%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV491+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:34:10 AM UTC 2025
% Result : Theorem 0.76s 1.00s
% Output : Proof 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWV491+4 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.10 % Command : run_E %s %d THM
% 0.09/0.30 % Computer : n004.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Fri Jun 20 09:53:07 EDT 2025
% 0.09/0.31 % CPUTime :
% 0.76/1.00 % SZS status Theorem
% 0.76/1.00 % SZS output start Proof
% 0.76/1.00 tff(real_zero_type, type, (
% 0.76/1.00 real_zero: $i)).
% 0.76/1.00 tff(a_type, type, (
% 0.76/1.00 a: ( $i * $i ) > $i)).
% 0.76/1.00 tff(tptp_fun_J_1_type, type, (
% 0.76/1.00 tptp_fun_J_1: $i)).
% 0.76/1.00 tff(tptp_fun_I_2_type, type, (
% 0.76/1.00 tptp_fun_I_2: $i)).
% 0.76/1.00 tff(plus_type, type, (
% 0.76/1.00 plus: ( $i * $i ) > $i)).
% 0.76/1.00 tff(tptp_fun_K_0_type, type, (
% 0.76/1.00 tptp_fun_K_0: ( $i * $i ) > $i)).
% 0.76/1.00 tff(int_leq_type, type, (
% 0.76/1.00 int_leq: ( $i * $i ) > $o)).
% 0.76/1.00 tff(int_one_type, type, (
% 0.76/1.00 int_one: $i)).
% 0.76/1.00 tff(int_zero_type, type, (
% 0.76/1.00 int_zero: $i)).
% 0.76/1.00 tff(int_less_type, type, (
% 0.76/1.00 int_less: ( $i * $i ) > $o)).
% 0.76/1.00 tff(real_one_type, type, (
% 0.76/1.00 real_one: $i)).
% 0.76/1.00 tff(n_type, type, (
% 0.76/1.00 n: $i)).
% 0.76/1.00 tff(1,plain,
% 0.76/1.00 (^[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))))))))),
% 0.76/1.00 inference(bind,[status(th)],[])).
% 0.76/1.00 tff(2,plain,
% 0.76/1.00 (![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)))))))),
% 0.76/1.00 inference(quant_intro,[status(thm)],[1])).
% 0.76/1.00 tff(3,plain,
% 0.76/1.00 (^[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))))))))),
% 0.76/1.00 inference(bind,[status(th)],[])).
% 0.76/1.00 tff(4,plain,
% 0.76/1.00 (![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)))))))),
% 0.76/1.00 inference(quant_intro,[status(thm)],[3])).
% 0.76/1.00 tff(5,plain,
% 0.76/1.00 (![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)))))))),
% 0.76/1.00 inference(transitivity,[status(thm)],[4, 2])).
% 0.76/1.00 tff(6,plain,
% 0.76/1.00 (^[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)))))))))),
% 0.76/1.00 inference(bind,[status(th)],[])).
% 0.76/1.00 tff(7,plain,
% 0.76/1.00 (![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)))))))),
% 0.76/1.00 inference(quant_intro,[status(thm)],[6])).
% 0.76/1.00 tff(8,plain,
% 0.76/1.00 (![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)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(9,axiom,(![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_and_inverse')).
% 0.76/1.00 tff(10,plain,
% 0.76/1.00 (![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.76/1.00 tff(11,plain,(
% 0.76/1.00 ![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)))))),
% 0.76/1.00 inference(skolemize,[status(sab)],[10])).
% 0.76/1.00 tff(12,plain,
% 0.76/1.00 (![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)))))))),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.76/1.00 tff(13,plain,
% 0.76/1.00 (![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)))))))),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.76/1.00 tff(14,plain,
% 0.76/1.00 (((~![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)))))))))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(15,plain,
% 0.76/1.00 ((~((~((~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))))))))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(16,plain,
% 0.76/1.01 (((~![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)))))))))),
% 0.76/1.01 inference(monotonicity,[status(thm)],[15])).
% 0.76/1.01 tff(17,plain,
% 0.76/1.01 (((~![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)))))))))),
% 0.76/1.01 inference(transitivity,[status(thm)],[16, 14])).
% 0.76/1.01 tff(18,plain,
% 0.76/1.01 ((~![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)))))))),
% 0.76/1.01 inference(quant_inst,[status(thm)],[])).
% 0.76/1.01 tff(19,plain,
% 0.76/1.01 ((~![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))))))))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.76/1.01 tff(20,plain,
% 0.76/1.01 (~((~(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)))))))),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.76/1.01 tff(21,plain,
% 0.76/1.01 (((~(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)))))),
% 0.76/1.01 inference(tautology,[status(thm)],[])).
% 0.76/1.01 tff(22,plain,
% 0.76/1.01 ((~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))))),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.76/1.01 tff(23,plain,
% 0.76/1.01 (^[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))))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(24,plain,
% 0.76/1.01 (![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)))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[23])).
% 0.76/1.01 tff(25,plain,
% 0.76/1.01 (![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)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(26,plain,
% 0.76/1.01 (^[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))))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(27,plain,
% 0.76/1.01 (![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)))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[26])).
% 0.76/1.01 tff(28,axiom,(![I: $i, J: $i] : (int_leq(I, J) <=> (int_less(I, J) | (I = J)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','int_leq')).
% 0.76/1.01 tff(29,plain,
% 0.76/1.01 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.76/1.01 tff(30,plain,
% 0.76/1.01 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.76/1.01 tff(31,plain,(
% 0.76/1.01 ![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.76/1.01 inference(skolemize,[status(sab)],[30])).
% 0.76/1.01 tff(32,plain,
% 0.76/1.01 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.76/1.01 tff(33,plain,
% 0.76/1.01 ((~![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)))),
% 0.76/1.01 inference(quant_inst,[status(thm)],[])).
% 0.76/1.01 tff(34,plain,
% 0.76/1.01 (int_leq(I!2, J!1) <=> ((I!2 = J!1) | int_less(I!2, J!1))),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.76/1.01 tff(35,assumption,(~int_leq(J!1, J!1)), introduced(assumption)).
% 0.76/1.01 tff(36,plain,
% 0.76/1.01 (((~![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))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(37,plain,
% 0.76/1.01 ((int_leq(J!1, J!1) <=> $true) <=> int_leq(J!1, J!1)),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(38,plain,
% 0.76/1.01 (($true | int_less(J!1, J!1)) <=> $true),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(39,plain,
% 0.76/1.01 ((J!1 = J!1) <=> $true),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(40,plain,
% 0.76/1.01 (((J!1 = J!1) | int_less(J!1, J!1)) <=> ($true | int_less(J!1, J!1))),
% 0.76/1.01 inference(monotonicity,[status(thm)],[39])).
% 0.76/1.01 tff(41,plain,
% 0.76/1.01 (((J!1 = J!1) | int_less(J!1, J!1)) <=> $true),
% 0.76/1.01 inference(transitivity,[status(thm)],[40, 38])).
% 0.76/1.01 tff(42,plain,
% 0.76/1.01 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> (int_leq(J!1, J!1) <=> $true)),
% 0.76/1.01 inference(monotonicity,[status(thm)],[41])).
% 0.76/1.01 tff(43,plain,
% 0.76/1.01 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> int_leq(J!1, J!1)),
% 0.76/1.01 inference(transitivity,[status(thm)],[42, 37])).
% 0.76/1.01 tff(44,plain,
% 0.76/1.01 (((~![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))),
% 0.76/1.01 inference(monotonicity,[status(thm)],[43])).
% 0.76/1.01 tff(45,plain,
% 0.76/1.01 (((~![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))),
% 0.76/1.01 inference(transitivity,[status(thm)],[44, 36])).
% 0.76/1.01 tff(46,plain,
% 0.76/1.01 ((~![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)))),
% 0.76/1.01 inference(quant_inst,[status(thm)],[])).
% 0.76/1.01 tff(47,plain,
% 0.76/1.01 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1)),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.76/1.01 tff(48,plain,
% 0.76/1.01 ($false),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[47, 32, 35])).
% 0.76/1.01 tff(49,plain,(int_leq(J!1, J!1)), inference(lemma,lemma(discharge,[]))).
% 0.76/1.01 tff(50,plain,
% 0.76/1.01 ((~![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_one))))) <=> (~![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_one)))))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(51,plain,
% 0.76/1.01 ((~![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_one))))) <=> (~![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_one)))))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(52,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_one))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','id')).
% 0.76/1.01 tff(53,plain,
% 0.76/1.01 (~![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_one))))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.76/1.01 tff(54,plain,
% 0.76/1.01 (~![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_one))))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.76/1.01 tff(55,plain,
% 0.76/1.01 (~![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_one))))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.76/1.01 tff(56,plain,
% 0.76/1.01 (~![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_one))))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[55, 50])).
% 0.76/1.01 tff(57,plain,(
% 0.76/1.01 ~((~(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_one))))),
% 0.76/1.01 inference(skolemize,[status(sab)],[56])).
% 0.76/1.01 tff(58,plain,
% 0.76/1.01 (int_leq(int_one, I!2) & int_leq(I!2, n) & int_leq(int_one, J!1) & int_leq(J!1, n)),
% 0.76/1.01 inference(or_elim,[status(thm)],[57])).
% 0.76/1.01 tff(59,plain,
% 0.76/1.01 (int_leq(J!1, n)),
% 0.76/1.01 inference(and_elim,[status(thm)],[58])).
% 0.76/1.01 tff(60,plain,
% 0.76/1.01 (int_leq(int_one, J!1)),
% 0.76/1.01 inference(and_elim,[status(thm)],[58])).
% 0.76/1.01 tff(61,plain,
% 0.76/1.01 (int_leq(I!2, n)),
% 0.76/1.01 inference(and_elim,[status(thm)],[58])).
% 0.76/1.01 tff(62,plain,
% 0.76/1.01 (int_leq(int_one, I!2)),
% 0.76/1.01 inference(and_elim,[status(thm)],[58])).
% 0.76/1.01 tff(63,plain,
% 0.76/1.01 (^[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)))))))))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(64,plain,
% 0.76/1.01 (![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))))))))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[63])).
% 0.76/1.01 tff(65,plain,
% 0.76/1.01 (^[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)))))))))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(66,plain,
% 0.76/1.01 (![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))))))))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[65])).
% 0.76/1.01 tff(67,plain,
% 0.76/1.01 (![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))))))))),
% 0.76/1.01 inference(transitivity,[status(thm)],[66, 64])).
% 0.76/1.01 tff(68,plain,
% 0.76/1.01 (^[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))))))))))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(69,plain,
% 0.76/1.01 (![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))))))))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[68])).
% 0.76/1.01 tff(70,plain,
% 0.76/1.01 (![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)))))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(71,plain,
% 0.76/1.01 (^[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)))))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(72,plain,
% 0.85/1.02 (![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)))))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[71])).
% 0.85/1.02 tff(73,axiom,(![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = real_zero))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qii')).
% 0.85/1.02 tff(74,plain,
% 0.85/1.02 (![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)))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.85/1.02 tff(75,plain,
% 0.85/1.02 (![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)))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.85/1.02 tff(76,plain,(
% 0.85/1.02 ![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)))))),
% 0.85/1.02 inference(skolemize,[status(sab)],[75])).
% 0.85/1.02 tff(77,plain,
% 0.85/1.02 (![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))))))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.85/1.02 tff(78,plain,
% 0.85/1.02 (![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))))))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.85/1.02 tff(79,plain,
% 0.85/1.02 (((~![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))))))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(80,plain,
% 0.85/1.02 (((~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))))))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(81,plain,
% 0.85/1.02 ((~((~![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)))))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(82,plain,
% 0.85/1.02 (((~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))))))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[81])).
% 0.85/1.02 tff(83,plain,
% 0.85/1.02 (((~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))))))))),
% 0.85/1.02 inference(transitivity,[status(thm)],[82, 80])).
% 0.85/1.02 tff(84,plain,
% 0.85/1.02 (((~![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)))))))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[83])).
% 0.85/1.02 tff(85,plain,
% 0.85/1.02 (((~![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))))))))),
% 0.85/1.02 inference(transitivity,[status(thm)],[84, 79])).
% 0.85/1.02 tff(86,plain,
% 0.85/1.02 ((~![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))))))))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(87,plain,
% 0.85/1.02 ((~![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)))))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.85/1.02 tff(88,plain,
% 0.85/1.02 (~((~![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))))))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[87, 78, 62, 61, 60, 59])).
% 0.85/1.02 tff(89,plain,
% 0.85/1.02 (((~![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)))),
% 0.85/1.02 inference(tautology,[status(thm)],[])).
% 0.85/1.02 tff(90,plain,
% 0.85/1.02 (![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.85/1.02 tff(91,plain,
% 0.85/1.02 (((~![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)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(92,plain,
% 0.85/1.02 (((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)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(93,plain,
% 0.85/1.02 (((~![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))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[92])).
% 0.85/1.02 tff(94,plain,
% 0.85/1.02 (((~![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)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[93, 91])).
% 0.85/1.02 tff(95,plain,
% 0.85/1.02 ((~![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)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(96,plain,
% 0.85/1.02 ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.85/1.02 tff(97,plain,
% 0.85/1.02 ((a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[96, 60, 90])).
% 0.85/1.02 tff(98,plain,
% 0.85/1.02 (a(J!1, J!1) = real_one),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[97, 49])).
% 0.85/1.02 tff(99,assumption,(~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one))), introduced(assumption)).
% 0.85/1.02 tff(100,plain,
% 0.85/1.02 (((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)) | (I!2 = J!1)),
% 0.85/1.02 inference(tautology,[status(thm)],[])).
% 0.85/1.02 tff(101,plain,
% 0.85/1.02 (I!2 = J!1),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.85/1.02 tff(102,plain,
% 0.85/1.02 (a(I!2, J!1) = a(J!1, J!1)),
% 0.85/1.02 inference(monotonicity,[status(thm)],[101])).
% 0.85/1.02 tff(103,plain,
% 0.85/1.02 (a(I!2, J!1) = real_one),
% 0.85/1.02 inference(transitivity,[status(thm)],[102, 98])).
% 0.85/1.02 tff(104,plain,
% 0.85/1.02 (((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)) | (~(a(I!2, J!1) = real_one))),
% 0.85/1.02 inference(tautology,[status(thm)],[])).
% 0.85/1.02 tff(105,plain,
% 0.85/1.02 (~(a(I!2, J!1) = real_one)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[104, 99])).
% 0.85/1.02 tff(106,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[105, 103])).
% 0.85/1.02 tff(107,plain,((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(108,plain,
% 0.85/1.02 ((~(~((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))))) <=> ((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(109,plain,
% 0.85/1.02 ((((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (a(I!2, J!1) = real_one))) <=> (~((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(110,plain,
% 0.85/1.02 ((~(((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))) <=> (~(~((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one))))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[109])).
% 0.85/1.02 tff(111,plain,
% 0.85/1.02 ((~(((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))) <=> ((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one))))),
% 0.85/1.03 inference(transitivity,[status(thm)],[110, 108])).
% 0.85/1.03 tff(112,plain,
% 0.85/1.03 (~(((I!2 = J!1) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))),
% 0.85/1.03 inference(or_elim,[status(thm)],[57])).
% 0.85/1.03 tff(113,plain,
% 0.85/1.03 ((~((I!2 = J!1) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.85/1.03 tff(114,plain,
% 0.85/1.03 (~((I!2 = J!1) | (a(I!2, J!1) = real_zero))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[113, 107])).
% 0.85/1.03 tff(115,plain,
% 0.85/1.03 (((I!2 = J!1) | (a(I!2, J!1) = real_zero)) | (~(a(I!2, J!1) = real_zero))),
% 0.85/1.03 inference(tautology,[status(thm)],[])).
% 0.85/1.03 tff(116,plain,
% 0.85/1.03 (~(a(I!2, J!1) = real_zero)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.85/1.03 tff(117,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)).
% 0.85/1.03 tff(118,plain,
% 0.85/1.03 (((~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)),
% 0.85/1.03 inference(tautology,[status(thm)],[])).
% 0.85/1.03 tff(119,plain,
% 0.85/1.03 (plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.85/1.03 tff(120,plain,
% 0.85/1.03 (I!2 = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.85/1.03 inference(symmetry,[status(thm)],[119])).
% 0.85/1.03 tff(121,plain,
% 0.85/1.03 (((~![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))))))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(122,plain,
% 0.85/1.03 ((~((~((~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)))))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(123,plain,
% 0.85/1.03 (((~![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))))))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[122])).
% 0.85/1.03 tff(124,plain,
% 0.85/1.03 (((~![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))))))))),
% 0.85/1.03 inference(transitivity,[status(thm)],[123, 121])).
% 0.85/1.03 tff(125,plain,
% 0.85/1.03 ((~![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)))))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(126,plain,
% 0.85/1.03 ((~![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)))))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.85/1.03 tff(127,plain,
% 0.85/1.03 (~((~((~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))))))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[126, 13])).
% 0.85/1.03 tff(128,plain,
% 0.85/1.03 (((~((~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)))))),
% 0.85/1.03 inference(tautology,[status(thm)],[])).
% 0.85/1.03 tff(129,plain,
% 0.85/1.03 ((~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))))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.85/1.03 tff(130,plain,
% 0.85/1.03 (^[I: $i] : refl((int_less(int_zero, I) <=> int_leq(int_one, I)) <=> (int_less(int_zero, I) <=> int_leq(int_one, I)))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(131,plain,
% 0.85/1.03 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[130])).
% 0.85/1.03 tff(132,plain,
% 0.85/1.03 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(133,axiom,(![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','one_successor_of_zero')).
% 0.85/1.03 tff(134,plain,
% 0.85/1.03 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.85/1.03 tff(135,plain,(
% 0.85/1.03 ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.85/1.03 inference(skolemize,[status(sab)],[134])).
% 0.85/1.03 tff(136,plain,
% 0.85/1.03 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.85/1.03 tff(137,plain,
% 0.85/1.03 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, I!2) <=> int_leq(int_one, I!2))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(138,plain,
% 0.85/1.03 (int_less(int_zero, I!2) <=> int_leq(int_one, I!2)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.85/1.03 tff(139,plain,
% 0.85/1.03 ((~(int_less(int_zero, I!2) <=> int_leq(int_one, I!2))) | int_less(int_zero, I!2) | (~int_leq(int_one, I!2))),
% 0.85/1.03 inference(tautology,[status(thm)],[])).
% 0.85/1.03 tff(140,plain,
% 0.85/1.03 ((~(int_less(int_zero, I!2) <=> int_leq(int_one, I!2))) | int_less(int_zero, I!2)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[139, 62])).
% 0.85/1.03 tff(141,plain,
% 0.85/1.03 (int_less(int_zero, I!2)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[140, 138])).
% 0.85/1.03 tff(142,plain,
% 0.85/1.03 ((~((~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))))),
% 0.85/1.03 inference(tautology,[status(thm)],[])).
% 0.85/1.03 tff(143,plain,
% 0.85/1.03 ((~((~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))))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.85/1.03 tff(144,plain,
% 0.85/1.03 (~((~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)))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[143, 129])).
% 0.85/1.03 tff(145,plain,
% 0.85/1.03 (((~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)),
% 0.85/1.03 inference(tautology,[status(thm)],[])).
% 0.85/1.03 tff(146,plain,
% 0.85/1.03 (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.85/1.03 tff(147,plain,
% 0.85/1.03 (^[I: $i, J: $i] : refl((plus(I, J) = plus(J, I)) <=> (plus(I, J) = plus(J, I)))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(148,plain,
% 0.85/1.03 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[147])).
% 0.85/1.03 tff(149,plain,
% 0.85/1.03 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(150,axiom,(![I: $i, J: $i] : (plus(I, J) = plus(J, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_commutative')).
% 0.85/1.03 tff(151,plain,
% 0.85/1.03 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.85/1.03 tff(152,plain,(
% 0.85/1.03 ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.85/1.03 inference(skolemize,[status(sab)],[151])).
% 0.85/1.03 tff(153,plain,
% 0.85/1.03 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.85/1.03 tff(154,plain,
% 0.85/1.03 ((~![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))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(155,plain,
% 0.85/1.03 (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = plus(tptp_fun_K_0(I!2, int_zero), int_zero)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.85/1.03 tff(156,plain,
% 0.85/1.03 (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = plus(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.85/1.03 inference(symmetry,[status(thm)],[155])).
% 0.85/1.03 tff(157,plain,
% 0.85/1.03 (^[I: $i] : refl((plus(I, int_zero) = I) <=> (plus(I, int_zero) = I))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(158,plain,
% 0.85/1.03 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.85/1.03 inference(quant_intro,[status(thm)],[157])).
% 0.85/1.03 tff(159,plain,
% 0.85/1.03 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(160,axiom,(![I: $i] : (plus(I, int_zero) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_zero')).
% 0.85/1.03 tff(161,plain,
% 0.85/1.03 (![I: $i] : (plus(I, int_zero) = I)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.85/1.03 tff(162,plain,(
% 0.85/1.03 ![I: $i] : (plus(I, int_zero) = I)),
% 0.85/1.03 inference(skolemize,[status(sab)],[161])).
% 0.85/1.03 tff(163,plain,
% 0.85/1.03 (![I: $i] : (plus(I, int_zero) = I)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.85/1.03 tff(164,plain,
% 0.85/1.03 ((~![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))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(165,plain,
% 0.85/1.03 (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = tptp_fun_K_0(I!2, int_zero)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.85/1.03 tff(166,plain,
% 0.85/1.03 (tptp_fun_K_0(I!2, int_zero) = plus(tptp_fun_K_0(I!2, int_zero), int_zero)),
% 0.85/1.03 inference(symmetry,[status(thm)],[165])).
% 0.85/1.03 tff(167,plain,
% 0.85/1.03 (tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.85/1.03 inference(transitivity,[status(thm)],[166, 156, 146, 120])).
% 0.85/1.03 tff(168,plain,
% 0.85/1.03 (((~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))),
% 0.85/1.03 inference(tautology,[status(thm)],[])).
% 0.85/1.03 tff(169,plain,
% 0.85/1.03 (int_less(int_zero, tptp_fun_K_0(I!2, J!1))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[168, 117])).
% 0.85/1.03 tff(170,plain,
% 0.85/1.03 (tptp_fun_K_0(I!2, int_zero) = I!2),
% 0.85/1.03 inference(transitivity,[status(thm)],[166, 156, 146])).
% 0.85/1.03 tff(171,plain,
% 0.85/1.03 (int_leq(tptp_fun_K_0(I!2, int_zero), n) <=> int_leq(I!2, n)),
% 0.85/1.03 inference(monotonicity,[status(thm)],[170])).
% 0.85/1.03 tff(172,plain,
% 0.85/1.03 (int_leq(I!2, n) <=> int_leq(tptp_fun_K_0(I!2, int_zero), n)),
% 0.85/1.03 inference(symmetry,[status(thm)],[171])).
% 0.85/1.03 tff(173,plain,
% 0.85/1.03 (int_leq(tptp_fun_K_0(I!2, int_zero), n)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[61, 172])).
% 0.85/1.03 tff(174,plain,
% 0.85/1.03 ((~![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)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(175,plain,
% 0.85/1.03 (int_less(int_zero, tptp_fun_K_0(I!2, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[174, 136])).
% 0.85/1.03 tff(176,plain,
% 0.85/1.03 (((~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))),
% 0.85/1.03 inference(tautology,[status(thm)],[])).
% 0.85/1.03 tff(177,plain,
% 0.85/1.03 (int_less(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[176, 144])).
% 0.85/1.03 tff(178,plain,
% 0.85/1.03 ((~(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))),
% 0.85/1.03 inference(tautology,[status(thm)],[])).
% 0.85/1.03 tff(179,plain,
% 0.85/1.03 ((~(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))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.85/1.03 tff(180,plain,
% 0.85/1.03 (int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[179, 175])).
% 0.85/1.03 tff(181,plain,
% 0.85/1.03 (((~![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))))))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(182,plain,
% 0.85/1.03 (((~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))))))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(183,plain,
% 0.85/1.03 ((~((~![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)))))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(184,plain,
% 0.85/1.03 (((~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))))))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[183])).
% 0.85/1.03 tff(185,plain,
% 0.85/1.03 (((~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))))))))),
% 0.85/1.03 inference(transitivity,[status(thm)],[184, 182])).
% 0.85/1.03 tff(186,plain,
% 0.85/1.03 (((~![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)))))))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[185])).
% 0.85/1.03 tff(187,plain,
% 0.85/1.03 (((~![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))))))))),
% 0.85/1.03 inference(transitivity,[status(thm)],[186, 181])).
% 0.85/1.03 tff(188,plain,
% 0.85/1.03 ((~![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)))))))))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(189,plain,
% 0.85/1.04 ((~![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)))))))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.85/1.04 tff(190,plain,
% 0.85/1.04 ((~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)))))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[189, 78, 60, 59, 180])).
% 0.85/1.04 tff(191,plain,
% 0.85/1.04 (~((~![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))))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[190, 173])).
% 0.85/1.04 tff(192,plain,
% 0.85/1.04 (((~![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))))),
% 0.85/1.04 inference(tautology,[status(thm)],[])).
% 0.85/1.04 tff(193,plain,
% 0.85/1.04 (![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))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.85/1.04 tff(194,plain,
% 0.85/1.04 (((~![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)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(195,plain,
% 0.85/1.04 (((~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)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(196,plain,
% 0.85/1.04 (((~![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))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[195])).
% 0.85/1.04 tff(197,plain,
% 0.85/1.04 (((~![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)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[196, 194])).
% 0.85/1.04 tff(198,plain,
% 0.85/1.04 ((~![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))))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(199,plain,
% 0.85/1.04 ((~![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))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.85/1.04 tff(200,plain,
% 0.85/1.04 (![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))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[199, 193, 169, 167])).
% 0.85/1.04 tff(201,plain,
% 0.85/1.04 (((~![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))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(202,plain,
% 0.85/1.04 ((~![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))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(203,plain,
% 0.85/1.04 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.85/1.04 tff(204,plain,
% 0.85/1.04 (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[203, 60, 49, 200])).
% 0.85/1.04 tff(205,plain,
% 0.85/1.04 (a(I!2, J!1) = a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1)),
% 0.85/1.04 inference(monotonicity,[status(thm)],[120])).
% 0.85/1.04 tff(206,plain,
% 0.85/1.04 (a(I!2, J!1) = real_zero),
% 0.85/1.04 inference(transitivity,[status(thm)],[205, 204])).
% 0.85/1.04 tff(207,assumption,(~(a(I!2, J!1) = real_zero)), introduced(assumption)).
% 0.85/1.04 tff(208,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.85/1.04 tff(209,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,[]))).
% 0.85/1.04 tff(210,plain,
% 0.85/1.04 ((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[209, 116])).
% 0.85/1.04 tff(211,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)).
% 0.85/1.04 tff(212,plain,
% 0.85/1.04 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(213,plain,
% 0.85/1.04 ((~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(214,plain,
% 0.85/1.04 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[213])).
% 0.85/1.04 tff(215,plain,
% 0.85/1.04 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2))))))))),
% 0.85/1.04 inference(transitivity,[status(thm)],[214, 212])).
% 0.85/1.04 tff(216,plain,
% 0.85/1.04 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)) | (~int_less(int_zero, tptp_fun_K_0(I!2, J!1))))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~(plus(J!1, K) = I!2)) | (~int_less(int_zero, K)))))))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(217,plain,
% 0.85/1.04 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.85/1.04 tff(218,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[217, 13, 211])).
% 0.85/1.04 tff(219,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,[]))).
% 0.85/1.04 tff(220,plain,
% 0.85/1.04 (((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~(int_less(J!1, I!2) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(J!1, K) = I!2)))))) | ((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))),
% 0.85/1.04 inference(tautology,[status(thm)],[])).
% 0.85/1.04 tff(221,plain,
% 0.85/1.04 ((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.85/1.04 tff(222,plain,
% 0.85/1.04 ((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2))))),
% 0.85/1.04 inference(tautology,[status(thm)],[])).
% 0.85/1.04 tff(223,plain,
% 0.85/1.04 ((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.85/1.04 tff(224,plain,
% 0.85/1.04 (~int_less(J!1, I!2)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[223, 210])).
% 0.85/1.04 tff(225,assumption,(~int_leq(I!2, J!1)), introduced(assumption)).
% 0.85/1.04 tff(226,plain,
% 0.85/1.04 (^[I: $i, J: $i] : refl((int_leq(J, I) | int_less(I, J)) <=> (int_leq(J, I) | int_less(I, J)))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(227,plain,
% 0.85/1.04 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[226])).
% 0.85/1.04 tff(228,plain,
% 0.85/1.04 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(229,plain,
% 0.85/1.04 (^[I: $i, J: $i] : rewrite((int_less(I, J) | int_leq(J, I)) <=> (int_leq(J, I) | int_less(I, J)))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(230,plain,
% 0.85/1.04 (![I: $i, J: $i] : (int_less(I, J) | int_leq(J, I)) <=> ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[229])).
% 0.85/1.04 tff(231,axiom,(![I: $i, J: $i] : (int_less(I, J) | int_leq(J, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','int_less_total')).
% 0.85/1.04 tff(232,plain,
% 0.85/1.04 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.85/1.04 tff(233,plain,
% 0.85/1.04 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.85/1.04 tff(234,plain,(
% 0.85/1.04 ![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.85/1.04 inference(skolemize,[status(sab)],[233])).
% 0.85/1.04 tff(235,plain,
% 0.85/1.04 (![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.85/1.04 tff(236,plain,
% 0.85/1.04 (((~![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))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(237,plain,
% 0.85/1.04 ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | (int_leq(I!2, J!1) | int_less(J!1, I!2))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(238,plain,
% 0.85/1.04 ((~![I: $i, J: $i] : (int_leq(J, I) | int_less(I, J))) | int_leq(I!2, J!1) | int_less(J!1, I!2)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.85/1.04 tff(239,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[238, 235, 225, 224])).
% 0.85/1.04 tff(240,plain,(int_leq(I!2, J!1)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(241,plain,
% 0.85/1.04 ((~(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))),
% 0.85/1.04 inference(tautology,[status(thm)],[])).
% 0.85/1.04 tff(242,plain,
% 0.85/1.04 ((~(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))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.85/1.04 tff(243,plain,
% 0.85/1.04 ((I!2 = J!1) | int_less(I!2, J!1)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[242, 34])).
% 0.85/1.04 tff(244,plain,
% 0.85/1.04 (((I!2 = J!1) | (a(I!2, J!1) = real_zero)) | (~(I!2 = J!1))),
% 0.85/1.04 inference(tautology,[status(thm)],[])).
% 0.85/1.04 tff(245,plain,
% 0.85/1.04 (~(I!2 = J!1)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[244, 114])).
% 0.85/1.04 tff(246,plain,
% 0.85/1.04 ((~((I!2 = J!1) | int_less(I!2, J!1))) | (I!2 = J!1) | int_less(I!2, J!1)),
% 0.85/1.04 inference(tautology,[status(thm)],[])).
% 0.85/1.04 tff(247,plain,
% 0.85/1.04 ((~((I!2 = J!1) | int_less(I!2, J!1))) | int_less(I!2, J!1)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.85/1.04 tff(248,plain,
% 0.85/1.04 (int_less(I!2, J!1)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[247, 243])).
% 0.85/1.04 tff(249,plain,
% 0.85/1.04 ((~((~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))))),
% 0.85/1.04 inference(tautology,[status(thm)],[])).
% 0.85/1.04 tff(250,plain,
% 0.85/1.04 ((~((~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))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.85/1.04 tff(251,plain,
% 0.85/1.04 (~((~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)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[250, 22])).
% 0.85/1.04 tff(252,plain,
% 0.85/1.04 (((~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)),
% 0.85/1.04 inference(tautology,[status(thm)],[])).
% 0.85/1.04 tff(253,plain,
% 0.85/1.04 (plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.85/1.04 tff(254,plain,
% 0.85/1.04 (J!1 = plus(I!2, tptp_fun_K_0(J!1, I!2))),
% 0.85/1.04 inference(symmetry,[status(thm)],[253])).
% 0.85/1.04 tff(255,plain,
% 0.85/1.04 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, 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))))))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(256,plain,
% 0.85/1.04 ((~((~((~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)))))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(257,plain,
% 0.85/1.04 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, 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))))))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[256])).
% 0.85/1.04 tff(258,plain,
% 0.85/1.04 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, 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))))))))),
% 0.85/1.04 inference(transitivity,[status(thm)],[257, 255])).
% 0.85/1.04 tff(259,plain,
% 0.85/1.04 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, 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)))))))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(260,plain,
% 0.85/1.04 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(int_zero, 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)))))))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.85/1.04 tff(261,plain,
% 0.85/1.04 (~((~((~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))))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[260, 13])).
% 0.85/1.04 tff(262,plain,
% 0.85/1.04 (((~((~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)))))),
% 0.85/1.04 inference(tautology,[status(thm)],[])).
% 0.85/1.04 tff(263,plain,
% 0.85/1.04 ((~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))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.85/1.04 tff(264,plain,
% 0.85/1.04 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, J!1) <=> int_leq(int_one, J!1))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(265,plain,
% 0.85/1.04 (int_less(int_zero, J!1) <=> int_leq(int_one, J!1)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[264, 136])).
% 0.85/1.04 tff(266,plain,
% 0.85/1.04 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1) | (~int_leq(int_one, J!1))),
% 0.85/1.04 inference(tautology,[status(thm)],[])).
% 0.85/1.04 tff(267,plain,
% 0.85/1.04 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[266, 60])).
% 0.85/1.04 tff(268,plain,
% 0.85/1.04 (int_less(int_zero, J!1)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[267, 265])).
% 0.85/1.04 tff(269,plain,
% 0.85/1.04 ((~((~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))))),
% 0.85/1.04 inference(tautology,[status(thm)],[])).
% 0.85/1.04 tff(270,plain,
% 0.85/1.04 ((~((~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))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[269, 268])).
% 0.85/1.04 tff(271,plain,
% 0.85/1.04 (~((~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)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[270, 263])).
% 0.85/1.04 tff(272,plain,
% 0.85/1.04 (((~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)),
% 0.85/1.04 inference(tautology,[status(thm)],[])).
% 0.85/1.04 tff(273,plain,
% 0.85/1.04 (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[272, 271])).
% 0.85/1.05 tff(274,plain,
% 0.85/1.05 ((~![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))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(275,plain,
% 0.85/1.05 (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = plus(tptp_fun_K_0(J!1, int_zero), int_zero)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[274, 153])).
% 0.85/1.05 tff(276,plain,
% 0.85/1.05 (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = plus(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.85/1.05 inference(symmetry,[status(thm)],[275])).
% 0.85/1.05 tff(277,plain,
% 0.85/1.05 ((~![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))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(278,plain,
% 0.85/1.05 (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = tptp_fun_K_0(J!1, int_zero)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[277, 163])).
% 0.85/1.05 tff(279,plain,
% 0.85/1.05 (tptp_fun_K_0(J!1, int_zero) = plus(tptp_fun_K_0(J!1, int_zero), int_zero)),
% 0.85/1.05 inference(symmetry,[status(thm)],[278])).
% 0.85/1.05 tff(280,plain,
% 0.85/1.05 (tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2))),
% 0.85/1.05 inference(transitivity,[status(thm)],[279, 276, 273, 254])).
% 0.85/1.05 tff(281,plain,
% 0.85/1.05 (((~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))),
% 0.85/1.05 inference(tautology,[status(thm)],[])).
% 0.85/1.05 tff(282,plain,
% 0.85/1.05 (int_less(int_zero, tptp_fun_K_0(J!1, I!2))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[281, 251])).
% 0.85/1.05 tff(283,plain,
% 0.85/1.05 (tptp_fun_K_0(J!1, int_zero) = J!1),
% 0.85/1.05 inference(transitivity,[status(thm)],[279, 276, 273])).
% 0.85/1.05 tff(284,plain,
% 0.85/1.05 (int_leq(tptp_fun_K_0(J!1, int_zero), n) <=> int_leq(J!1, n)),
% 0.85/1.05 inference(monotonicity,[status(thm)],[283])).
% 0.85/1.05 tff(285,plain,
% 0.85/1.05 (int_leq(J!1, n) <=> int_leq(tptp_fun_K_0(J!1, int_zero), n)),
% 0.85/1.05 inference(symmetry,[status(thm)],[284])).
% 0.85/1.05 tff(286,plain,
% 0.85/1.05 (int_leq(tptp_fun_K_0(J!1, int_zero), n)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[59, 285])).
% 0.85/1.05 tff(287,plain,
% 0.85/1.05 ((~![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)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(288,plain,
% 0.85/1.05 (int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[287, 136])).
% 0.85/1.05 tff(289,plain,
% 0.85/1.05 (((~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))),
% 0.85/1.05 inference(tautology,[status(thm)],[])).
% 0.85/1.05 tff(290,plain,
% 0.85/1.05 (int_less(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[289, 271])).
% 0.85/1.05 tff(291,plain,
% 0.85/1.05 ((~(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))),
% 0.85/1.05 inference(tautology,[status(thm)],[])).
% 0.85/1.05 tff(292,plain,
% 0.85/1.05 ((~(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))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.85/1.05 tff(293,plain,
% 0.85/1.05 (int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[292, 288])).
% 0.85/1.05 tff(294,plain,
% 0.85/1.05 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![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)))))))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(295,plain,
% 0.85/1.05 (((~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)))))))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(296,plain,
% 0.85/1.05 ((~((~![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))))))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(297,plain,
% 0.85/1.05 (((~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)))))))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[296])).
% 0.85/1.05 tff(298,plain,
% 0.85/1.05 (((~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)))))))))),
% 0.85/1.05 inference(transitivity,[status(thm)],[297, 295])).
% 0.85/1.05 tff(299,plain,
% 0.85/1.05 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![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))))))))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[298])).
% 0.85/1.05 tff(300,plain,
% 0.85/1.05 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![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)))))))))),
% 0.85/1.05 inference(transitivity,[status(thm)],[299, 294])).
% 0.85/1.05 tff(301,plain,
% 0.85/1.05 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![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))))))))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(302,plain,
% 0.85/1.05 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(I, n)) | (~int_leq(int_one, J)) | (~int_leq(J, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![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))))))))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.85/1.05 tff(303,plain,
% 0.85/1.05 ((~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))))))))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[302, 78, 62, 61, 293])).
% 0.85/1.05 tff(304,plain,
% 0.85/1.05 (~((~![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)))))))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[303, 286])).
% 0.85/1.05 tff(305,plain,
% 0.85/1.05 (((~![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))))),
% 0.85/1.05 inference(tautology,[status(thm)],[])).
% 0.85/1.05 tff(306,plain,
% 0.85/1.05 (![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))))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[305, 304])).
% 0.85/1.05 tff(307,plain,
% 0.85/1.05 (((~![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)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(308,plain,
% 0.85/1.05 (((~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)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(309,plain,
% 0.85/1.05 (((~![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))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[308])).
% 0.85/1.05 tff(310,plain,
% 0.85/1.05 (((~![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)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[309, 307])).
% 0.85/1.05 tff(311,plain,
% 0.85/1.05 ((~![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))))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(312,plain,
% 0.85/1.05 ((~![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))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.85/1.05 tff(313,plain,
% 0.85/1.05 (![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))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[312, 306, 282, 280])).
% 0.85/1.05 tff(314,assumption,(~int_leq(I!2, I!2)), introduced(assumption)).
% 0.85/1.05 tff(315,plain,
% 0.85/1.05 (((~![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))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(316,plain,
% 0.85/1.05 ((int_leq(I!2, I!2) <=> $true) <=> int_leq(I!2, I!2)),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(317,plain,
% 0.85/1.05 (($true | int_less(I!2, I!2)) <=> $true),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(318,plain,
% 0.85/1.05 ((I!2 = I!2) <=> $true),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(319,plain,
% 0.85/1.05 (((I!2 = I!2) | int_less(I!2, I!2)) <=> ($true | int_less(I!2, I!2))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[318])).
% 0.85/1.05 tff(320,plain,
% 0.85/1.05 (((I!2 = I!2) | int_less(I!2, I!2)) <=> $true),
% 0.85/1.05 inference(transitivity,[status(thm)],[319, 317])).
% 0.85/1.05 tff(321,plain,
% 0.85/1.05 ((int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2))) <=> (int_leq(I!2, I!2) <=> $true)),
% 0.85/1.05 inference(monotonicity,[status(thm)],[320])).
% 0.85/1.05 tff(322,plain,
% 0.85/1.05 ((int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2))) <=> int_leq(I!2, I!2)),
% 0.85/1.05 inference(transitivity,[status(thm)],[321, 316])).
% 0.85/1.05 tff(323,plain,
% 0.85/1.05 (((~![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))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[322])).
% 0.85/1.05 tff(324,plain,
% 0.85/1.05 (((~![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))),
% 0.85/1.05 inference(transitivity,[status(thm)],[323, 315])).
% 0.85/1.05 tff(325,plain,
% 0.85/1.05 ((~![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)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(326,plain,
% 0.85/1.05 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.85/1.05 tff(327,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[326, 32, 314])).
% 0.85/1.05 tff(328,plain,(int_leq(I!2, I!2)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(329,plain,
% 0.85/1.05 (((~![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))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(330,plain,
% 0.85/1.05 ((~![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))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(331,plain,
% 0.85/1.05 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.85/1.05 tff(332,plain,
% 0.85/1.05 (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[331, 62, 328, 313])).
% 0.85/1.05 tff(333,plain,
% 0.85/1.05 (a(I!2, J!1) = a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2)))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[254])).
% 0.85/1.06 tff(334,plain,
% 0.85/1.06 (a(I!2, J!1) = real_zero),
% 0.85/1.06 inference(transitivity,[status(thm)],[333, 332])).
% 0.85/1.06 tff(335,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[116, 334])).
% 0.85/1.06 % SZS output end Proof
% 0.85/1.06 % E exiting
%------------------------------------------------------------------------------