 = n) | int_less(I!2, n)))) | int_leq(I!2, n)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.53 tff(167,plain,
% 0.19/0.53 (int_leq(I!2, n)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[166, 123])).
% 0.19/0.53 tff(168,plain,
% 0.19/0.53 (tptp_fun_K_0(J!1, int_zero) = J!1),
% 0.19/0.53 inference(transitivity,[status(thm)],[110, 100, 90])).
% 0.19/0.53 tff(169,plain,
% 0.19/0.53 (int_leq(tptp_fun_K_0(J!1, int_zero), n) <=> int_leq(J!1, n)),
% 0.19/0.53 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.53 tff(170,plain,
% 0.19/0.53 (int_leq(J!1, n) <=> int_leq(tptp_fun_K_0(J!1, int_zero), n)),
% 0.19/0.53 inference(symmetry,[status(thm)],[169])).
% 0.19/0.53 tff(171,plain,
% 0.19/0.53 (int_leq(tptp_fun_K_0(J!1, int_zero), n)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[148, 170])).
% 0.19/0.53 tff(172,plain,
% 0.19/0.53 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(173,plain,
% 0.19/0.53 (int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[172, 60])).
% 0.19/0.53 tff(174,plain,
% 0.19/0.53 (((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1))) | int_less(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(175,plain,
% 0.19/0.53 (int_less(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[174, 88])).
% 0.19/0.53 tff(176,plain,
% 0.19/0.53 ((~(int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero)))) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(177,plain,
% 0.19/0.53 ((~(int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero)))) | int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.19/0.53 tff(178,plain,
% 0.19/0.53 (int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[177, 173])).
% 0.19/0.53 tff(179,plain,
% 0.19/0.53 (^[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) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(180,plain,
% 0.19/0.53 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[179])).
% 0.19/0.53 tff(181,plain,
% 0.19/0.53 (^[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) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(182,plain,
% 0.19/0.53 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[181])).
% 0.19/0.53 tff(183,plain,
% 0.19/0.53 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[182, 180])).
% 0.19/0.53 tff(184,plain,
% 0.19/0.53 (^[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) = lu(plus(K, C), K))) <=> (((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K))))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K))) <=> ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J)))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K))) <=> ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~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) = lu(plus(K, C), K))) <=> ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~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) = lu(plus(K, C), K)))) <=> (((~int_less(int_zero, C)) | (~(I = plus(J, C)))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~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) = lu(plus(K, C), K)) | (~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) = lu(plus(K, C), K)) | (~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) = lu(plus(K, C), K)))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~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) = lu(plus(K, C), K)))) <=> ![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), quant_intro(proof_bind(^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, K) & int_leq(K, J)) <=> (~((~int_leq(int_one, K)) | (~int_leq(K, J))))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> (~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))))), rewrite((~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J)))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) <=> (((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(K, K) = real_one)))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(K, K) = real_one)) <=> ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) <=> ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) <=> ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_less(int_zero, C) & (J = plus(I, C))) <=> (~((~int_less(int_zero, C)) | (~(J = plus(I, C)))))), ((~(int_less(int_zero, C) & (J = plus(I, C)))) <=> (~(~((~int_less(int_zero, C)) | (~(J = plus(I, C)))))))), rewrite((~(~((~int_less(int_zero, C)) | (~(J = plus(I, C)))))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C))))), ((~(int_less(int_zero, C) & (J = plus(I, C)))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C)))))), quant_intro(proof_bind(^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, K) & int_leq(K, I)) <=> (~((~int_leq(int_one, K)) | (~int_leq(K, I))))), ((~(int_leq(int_one, K) & int_leq(K, I))) <=> (~(~((~int_leq(int_one, K)) | (~int_leq(K, I))))))), rewrite((~(~((~int_leq(int_one, K)) | (~int_leq(K, I))))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, I)))), ((~(int_leq(int_one, K) & int_leq(K, I))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> (((~int_leq(int_one, K)) | (~int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))), (((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> (((~int_less(int_zero, C)) | (~(J = plus(I, C)))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), rewrite((((~int_less(int_zero, C)) | (~(J = plus(I, C)))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))), (![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> ![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))) <=> (![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) & ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J))) & ![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))), rewrite((![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) & ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J))) & ![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))), ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))), (((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> (((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))), rewrite((((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))), (((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(185,plain,
% 0.19/0.54 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[184])).
% 0.19/0.54 tff(186,plain,
% 0.19/0.54 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(187,plain,
% 0.19/0.54 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite(((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) <=> (int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J))), ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) <=> ((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J)) & int_leq(J, n)))), rewrite(((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J)) & int_leq(J, n)) <=> (int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))), ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) <=> (int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)))), trans(monotonicity(rewrite((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[K: $i] : rewrite(((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)) <=> ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), (![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)) <=> ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), (((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))) <=> ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))), rewrite(((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), (((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))) <=> ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), (![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))) <=> ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))), (((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))) <=> ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one))) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), rewrite(((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one))) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))), (((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), (((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))))) <=> ((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) => (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))))), rewrite(((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) => (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), (((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))))) <=> ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(188,plain,
% 0.19/0.54 (![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))))) <=> ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[187])).
% 0.19/0.54 tff(189,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) = lu(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qil')).
% 0.19/0.54 tff(190,plain,
% 0.19/0.54 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.19/0.54 tff(191,plain,
% 0.19/0.54 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.19/0.54 tff(192,plain,(
% 0.19/0.54 ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = lu(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.19/0.54 inference(skolemize,[status(sab)],[191])).
% 0.19/0.54 tff(193,plain,
% 0.19/0.54 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.19/0.54 tff(194,plain,
% 0.19/0.54 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[193, 183])).
% 0.19/0.54 tff(195,plain,
% 0.19/0.54 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, 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) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(196,plain,
% 0.19/0.55 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))))) <=> ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(197,plain,
% 0.19/0.55 ((~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(198,plain,
% 0.19/0.55 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))) <=> ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[197])).
% 0.19/0.55 tff(199,plain,
% 0.19/0.55 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))) <=> ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[198, 196])).
% 0.19/0.55 tff(200,plain,
% 0.19/0.55 (((~![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) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[199])).
% 0.19/0.55 tff(201,plain,
% 0.19/0.55 (((~![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) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[200, 195])).
% 0.19/0.55 tff(202,plain,
% 0.19/0.55 ((~![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) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(203,plain,
% 0.19/0.55 ((~![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) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.19/0.55 tff(204,plain,
% 0.19/0.55 ((~int_leq(I!2, n)) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[203, 194, 63, 178])).
% 0.19/0.55 tff(205,plain,
% 0.19/0.55 ((~int_leq(I!2, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[204, 171])).
% 0.19/0.55 tff(206,plain,
% 0.19/0.55 (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[205, 167])).
% 0.19/0.55 tff(207,plain,
% 0.19/0.55 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = lu(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))) | ![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(208,plain,
% 0.19/0.55 (![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.19/0.55 tff(209,plain,
% 0.19/0.55 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero)))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(210,plain,
% 0.19/0.55 (((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))) <=> ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(211,plain,
% 0.19/0.55 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[210])).
% 0.19/0.55 tff(212,plain,
% 0.19/0.55 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[211, 209])).
% 0.19/0.56 tff(213,plain,
% 0.19/0.56 ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(214,plain,
% 0.19/0.56 ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.56 tff(215,plain,
% 0.19/0.56 (![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[214, 140, 208, 111])).
% 0.19/0.56 tff(216,plain,
% 0.19/0.56 (((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero))) <=> ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(217,plain,
% 0.19/0.56 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(218,plain,
% 0.19/0.56 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.19/0.56 tff(219,plain,
% 0.19/0.56 ((~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[218, 63, 215])).
% 0.19/0.56 tff(220,plain,
% 0.19/0.56 (~int_leq(I!2, I!2)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[219, 43])).
% 0.19/0.56 tff(221,plain,
% 0.19/0.56 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2)) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(222,plain,
% 0.19/0.56 ((int_leq(I!2, I!2) <=> $true) <=> int_leq(I!2, I!2)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(223,plain,
% 0.19/0.56 (($true | int_less(I!2, I!2)) <=> $true),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(224,plain,
% 0.19/0.56 ((I!2 = I!2) <=> $true),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(225,plain,
% 0.19/0.56 (((I!2 = I!2) | int_less(I!2, I!2)) <=> ($true | int_less(I!2, I!2))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[224])).
% 0.19/0.56 tff(226,plain,
% 0.19/0.56 (((I!2 = I!2) | int_less(I!2, I!2)) <=> $true),
% 0.19/0.56 inference(transitivity,[status(thm)],[225, 223])).
% 0.19/0.56 tff(227,plain,
% 0.19/0.56 ((int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2))) <=> (int_leq(I!2, I!2) <=> $true)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[226])).
% 0.19/0.56 tff(228,plain,
% 0.19/0.56 ((int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2))) <=> int_leq(I!2, I!2)),
% 0.19/0.56 inference(transitivity,[status(thm)],[227, 222])).
% 0.19/0.56 tff(229,plain,
% 0.19/0.56 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2)))) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[228])).
% 0.19/0.56 tff(230,plain,
% 0.19/0.56 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2)))) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2))),
% 0.39/0.56 inference(transitivity,[status(thm)],[229, 221])).
% 0.39/0.56 tff(231,plain,
% 0.39/0.56 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2)))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(232,plain,
% 0.39/0.56 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2)),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.39/0.56 tff(233,plain,
% 0.39/0.56 ($false),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[232, 121, 220])).
% 0.39/0.56 % SZS output end Proof
% 0.39/0.56 % E exiting
%------------------------------------------------------------------------------