%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV491+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.90s 1.11s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV491+3 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:54:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.90/1.11 % SZS status Theorem
% 0.90/1.11 % SZS output start Proof
% 0.90/1.11 tff(real_zero_type, type, (
% 0.90/1.11 real_zero: $i)).
% 0.90/1.11 tff(a_type, type, (
% 0.90/1.11 a: ( $i * $i ) > $i)).
% 0.90/1.11 tff(tptp_fun_J_1_type, type, (
% 0.90/1.11 tptp_fun_J_1: $i)).
% 0.90/1.11 tff(tptp_fun_I_2_type, type, (
% 0.90/1.11 tptp_fun_I_2: $i)).
% 0.90/1.11 tff(int_less_type, type, (
% 0.90/1.11 int_less: ( $i * $i ) > $o)).
% 0.90/1.11 tff(real_one_type, type, (
% 0.90/1.11 real_one: $i)).
% 0.90/1.11 tff(int_leq_type, type, (
% 0.90/1.11 int_leq: ( $i * $i ) > $o)).
% 0.90/1.11 tff(int_one_type, type, (
% 0.90/1.11 int_one: $i)).
% 0.90/1.11 tff(plus_type, type, (
% 0.90/1.11 plus: ( $i * $i ) > $i)).
% 0.90/1.11 tff(int_zero_type, type, (
% 0.90/1.11 int_zero: $i)).
% 0.90/1.11 tff(n_type, type, (
% 0.90/1.11 n: $i)).
% 0.90/1.11 tff(tptp_fun_K_0_type, type, (
% 0.90/1.11 tptp_fun_K_0: ( $i * $i ) > $i)).
% 0.90/1.11 tff(1,assumption,(~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one))), introduced(assumption)).
% 0.90/1.11 tff(2,plain,
% 0.90/1.11 (((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)) | (I!2 = J!1)),
% 0.90/1.11 inference(tautology,[status(thm)],[])).
% 0.90/1.11 tff(3,plain,
% 0.90/1.11 (I!2 = J!1),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.90/1.11 tff(4,plain,
% 0.90/1.11 (((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)) | (~(a(I!2, J!1) = real_one))),
% 0.90/1.11 inference(tautology,[status(thm)],[])).
% 0.90/1.11 tff(5,plain,
% 0.90/1.11 (~(a(I!2, J!1) = real_one)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.90/1.11 tff(6,assumption,(~int_leq(J!1, J!1)), introduced(assumption)).
% 0.90/1.11 tff(7,plain,
% 0.90/1.11 (^[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))))),
% 0.90/1.11 inference(bind,[status(th)],[])).
% 0.90/1.11 tff(8,plain,
% 0.90/1.11 (![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)))),
% 0.90/1.11 inference(quant_intro,[status(thm)],[7])).
% 0.90/1.11 tff(9,plain,
% 0.90/1.11 (![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)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(10,plain,
% 0.90/1.11 (^[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))))),
% 0.90/1.11 inference(bind,[status(th)],[])).
% 0.90/1.11 tff(11,plain,
% 0.90/1.11 (![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)))),
% 0.90/1.11 inference(quant_intro,[status(thm)],[10])).
% 0.90/1.11 tff(12,axiom,(![I: $i, J: $i] : (int_leq(I, J) <=> (int_less(I, J) | (I = J)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','int_leq')).
% 0.90/1.11 tff(13,plain,
% 0.90/1.11 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.90/1.11 tff(14,plain,
% 0.90/1.11 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.90/1.11 tff(15,plain,(
% 0.90/1.11 ![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.90/1.11 inference(skolemize,[status(sab)],[14])).
% 0.90/1.11 tff(16,plain,
% 0.90/1.11 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.90/1.11 tff(17,plain,
% 0.90/1.11 (((~![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))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(18,plain,
% 0.90/1.11 ((int_leq(J!1, J!1) <=> $true) <=> int_leq(J!1, J!1)),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(19,plain,
% 0.90/1.11 (($true | int_less(J!1, J!1)) <=> $true),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(20,plain,
% 0.90/1.11 ((J!1 = J!1) <=> $true),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(21,plain,
% 0.90/1.11 (((J!1 = J!1) | int_less(J!1, J!1)) <=> ($true | int_less(J!1, J!1))),
% 0.90/1.11 inference(monotonicity,[status(thm)],[20])).
% 0.90/1.11 tff(22,plain,
% 0.90/1.11 (((J!1 = J!1) | int_less(J!1, J!1)) <=> $true),
% 0.90/1.11 inference(transitivity,[status(thm)],[21, 19])).
% 0.90/1.11 tff(23,plain,
% 0.90/1.11 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> (int_leq(J!1, J!1) <=> $true)),
% 0.90/1.11 inference(monotonicity,[status(thm)],[22])).
% 0.90/1.11 tff(24,plain,
% 0.90/1.11 ((int_leq(J!1, J!1) <=> ((J!1 = J!1) | int_less(J!1, J!1))) <=> int_leq(J!1, J!1)),
% 0.90/1.11 inference(transitivity,[status(thm)],[23, 18])).
% 0.90/1.11 tff(25,plain,
% 0.90/1.11 (((~![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))),
% 0.90/1.11 inference(monotonicity,[status(thm)],[24])).
% 0.90/1.11 tff(26,plain,
% 0.90/1.11 (((~![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))),
% 0.90/1.11 inference(transitivity,[status(thm)],[25, 17])).
% 0.90/1.11 tff(27,plain,
% 0.90/1.11 ((~![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)))),
% 0.90/1.11 inference(quant_inst,[status(thm)],[])).
% 0.90/1.11 tff(28,plain,
% 0.90/1.11 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!1, J!1)),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.90/1.11 tff(29,plain,
% 0.90/1.11 ($false),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[28, 16, 6])).
% 0.90/1.11 tff(30,plain,(int_leq(J!1, J!1)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.11 tff(31,plain,
% 0.90/1.11 ((~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((~int_less(I, J)) | (a(I, J) = real_zero)) & ((~int_less(J, I)) | (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))) | (((~int_less(I, J)) | (a(I, J) = real_zero)) & ((~int_less(J, I)) | (a(I, J) = real_zero)) & ((~(I = J)) | (a(I, J) = real_one)))))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(32,plain,
% 0.90/1.11 ((~![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => (((int_less(I, J) => (a(I, J) = real_zero)) & (int_less(J, I) => (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))) | (((~int_less(I, J)) | (a(I, J) = real_zero)) & ((~int_less(J, I)) | (a(I, J) = real_zero)) & ((~(I = J)) | (a(I, J) = real_one)))))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(33,axiom,(~![I: $i, J: $i] : ((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => (((int_less(I, J) => (a(I, J) = real_zero)) & (int_less(J, I) => (a(I, J) = real_zero))) & ((I = J) => (a(I, J) = real_one))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diag')).
% 0.90/1.11 tff(34,plain,
% 0.90/1.11 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((~int_less(I, J)) | (a(I, J) = real_zero)) & ((~int_less(J, I)) | (a(I, J) = real_zero)) & ((~(I = J)) | (a(I, J) = real_one))))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.90/1.11 tff(35,plain,
% 0.90/1.11 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((~int_less(I, J)) | (a(I, J) = real_zero)) & ((~int_less(J, I)) | (a(I, J) = real_zero)) & ((~(I = J)) | (a(I, J) = real_one))))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.90/1.11 tff(36,plain,
% 0.90/1.11 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((~int_less(I, J)) | (a(I, J) = real_zero)) & ((~int_less(J, I)) | (a(I, J) = real_zero)) & ((~(I = J)) | (a(I, J) = real_one))))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.90/1.11 tff(37,plain,
% 0.90/1.11 (~![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (((~int_less(I, J)) | (a(I, J) = real_zero)) & ((~int_less(J, I)) | (a(I, J) = real_zero)) & ((~(I = J)) | (a(I, J) = real_one))))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.90/1.11 tff(38,plain,(
% 0.90/1.11 ~((~(int_leq(int_one, I!2) & int_leq(I!2, n) & int_leq(int_one, J!1) & int_leq(J!1, n))) | (((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero)) & ((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (a(I!2, J!1) = real_one))))),
% 0.90/1.11 inference(skolemize,[status(sab)],[37])).
% 0.90/1.11 tff(39,plain,
% 0.90/1.11 (int_leq(int_one, I!2) & int_leq(I!2, n) & int_leq(int_one, J!1) & int_leq(J!1, n)),
% 0.90/1.11 inference(or_elim,[status(thm)],[38])).
% 0.90/1.11 tff(40,plain,
% 0.90/1.11 (int_leq(J!1, n)),
% 0.90/1.11 inference(and_elim,[status(thm)],[39])).
% 0.90/1.11 tff(41,plain,
% 0.90/1.11 (int_leq(int_one, J!1)),
% 0.90/1.11 inference(and_elim,[status(thm)],[39])).
% 0.90/1.11 tff(42,plain,
% 0.90/1.11 (int_leq(I!2, n)),
% 0.90/1.11 inference(and_elim,[status(thm)],[39])).
% 0.90/1.11 tff(43,plain,
% 0.90/1.11 (int_leq(int_one, I!2)),
% 0.90/1.11 inference(and_elim,[status(thm)],[39])).
% 0.90/1.11 tff(44,plain,
% 0.90/1.11 (^[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)))))))))),
% 0.90/1.11 inference(bind,[status(th)],[])).
% 0.90/1.11 tff(45,plain,
% 0.90/1.11 (![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))))))))),
% 0.90/1.11 inference(quant_intro,[status(thm)],[44])).
% 0.90/1.11 tff(46,plain,
% 0.90/1.11 (^[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)))))))))),
% 0.90/1.11 inference(bind,[status(th)],[])).
% 0.90/1.11 tff(47,plain,
% 0.90/1.11 (![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))))))))),
% 0.90/1.11 inference(quant_intro,[status(thm)],[46])).
% 0.90/1.11 tff(48,plain,
% 0.90/1.11 (![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))))))))),
% 0.90/1.11 inference(transitivity,[status(thm)],[47, 45])).
% 0.90/1.11 tff(49,plain,
% 0.90/1.11 (^[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))))))))))),
% 0.90/1.12 inference(bind,[status(th)],[])).
% 0.90/1.12 tff(50,plain,
% 0.90/1.12 (![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))))))))),
% 0.90/1.12 inference(quant_intro,[status(thm)],[49])).
% 0.90/1.12 tff(51,plain,
% 0.90/1.12 (![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)))))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(52,plain,
% 0.90/1.12 (^[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)))))))),
% 0.90/1.12 inference(bind,[status(th)],[])).
% 0.90/1.12 tff(53,plain,
% 0.90/1.12 (![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)))))),
% 0.90/1.12 inference(quant_intro,[status(thm)],[52])).
% 0.90/1.12 tff(54,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','qih')).
% 0.90/1.12 tff(55,plain,
% 0.90/1.12 (![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)))))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.90/1.12 tff(56,plain,
% 0.90/1.12 (![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)))))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.90/1.12 tff(57,plain,(
% 0.90/1.12 ![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)))))),
% 0.90/1.12 inference(skolemize,[status(sab)],[56])).
% 0.90/1.12 tff(58,plain,
% 0.90/1.12 (![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))))))))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.90/1.12 tff(59,plain,
% 0.90/1.12 (![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))))))))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.90/1.12 tff(60,plain,
% 0.90/1.12 (((~![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))))))))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(61,plain,
% 0.90/1.12 (((~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))))))))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(62,plain,
% 0.90/1.12 ((~((~![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)))))))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(63,plain,
% 0.90/1.12 (((~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))))))))),
% 0.90/1.12 inference(monotonicity,[status(thm)],[62])).
% 0.90/1.12 tff(64,plain,
% 0.90/1.12 (((~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))))))))),
% 0.90/1.12 inference(transitivity,[status(thm)],[63, 61])).
% 0.90/1.12 tff(65,plain,
% 0.90/1.12 (((~![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)))))))))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[64])).
% 0.90/1.13 tff(66,plain,
% 0.90/1.13 (((~![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))))))))),
% 0.90/1.13 inference(transitivity,[status(thm)],[65, 60])).
% 0.90/1.13 tff(67,plain,
% 0.90/1.13 ((~![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))))))))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(68,plain,
% 0.90/1.13 ((~![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)))))))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.90/1.13 tff(69,plain,
% 0.90/1.13 (~((~![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))))))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[68, 59, 43, 42, 41, 40])).
% 0.90/1.13 tff(70,plain,
% 0.90/1.13 (((~![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)))),
% 0.90/1.13 inference(tautology,[status(thm)],[])).
% 0.90/1.13 tff(71,plain,
% 0.90/1.13 (![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.90/1.13 tff(72,plain,
% 0.90/1.13 (((~![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)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(73,plain,
% 0.90/1.13 (((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)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(74,plain,
% 0.90/1.13 (((~![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))))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[73])).
% 0.90/1.13 tff(75,plain,
% 0.90/1.13 (((~![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)))),
% 0.90/1.13 inference(transitivity,[status(thm)],[74, 72])).
% 0.90/1.13 tff(76,plain,
% 0.90/1.13 ((~![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)))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(77,plain,
% 0.90/1.13 ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!1)))) | (~int_leq(int_one, J!1)) | (a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.90/1.13 tff(78,plain,
% 0.90/1.13 ((a(J!1, J!1) = real_one) | (~int_leq(J!1, J!1))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[77, 41, 71])).
% 0.90/1.13 tff(79,plain,
% 0.90/1.13 (a(J!1, J!1) = real_one),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[78, 30])).
% 0.90/1.13 tff(80,assumption,(I!2 = J!1), introduced(assumption)).
% 0.90/1.13 tff(81,plain,
% 0.90/1.13 (a(I!2, J!1) = a(J!1, J!1)),
% 0.90/1.13 inference(monotonicity,[status(thm)],[80])).
% 0.90/1.13 tff(82,plain,
% 0.90/1.13 (a(I!2, J!1) = real_one),
% 0.90/1.13 inference(transitivity,[status(thm)],[81, 79])).
% 0.90/1.13 tff(83,assumption,(~(a(I!2, J!1) = real_one)), introduced(assumption)).
% 0.90/1.13 tff(84,plain,
% 0.90/1.13 ($false),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.90/1.13 tff(85,plain,((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.13 tff(86,plain,
% 0.90/1.13 ($false),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[85, 5, 3])).
% 0.90/1.13 tff(87,plain,((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.13 tff(88,plain,
% 0.90/1.13 (^[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))))))))),
% 0.90/1.13 inference(bind,[status(th)],[])).
% 0.90/1.13 tff(89,plain,
% 0.90/1.13 (![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)))))))),
% 0.90/1.13 inference(quant_intro,[status(thm)],[88])).
% 0.90/1.13 tff(90,plain,
% 0.90/1.13 (^[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))))))))),
% 0.90/1.13 inference(bind,[status(th)],[])).
% 0.90/1.13 tff(91,plain,
% 0.90/1.13 (![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)))))))),
% 0.90/1.13 inference(quant_intro,[status(thm)],[90])).
% 0.90/1.13 tff(92,plain,
% 0.90/1.13 (![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)))))))),
% 0.90/1.13 inference(transitivity,[status(thm)],[91, 89])).
% 0.90/1.13 tff(93,plain,
% 0.90/1.13 (^[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)))))))))),
% 0.90/1.13 inference(bind,[status(th)],[])).
% 0.90/1.13 tff(94,plain,
% 0.90/1.13 (![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)))))))),
% 0.90/1.13 inference(quant_intro,[status(thm)],[93])).
% 0.90/1.13 tff(95,plain,
% 0.90/1.13 (![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)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(96,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')).
% 0.90/1.13 tff(97,plain,
% 0.90/1.13 (![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.90/1.13 tff(98,plain,(
% 0.90/1.13 ![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)))))),
% 0.90/1.13 inference(skolemize,[status(sab)],[97])).
% 0.90/1.13 tff(99,plain,
% 0.90/1.13 (![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)))))))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.90/1.13 tff(100,plain,
% 0.90/1.13 (![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)))))))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.90/1.13 tff(101,plain,
% 0.90/1.13 (((~![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))))))))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(102,plain,
% 0.90/1.13 ((~((~((~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)))))))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(103,plain,
% 0.90/1.13 (((~![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))))))))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[102])).
% 0.90/1.13 tff(104,plain,
% 0.90/1.13 (((~![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))))))))),
% 0.90/1.13 inference(transitivity,[status(thm)],[103, 101])).
% 0.90/1.13 tff(105,plain,
% 0.90/1.13 ((~![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)))))))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(106,plain,
% 0.90/1.13 ((~![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)))))))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.90/1.13 tff(107,plain,
% 0.90/1.13 (~((~((~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))))))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[106, 100])).
% 0.90/1.13 tff(108,plain,
% 0.90/1.13 (((~((~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)))))),
% 0.90/1.13 inference(tautology,[status(thm)],[])).
% 0.90/1.13 tff(109,plain,
% 0.90/1.13 ((~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))))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.90/1.13 tff(110,assumption,(~((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero))), introduced(assumption)).
% 0.90/1.13 tff(111,plain,
% 0.90/1.13 (((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero)) | int_less(J!1, I!2)),
% 0.90/1.13 inference(tautology,[status(thm)],[])).
% 0.90/1.13 tff(112,plain,
% 0.90/1.13 (int_less(J!1, I!2)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.90/1.13 tff(113,plain,
% 0.90/1.13 ((~((~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))))),
% 0.90/1.13 inference(tautology,[status(thm)],[])).
% 0.90/1.13 tff(114,plain,
% 0.90/1.13 ((~((~int_less(J!1, I!2)) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2)))))) | (~((~int_less(int_zero, tptp_fun_K_0(I!2, J!1))) | (~(plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2))))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.90/1.13 tff(115,plain,
% 0.90/1.13 (~((~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)))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[114, 109])).
% 0.90/1.13 tff(116,plain,
% 0.90/1.13 (((~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)),
% 0.90/1.13 inference(tautology,[status(thm)],[])).
% 0.90/1.13 tff(117,plain,
% 0.90/1.13 (plus(J!1, tptp_fun_K_0(I!2, J!1)) = I!2),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.90/1.13 tff(118,plain,
% 0.90/1.13 (I!2 = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.90/1.13 inference(symmetry,[status(thm)],[117])).
% 0.90/1.13 tff(119,plain,
% 0.90/1.13 (((~![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))))))))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(120,plain,
% 0.90/1.13 ((~((~((~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)))))))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(121,plain,
% 0.90/1.13 (((~![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))))))))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[120])).
% 0.90/1.13 tff(122,plain,
% 0.90/1.13 (((~![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))))))))),
% 0.90/1.13 inference(transitivity,[status(thm)],[121, 119])).
% 0.90/1.13 tff(123,plain,
% 0.90/1.13 ((~![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)))))))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(124,plain,
% 0.90/1.13 ((~![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)))))))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.90/1.13 tff(125,plain,
% 0.90/1.13 (~((~((~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))))))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[124, 100])).
% 0.90/1.13 tff(126,plain,
% 0.90/1.13 (((~((~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)))))),
% 0.90/1.13 inference(tautology,[status(thm)],[])).
% 0.90/1.13 tff(127,plain,
% 0.90/1.13 ((~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))))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.90/1.13 tff(128,plain,
% 0.90/1.13 (^[I: $i] : refl((int_less(int_zero, I) <=> int_leq(int_one, I)) <=> (int_less(int_zero, I) <=> int_leq(int_one, I)))),
% 0.90/1.13 inference(bind,[status(th)],[])).
% 0.90/1.13 tff(129,plain,
% 0.90/1.13 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.90/1.13 inference(quant_intro,[status(thm)],[128])).
% 0.90/1.13 tff(130,plain,
% 0.90/1.13 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I)) <=> ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(131,axiom,(![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','one_successor_of_zero')).
% 0.90/1.13 tff(132,plain,
% 0.90/1.13 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.90/1.13 tff(133,plain,(
% 0.90/1.13 ![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.90/1.13 inference(skolemize,[status(sab)],[132])).
% 0.90/1.13 tff(134,plain,
% 0.90/1.13 (![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.90/1.13 tff(135,plain,
% 0.90/1.13 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, I!2) <=> int_leq(int_one, I!2))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(136,plain,
% 0.90/1.14 (int_less(int_zero, I!2) <=> int_leq(int_one, I!2)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.90/1.14 tff(137,plain,
% 0.90/1.14 ((~(int_less(int_zero, I!2) <=> int_leq(int_one, I!2))) | int_less(int_zero, I!2) | (~int_leq(int_one, I!2))),
% 0.90/1.14 inference(tautology,[status(thm)],[])).
% 0.90/1.14 tff(138,plain,
% 0.90/1.14 ((~(int_less(int_zero, I!2) <=> int_leq(int_one, I!2))) | int_less(int_zero, I!2)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[137, 43])).
% 0.90/1.14 tff(139,plain,
% 0.90/1.14 (int_less(int_zero, I!2)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[138, 136])).
% 0.90/1.14 tff(140,plain,
% 0.90/1.14 ((~((~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))))),
% 0.90/1.14 inference(tautology,[status(thm)],[])).
% 0.90/1.14 tff(141,plain,
% 0.90/1.14 ((~((~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))))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.90/1.14 tff(142,plain,
% 0.90/1.14 (~((~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)))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[141, 127])).
% 0.90/1.14 tff(143,plain,
% 0.90/1.14 (((~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)),
% 0.90/1.14 inference(tautology,[status(thm)],[])).
% 0.90/1.14 tff(144,plain,
% 0.90/1.14 (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = I!2),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.90/1.14 tff(145,plain,
% 0.90/1.14 (^[I: $i, J: $i] : refl((plus(I, J) = plus(J, I)) <=> (plus(I, J) = plus(J, I)))),
% 0.90/1.14 inference(bind,[status(th)],[])).
% 0.90/1.14 tff(146,plain,
% 0.90/1.14 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.90/1.14 inference(quant_intro,[status(thm)],[145])).
% 0.90/1.14 tff(147,plain,
% 0.90/1.14 (![I: $i, J: $i] : (plus(I, J) = plus(J, I)) <=> ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(148,axiom,(![I: $i, J: $i] : (plus(I, J) = plus(J, I))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_commutative')).
% 0.90/1.14 tff(149,plain,
% 0.90/1.14 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.90/1.14 tff(150,plain,(
% 0.90/1.14 ![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.90/1.14 inference(skolemize,[status(sab)],[149])).
% 0.90/1.14 tff(151,plain,
% 0.90/1.14 (![I: $i, J: $i] : (plus(I, J) = plus(J, I))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.90/1.14 tff(152,plain,
% 0.90/1.14 ((~![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))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(153,plain,
% 0.90/1.14 (plus(int_zero, tptp_fun_K_0(I!2, int_zero)) = plus(tptp_fun_K_0(I!2, int_zero), int_zero)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.90/1.14 tff(154,plain,
% 0.90/1.14 (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = plus(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.90/1.14 inference(symmetry,[status(thm)],[153])).
% 0.90/1.14 tff(155,plain,
% 0.90/1.14 (^[I: $i] : refl((plus(I, int_zero) = I) <=> (plus(I, int_zero) = I))),
% 0.90/1.14 inference(bind,[status(th)],[])).
% 0.90/1.14 tff(156,plain,
% 0.90/1.14 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.90/1.14 inference(quant_intro,[status(thm)],[155])).
% 0.90/1.14 tff(157,plain,
% 0.90/1.14 (![I: $i] : (plus(I, int_zero) = I) <=> ![I: $i] : (plus(I, int_zero) = I)),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(158,axiom,(![I: $i] : (plus(I, int_zero) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_zero')).
% 0.90/1.14 tff(159,plain,
% 0.90/1.14 (![I: $i] : (plus(I, int_zero) = I)),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.90/1.14 tff(160,plain,(
% 0.90/1.14 ![I: $i] : (plus(I, int_zero) = I)),
% 0.90/1.14 inference(skolemize,[status(sab)],[159])).
% 0.90/1.14 tff(161,plain,
% 0.90/1.14 (![I: $i] : (plus(I, int_zero) = I)),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.90/1.14 tff(162,plain,
% 0.90/1.14 ((~![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))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(163,plain,
% 0.90/1.14 (plus(tptp_fun_K_0(I!2, int_zero), int_zero) = tptp_fun_K_0(I!2, int_zero)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.90/1.14 tff(164,plain,
% 0.90/1.14 (tptp_fun_K_0(I!2, int_zero) = plus(tptp_fun_K_0(I!2, int_zero), int_zero)),
% 0.90/1.14 inference(symmetry,[status(thm)],[163])).
% 0.90/1.14 tff(165,plain,
% 0.90/1.14 (tptp_fun_K_0(I!2, int_zero) = plus(J!1, tptp_fun_K_0(I!2, J!1))),
% 0.90/1.14 inference(transitivity,[status(thm)],[164, 154, 144, 118])).
% 0.90/1.14 tff(166,plain,
% 0.90/1.14 (((~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))),
% 0.90/1.14 inference(tautology,[status(thm)],[])).
% 0.90/1.14 tff(167,plain,
% 0.90/1.14 (int_less(int_zero, tptp_fun_K_0(I!2, J!1))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[166, 115])).
% 0.90/1.14 tff(168,plain,
% 0.90/1.14 (tptp_fun_K_0(I!2, int_zero) = I!2),
% 0.90/1.14 inference(transitivity,[status(thm)],[164, 154, 144])).
% 0.90/1.14 tff(169,plain,
% 0.90/1.14 (int_leq(tptp_fun_K_0(I!2, int_zero), n) <=> int_leq(I!2, n)),
% 0.90/1.14 inference(monotonicity,[status(thm)],[168])).
% 0.90/1.14 tff(170,plain,
% 0.90/1.14 (int_leq(I!2, n) <=> int_leq(tptp_fun_K_0(I!2, int_zero), n)),
% 0.90/1.14 inference(symmetry,[status(thm)],[169])).
% 0.90/1.14 tff(171,plain,
% 0.90/1.14 (int_leq(tptp_fun_K_0(I!2, int_zero), n)),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[42, 170])).
% 0.90/1.14 tff(172,plain,
% 0.90/1.14 ((~![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)))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(173,plain,
% 0.90/1.14 (int_less(int_zero, tptp_fun_K_0(I!2, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[172, 134])).
% 0.90/1.14 tff(174,plain,
% 0.90/1.14 (((~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))),
% 0.90/1.14 inference(tautology,[status(thm)],[])).
% 0.90/1.14 tff(175,plain,
% 0.90/1.14 (int_less(int_zero, tptp_fun_K_0(I!2, int_zero))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[174, 142])).
% 0.90/1.14 tff(176,plain,
% 0.90/1.14 ((~(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))),
% 0.90/1.14 inference(tautology,[status(thm)],[])).
% 0.90/1.14 tff(177,plain,
% 0.90/1.14 ((~(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))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.90/1.14 tff(178,plain,
% 0.90/1.14 (int_leq(int_one, tptp_fun_K_0(I!2, int_zero))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[177, 173])).
% 0.90/1.14 tff(179,plain,
% 0.90/1.14 (((~![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))))))))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(180,plain,
% 0.90/1.14 (((~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))))))))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(181,plain,
% 0.90/1.14 ((~((~![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)))))))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(182,plain,
% 0.90/1.14 (((~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))))))))),
% 0.90/1.14 inference(monotonicity,[status(thm)],[181])).
% 0.90/1.14 tff(183,plain,
% 0.90/1.14 (((~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))))))))),
% 0.90/1.14 inference(transitivity,[status(thm)],[182, 180])).
% 0.90/1.14 tff(184,plain,
% 0.90/1.14 (((~![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)))))))))),
% 0.90/1.14 inference(monotonicity,[status(thm)],[183])).
% 0.90/1.14 tff(185,plain,
% 0.90/1.14 (((~![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))))))))),
% 0.90/1.14 inference(transitivity,[status(thm)],[184, 179])).
% 0.90/1.14 tff(186,plain,
% 0.90/1.14 ((~![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)))))))))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(187,plain,
% 0.90/1.14 ((~![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)))))))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.90/1.14 tff(188,plain,
% 0.90/1.14 ((~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)))))))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[187, 59, 41, 40, 178])).
% 0.90/1.14 tff(189,plain,
% 0.90/1.14 (~((~![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))))))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[188, 171])).
% 0.90/1.14 tff(190,plain,
% 0.90/1.14 (((~![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))))),
% 0.90/1.14 inference(tautology,[status(thm)],[])).
% 0.90/1.14 tff(191,plain,
% 0.90/1.14 (![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))))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.90/1.14 tff(192,plain,
% 0.90/1.14 (((~![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)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(193,plain,
% 0.90/1.15 (((~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)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(194,plain,
% 0.90/1.15 (((~![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))))),
% 0.90/1.15 inference(monotonicity,[status(thm)],[193])).
% 0.90/1.15 tff(195,plain,
% 0.90/1.15 (((~![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)))),
% 0.90/1.15 inference(transitivity,[status(thm)],[194, 192])).
% 0.90/1.15 tff(196,plain,
% 0.90/1.15 ((~![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))))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(197,plain,
% 0.90/1.15 ((~![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))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.90/1.15 tff(198,plain,
% 0.90/1.15 (![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))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[197, 191, 167, 165])).
% 0.90/1.15 tff(199,plain,
% 0.90/1.15 (((~![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))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(200,plain,
% 0.90/1.15 ((~![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))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(201,plain,
% 0.90/1.15 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, J!1)) | (a(plus(K, tptp_fun_K_0(I!2, J!1)), K) = real_zero))) | (~int_leq(int_one, J!1)) | (~int_leq(J!1, J!1)) | (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero)),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.90/1.15 tff(202,plain,
% 0.90/1.15 (a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1) = real_zero),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[201, 41, 30, 198])).
% 0.90/1.15 tff(203,plain,
% 0.90/1.15 (a(I!2, J!1) = a(plus(J!1, tptp_fun_K_0(I!2, J!1)), J!1)),
% 0.90/1.15 inference(monotonicity,[status(thm)],[118])).
% 0.90/1.15 tff(204,plain,
% 0.90/1.15 (a(I!2, J!1) = real_zero),
% 0.90/1.15 inference(transitivity,[status(thm)],[203, 202])).
% 0.90/1.15 tff(205,plain,
% 0.90/1.15 (((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero)) | (~(a(I!2, J!1) = real_zero))),
% 0.90/1.15 inference(tautology,[status(thm)],[])).
% 0.90/1.15 tff(206,plain,
% 0.90/1.15 (~(a(I!2, J!1) = real_zero)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[205, 110])).
% 0.90/1.15 tff(207,plain,
% 0.90/1.15 ($false),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[206, 204])).
% 0.90/1.15 tff(208,plain,((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.15 tff(209,plain,
% 0.90/1.15 ((~(~((~((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero))) | (~((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))))) <=> ((~((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero))) | (~((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one))))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(210,plain,
% 0.90/1.15 ((((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero)) & ((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (a(I!2, J!1) = real_one))) <=> (~((~((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero))) | (~((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(211,plain,
% 0.90/1.15 ((~(((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero)) & ((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))) <=> (~(~((~((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero))) | (~((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one))))))),
% 0.90/1.15 inference(monotonicity,[status(thm)],[210])).
% 0.90/1.15 tff(212,plain,
% 0.90/1.15 ((~(((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero)) & ((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))) <=> ((~((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero))) | (~((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one))))),
% 0.90/1.15 inference(transitivity,[status(thm)],[211, 209])).
% 0.90/1.15 tff(213,plain,
% 0.90/1.15 (~(((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero)) & ((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero)) & ((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))),
% 0.90/1.15 inference(or_elim,[status(thm)],[38])).
% 0.90/1.15 tff(214,plain,
% 0.90/1.15 ((~((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero))) | (~((~int_less(J!1, I!2)) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.90/1.15 tff(215,plain,
% 0.90/1.15 ((~((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero))) | (~((~(I!2 = J!1)) | (a(I!2, J!1) = real_one)))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[214, 208])).
% 0.90/1.15 tff(216,plain,
% 0.90/1.15 (~((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[215, 87])).
% 0.90/1.15 tff(217,plain,
% 0.90/1.15 (((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero)) | (~(a(I!2, J!1) = real_zero))),
% 0.90/1.15 inference(tautology,[status(thm)],[])).
% 0.90/1.15 tff(218,plain,
% 0.90/1.15 (~(a(I!2, J!1) = real_zero)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.90/1.15 tff(219,plain,
% 0.90/1.15 (((~int_less(I!2, J!1)) | (a(I!2, J!1) = real_zero)) | int_less(I!2, J!1)),
% 0.90/1.15 inference(tautology,[status(thm)],[])).
% 0.90/1.15 tff(220,plain,
% 0.90/1.15 (int_less(I!2, J!1)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[219, 216])).
% 0.90/1.15 tff(221,assumption,((~(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))))))), introduced(assumption)).
% 0.90/1.15 tff(222,plain,
% 0.90/1.15 (((~![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)))))))))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(223,plain,
% 0.90/1.15 ((~((~((~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))))))))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(224,plain,
% 0.90/1.15 (((~![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)))))))))),
% 0.90/1.15 inference(monotonicity,[status(thm)],[223])).
% 0.90/1.15 tff(225,plain,
% 0.90/1.15 (((~![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)))))))))),
% 0.90/1.15 inference(transitivity,[status(thm)],[224, 222])).
% 0.90/1.15 tff(226,plain,
% 0.90/1.15 ((~![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)))))))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(227,plain,
% 0.90/1.15 ((~![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: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))) | (~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1))))))))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.90/1.15 tff(228,plain,
% 0.90/1.15 ($false),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[227, 100, 221])).
% 0.90/1.15 tff(229,plain,(~((~(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)))))))), inference(lemma,lemma(discharge,[]))).
% 0.90/1.15 tff(230,plain,
% 0.90/1.15 (((~(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)))))),
% 0.90/1.15 inference(tautology,[status(thm)],[])).
% 0.90/1.15 tff(231,plain,
% 0.90/1.15 ((~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))))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.90/1.15 tff(232,plain,
% 0.90/1.15 ((~((~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))))),
% 0.90/1.15 inference(tautology,[status(thm)],[])).
% 0.90/1.15 tff(233,plain,
% 0.90/1.15 ((~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))))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.90/1.15 tff(234,plain,
% 0.90/1.15 (~((~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)))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[233, 220])).
% 0.90/1.15 tff(235,assumption,(~((~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)))), introduced(assumption)).
% 0.90/1.15 tff(236,plain,
% 0.90/1.15 (((~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)),
% 0.90/1.15 inference(tautology,[status(thm)],[])).
% 0.90/1.15 tff(237,plain,
% 0.90/1.15 (plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.90/1.15 tff(238,plain,
% 0.90/1.15 (J!1 = plus(I!2, tptp_fun_K_0(J!1, I!2))),
% 0.90/1.15 inference(symmetry,[status(thm)],[237])).
% 0.90/1.15 tff(239,plain,
% 0.90/1.15 (((~![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))))))))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(240,plain,
% 0.90/1.15 ((~((~((~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)))))))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(241,plain,
% 0.90/1.15 (((~![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))))))))),
% 0.90/1.15 inference(monotonicity,[status(thm)],[240])).
% 0.90/1.15 tff(242,plain,
% 0.90/1.15 (((~![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))))))))),
% 0.90/1.15 inference(transitivity,[status(thm)],[241, 239])).
% 0.90/1.15 tff(243,plain,
% 0.90/1.15 ((~![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)))))))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(244,plain,
% 0.90/1.15 ((~![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)))))))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.90/1.15 tff(245,plain,
% 0.90/1.15 (~((~((~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))))))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[244, 100])).
% 0.90/1.15 tff(246,plain,
% 0.90/1.15 (((~((~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)))))),
% 0.90/1.15 inference(tautology,[status(thm)],[])).
% 0.90/1.15 tff(247,plain,
% 0.90/1.15 ((~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))))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.90/1.15 tff(248,plain,
% 0.90/1.15 ((~![I: $i] : (int_less(int_zero, I) <=> int_leq(int_one, I))) | (int_less(int_zero, J!1) <=> int_leq(int_one, J!1))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(249,plain,
% 0.90/1.15 (int_less(int_zero, J!1) <=> int_leq(int_one, J!1)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[248, 134])).
% 0.90/1.15 tff(250,plain,
% 0.90/1.15 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1) | (~int_leq(int_one, J!1))),
% 0.90/1.15 inference(tautology,[status(thm)],[])).
% 0.90/1.15 tff(251,plain,
% 0.90/1.15 ((~(int_less(int_zero, J!1) <=> int_leq(int_one, J!1))) | int_less(int_zero, J!1)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[250, 41])).
% 0.90/1.15 tff(252,plain,
% 0.90/1.15 (int_less(int_zero, J!1)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[251, 249])).
% 0.90/1.15 tff(253,plain,
% 0.90/1.15 ((~((~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))))),
% 0.90/1.15 inference(tautology,[status(thm)],[])).
% 0.90/1.15 tff(254,plain,
% 0.90/1.15 ((~((~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))))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[253, 252])).
% 0.90/1.15 tff(255,plain,
% 0.90/1.15 (~((~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)))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[254, 247])).
% 0.90/1.15 tff(256,plain,
% 0.90/1.15 (((~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)),
% 0.90/1.15 inference(tautology,[status(thm)],[])).
% 0.90/1.15 tff(257,plain,
% 0.90/1.15 (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = J!1),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[256, 255])).
% 0.90/1.15 tff(258,plain,
% 0.90/1.15 ((~![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))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(259,plain,
% 0.90/1.15 (plus(int_zero, tptp_fun_K_0(J!1, int_zero)) = plus(tptp_fun_K_0(J!1, int_zero), int_zero)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[258, 151])).
% 0.90/1.15 tff(260,plain,
% 0.90/1.15 (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = plus(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.90/1.15 inference(symmetry,[status(thm)],[259])).
% 0.90/1.15 tff(261,plain,
% 0.90/1.15 ((~![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))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(262,plain,
% 0.90/1.15 (plus(tptp_fun_K_0(J!1, int_zero), int_zero) = tptp_fun_K_0(J!1, int_zero)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[261, 161])).
% 0.90/1.15 tff(263,plain,
% 0.90/1.15 (tptp_fun_K_0(J!1, int_zero) = plus(tptp_fun_K_0(J!1, int_zero), int_zero)),
% 0.90/1.15 inference(symmetry,[status(thm)],[262])).
% 0.90/1.15 tff(264,plain,
% 0.90/1.15 (tptp_fun_K_0(J!1, int_zero) = plus(I!2, tptp_fun_K_0(J!1, I!2))),
% 0.90/1.15 inference(transitivity,[status(thm)],[263, 260, 257, 238])).
% 0.90/1.15 tff(265,plain,
% 0.90/1.15 (((~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))),
% 0.90/1.16 inference(tautology,[status(thm)],[])).
% 0.90/1.16 tff(266,plain,
% 0.90/1.16 (int_less(int_zero, tptp_fun_K_0(J!1, I!2))),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[265, 235])).
% 0.90/1.16 tff(267,plain,
% 0.90/1.16 (tptp_fun_K_0(J!1, int_zero) = J!1),
% 0.90/1.16 inference(transitivity,[status(thm)],[263, 260, 257])).
% 0.90/1.16 tff(268,plain,
% 0.90/1.16 (int_leq(tptp_fun_K_0(J!1, int_zero), n) <=> int_leq(J!1, n)),
% 0.90/1.16 inference(monotonicity,[status(thm)],[267])).
% 0.90/1.16 tff(269,plain,
% 0.90/1.16 (int_leq(J!1, n) <=> int_leq(tptp_fun_K_0(J!1, int_zero), n)),
% 0.90/1.16 inference(symmetry,[status(thm)],[268])).
% 0.90/1.16 tff(270,plain,
% 0.90/1.16 (int_leq(tptp_fun_K_0(J!1, int_zero), n)),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[40, 269])).
% 0.90/1.16 tff(271,plain,
% 0.90/1.16 ((~![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)))),
% 0.90/1.16 inference(quant_inst,[status(thm)],[])).
% 0.90/1.16 tff(272,plain,
% 0.90/1.16 (int_less(int_zero, tptp_fun_K_0(J!1, int_zero)) <=> int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[271, 134])).
% 0.90/1.16 tff(273,plain,
% 0.90/1.16 (((~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))),
% 0.90/1.16 inference(tautology,[status(thm)],[])).
% 0.90/1.16 tff(274,plain,
% 0.90/1.16 (int_less(int_zero, tptp_fun_K_0(J!1, int_zero))),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[273, 255])).
% 0.90/1.16 tff(275,plain,
% 0.90/1.16 ((~(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))),
% 0.90/1.16 inference(tautology,[status(thm)],[])).
% 0.90/1.16 tff(276,plain,
% 0.90/1.16 ((~(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))),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[275, 274])).
% 0.90/1.16 tff(277,plain,
% 0.90/1.16 (int_leq(int_one, tptp_fun_K_0(J!1, int_zero))),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[276, 272])).
% 0.90/1.16 tff(278,plain,
% 0.90/1.16 (((~![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)))))))))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(279,plain,
% 0.90/1.16 (((~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)))))))))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(280,plain,
% 0.90/1.16 ((~((~![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))))))))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(281,plain,
% 0.90/1.16 (((~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)))))))))),
% 0.90/1.16 inference(monotonicity,[status(thm)],[280])).
% 0.90/1.16 tff(282,plain,
% 0.90/1.16 (((~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)))))))))),
% 0.90/1.16 inference(transitivity,[status(thm)],[281, 279])).
% 0.90/1.16 tff(283,plain,
% 0.90/1.16 (((~![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))))))))))),
% 0.90/1.16 inference(monotonicity,[status(thm)],[282])).
% 0.90/1.16 tff(284,plain,
% 0.90/1.16 (((~![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)))))))))),
% 0.90/1.16 inference(transitivity,[status(thm)],[283, 278])).
% 0.90/1.16 tff(285,plain,
% 0.90/1.16 ((~![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))))))))),
% 0.90/1.16 inference(quant_inst,[status(thm)],[])).
% 0.90/1.16 tff(286,plain,
% 0.90/1.16 ((~![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))))))))),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.90/1.16 tff(287,plain,
% 0.90/1.16 ((~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))))))))),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[286, 59, 43, 42, 277])).
% 0.90/1.16 tff(288,plain,
% 0.90/1.16 (~((~![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)))))))),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[287, 270])).
% 0.90/1.16 tff(289,plain,
% 0.90/1.16 (((~![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))))),
% 0.90/1.16 inference(tautology,[status(thm)],[])).
% 0.90/1.16 tff(290,plain,
% 0.90/1.16 (![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))))),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[289, 288])).
% 0.90/1.16 tff(291,plain,
% 0.90/1.16 (((~![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)))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(292,plain,
% 0.90/1.16 (((~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)))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(293,plain,
% 0.90/1.16 (((~![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))))),
% 0.90/1.16 inference(monotonicity,[status(thm)],[292])).
% 0.90/1.16 tff(294,plain,
% 0.90/1.16 (((~![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)))),
% 0.90/1.16 inference(transitivity,[status(thm)],[293, 291])).
% 0.90/1.16 tff(295,plain,
% 0.90/1.16 ((~![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))))),
% 0.90/1.16 inference(quant_inst,[status(thm)],[])).
% 0.90/1.16 tff(296,plain,
% 0.90/1.16 ((~![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))),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.90/1.16 tff(297,plain,
% 0.90/1.16 (![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))),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[296, 290, 266, 264])).
% 0.90/1.16 tff(298,assumption,(~int_leq(I!2, I!2)), introduced(assumption)).
% 0.90/1.16 tff(299,plain,
% 0.90/1.16 (((~![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))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(300,plain,
% 0.90/1.16 ((int_leq(I!2, I!2) <=> $true) <=> int_leq(I!2, I!2)),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(301,plain,
% 0.90/1.16 (($true | int_less(I!2, I!2)) <=> $true),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(302,plain,
% 0.90/1.16 ((I!2 = I!2) <=> $true),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(303,plain,
% 0.90/1.16 (((I!2 = I!2) | int_less(I!2, I!2)) <=> ($true | int_less(I!2, I!2))),
% 0.90/1.16 inference(monotonicity,[status(thm)],[302])).
% 0.90/1.16 tff(304,plain,
% 0.90/1.16 (((I!2 = I!2) | int_less(I!2, I!2)) <=> $true),
% 0.90/1.16 inference(transitivity,[status(thm)],[303, 301])).
% 0.90/1.16 tff(305,plain,
% 0.90/1.16 ((int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2))) <=> (int_leq(I!2, I!2) <=> $true)),
% 0.90/1.17 inference(monotonicity,[status(thm)],[304])).
% 0.90/1.17 tff(306,plain,
% 0.90/1.17 ((int_leq(I!2, I!2) <=> ((I!2 = I!2) | int_less(I!2, I!2))) <=> int_leq(I!2, I!2)),
% 0.90/1.17 inference(transitivity,[status(thm)],[305, 300])).
% 0.90/1.17 tff(307,plain,
% 0.90/1.17 (((~![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))),
% 0.90/1.17 inference(monotonicity,[status(thm)],[306])).
% 0.90/1.17 tff(308,plain,
% 0.90/1.17 (((~![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))),
% 0.90/1.17 inference(transitivity,[status(thm)],[307, 299])).
% 0.90/1.17 tff(309,plain,
% 0.90/1.17 ((~![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)))),
% 0.90/1.17 inference(quant_inst,[status(thm)],[])).
% 0.90/1.17 tff(310,plain,
% 0.90/1.17 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(I!2, I!2)),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.90/1.17 tff(311,plain,
% 0.90/1.17 ($false),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[310, 16, 298])).
% 0.90/1.17 tff(312,plain,(int_leq(I!2, I!2)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.17 tff(313,plain,
% 0.90/1.17 (((~![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))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(314,plain,
% 0.90/1.17 ((~![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))),
% 0.90/1.17 inference(quant_inst,[status(thm)],[])).
% 0.90/1.17 tff(315,plain,
% 0.90/1.17 ((~![K: $i] : ((~int_leq(int_one, K)) | (~int_leq(K, I!2)) | (a(K, plus(K, tptp_fun_K_0(J!1, I!2))) = real_zero))) | (~int_leq(int_one, I!2)) | (~int_leq(I!2, I!2)) | (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero)),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.90/1.17 tff(316,plain,
% 0.90/1.17 (a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2))) = real_zero),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[315, 43, 312, 297])).
% 0.90/1.17 tff(317,plain,
% 0.90/1.17 (a(I!2, J!1) = a(I!2, plus(I!2, tptp_fun_K_0(J!1, I!2)))),
% 0.90/1.17 inference(monotonicity,[status(thm)],[238])).
% 0.90/1.17 tff(318,plain,
% 0.90/1.17 (a(I!2, J!1) = real_zero),
% 0.90/1.17 inference(transitivity,[status(thm)],[317, 316])).
% 0.90/1.17 tff(319,assumption,(~(a(I!2, J!1) = real_zero)), introduced(assumption)).
% 0.90/1.17 tff(320,plain,
% 0.90/1.17 ($false),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[319, 318])).
% 0.90/1.17 tff(321,plain,(((~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))) | (a(I!2, J!1) = real_zero)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.17 tff(322,plain,
% 0.90/1.17 ($false),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[321, 234, 218])).
% 0.90/1.17 % SZS output end Proof
% 0.90/1.17 % E exiting
%------------------------------------------------------------------------------