%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV490+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:34:10 AM UTC 2025
% Result : Theorem 0.41s 0.58s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV490+3 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:53:20 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.41/0.58 % SZS status Theorem
% 0.41/0.58 % SZS output start Proof
% 0.41/0.58 tff(real_zero_type, type, (
% 0.41/0.58 real_zero: $i)).
% 0.41/0.58 tff(a_type, type, (
% 0.41/0.58 a: ( $i * $i ) > $i)).
% 0.41/0.58 tff(tptp_fun_J_1_type, type, (
% 0.41/0.58 tptp_fun_J_1: $i)).
% 0.41/0.58 tff(tptp_fun_I_2_type, type, (
% 0.41/0.58 tptp_fun_I_2: $i)).
% 0.41/0.58 tff(plus_type, type, (
% 0.41/0.58 plus: ( $i * $i ) > $i)).
% 0.41/0.58 tff(tptp_fun_K_0_type, type, (
% 0.41/0.58 tptp_fun_K_0: ( $i * $i ) > $i)).
% 0.41/0.58 tff(int_leq_type, type, (
% 0.41/0.58 int_leq: ( $i * $i ) > $o)).
% 0.41/0.58 tff(int_one_type, type, (
% 0.41/0.58 int_one: $i)).
% 0.41/0.58 tff(int_zero_type, type, (
% 0.41/0.58 int_zero: $i)).
% 0.41/0.58 tff(int_less_type, type, (
% 0.41/0.58 int_less: ( $i * $i ) > $o)).
% 0.41/0.58 tff(real_one_type, type, (
% 0.41/0.58 real_one: $i)).
% 0.41/0.58 tff(n_type, type, (
% 0.41/0.58 n: $i)).
% 0.41/0.58 tff(1,plain,
% 0.41/0.58 (^[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))))))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(2,plain,
% 0.41/0.58 (![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)))))))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[1])).
% 0.41/0.58 tff(3,plain,
% 0.41/0.58 (^[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))))))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(4,plain,
% 0.41/0.58 (![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)))))))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[3])).
% 0.41/0.58 tff(5,plain,
% 0.41/0.58 (![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)))))))),
% 0.41/0.58 inference(transitivity,[status(thm)],[4, 2])).
% 0.41/0.58 tff(6,plain,
% 0.41/0.58 (^[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)))))))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(7,plain,
% 0.41/0.58 (![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)))))))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[6])).
% 0.41/0.58 tff(8,plain,
% 0.41/0.58 (![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)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(9,axiom,(![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus_and_inverse')).
% 0.41/0.58 tff(10,plain,
% 0.41/0.58 (![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.41/0.58 tff(11,plain,(
% 0.41/0.58 ![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)))))),
% 0.41/0.58 inference(skolemize,[status(sab)],[10])).
% 0.41/0.58 tff(12,plain,
% 0.41/0.58 (![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)))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.41/0.58 tff(13,plain,
% 0.41/0.58 (![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)))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.41/0.58 tff(14,plain,
% 0.41/0.58 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(15,plain,
% 0.41/0.58 ((~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K))))))) <=> (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(16,plain,
% 0.41/0.58 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))))))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[15])).
% 0.41/0.58 tff(17,plain,
% 0.41/0.58 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))))))),
% 0.41/0.58 inference(transitivity,[status(thm)],[16, 14])).
% 0.41/0.58 tff(18,plain,
% 0.41/0.58 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K)))))))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(19,plain,
% 0.41/0.58 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.41/0.58 tff(20,plain,
% 0.41/0.58 (~((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.41/0.58 tff(21,plain,
% 0.41/0.58 (((~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))))))) | ((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(22,plain,
% 0.41/0.58 ((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.41/0.58 tff(23,plain,
% 0.41/0.58 (^[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))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(24,plain,
% 0.41/0.58 (![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)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[23])).
% 0.41/0.58 tff(25,plain,
% 0.41/0.58 (![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)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(26,plain,
% 0.41/0.58 (^[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))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(27,plain,
% 0.41/0.58 (![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)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[26])).
% 0.41/0.58 tff(28,axiom,(![I: $i, J: $i] : (int_leq(I, J) <=> (int_less(I, J) | (I = J)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','int_leq')).
% 0.41/0.58 tff(29,plain,
% 0.41/0.58 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.41/0.58 tff(30,plain,
% 0.41/0.58 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.41/0.58 tff(31,plain,(
% 0.41/0.58 ![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.41/0.58 inference(skolemize,[status(sab)],[30])).
% 0.41/0.58 tff(32,plain,
% 0.41/0.58 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.41/0.58 tff(33,plain,
% 0.41/0.58 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(I!2, J!1) <=> ((I!2 = J!1) | int_less(I!2, J!1)))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(34,plain,
% 0.41/0.58 (int_leq(I!2, J!1) <=> ((I!2 = J!1) | int_less(I!2, J!1))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.41/0.58 tff(35,assumption,((~((~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)))))), introduced(assumption)).
% 0.41/0.58 tff(36,plain,
% 0.41/0.58 (((~![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))))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(37,plain,
% 0.41/0.58 ((~((~((~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)))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(38,plain,
% 0.41/0.58 (((~![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))))))))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[37])).
% 0.41/0.58 tff(39,plain,
% 0.41/0.58 (((~![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))))))))),
% 0.41/0.59 inference(transitivity,[status(thm)],[38, 36])).
% 0.41/0.59 tff(40,plain,
% 0.41/0.59 ((~![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)))))))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(41,plain,
% 0.41/0.59 ((~![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: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.41/0.59 tff(42,plain,
% 0.41/0.59 ($false),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[41, 13, 35])).
% 0.41/0.59 tff(43,plain,(~((~((~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))))))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.59 tff(44,plain,
% 0.41/0.59 (((~((~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)))))),
% 0.41/0.59 inference(tautology,[status(thm)],[])).
% 0.41/0.59 tff(45,plain,
% 0.41/0.59 ((~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))))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.41/0.59 tff(46,assumption,(~int_leq(J!1, J!1)), introduced(assumption)).
% 0.41/0.59 tff(47,plain,
% 0.41/0.59 (((~![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))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(48,plain,
% 0.41/0.59 ((int_leq(J!1, J!1) <=> $true) <=> int_leq(J!1, J!1)),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(49,plain,
% 0.41/0.59 (($true | int_less(J!1, J!1)) <=> $true),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(50,plain,
% 0.41/0.59 ((J!1 = J!1) <=> $true),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(51,plain,
% 0.41/0.59 (((J!1 = J!1) | int_less(J!1, J!1)) <=> ($true | int_less(J!1, J!1))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[50])).
% 0.41/0.59 tff(52,plain,
% 0.41/0.59 (((J!1 = J!1) | int_less(J!1, J!1)) <=> $true),
% 0.41/0.59 inference(transitivity,[status(thm)],[51, 49])).
% 0.41/0.59 tff(53,plain,
% 0.41/0.59 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> (int_leq(J!1, J!1) <=> $true)),
% 0.41/0.59 inference(monotonicity,[status(thm)],[52])).
% 0.41/0.59 tff(54,plain,
% 0.41/0.59 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> int_leq(J!1, J!1)),
% 0.41/0.59 inference(transitivity,[status(thm)],[53, 48])).
% 0.41/0.59 tff(55,plain,
% 0.41/0.59 (((~![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))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[54])).
% 0.41/0.59 tff(56,plain,
% 0.41/0.59 (((~![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))),
% 0.41/0.59 inference(transitivity,[status(thm)],[55, 47])).
% 0.41/0.59 tff(57,plain,
% 0.41/0.59 ((~![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)))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(58,plain,
% 0.41/0.59 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.41/0.59 tff(59,plain,
% 0.41/0.59 ($false),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[58, 32, 46])).
% 0.41/0.59 tff(60,plain,(int_leq(J!1, J!1)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.59 tff(61,plain,
% 0.41/0.59 ((~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))) <=> (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(62,plain,
% 0.41/0.59 ((~![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => (((~(I = J)) => (a(I, J) = real_zero)) & ((I = J) => (~(a(I, J) = real_zero)))))) <=> (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(63,axiom,(~![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => (((~(I = J)) => (a(I, J) = real_zero)) & ((I = J) => (~(a(I, J) = real_zero)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','di')).
% 0.41/0.59 tff(64,plain,
% 0.41/0.59 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.41/0.59 tff(65,plain,
% 0.41/0.59 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[64, 61])).
% 0.41/0.59 tff(66,plain,
% 0.41/0.59 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.41/0.59 tff(67,plain,
% 0.41/0.59 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((I = J) | (a(I, J) = real_zero)) & ((~(I = J)) | (~(a(I, J) = real_zero)))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[66, 61])).
% 0.41/0.59 tff(68,plain,(
% 0.41/0.59 ~((~(int_leq(int_one, I!2) & int_leq(I!2, n) & int_leq(int_one, J!1) & int_leq(J!1, n))) | (((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero)))))),
% 0.41/0.59 inference(skolemize,[status(sab)],[67])).
% 0.41/0.59 tff(69,plain,
% 0.41/0.59 (int_leq(int_one, I!2) & int_leq(I!2, n) & int_leq(int_one, J!1) & int_leq(J!1, n)),
% 0.41/0.59 inference(or_elim,[status(thm)],[68])).
% 0.41/0.59 tff(70,plain,
% 0.41/0.59 (int_leq(J!1, n)),
% 0.41/0.59 inference(and_elim,[status(thm)],[69])).
% 0.41/0.59 tff(71,plain,
% 0.41/0.59 (int_leq(int_one, J!1)),
% 0.41/0.59 inference(and_elim,[status(thm)],[69])).
% 0.41/0.59 tff(72,plain,
% 0.41/0.59 (int_leq(I!2, n)),
% 0.41/0.59 inference(and_elim,[status(thm)],[69])).
% 0.41/0.59 tff(73,plain,
% 0.41/0.59 (int_leq(int_one, I!2)),
% 0.41/0.59 inference(and_elim,[status(thm)],[69])).
% 0.41/0.59 tff(74,plain,
% 0.41/0.59 (^[I: $i, J: $i] : refl(((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(75,plain,
% 0.41/0.59 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[74])).
% 0.41/0.59 tff(76,plain,
% 0.41/0.59 (^[I: $i, J: $i] : rewrite(((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(77,plain,
% 0.41/0.59 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[76])).
% 0.43/0.59 tff(78,plain,
% 0.43/0.59 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[77, 75])).
% 0.43/0.59 tff(79,plain,
% 0.43/0.59 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) <=> (~((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))))), ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) <=> (~(~((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))))))), rewrite((~(~((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)))), ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))))), trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_less(int_zero, C) & (I = plus(J, C))) <=> (~((~int_less(int_zero, C)) | (~(I = plus(J, C)))))), ((~(int_less(int_zero, C) & (I = plus(J, C)))) <=> (~(~((~int_less(int_zero, C)) | (~(I = plus(J, C)))))))), rewrite((~(~((~int_less(int_zero, C)) | (~(I = plus(J, C)))))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C))))), ((~(int_less(int_zero, C) & (I = plus(J, C)))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C)))))), quant_intro(proof_bind(^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, K) & int_leq(K, J)) <=> (~((~int_leq(int_one, K)) | (~int_leq(K, J))))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> (~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))))), rewrite((~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J)))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero)) <=> (((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(plus(K, C), K) = real_zero)))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(plus(K, C), K) = real_zero)) <=> ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero)) <=> ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero)) <=> ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) <=> (((~int_less(int_zero, C)) | (~(I = plus(J, C)))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), rewrite((((~int_less(int_zero, C)) | (~(I = plus(J, C)))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))))), (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) <=> ![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), quant_intro(proof_bind(^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, K) & int_leq(K, J)) <=> (~((~int_leq(int_one, K)) | (~int_leq(K, J))))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> (~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))))), rewrite((~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J)))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) <=> (((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(K, K) = real_one)))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(K, K) = real_one)) <=> ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) <=> ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) <=> ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_less(int_zero, C) & (J = plus(I, C))) <=> (~((~int_less(int_zero, C)) | (~(J = plus(I, C)))))), ((~(int_less(int_zero, C) & (J = plus(I, C)))) <=> (~(~((~int_less(int_zero, C)) | (~(J = plus(I, C)))))))), rewrite((~(~((~int_less(int_zero, C)) | (~(J = plus(I, C)))))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C))))), ((~(int_less(int_zero, C) & (J = plus(I, C)))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C)))))), quant_intro(proof_bind(^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, K) & int_leq(K, I)) <=> (~((~int_leq(int_one, K)) | (~int_leq(K, I))))), ((~(int_leq(int_one, K) & int_leq(K, I))) <=> (~(~((~int_leq(int_one, K)) | (~int_leq(K, I))))))), rewrite((~(~((~int_leq(int_one, K)) | (~int_leq(K, I))))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, I)))), ((~(int_leq(int_one, K) & int_leq(K, I))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> (((~int_leq(int_one, K)) | (~int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))), (((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> (((~int_less(int_zero, C)) | (~(J = plus(I, C)))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), rewrite((((~int_less(int_zero, C)) | (~(J = plus(I, C)))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))), (![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> ![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))) <=> (![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) & ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J))) & ![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))), rewrite((![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) & ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J))) & ![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))), ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))), (((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> (((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))), rewrite((((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n))) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))), (((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(80,plain,
% 0.43/0.60 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[79])).
% 0.43/0.60 tff(81,plain,
% 0.43/0.60 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(82,plain,
% 0.43/0.60 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite(((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) <=> (int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J))), ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) <=> ((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J)) & int_leq(J, n)))), rewrite(((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J)) & int_leq(J, n)) <=> (int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))), ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) <=> (int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)))), trans(monotonicity(rewrite((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[K: $i] : rewrite(((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)) <=> ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), (![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)) <=> ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), (((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))) <=> ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))), rewrite(((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), (((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))) <=> ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), (![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))) <=> ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))), (((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))) <=> ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one))) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), rewrite(((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one))) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))), (((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), (((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))))) <=> ((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) => (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))))), rewrite(((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) => (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), (((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))))) <=> ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(83,plain,
% 0.43/0.60 (![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))))) <=> ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[82])).
% 0.43/0.60 tff(84,axiom,(![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qii')).
% 0.43/0.60 tff(85,plain,
% 0.43/0.60 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.43/0.60 tff(86,plain,
% 0.43/0.60 (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.43/0.60 tff(87,plain,(
% 0.43/0.60 ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 0.43/0.60 inference(skolemize,[status(sab)],[86])).
% 0.43/0.60 tff(88,plain,
% 0.43/0.60 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.43/0.60 tff(89,plain,
% 0.43/0.60 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[88, 78])).
% 0.43/0.60 tff(90,plain,
% 0.43/0.60 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(91,plain,
% 0.43/0.60 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))) <=> ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(92,plain,
% 0.43/0.60 ((~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(93,plain,
% 0.43/0.60 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))) <=> ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[92])).
% 0.43/0.60 tff(94,plain,
% 0.43/0.60 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))) <=> ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))),
% 0.43/0.60 inference(transitivity,[status(thm)],[93, 91])).
% 0.43/0.60 tff(95,plain,
% 0.43/0.60 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[94])).
% 0.43/0.61 tff(96,plain,
% 0.43/0.61 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[95, 90])).
% 0.43/0.61 tff(97,plain,
% 0.43/0.61 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(98,plain,
% 0.43/0.61 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.43/0.61 tff(99,plain,
% 0.43/0.61 (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[98, 89, 73, 72, 71, 70])).
% 0.43/0.61 tff(100,plain,
% 0.43/0.61 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))) | ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))),
% 0.43/0.61 inference(tautology,[status(thm)],[])).
% 0.43/0.61 tff(101,plain,
% 0.43/0.61 (![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.43/0.61 tff(102,plain,
% 0.43/0.61 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | ((~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1)))) <=> ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(103,plain,
% 0.43/0.61 (((a(J!1, J!1) = real_one) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1))) <=> ((~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(104,plain,
% 0.43/0.61 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | ((a(J!1, J!1) = real_one) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)))) <=> ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | ((~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[103])).
% 0.43/0.61 tff(105,plain,
% 0.43/0.61 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | ((a(J!1, J!1) = real_one) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)))) <=> ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1)))),
% 0.43/0.61 inference(transitivity,[status(thm)],[104, 102])).
% 0.43/0.61 tff(106,plain,
% 0.43/0.61 ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | ((a(J!1, J!1) = real_one) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(107,plain,
% 0.43/0.61 ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.43/0.61 tff(108,plain,
% 0.43/0.61 ((a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[107, 71, 101])).
% 0.43/0.61 tff(109,plain,
% 0.43/0.61 (a(J!1, J!1) = real_one),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[108, 60])).
% 0.43/0.61 tff(110,assumption,(a(I!2, J!1) = real_zero), introduced(assumption)).
% 0.43/0.61 tff(111,plain,
% 0.43/0.61 (((I!2 = J!1) | (a(I!2, J!1) = real_zero)) | (~(a(I!2, J!1) = real_zero))),
% 0.43/0.61 inference(tautology,[status(thm)],[])).
% 0.43/0.61 tff(112,plain,
% 0.43/0.61 ((I!2 = J!1) | (a(I!2, J!1) = real_zero)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.43/0.61 tff(113,plain,
% 0.43/0.61 ((~(~((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))))))) <=> ((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero)))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(114,plain,
% 0.43/0.61 ((((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero)))) <=> (~((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(115,plain,
% 0.43/0.61 ((~(((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))))) <=> (~(~((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero)))))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[114])).
% 0.43/0.61 tff(116,plain,
% 0.43/0.61 ((~(((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))))) <=> ((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero)))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[115, 113])).
% 0.43/0.61 tff(117,plain,
% 0.43/0.61 (~(((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))))),
% 0.43/0.61 inference(or_elim,[status(thm)],[68])).
% 0.43/0.61 tff(118,plain,
% 0.43/0.61 ((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.43/0.61 tff(119,plain,
% 0.43/0.61 (~((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero)))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[118, 112])).
% 0.43/0.61 tff(120,plain,
% 0.43/0.61 (((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))) | (I!2 = J!1)),
% 0.43/0.61 inference(tautology,[status(thm)],[])).
% 0.43/0.61 tff(121,plain,
% 0.43/0.61 (I!2 = J!1),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.43/0.61 tff(122,plain,
% 0.43/0.61 (a(I!2, J!1) = a(J!1, J!1)),
% 0.43/0.61 inference(monotonicity,[status(thm)],[121])).
% 0.43/0.61 tff(123,plain,
% 0.43/0.61 (real_zero = a(I!2, J!1)),
% 0.43/0.61 inference(symmetry,[status(thm)],[110])).
% 0.43/0.61 tff(124,plain,
% 0.43/0.61 (real_zero = real_one),
% 0.43/0.61 inference(transitivity,[status(thm)],[123, 122, 109])).
% 0.43/0.61 tff(125,plain,
% 0.43/0.61 ((~(real_zero = real_one)) <=> (~(real_zero = real_one))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(126,axiom,(~(real_zero = real_one)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','real_constants')).
% 0.43/0.61 tff(127,plain,
% 0.43/0.61 (~(real_zero = real_one)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.43/0.61 tff(128,plain,
% 0.43/0.61 ($false),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[127, 124])).
% 0.43/0.61 tff(129,plain,(~(a(I!2, J!1) = real_zero)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.61 tff(130,assumption,(~((~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)))), introduced(assumption)).
% 0.43/0.61 tff(131,plain,
% 0.43/0.61 (((~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)),
% 0.43/0.61 inference(tautology,[status(thm)],[])).
% 0.43/0.61 tff(132,plain,
% 0.43/0.61 (plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.43/0.61 tff(133,plain,
% 0.43/0.61 (I!2 = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.43/0.61 inference(symmetry,[status(thm)],[132])).
% 0.43/0.61 tff(134,plain,
% 0.43/0.61 (((~![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))))))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(135,plain,
% 0.43/0.61 ((~((~((~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)))))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(136,plain,
% 0.43/0.61 (((~![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))))))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[135])).
% 0.43/0.61 tff(137,plain,
% 0.43/0.61 (((~![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))))))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[136, 134])).
% 0.43/0.61 tff(138,plain,
% 0.43/0.61 ((~![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)))))))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(139,plain,
% 0.43/0.61 ((~![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)))))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.43/0.61 tff(140,plain,
% 0.43/0.61 (~((~((~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))))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[139, 13])).
% 0.43/0.61 tff(141,plain,
% 0.43/0.61 (((~((~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)))))),
% 0.43/0.61 inference(tautology,[status(thm)],[])).
% 0.43/0.61 tff(142,plain,
% 0.43/0.61 ((~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))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.43/0.61 tff(143,plain,
% 0.43/0.61 (^[I: $i] : refl((int_less(int_zero, I) <=> int_leq(int_one, I)) <=> (int_less(int_zero, I) <=> int_leq(int_one, I)))),
% 0.43/0.61 inference(bind,[status(th)],[])).
% 0.43/0.61 tff(144,plain,
% 0.43/0.61 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.43/0.61 inference(quant_intro,[status(thm)],[143])).
% 0.43/0.61 tff(145,plain,
% 0.43/0.61 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(146,axiom,(![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','one_successor_of_zero')).
% 0.43/0.61 tff(147,plain,
% 0.43/0.61 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.43/0.61 tff(148,plain,(
% 0.43/0.61 ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.43/0.61 inference(skolemize,[status(sab)],[147])).
% 0.43/0.61 tff(149,plain,
% 0.43/0.61 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.43/0.61 tff(150,plain,
% 0.43/0.61 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, I!2) <=> int_leq(int_one, I!2))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(151,plain,
% 0.43/0.61 (int_less(int_zero, I!2) <=> int_leq(int_one, I!2)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.43/0.61 tff(152,plain,
% 0.43/0.61 ((~(int_less(int_zero, I!2) <=> int_leq(int_one, I!2))) | int_less(int_zero, I!2) | (~int_leq(int_one, I!2))),
% 0.43/0.61 inference(tautology,[status(thm)],[])).
% 0.43/0.61 tff(153,plain,
% 0.43/0.61 ((~(int_less(int_zero, I!2) <=> int_leq(int_one, I!2))) | int_less(int_zero, I!2)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[152, 73])).
% 0.43/0.61 tff(154,plain,
% 0.43/0.61 (int_less(int_zero, I!2)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[153, 151])).
% 0.43/0.61 tff(155,plain,
% 0.43/0.61 ((~((~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))))),
% 0.43/0.62 inference(tautology,[status(thm)],[])).
% 0.43/0.62 tff(156,plain,
% 0.43/0.62 ((~((~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))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.43/0.62 tff(157,plain,
% 0.43/0.62 (~((~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)))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[156, 142])).
% 0.43/0.62 tff(158,plain,
% 0.43/0.62 (((~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)),
% 0.43/0.62 inference(tautology,[status(thm)],[])).
% 0.43/0.62 tff(159,plain,
% 0.43/0.62 (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.43/0.62 tff(160,plain,
% 0.43/0.62 (^[I: $i, J: $i] : refl((plus(I, J) = plus(J, I)) <=> (plus(I, J) = plus(J, I)))),
% 0.43/0.62 inference(bind,[status(th)],[])).
% 0.43/0.62 tff(161,plain,
% 0.43/0.62 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.43/0.62 inference(quant_intro,[status(thm)],[160])).
% 0.43/0.62 tff(162,plain,
% 0.43/0.62 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(163,axiom,(![I: $i, J: $i] : (plus(I, J) = plus(J, I))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus_commutative')).
% 0.43/0.62 tff(164,plain,
% 0.43/0.62 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.43/0.62 tff(165,plain,(
% 0.43/0.62 ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.43/0.62 inference(skolemize,[status(sab)],[164])).
% 0.43/0.62 tff(166,plain,
% 0.43/0.62 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.43/0.62 tff(167,plain,
% 0.43/0.62 ((~![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))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(168,plain,
% 0.43/0.62 (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = plus(tptp_fun_K_0(I!2, int_zero), int_zero)),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.43/0.62 tff(169,plain,
% 0.43/0.62 (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = plus(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.43/0.62 inference(symmetry,[status(thm)],[168])).
% 0.43/0.62 tff(170,plain,
% 0.43/0.62 (^[I: $i] : refl((plus(I, int_zero) = I) <=> (plus(I, int_zero) = I))),
% 0.43/0.62 inference(bind,[status(th)],[])).
% 0.43/0.62 tff(171,plain,
% 0.43/0.62 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.43/0.62 inference(quant_intro,[status(thm)],[170])).
% 0.43/0.62 tff(172,plain,
% 0.43/0.62 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(173,axiom,(![I: $i] : (plus(I, int_zero) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus_zero')).
% 0.43/0.62 tff(174,plain,
% 0.43/0.62 (![I: $i] : (plus(I, int_zero) = I)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.43/0.62 tff(175,plain,(
% 0.43/0.62 ![I: $i] : (plus(I, int_zero) = I)),
% 0.43/0.62 inference(skolemize,[status(sab)],[174])).
% 0.43/0.62 tff(176,plain,
% 0.43/0.62 (![I: $i] : (plus(I, int_zero) = I)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.43/0.62 tff(177,plain,
% 0.43/0.62 ((~![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))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(178,plain,
% 0.43/0.62 (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = tptp_fun_K_0(I!2, int_zero)),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.43/0.62 tff(179,plain,
% 0.43/0.62 (tptp_fun_K_0(I!2, int_zero) = plus(tptp_fun_K_0(I!2, int_zero), int_zero)),
% 0.43/0.62 inference(symmetry,[status(thm)],[178])).
% 0.43/0.62 tff(180,plain,
% 0.43/0.62 (tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.43/0.62 inference(transitivity,[status(thm)],[179, 169, 159, 133])).
% 0.43/0.62 tff(181,plain,
% 0.43/0.62 (((~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))),
% 0.43/0.62 inference(tautology,[status(thm)],[])).
% 0.43/0.62 tff(182,plain,
% 0.43/0.62 (int_less(int_zero, tptp_fun_K_0(I!2, J!1))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[181, 130])).
% 0.43/0.62 tff(183,plain,
% 0.43/0.62 (tptp_fun_K_0(I!2, int_zero) = I!2),
% 0.43/0.62 inference(transitivity,[status(thm)],[179, 169, 159])).
% 0.43/0.62 tff(184,plain,
% 0.43/0.62 (int_leq(tptp_fun_K_0(I!2, int_zero), n) <=> int_leq(I!2, n)),
% 0.43/0.62 inference(monotonicity,[status(thm)],[183])).
% 0.43/0.62 tff(185,plain,
% 0.43/0.62 (int_leq(I!2, n) <=> int_leq(tptp_fun_K_0(I!2, int_zero), n)),
% 0.43/0.62 inference(symmetry,[status(thm)],[184])).
% 0.43/0.62 tff(186,plain,
% 0.43/0.62 (int_leq(tptp_fun_K_0(I!2, int_zero), n)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[72, 185])).
% 0.43/0.62 tff(187,plain,
% 0.43/0.62 ((~![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)))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(188,plain,
% 0.43/0.62 (int_less(int_zero, tptp_fun_K_0(I!2, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[187, 149])).
% 0.43/0.62 tff(189,plain,
% 0.43/0.62 (((~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))),
% 0.43/0.62 inference(tautology,[status(thm)],[])).
% 0.43/0.62 tff(190,plain,
% 0.43/0.62 (int_less(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[189, 157])).
% 0.43/0.62 tff(191,plain,
% 0.43/0.62 ((~(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))),
% 0.43/0.62 inference(tautology,[status(thm)],[])).
% 0.43/0.62 tff(192,plain,
% 0.43/0.62 ((~(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))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.43/0.62 tff(193,plain,
% 0.43/0.62 (int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[192, 188])).
% 0.43/0.62 tff(194,plain,
% 0.43/0.62 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![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))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![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))))))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(195,plain,
% 0.43/0.62 (((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))) <=> ((~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![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))))))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(196,plain,
% 0.43/0.62 ((~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))) <=> (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(197,plain,
% 0.43/0.62 (((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))) <=> ((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[196])).
% 0.43/0.62 tff(198,plain,
% 0.43/0.62 (((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero))))))))) <=> ((~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![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))))))))),
% 0.43/0.62 inference(transitivity,[status(thm)],[197, 195])).
% 0.43/0.62 tff(199,plain,
% 0.43/0.62 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![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)))))))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[198])).
% 0.43/0.62 tff(200,plain,
% 0.43/0.62 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![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))))))))),
% 0.43/0.62 inference(transitivity,[status(thm)],[199, 194])).
% 0.43/0.62 tff(201,plain,
% 0.43/0.62 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))))))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(202,plain,
% 0.43/0.62 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(J!1, n)) | (~int_leq(int_one, J!1)) | (~int_leq(int_one, tptp_fun_K_0(I!2, int_zero))) | (~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![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)))))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.43/0.62 tff(203,plain,
% 0.43/0.62 ((~int_leq(tptp_fun_K_0(I!2, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(I!2, int_zero) = plus(J!1, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[202, 89, 71, 70, 193])).
% 0.43/0.62 tff(204,plain,
% 0.43/0.62 (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![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))))))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[203, 186])).
% 0.46/0.63 tff(205,plain,
% 0.46/0.63 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!1 = plus(tptp_fun_K_0(I!2, int_zero), C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(I!2, int_zero)))))) | (~![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))))),
% 0.46/0.63 inference(tautology,[status(thm)],[])).
% 0.46/0.63 tff(206,plain,
% 0.46/0.63 (![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))))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.46/0.63 tff(207,plain,
% 0.46/0.63 (((~![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)))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(208,plain,
% 0.46/0.63 (((~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)))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(209,plain,
% 0.46/0.63 (((~![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))))),
% 0.46/0.63 inference(monotonicity,[status(thm)],[208])).
% 0.46/0.63 tff(210,plain,
% 0.46/0.63 (((~![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)))),
% 0.46/0.63 inference(transitivity,[status(thm)],[209, 207])).
% 0.46/0.63 tff(211,plain,
% 0.46/0.63 ((~![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))))),
% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(212,plain,
% 0.46/0.63 ((~![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))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.46/0.63 tff(213,plain,
% 0.46/0.63 (![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))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[212, 206, 182, 180])).
% 0.46/0.63 tff(214,plain,
% 0.46/0.63 (((~![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))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(215,plain,
% 0.46/0.63 ((~![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))),
% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(216,plain,
% 0.46/0.63 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero)),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.46/0.63 tff(217,plain,
% 0.46/0.63 (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[216, 71, 60, 213])).
% 0.46/0.63 tff(218,plain,
% 0.46/0.63 (a(I!2, J!1) = a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1)),
% 0.46/0.63 inference(monotonicity,[status(thm)],[133])).
% 0.46/0.63 tff(219,plain,
% 0.46/0.63 (a(I!2, J!1) = real_zero),
% 0.46/0.63 inference(transitivity,[status(thm)],[218, 217])).
% 0.46/0.63 tff(220,assumption,(~(a(I!2, J!1) = real_zero)), introduced(assumption)).
% 0.46/0.63 tff(221,plain,
% 0.46/0.63 ($false),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.46/0.63 tff(222,plain,(((~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))) | (a(I!2, J!1) = real_zero)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.63 tff(223,plain,
% 0.46/0.63 ((~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))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[222, 129])).
% 0.46/0.63 tff(224,plain,
% 0.46/0.63 ((~((~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))))),
% 0.46/0.63 inference(tautology,[status(thm)],[])).
% 0.46/0.63 tff(225,plain,
% 0.46/0.63 (~int_less(J!1, I!2)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[224, 223, 45])).
% 0.46/0.63 tff(226,assumption,(~int_less(J!1, I!2)), introduced(assumption)).
% 0.46/0.63 tff(227,assumption,(~int_leq(I!2, J!1)), introduced(assumption)).
% 0.46/0.63 tff(228,plain,
% 0.46/0.63 (^[I: $i, J: $i] : refl((int_leq(J, I) | int_less(I, J)) <=> (int_leq(J, I) | int_less(I, J)))),
% 0.46/0.63 inference(bind,[status(th)],[])).
% 0.46/0.63 tff(229,plain,
% 0.46/0.63 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.46/0.63 inference(quant_intro,[status(thm)],[228])).
% 0.46/0.63 tff(230,plain,
% 0.46/0.63 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(231,plain,
% 0.46/0.63 (^[I: $i, J: $i] : rewrite((int_less(I, J) | int_leq(J, I)) <=> (int_leq(J, I) | int_less(I, J)))),
% 0.46/0.63 inference(bind,[status(th)],[])).
% 0.46/0.63 tff(232,plain,
% 0.46/0.63 (![I: $i, J: $i] : (int_less(I, J) | int_leq(J, I)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.46/0.63 inference(quant_intro,[status(thm)],[231])).
% 0.46/0.63 tff(233,axiom,(![I: $i, J: $i] : (int_less(I, J) | int_leq(J, I))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','int_less_total')).
% 0.46/0.63 tff(234,plain,
% 0.46/0.63 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.46/0.63 tff(235,plain,
% 0.46/0.63 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.46/0.63 tff(236,plain,(
% 0.46/0.63 ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.46/0.63 inference(skolemize,[status(sab)],[235])).
% 0.46/0.63 tff(237,plain,
% 0.46/0.63 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[236, 229])).
% 0.46/0.63 tff(238,plain,
% 0.46/0.63 (((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | (int_leq(I!2, J!1) | int_less(J!1, I!2))) <=> ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | int_leq(I!2, J!1) | int_less(J!1, I!2))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(239,plain,
% 0.46/0.63 ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | (int_leq(I!2, J!1) | int_less(J!1, I!2))),
% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(240,plain,
% 0.46/0.63 ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | int_leq(I!2, J!1) | int_less(J!1, I!2)),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.46/0.63 tff(241,plain,
% 0.46/0.63 ($false),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[240, 237, 227, 226])).
% 0.46/0.63 tff(242,plain,(int_leq(I!2, J!1) | int_less(J!1, I!2)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.63 tff(243,plain,
% 0.46/0.63 (int_leq(I!2, J!1)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[242, 225])).
% 0.46/0.63 tff(244,plain,
% 0.46/0.63 ((~(int_leq(I!2, J!1) <=> ((I!2 = J!1) | int_less(I!2, J!1)))) | (~int_leq(I!2, J!1)) | ((I!2 = J!1) | int_less(I!2, J!1))),
% 0.46/0.63 inference(tautology,[status(thm)],[])).
% 0.46/0.63 tff(245,plain,
% 0.46/0.63 ((~(int_leq(I!2, J!1) <=> ((I!2 = J!1) | int_less(I!2, J!1)))) | ((I!2 = J!1) | int_less(I!2, J!1))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.46/0.63 tff(246,plain,
% 0.46/0.63 ((I!2 = J!1) | int_less(I!2, J!1)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[245, 34])).
% 0.46/0.63 tff(247,plain,
% 0.46/0.63 (((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))) | (a(I!2, J!1) = real_zero)),
% 0.46/0.63 inference(tautology,[status(thm)],[])).
% 0.46/0.63 tff(248,plain,
% 0.46/0.63 ((~(I!2 = J!1)) | (~(a(I!2, J!1) = real_zero))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[247, 129])).
% 0.46/0.63 tff(249,plain,
% 0.46/0.63 (~((I!2 = J!1) | (a(I!2, J!1) = real_zero))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[118, 248])).
% 0.46/0.63 tff(250,plain,
% 0.46/0.63 (((I!2 = J!1) | (a(I!2, J!1) = real_zero)) | (~(I!2 = J!1))),
% 0.46/0.63 inference(tautology,[status(thm)],[])).
% 0.46/0.63 tff(251,plain,
% 0.46/0.63 (~(I!2 = J!1)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[250, 249])).
% 0.46/0.63 tff(252,plain,
% 0.46/0.63 ((~((I!2 = J!1) | int_less(I!2, J!1))) | (I!2 = J!1) | int_less(I!2, J!1)),
% 0.46/0.63 inference(tautology,[status(thm)],[])).
% 0.46/0.63 tff(253,plain,
% 0.46/0.63 ((~((I!2 = J!1) | int_less(I!2, J!1))) | int_less(I!2, J!1)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.46/0.63 tff(254,plain,
% 0.46/0.63 (int_less(I!2, J!1)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[253, 246])).
% 0.46/0.63 tff(255,plain,
% 0.46/0.63 ((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))))),
% 0.47/0.63 inference(tautology,[status(thm)],[])).
% 0.47/0.63 tff(256,plain,
% 0.47/0.63 ((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.47/0.63 tff(257,plain,
% 0.47/0.63 (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[256, 22])).
% 0.47/0.63 tff(258,plain,
% 0.47/0.63 (((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))) | (plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)),
% 0.47/0.63 inference(tautology,[status(thm)],[])).
% 0.47/0.63 tff(259,plain,
% 0.47/0.63 (plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.47/0.63 tff(260,plain,
% 0.47/0.63 (J!1 = plus(I!2, tptp_fun_K_0(J!1, I!2))),
% 0.47/0.63 inference(symmetry,[status(thm)],[259])).
% 0.47/0.63 tff(261,plain,
% 0.47/0.63 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1))))))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(262,plain,
% 0.47/0.63 ((~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~(plus(int_zero, K) = J!1)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1)))))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(263,plain,
% 0.47/0.63 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~(plus(int_zero, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1))))))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[262])).
% 0.47/0.63 tff(264,plain,
% 0.47/0.63 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~(plus(int_zero, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1))))))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[263, 261])).
% 0.47/0.63 tff(265,plain,
% 0.47/0.63 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~(plus(int_zero, K) = J!1)) | (~int_less(int_zero, K)))))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(266,plain,
% 0.47/0.63 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1)))))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.47/0.63 tff(267,plain,
% 0.47/0.63 (~((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1))))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[266, 13])).
% 0.47/0.63 tff(268,plain,
% 0.47/0.63 (((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~(int_less(int_zero, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(int_zero, K) = J!1)))))) | ((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))),
% 0.47/0.63 inference(tautology,[status(thm)],[])).
% 0.47/0.63 tff(269,plain,
% 0.47/0.63 ((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.47/0.63 tff(270,plain,
% 0.47/0.63 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, J!1) <=> int_leq(int_one, J!1))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(271,plain,
% 0.47/0.63 (int_less(int_zero, J!1) <=> int_leq(int_one, J!1)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[270, 149])).
% 0.47/0.63 tff(272,plain,
% 0.47/0.63 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1) | (~int_leq(int_one, J!1))),
% 0.47/0.63 inference(tautology,[status(thm)],[])).
% 0.47/0.63 tff(273,plain,
% 0.47/0.63 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[272, 71])).
% 0.47/0.63 tff(274,plain,
% 0.47/0.63 (int_less(int_zero, J!1)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[273, 271])).
% 0.47/0.63 tff(275,plain,
% 0.47/0.63 ((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1))))),
% 0.47/0.63 inference(tautology,[status(thm)],[])).
% 0.47/0.63 tff(276,plain,
% 0.47/0.63 ((~((~int_less(int_zero, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))))) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[275, 274])).
% 0.47/0.64 tff(277,plain,
% 0.47/0.64 (~((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[276, 269])).
% 0.47/0.64 tff(278,plain,
% 0.47/0.64 (((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1))) | (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1)),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(279,plain,
% 0.47/0.64 (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[278, 277])).
% 0.47/0.64 tff(280,plain,
% 0.47/0.64 ((~![I: $i, J: $i] : (plus(I, J) = plus(J, I))) | (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = plus(tptp_fun_K_0(J!1, int_zero), int_zero))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(281,plain,
% 0.47/0.64 (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = plus(tptp_fun_K_0(J!1, int_zero), int_zero)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[280, 166])).
% 0.47/0.64 tff(282,plain,
% 0.47/0.64 (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = plus(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.47/0.64 inference(symmetry,[status(thm)],[281])).
% 0.47/0.64 tff(283,plain,
% 0.47/0.64 ((~![I: $i] : (plus(I, int_zero) = I)) | (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = tptp_fun_K_0(J!1, int_zero))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(284,plain,
% 0.47/0.64 (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = tptp_fun_K_0(J!1, int_zero)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[283, 176])).
% 0.47/0.64 tff(285,plain,
% 0.47/0.64 (tptp_fun_K_0(J!1, int_zero) = plus(tptp_fun_K_0(J!1, int_zero), int_zero)),
% 0.47/0.64 inference(symmetry,[status(thm)],[284])).
% 0.47/0.64 tff(286,plain,
% 0.47/0.64 (tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2))),
% 0.47/0.64 inference(transitivity,[status(thm)],[285, 282, 279, 260])).
% 0.47/0.64 tff(287,plain,
% 0.47/0.64 (((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))) | int_less(int_zero, tptp_fun_K_0(J!1, I!2))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(288,plain,
% 0.47/0.64 (int_less(int_zero, tptp_fun_K_0(J!1, I!2))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[287, 257])).
% 0.47/0.64 tff(289,plain,
% 0.47/0.64 (tptp_fun_K_0(J!1, int_zero) = J!1),
% 0.47/0.64 inference(transitivity,[status(thm)],[285, 282, 279])).
% 0.47/0.64 tff(290,plain,
% 0.47/0.64 (int_leq(tptp_fun_K_0(J!1, int_zero), n) <=> int_leq(J!1, n)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[289])).
% 0.47/0.64 tff(291,plain,
% 0.47/0.64 (int_leq(J!1, n) <=> int_leq(tptp_fun_K_0(J!1, int_zero), n)),
% 0.47/0.64 inference(symmetry,[status(thm)],[290])).
% 0.47/0.64 tff(292,plain,
% 0.47/0.64 (int_leq(tptp_fun_K_0(J!1, int_zero), n)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[70, 291])).
% 0.47/0.64 tff(293,plain,
% 0.47/0.64 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(294,plain,
% 0.47/0.64 (int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[293, 149])).
% 0.47/0.64 tff(295,plain,
% 0.47/0.64 (((~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | (~(plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1))) | int_less(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(296,plain,
% 0.47/0.64 (int_less(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[295, 277])).
% 0.47/0.64 tff(297,plain,
% 0.47/0.64 ((~(int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero)))) | (~int_less(int_zero, tptp_fun_K_0(J!1, int_zero))) | int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(298,plain,
% 0.47/0.64 ((~(int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero)))) | int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[297, 296])).
% 0.47/0.64 tff(299,plain,
% 0.47/0.64 (int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[298, 294])).
% 0.47/0.64 tff(300,plain,
% 0.47/0.64 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(301,plain,
% 0.47/0.64 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))))) <=> ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(302,plain,
% 0.47/0.64 ((~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))) <=> (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(303,plain,
% 0.47/0.64 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))) <=> ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[302])).
% 0.47/0.64 tff(304,plain,
% 0.47/0.64 (((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))))))) <=> ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[303, 301])).
% 0.47/0.64 tff(305,plain,
% 0.47/0.64 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[304])).
% 0.47/0.64 tff(306,plain,
% 0.47/0.64 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[305, 300])).
% 0.47/0.64 tff(307,plain,
% 0.47/0.64 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(308,plain,
% 0.47/0.64 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, n)) | (~int_leq(int_one, tptp_fun_K_0(J!1, int_zero))) | (~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.47/0.64 tff(309,plain,
% 0.47/0.64 ((~int_leq(tptp_fun_K_0(J!1, int_zero), n)) | (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[308, 89, 73, 72, 299])).
% 0.47/0.64 tff(310,plain,
% 0.47/0.64 (~((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero)))))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[309, 292])).
% 0.47/0.64 tff(311,plain,
% 0.47/0.64 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(I!2 = plus(tptp_fun_K_0(J!1, int_zero), C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, tptp_fun_K_0(J!1, int_zero))))))) | ![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(312,plain,
% 0.47/0.65 (![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[311, 310])).
% 0.47/0.65 tff(313,plain,
% 0.47/0.65 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero)))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(314,plain,
% 0.47/0.65 (((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2)))) <=> ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(315,plain,
% 0.47/0.65 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[314])).
% 0.47/0.65 tff(316,plain,
% 0.47/0.65 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) <=> ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[315, 313])).
% 0.47/0.65 tff(317,plain,
% 0.47/0.65 ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | ((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(318,plain,
% 0.47/0.65 ((~![C: $i] : ((~int_less(int_zero, C)) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I!2))))) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2)))) | ![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.47/0.65 tff(319,plain,
% 0.47/0.65 (![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[318, 312, 288, 286])).
% 0.47/0.65 tff(320,assumption,(~int_leq(I!2, I!2)), introduced(assumption)).
% 0.47/0.65 tff(321,plain,
% 0.47/0.65 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2)) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(322,plain,
% 0.47/0.65 ((int_leq(I!2, I!2) <=> $true) <=> int_leq(I!2, I!2)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(323,plain,
% 0.47/0.65 (($true | int_less(I!2, I!2)) <=> $true),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(324,plain,
% 0.47/0.65 ((I!2 = I!2) <=> $true),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(325,plain,
% 0.47/0.65 (((I!2 = I!2) | int_less(I!2, I!2)) <=> ($true | int_less(I!2, I!2))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[324])).
% 0.47/0.65 tff(326,plain,
% 0.47/0.65 (((I!2 = I!2) | int_less(I!2, I!2)) <=> $true),
% 0.47/0.65 inference(transitivity,[status(thm)],[325, 323])).
% 0.47/0.65 tff(327,plain,
% 0.47/0.65 ((int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2))) <=> (int_leq(I!2, I!2) <=> $true)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[326])).
% 0.47/0.65 tff(328,plain,
% 0.47/0.65 ((int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2))) <=> int_leq(I!2, I!2)),
% 0.47/0.65 inference(transitivity,[status(thm)],[327, 322])).
% 0.47/0.65 tff(329,plain,
% 0.47/0.65 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2)))) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[328])).
% 0.47/0.65 tff(330,plain,
% 0.47/0.65 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2)))) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2))),
% 0.47/0.65 inference(transitivity,[status(thm)],[329, 321])).
% 0.47/0.65 tff(331,plain,
% 0.47/0.65 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(332,plain,
% 0.47/0.65 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.47/0.65 tff(333,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[332, 32, 320])).
% 0.47/0.65 tff(334,plain,(int_leq(I!2, I!2)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(335,plain,
% 0.47/0.65 (((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero))) <=> ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(336,plain,
% 0.47/0.65 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | ((~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(337,plain,
% 0.47/0.65 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.47/0.65 tff(338,plain,
% 0.47/0.65 (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[337, 73, 334, 319])).
% 0.47/0.65 tff(339,plain,
% 0.47/0.65 (a(I!2, J!1) = a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2)))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[260])).
% 0.47/0.65 tff(340,plain,
% 0.47/0.65 (a(I!2, J!1) = real_zero),
% 0.47/0.65 inference(transitivity,[status(thm)],[339, 338])).
% 0.47/0.65 tff(341,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[129, 340])).
% 0.47/0.65 % SZS output end Proof
% 0.47/0.65 % E exiting
%------------------------------------------------------------------------------