%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV487+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 0.87s 1.04s
% Output : Proof 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV487+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:52:52 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.87/1.04 % SZS status Theorem
% 0.87/1.04 % SZS output start Proof
% 0.87/1.04 tff(int_less_type, type, (
% 0.87/1.04 int_less: ( $i * $i ) > $o)).
% 0.87/1.04 tff(n_type, type, (
% 0.87/1.04 n: $i)).
% 0.87/1.04 tff(tptp_fun_J_1_type, type, (
% 0.87/1.04 tptp_fun_J_1: $i)).
% 0.87/1.04 tff(int_leq_type, type, (
% 0.87/1.04 int_leq: ( $i * $i ) > $o)).
% 0.87/1.04 tff(int_one_type, type, (
% 0.87/1.04 int_one: $i)).
% 0.87/1.04 tff(real_zero_type, type, (
% 0.87/1.04 real_zero: $i)).
% 0.87/1.04 tff(a_type, type, (
% 0.87/1.04 a: ( $i * $i ) > $i)).
% 0.87/1.04 tff(plus_type, type, (
% 0.87/1.04 plus: ( $i * $i ) > $i)).
% 0.87/1.04 tff(tptp_fun_K_0_type, type, (
% 0.87/1.04 tptp_fun_K_0: ( $i * $i ) > $i)).
% 0.87/1.04 tff(int_zero_type, type, (
% 0.87/1.04 int_zero: $i)).
% 0.87/1.04 tff(tptp_fun_I_2_type, type, (
% 0.87/1.04 tptp_fun_I_2: $i)).
% 0.87/1.04 tff(lu_type, type, (
% 0.87/1.04 lu: ( $i * $i ) > $i)).
% 0.87/1.04 tff(1,plain,
% 0.87/1.04 (^[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))))),
% 0.87/1.04 inference(bind,[status(th)],[])).
% 0.87/1.04 tff(2,plain,
% 0.87/1.04 (![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)))),
% 0.87/1.04 inference(quant_intro,[status(thm)],[1])).
% 0.87/1.04 tff(3,plain,
% 0.87/1.04 (![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)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(4,plain,
% 0.87/1.04 (^[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))))),
% 0.87/1.04 inference(bind,[status(th)],[])).
% 0.87/1.04 tff(5,plain,
% 0.87/1.04 (![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)))),
% 0.87/1.04 inference(quant_intro,[status(thm)],[4])).
% 0.87/1.04 tff(6,axiom,(![I: $i, J: $i] : (int_leq(I, J) <=> (int_less(I, J) | (I = J)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','int_leq')).
% 0.87/1.04 tff(7,plain,
% 0.87/1.04 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.87/1.04 tff(8,plain,
% 0.87/1.04 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.87/1.04 tff(9,plain,(
% 0.87/1.04 ![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.87/1.04 inference(skolemize,[status(sab)],[8])).
% 0.87/1.04 tff(10,plain,
% 0.87/1.04 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.87/1.04 tff(11,plain,
% 0.87/1.04 ((~![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)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(12,plain,
% 0.87/1.04 (int_leq(J!1, n) <=> ((J!1 = n) | int_less(J!1, n))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.87/1.04 tff(13,plain,
% 0.87/1.04 (^[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))))))))),
% 0.87/1.04 inference(bind,[status(th)],[])).
% 0.87/1.04 tff(14,plain,
% 0.87/1.04 (![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)))))))),
% 0.87/1.04 inference(quant_intro,[status(thm)],[13])).
% 0.87/1.04 tff(15,plain,
% 0.87/1.04 (^[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))))))))),
% 0.87/1.04 inference(bind,[status(th)],[])).
% 0.87/1.04 tff(16,plain,
% 0.87/1.04 (![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)))))))),
% 0.87/1.04 inference(quant_intro,[status(thm)],[15])).
% 0.87/1.04 tff(17,plain,
% 0.87/1.04 (![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)))))))),
% 0.87/1.04 inference(transitivity,[status(thm)],[16, 14])).
% 0.87/1.04 tff(18,plain,
% 0.87/1.04 (^[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)))))))))),
% 0.87/1.04 inference(bind,[status(th)],[])).
% 0.87/1.04 tff(19,plain,
% 0.87/1.04 (![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)))))))),
% 0.87/1.04 inference(quant_intro,[status(thm)],[18])).
% 0.87/1.04 tff(20,plain,
% 0.87/1.04 (![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)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(21,axiom,(![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_and_inverse')).
% 0.87/1.04 tff(22,plain,
% 0.87/1.04 (![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.87/1.04 tff(23,plain,(
% 0.87/1.04 ![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)))))),
% 0.87/1.04 inference(skolemize,[status(sab)],[22])).
% 0.87/1.04 tff(24,plain,
% 0.87/1.04 (![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)))))))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.87/1.04 tff(25,plain,
% 0.87/1.04 (![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)))))))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.87/1.04 tff(26,plain,
% 0.87/1.04 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(27,plain,
% 0.87/1.04 ((~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(28,plain,
% 0.87/1.04 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[27])).
% 0.87/1.04 tff(29,plain,
% 0.87/1.04 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))))),
% 0.87/1.04 inference(transitivity,[status(thm)],[28, 26])).
% 0.87/1.04 tff(30,plain,
% 0.87/1.04 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K)))))))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(31,plain,
% 0.87/1.04 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.87/1.04 tff(32,plain,
% 0.87/1.04 (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.87/1.04 tff(33,plain,
% 0.87/1.04 (((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))) | ((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))),
% 0.87/1.04 inference(tautology,[status(thm)],[])).
% 0.87/1.04 tff(34,plain,
% 0.87/1.04 ((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.87/1.04 tff(35,plain,
% 0.87/1.04 ((~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))) <=> (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(36,plain,
% 0.87/1.04 ((~![I: $i, J: $i] : (((int_leq(int_one, J) & int_less(J, I)) & int_leq(I, n)) => (a(I, J) = real_zero))) <=> (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(37,axiom,(~![I: $i, J: $i] : (((int_leq(int_one, J) & int_less(J, I)) & int_leq(I, n)) => (a(I, J) = real_zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ut')).
% 0.87/1.04 tff(38,plain,
% 0.87/1.04 (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.87/1.04 tff(39,plain,
% 0.87/1.04 (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.87/1.04 tff(40,plain,
% 0.87/1.04 (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.87/1.04 tff(41,plain,
% 0.87/1.04 (~![I: $i, J: $i] : ((~(int_leq(int_one, J) & int_less(J, I) & int_leq(I, n))) | (a(I, J) = real_zero))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.87/1.04 tff(42,plain,(
% 0.87/1.04 ~((~(int_leq(int_one, J!1) & int_less(J!1, I!2) & int_leq(I!2, n))) | (a(I!2, J!1) = real_zero))),
% 0.87/1.04 inference(skolemize,[status(sab)],[41])).
% 0.87/1.04 tff(43,plain,
% 0.87/1.04 (int_leq(int_one, J!1) & int_less(J!1, I!2) & int_leq(I!2, n)),
% 0.87/1.04 inference(or_elim,[status(thm)],[42])).
% 0.87/1.04 tff(44,plain,
% 0.87/1.04 (int_less(J!1, I!2)),
% 0.87/1.04 inference(and_elim,[status(thm)],[43])).
% 0.87/1.04 tff(45,plain,
% 0.87/1.04 ((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2))))),
% 0.87/1.04 inference(tautology,[status(thm)],[])).
% 0.87/1.04 tff(46,plain,
% 0.87/1.04 ((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.87/1.04 tff(47,plain,
% 0.87/1.04 (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[46, 34])).
% 0.87/1.04 tff(48,plain,
% 0.87/1.04 (((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2))) | (plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)),
% 0.87/1.04 inference(tautology,[status(thm)],[])).
% 0.87/1.04 tff(49,plain,
% 0.87/1.04 (plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.87/1.04 tff(50,plain,
% 0.87/1.04 (I!2 = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.87/1.04 inference(symmetry,[status(thm)],[49])).
% 0.87/1.04 tff(51,plain,
% 0.87/1.04 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2))))))))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(52,plain,
% 0.87/1.04 ((~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~(plus(int_zero, K) = I!2)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2)))))))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(53,plain,
% 0.87/1.05 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~(plus(int_zero, K) = I!2)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2))))))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[52])).
% 0.87/1.05 tff(54,plain,
% 0.87/1.05 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~(plus(int_zero, K) = I!2)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2))))))))),
% 0.87/1.05 inference(transitivity,[status(thm)],[53, 51])).
% 0.87/1.05 tff(55,plain,
% 0.87/1.05 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~(plus(int_zero, K) = I!2)) | (~int_less(int_zero, K)))))))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(56,plain,
% 0.87/1.05 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2)))))))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.87/1.05 tff(57,plain,
% 0.87/1.05 (~((~((~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2))))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[56, 25])).
% 0.87/1.05 tff(58,plain,
% 0.87/1.05 (((~((~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)))))) | (~(int_less(int_zero, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = I!2)))))) | ((~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)))))),
% 0.87/1.05 inference(tautology,[status(thm)],[])).
% 0.87/1.05 tff(59,plain,
% 0.87/1.05 ((~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.87/1.05 tff(60,plain,
% 0.87/1.05 (^[I: $i] : refl((int_less(int_zero, I) <=> int_leq(int_one, I)) <=> (int_less(int_zero, I) <=> int_leq(int_one, I)))),
% 0.87/1.05 inference(bind,[status(th)],[])).
% 0.87/1.05 tff(61,plain,
% 0.87/1.05 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.87/1.05 inference(quant_intro,[status(thm)],[60])).
% 0.87/1.05 tff(62,plain,
% 0.87/1.05 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(63,axiom,(![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','one_successor_of_zero')).
% 0.87/1.05 tff(64,plain,
% 0.87/1.05 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.87/1.05 tff(65,plain,(
% 0.87/1.05 ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.87/1.05 inference(skolemize,[status(sab)],[64])).
% 0.87/1.05 tff(66,plain,
% 0.87/1.05 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.87/1.05 tff(67,plain,
% 0.87/1.05 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, J!1) <=> int_leq(int_one, J!1))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(68,plain,
% 0.87/1.05 (int_less(int_zero, J!1) <=> int_leq(int_one, J!1)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.87/1.05 tff(69,plain,
% 0.87/1.05 (int_leq(int_one, J!1)),
% 0.87/1.05 inference(and_elim,[status(thm)],[43])).
% 0.87/1.05 tff(70,plain,
% 0.87/1.05 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1) | (~int_leq(int_one, J!1))),
% 0.87/1.05 inference(tautology,[status(thm)],[])).
% 0.87/1.05 tff(71,plain,
% 0.87/1.05 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.87/1.05 tff(72,plain,
% 0.87/1.05 (int_less(int_zero, J!1)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.87/1.05 tff(73,plain,
% 0.87/1.05 (![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)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(74,plain,
% 0.87/1.05 (^[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)))))),
% 0.87/1.05 inference(bind,[status(th)],[])).
% 0.87/1.05 tff(75,plain,
% 0.87/1.05 (![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)))),
% 0.87/1.05 inference(quant_intro,[status(thm)],[74])).
% 0.87/1.05 tff(76,plain,
% 0.87/1.05 (![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))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(77,plain,
% 0.87/1.05 (^[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)))),
% 0.87/1.05 inference(bind,[status(th)],[])).
% 0.87/1.05 tff(78,plain,
% 0.87/1.05 (![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))),
% 0.87/1.05 inference(quant_intro,[status(thm)],[77])).
% 0.87/1.05 tff(79,axiom,(![I: $i, J: $i, K: $i] : ((int_less(I, J) & int_less(J, K)) => int_less(I, K))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','int_less_transitive')).
% 0.87/1.05 tff(80,plain,
% 0.87/1.05 (![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.87/1.05 tff(81,plain,
% 0.87/1.05 (![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.87/1.05 tff(82,plain,(
% 0.87/1.05 ![I: $i, J: $i, K: $i] : ((~(int_less(I, J) & int_less(J, K))) | int_less(I, K))),
% 0.87/1.05 inference(skolemize,[status(sab)],[81])).
% 0.87/1.05 tff(83,plain,
% 0.87/1.05 (![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.87/1.05 tff(84,plain,
% 0.87/1.05 (![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.87/1.05 tff(85,plain,
% 0.87/1.05 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | ((~int_less(int_zero, J!1)) | (~int_less(J!1, I!2)) | int_less(int_zero, I!2))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(int_zero, J!1)) | (~int_less(J!1, I!2)) | int_less(int_zero, I!2))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(86,plain,
% 0.87/1.05 ((int_less(int_zero, I!2) | (~int_less(J!1, I!2)) | (~int_less(int_zero, J!1))) <=> ((~int_less(int_zero, J!1)) | (~int_less(J!1, I!2)) | int_less(int_zero, I!2))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(87,plain,
% 0.87/1.05 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(int_zero, I!2) | (~int_less(J!1, I!2)) | (~int_less(int_zero, J!1)))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | ((~int_less(int_zero, J!1)) | (~int_less(J!1, I!2)) | int_less(int_zero, I!2)))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[86])).
% 0.87/1.05 tff(88,plain,
% 0.87/1.05 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(int_zero, I!2) | (~int_less(J!1, I!2)) | (~int_less(int_zero, J!1)))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(int_zero, J!1)) | (~int_less(J!1, I!2)) | int_less(int_zero, I!2))),
% 0.87/1.05 inference(transitivity,[status(thm)],[87, 85])).
% 0.87/1.05 tff(89,plain,
% 0.87/1.05 ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(int_zero, I!2) | (~int_less(J!1, I!2)) | (~int_less(int_zero, J!1)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(90,plain,
% 0.87/1.05 ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(int_zero, J!1)) | (~int_less(J!1, I!2)) | int_less(int_zero, I!2)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.87/1.05 tff(91,plain,
% 0.87/1.05 (int_less(int_zero, I!2)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[90, 84, 44, 72])).
% 0.87/1.05 tff(92,plain,
% 0.87/1.05 ((~((~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)))))) | (~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2))))),
% 0.87/1.05 inference(tautology,[status(thm)],[])).
% 0.87/1.05 tff(93,plain,
% 0.87/1.05 ((~((~int_less(int_zero, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)))))) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.87/1.05 tff(94,plain,
% 0.87/1.05 (~((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[93, 59])).
% 0.87/1.05 tff(95,plain,
% 0.87/1.05 (((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2))) | (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2)),
% 0.87/1.05 inference(tautology,[status(thm)],[])).
% 0.87/1.05 tff(96,plain,
% 0.87/1.05 (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.87/1.05 tff(97,plain,
% 0.87/1.05 (^[I: $i, J: $i] : refl((plus(I, J) = plus(J, I)) <=> (plus(I, J) = plus(J, I)))),
% 0.87/1.05 inference(bind,[status(th)],[])).
% 0.87/1.05 tff(98,plain,
% 0.87/1.05 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.87/1.05 inference(quant_intro,[status(thm)],[97])).
% 0.87/1.05 tff(99,plain,
% 0.87/1.05 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(100,axiom,(![I: $i, J: $i] : (plus(I, J) = plus(J, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_commutative')).
% 0.87/1.05 tff(101,plain,
% 0.87/1.05 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.87/1.05 tff(102,plain,(
% 0.87/1.05 ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.87/1.05 inference(skolemize,[status(sab)],[101])).
% 0.87/1.05 tff(103,plain,
% 0.87/1.05 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.87/1.05 tff(104,plain,
% 0.87/1.05 ((~![I: $i, J: $i] : (plus(I, J) = plus(J, I))) | (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = plus(tptp_fun_K_0(I!2, int_zero), int_zero))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(105,plain,
% 0.87/1.05 (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = plus(tptp_fun_K_0(I!2, int_zero), int_zero)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.87/1.05 tff(106,plain,
% 0.87/1.05 (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = plus(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.87/1.05 inference(symmetry,[status(thm)],[105])).
% 0.87/1.05 tff(107,plain,
% 0.87/1.05 (^[I: $i] : refl((plus(I, int_zero) = I) <=> (plus(I, int_zero) = I))),
% 0.87/1.05 inference(bind,[status(th)],[])).
% 0.87/1.05 tff(108,plain,
% 0.87/1.05 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.87/1.05 inference(quant_intro,[status(thm)],[107])).
% 0.87/1.05 tff(109,plain,
% 0.87/1.05 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(110,axiom,(![I: $i] : (plus(I, int_zero) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_zero')).
% 0.87/1.05 tff(111,plain,
% 0.87/1.05 (![I: $i] : (plus(I, int_zero) = I)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.87/1.05 tff(112,plain,(
% 0.87/1.05 ![I: $i] : (plus(I, int_zero) = I)),
% 0.87/1.05 inference(skolemize,[status(sab)],[111])).
% 0.87/1.05 tff(113,plain,
% 0.87/1.05 (![I: $i] : (plus(I, int_zero) = I)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.87/1.05 tff(114,plain,
% 0.87/1.05 ((~![I: $i] : (plus(I, int_zero) = I)) | (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = tptp_fun_K_0(I!2, int_zero))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(115,plain,
% 0.87/1.05 (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = tptp_fun_K_0(I!2, int_zero)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.87/1.05 tff(116,plain,
% 0.87/1.05 (tptp_fun_K_0(I!2, int_zero) = plus(tptp_fun_K_0(I!2, int_zero), int_zero)),
% 0.87/1.05 inference(symmetry,[status(thm)],[115])).
% 0.87/1.05 tff(117,plain,
% 0.87/1.05 (tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.87/1.05 inference(transitivity,[status(thm)],[116, 106, 96, 50])).
% 0.87/1.05 tff(118,assumption,(![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))), introduced(assumption)).
% 0.87/1.05 tff(119,assumption,(a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero), introduced(assumption)).
% 0.87/1.05 tff(120,plain,
% 0.87/1.05 (a(I!2, J!1) = a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1)),
% 0.87/1.05 inference(monotonicity,[status(thm)],[50])).
% 0.87/1.05 tff(121,plain,
% 0.87/1.05 (a(I!2, J!1) = real_zero),
% 0.87/1.05 inference(transitivity,[status(thm)],[120, 119])).
% 0.87/1.05 tff(122,plain,
% 0.87/1.05 (~(a(I!2, J!1) = real_zero)),
% 0.87/1.05 inference(or_elim,[status(thm)],[42])).
% 0.87/1.05 tff(123,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.87/1.05 tff(124,plain,(~(a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(125,assumption,(~int_leq(J!1, J!1)), introduced(assumption)).
% 0.87/1.05 tff(126,plain,
% 0.87/1.05 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1)) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(127,plain,
% 0.87/1.05 ((int_leq(J!1, J!1) <=> $true) <=> int_leq(J!1, J!1)),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(128,plain,
% 0.87/1.05 (($true | int_less(J!1, J!1)) <=> $true),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(129,plain,
% 0.87/1.05 ((J!1 = J!1) <=> $true),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(130,plain,
% 0.87/1.05 (((J!1 = J!1) | int_less(J!1, J!1)) <=> ($true | int_less(J!1, J!1))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[129])).
% 0.87/1.05 tff(131,plain,
% 0.87/1.05 (((J!1 = J!1) | int_less(J!1, J!1)) <=> $true),
% 0.87/1.05 inference(transitivity,[status(thm)],[130, 128])).
% 0.87/1.05 tff(132,plain,
% 0.87/1.05 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> (int_leq(J!1, J!1) <=> $true)),
% 0.87/1.05 inference(monotonicity,[status(thm)],[131])).
% 0.87/1.05 tff(133,plain,
% 0.87/1.05 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> int_leq(J!1, J!1)),
% 0.87/1.05 inference(transitivity,[status(thm)],[132, 127])).
% 0.87/1.05 tff(134,plain,
% 0.87/1.05 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1)))) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[133])).
% 0.87/1.05 tff(135,plain,
% 0.87/1.05 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1)))) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1))),
% 0.87/1.05 inference(transitivity,[status(thm)],[134, 126])).
% 0.87/1.05 tff(136,plain,
% 0.87/1.05 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(137,plain,
% 0.87/1.05 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.87/1.05 tff(138,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[137, 10, 125])).
% 0.87/1.05 tff(139,plain,(int_leq(J!1, J!1)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(140,plain,
% 0.87/1.05 (((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))) | ((~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero))) <=> ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(141,plain,
% 0.87/1.05 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))) | ((~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(142,plain,
% 0.87/1.05 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.87/1.05 tff(143,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[142, 69, 139, 124, 118])).
% 0.87/1.05 tff(144,plain,(~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(145,assumption,(![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))), introduced(assumption)).
% 0.87/1.05 tff(146,plain,
% 0.87/1.05 (((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2))) | int_less(int_zero, tptp_fun_K_0(I!2, J!1))),
% 0.87/1.05 inference(tautology,[status(thm)],[])).
% 0.87/1.05 tff(147,plain,
% 0.87/1.05 (int_less(int_zero, tptp_fun_K_0(I!2, J!1))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[146, 47])).
% 0.87/1.05 tff(148,plain,
% 0.87/1.05 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero)))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(149,plain,
% 0.87/1.05 (((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) <=> ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(150,plain,
% 0.87/1.05 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[149])).
% 0.87/1.05 tff(151,plain,
% 0.87/1.05 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[150, 148])).
% 0.87/1.05 tff(152,plain,
% 0.87/1.05 ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(153,plain,
% 0.87/1.05 ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.87/1.05 tff(154,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[153, 147, 145, 144, 117])).
% 0.87/1.05 tff(155,plain,(~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(156,plain,
% 0.87/1.05 (((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))) | ![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))),
% 0.87/1.05 inference(tautology,[status(thm)],[])).
% 0.87/1.05 tff(157,plain,
% 0.87/1.05 ((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.87/1.05 tff(158,plain,
% 0.87/1.05 (tptp_fun_K_0(I!2, int_zero) = I!2),
% 0.87/1.05 inference(transitivity,[status(thm)],[116, 106, 96])).
% 0.87/1.05 tff(159,plain,
% 0.87/1.05 (int_leq(tptp_fun_K_0(I!2, int_zero), n) <=> int_leq(I!2, n)),
% 0.87/1.05 inference(monotonicity,[status(thm)],[158])).
% 0.87/1.05 tff(160,plain,
% 0.87/1.05 (int_leq(I!2, n) <=> int_leq(tptp_fun_K_0(I!2, int_zero), n)),
% 0.87/1.05 inference(symmetry,[status(thm)],[159])).
% 0.87/1.05 tff(161,plain,
% 0.87/1.05 (int_leq(I!2, n)),
% 0.87/1.05 inference(and_elim,[status(thm)],[43])).
% 0.87/1.05 tff(162,plain,
% 0.87/1.05 (int_leq(tptp_fun_K_0(I!2, int_zero), n)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.87/1.05 tff(163,plain,
% 0.87/1.05 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, tptp_fun_K_0(I!2, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(I!2, int_zero)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(164,plain,
% 0.87/1.05 (int_less(int_zero, tptp_fun_K_0(I!2, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[163, 66])).
% 0.87/1.05 tff(165,plain,
% 0.87/1.05 (((~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2))) | int_less(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.87/1.05 inference(tautology,[status(thm)],[])).
% 0.87/1.05 tff(166,plain,
% 0.87/1.05 (int_less(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[165, 94])).
% 0.87/1.05 tff(167,plain,
% 0.87/1.05 ((~(int_less(int_zero, tptp_fun_K_0(I!2, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(I!2, int_zero)))) | (~int_less(int_zero, tptp_fun_K_0(I!2, int_zero))) | int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.87/1.05 inference(tautology,[status(thm)],[])).
% 0.87/1.05 tff(168,plain,
% 0.87/1.05 ((~(int_less(int_zero, tptp_fun_K_0(I!2, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(I!2, int_zero)))) | int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.87/1.05 tff(169,plain,
% 0.87/1.05 (int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[168, 164])).
% 0.87/1.05 tff(170,plain,
% 0.87/1.05 (^[I: $i, J: $i] : refl(((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))),
% 0.87/1.05 inference(bind,[status(th)],[])).
% 0.87/1.05 tff(171,plain,
% 0.87/1.05 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.87/1.05 inference(quant_intro,[status(thm)],[170])).
% 0.87/1.05 tff(172,plain,
% 0.87/1.05 (^[I: $i, J: $i] : rewrite(((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))),
% 0.87/1.06 inference(bind,[status(th)],[])).
% 0.87/1.06 tff(173,plain,
% 0.87/1.06 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.87/1.06 inference(quant_intro,[status(thm)],[172])).
% 0.87/1.06 tff(174,plain,
% 0.87/1.06 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.87/1.06 inference(transitivity,[status(thm)],[173, 171])).
% 0.87/1.06 tff(175,plain,
% 0.87/1.06 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) <=> (~((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))))), ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) <=> (~(~((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))))))), rewrite((~(~((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)))), ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))))), trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_less(int_zero, C) & (I = plus(J, C))) <=> (~((~int_less(int_zero, C)) | (~(I = plus(J, C)))))), ((~(int_less(int_zero, C) & (I = plus(J, C)))) <=> (~(~((~int_less(int_zero, C)) | (~(I = plus(J, C)))))))), rewrite((~(~((~int_less(int_zero, C)) | (~(I = plus(J, C)))))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C))))), ((~(int_less(int_zero, C) & (I = plus(J, C)))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C)))))), quant_intro(proof_bind(^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, K) & int_leq(K, J)) <=> (~((~int_leq(int_one, K)) | (~int_leq(K, J))))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> (~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))))), rewrite((~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J)))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero)) <=> (((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(plus(K, C), K) = real_zero)))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(plus(K, C), K) = real_zero)) <=> ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero)) <=> ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero)) <=> ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) <=> (((~int_less(int_zero, C)) | (~(I = plus(J, C)))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), rewrite((((~int_less(int_zero, C)) | (~(I = plus(J, C)))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))))), (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) <=> ![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_zero, C) & (J = plus(I, C))) <=> (~((~int_leq(int_zero, C)) | (~(J = plus(I, C)))))), ((~(int_leq(int_zero, C) & (J = plus(I, C)))) <=> (~(~((~int_leq(int_zero, C)) | (~(J = plus(I, C)))))))), rewrite((~(~((~int_leq(int_zero, C)) | (~(J = plus(I, C)))))) <=> ((~int_leq(int_zero, C)) | (~(J = plus(I, C))))), ((~(int_leq(int_zero, C) & (J = plus(I, C)))) <=> ((~int_leq(int_zero, C)) | (~(J = plus(I, C)))))), quant_intro(proof_bind(^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, K) & int_leq(K, I)) <=> (~((~int_leq(int_one, K)) | (~int_leq(K, I))))), ((~(int_leq(int_one, K) & int_leq(K, I))) <=> (~(~((~int_leq(int_one, K)) | (~int_leq(K, I))))))), rewrite((~(~((~int_leq(int_one, K)) | (~int_leq(K, I))))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, I)))), ((~(int_leq(int_one, K) & int_leq(K, I))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))) <=> (((~int_leq(int_one, K)) | (~int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))) <=> ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))), (((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))) <=> ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))) <=> ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))) <=> (((~int_leq(int_zero, C)) | (~(J = plus(I, C)))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), rewrite((((~int_leq(int_zero, C)) | (~(J = plus(I, C)))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))) <=> ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))) <=> ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))), (![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))) <=> ![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))) <=> (![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) & ![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))), rewrite((![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) & ![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))), ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))), (((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> (((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))), rewrite((((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))), (((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))))),
% 0.87/1.06 inference(bind,[status(th)],[])).
% 0.87/1.06 tff(176,plain,
% 0.87/1.06 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.87/1.06 inference(quant_intro,[status(thm)],[175])).
% 0.87/1.06 tff(177,plain,
% 0.87/1.06 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(178,plain,
% 0.87/1.06 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite(((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) <=> (int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J))), ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) <=> ((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J)) & int_leq(J, n)))), rewrite(((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J)) & int_leq(J, n)) <=> (int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))), ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) <=> (int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)))), rewrite((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((int_leq(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = lu(K, plus(K, C)))))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))), (((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => (![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((int_leq(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) => (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))))), rewrite(((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) => (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))), (((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => (![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((int_leq(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))))),
% 0.87/1.06 inference(bind,[status(th)],[])).
% 0.87/1.06 tff(179,plain,
% 0.87/1.06 (![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => (![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((int_leq(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = lu(K, plus(K, C))))))) <=> ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))),
% 0.87/1.06 inference(quant_intro,[status(thm)],[178])).
% 0.87/1.06 tff(180,axiom,(![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => (![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((int_leq(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = lu(K, plus(K, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qiu')).
% 0.87/1.06 tff(181,plain,
% 0.87/1.06 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.87/1.06 tff(182,plain,
% 0.87/1.06 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.87/1.06 tff(183,plain,(
% 0.87/1.06 ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![C: $i] : ((~(int_leq(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = lu(K, plus(K, C)))))))),
% 0.87/1.06 inference(skolemize,[status(sab)],[182])).
% 0.87/1.06 tff(184,plain,
% 0.87/1.06 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[183, 176])).
% 0.87/1.06 tff(185,plain,
% 0.87/1.06 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[184, 174])).
% 0.87/1.06 tff(186,plain,
% 0.87/1.06 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(187,plain,
% 0.87/1.06 (((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))) <=> ((~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(188,plain,
% 0.87/1.06 ((~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))) <=> (~((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(189,plain,
% 0.87/1.06 (((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))) <=> ((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[188])).
% 0.87/1.06 tff(190,plain,
% 0.87/1.06 (((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))) <=> ((~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))),
% 0.87/1.07 inference(transitivity,[status(thm)],[189, 187])).
% 0.87/1.07 tff(191,plain,
% 0.87/1.07 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[190])).
% 0.87/1.07 tff(192,plain,
% 0.87/1.07 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))),
% 0.87/1.07 inference(transitivity,[status(thm)],[191, 186])).
% 0.87/1.07 tff(193,plain,
% 0.87/1.07 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(194,plain,
% 0.87/1.07 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![C: $i] : ((~int_leq(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.87/1.07 tff(195,plain,
% 0.87/1.07 ((~int_leq(J!1, n)) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[194, 185, 69, 169])).
% 0.87/1.07 tff(196,plain,
% 0.87/1.07 ((~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_leq(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = lu(K, plus(K, C))) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[195, 162])).
% 0.87/1.07 tff(197,plain,
% 0.87/1.07 (~int_leq(J!1, n)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[196, 157])).
% 0.87/1.07 tff(198,plain,
% 0.87/1.07 ((~(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)))),
% 0.87/1.07 inference(tautology,[status(thm)],[])).
% 0.87/1.07 tff(199,plain,
% 0.87/1.07 ((~(int_leq(J!1, n) <=> ((J!1 = n) | int_less(J!1, n)))) | (~((J!1 = n) | int_less(J!1, n)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.87/1.07 tff(200,plain,
% 0.87/1.07 (~((J!1 = n) | int_less(J!1, n))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[199, 12])).
% 0.87/1.07 tff(201,plain,
% 0.87/1.07 (((J!1 = n) | int_less(J!1, n)) | (~int_less(J!1, n))),
% 0.87/1.07 inference(tautology,[status(thm)],[])).
% 0.87/1.07 tff(202,plain,
% 0.87/1.07 (~int_less(J!1, n)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.87/1.07 tff(203,plain,
% 0.87/1.07 ((plus(J!1, tptp_fun_K_0(I!2, J!1)) = n) <=> (I!2 = n)),
% 0.87/1.07 inference(monotonicity,[status(thm)],[49])).
% 0.87/1.07 tff(204,plain,
% 0.87/1.07 ((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = n)) <=> (~(I!2 = n))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[203])).
% 0.87/1.07 tff(205,plain,
% 0.87/1.07 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~(int_less(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n))))) | (~((~int_less(J!1, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, J!1))) | (~(plus(J!1, tptp_fun_K_0(n, J!1)) = 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(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n))))) | (~((~int_less(J!1, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, J!1))) | (~(plus(J!1, tptp_fun_K_0(n, J!1)) = n)))))))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(206,plain,
% 0.87/1.07 ((~((~((~int_less(J!1, n)) | (~((~(plus(J!1, tptp_fun_K_0(n, J!1)) = n)) | (~int_less(int_zero, tptp_fun_K_0(n, J!1))))))) | (~(int_less(J!1, n) | ![K: $i] : ((~(plus(J!1, K) = n)) | (~int_less(int_zero, K))))))) <=> (~((~(int_less(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n))))) | (~((~int_less(J!1, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, J!1))) | (~(plus(J!1, tptp_fun_K_0(n, J!1)) = n))))))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(207,plain,
% 0.87/1.07 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, n)) | (~((~(plus(J!1, tptp_fun_K_0(n, J!1)) = n)) | (~int_less(int_zero, tptp_fun_K_0(n, J!1))))))) | (~(int_less(J!1, n) | ![K: $i] : ((~(plus(J!1, 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(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n))))) | (~((~int_less(J!1, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, J!1))) | (~(plus(J!1, tptp_fun_K_0(n, J!1)) = n)))))))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[206])).
% 0.87/1.07 tff(208,plain,
% 0.87/1.07 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, n)) | (~((~(plus(J!1, tptp_fun_K_0(n, J!1)) = n)) | (~int_less(int_zero, tptp_fun_K_0(n, J!1))))))) | (~(int_less(J!1, n) | ![K: $i] : ((~(plus(J!1, 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(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n))))) | (~((~int_less(J!1, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, J!1))) | (~(plus(J!1, tptp_fun_K_0(n, J!1)) = n)))))))))),
% 0.87/1.07 inference(transitivity,[status(thm)],[207, 205])).
% 0.87/1.07 tff(209,plain,
% 0.87/1.07 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, n)) | (~((~(plus(J!1, tptp_fun_K_0(n, J!1)) = n)) | (~int_less(int_zero, tptp_fun_K_0(n, J!1))))))) | (~(int_less(J!1, n) | ![K: $i] : ((~(plus(J!1, K) = n)) | (~int_less(int_zero, K)))))))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(210,plain,
% 0.87/1.07 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~(int_less(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n))))) | (~((~int_less(J!1, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, J!1))) | (~(plus(J!1, tptp_fun_K_0(n, J!1)) = n))))))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.87/1.07 tff(211,plain,
% 0.87/1.07 (~((~(int_less(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n))))) | (~((~int_less(J!1, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, J!1))) | (~(plus(J!1, tptp_fun_K_0(n, J!1)) = n)))))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[210, 25])).
% 0.87/1.07 tff(212,plain,
% 0.87/1.07 (((~(int_less(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n))))) | (~((~int_less(J!1, n)) | (~((~int_less(int_zero, tptp_fun_K_0(n, J!1))) | (~(plus(J!1, tptp_fun_K_0(n, J!1)) = n))))))) | (int_less(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n))))),
% 0.87/1.07 inference(tautology,[status(thm)],[])).
% 0.87/1.07 tff(213,plain,
% 0.87/1.07 (int_less(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.87/1.07 tff(214,plain,
% 0.87/1.07 ((~(int_less(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n))))) | int_less(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n)))),
% 0.87/1.07 inference(tautology,[status(thm)],[])).
% 0.87/1.07 tff(215,plain,
% 0.87/1.07 ((~(int_less(J!1, n) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n))))) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[214, 202])).
% 0.87/1.07 tff(216,plain,
% 0.87/1.07 (![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[215, 213])).
% 0.87/1.07 tff(217,plain,
% 0.87/1.07 (((~![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n)))) | ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = n)))) <=> ((~![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n)))) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = n)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(218,plain,
% 0.87/1.07 ((~![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n)))) | ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = n)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(219,plain,
% 0.87/1.07 ((~![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = n)))) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = n))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.87/1.07 tff(220,plain,
% 0.87/1.07 (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = n)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[219, 147, 216])).
% 0.87/1.07 tff(221,plain,
% 0.87/1.07 (~(I!2 = n)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[220, 204])).
% 0.87/1.07 tff(222,plain,
% 0.87/1.07 ((~![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)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(223,plain,
% 0.87/1.07 (int_leq(I!2, n) <=> ((I!2 = n) | int_less(I!2, n))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[222, 10])).
% 0.87/1.07 tff(224,plain,
% 0.87/1.07 ((~(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))),
% 0.87/1.07 inference(tautology,[status(thm)],[])).
% 0.87/1.07 tff(225,plain,
% 0.87/1.07 ((~(int_leq(I!2, n) <=> ((I!2 = n) | int_less(I!2, n)))) | ((I!2 = n) | int_less(I!2, n))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[224, 161])).
% 0.87/1.07 tff(226,plain,
% 0.87/1.07 ((I!2 = n) | int_less(I!2, n)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[225, 223])).
% 0.87/1.07 tff(227,plain,
% 0.87/1.07 ((~((I!2 = n) | int_less(I!2, n))) | (I!2 = n) | int_less(I!2, n)),
% 0.87/1.07 inference(tautology,[status(thm)],[])).
% 0.87/1.07 tff(228,plain,
% 0.87/1.07 ((I!2 = n) | int_less(I!2, n)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.87/1.07 tff(229,plain,
% 0.87/1.07 (int_less(I!2, n)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[228, 221])).
% 0.87/1.07 tff(230,plain,
% 0.87/1.07 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | ((~int_less(I!2, n)) | (~int_less(J!1, I!2)) | int_less(J!1, n))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(I!2, n)) | (~int_less(J!1, I!2)) | int_less(J!1, n))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(231,plain,
% 0.87/1.07 ((int_less(J!1, n) | (~int_less(I!2, n)) | (~int_less(J!1, I!2))) <=> ((~int_less(I!2, n)) | (~int_less(J!1, I!2)) | int_less(J!1, n))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(232,plain,
% 0.87/1.07 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(J!1, n) | (~int_less(I!2, n)) | (~int_less(J!1, I!2)))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | ((~int_less(I!2, n)) | (~int_less(J!1, I!2)) | int_less(J!1, n)))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[231])).
% 0.87/1.07 tff(233,plain,
% 0.87/1.07 (((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(J!1, n) | (~int_less(I!2, n)) | (~int_less(J!1, I!2)))) <=> ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(I!2, n)) | (~int_less(J!1, I!2)) | int_less(J!1, n))),
% 0.87/1.07 inference(transitivity,[status(thm)],[232, 230])).
% 0.87/1.07 tff(234,plain,
% 0.87/1.07 ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (int_less(J!1, n) | (~int_less(I!2, n)) | (~int_less(J!1, I!2)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(235,plain,
% 0.87/1.07 ((~![I: $i, J: $i, K: $i] : (int_less(I, K) | (~int_less(J, K)) | (~int_less(I, J)))) | (~int_less(I!2, n)) | (~int_less(J!1, I!2)) | int_less(J!1, n)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.87/1.07 tff(236,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[235, 84, 44, 229, 202])).
% 0.87/1.07 % SZS output end Proof
% 0.87/1.08 % E exiting
%------------------------------------------------------------------------------