%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV492+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 163.43s 163.67s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV492+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:53:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 163.43/163.67 % SZS status Theorem
% 163.43/163.67 % SZS output start Proof
% 163.43/163.67 tff(int_less_type, type, (
% 163.43/163.67 int_less: ( $i * $i ) > $o)).
% 163.43/163.67 tff(n_type, type, (
% 163.43/163.67 n: $i)).
% 163.43/163.67 tff(tptp_fun_I_2_type, type, (
% 163.43/163.67 tptp_fun_I_2: $i)).
% 163.43/163.67 tff(int_leq_type, type, (
% 163.43/163.67 int_leq: ( $i * $i ) > $o)).
% 163.43/163.67 tff(tptp_fun_J_1_type, type, (
% 163.43/163.67 tptp_fun_J_1: $i)).
% 163.43/163.67 tff(int_one_type, type, (
% 163.43/163.67 int_one: $i)).
% 163.43/163.67 tff(real_one_type, type, (
% 163.43/163.67 real_one: $i)).
% 163.43/163.67 tff(a_type, type, (
% 163.43/163.67 a: ( $i * $i ) > $i)).
% 163.43/163.67 tff(real_zero_type, type, (
% 163.43/163.67 real_zero: $i)).
% 163.43/163.67 tff(plus_type, type, (
% 163.43/163.67 plus: ( $i * $i ) > $i)).
% 163.43/163.67 tff(int_zero_type, type, (
% 163.43/163.67 int_zero: $i)).
% 163.43/163.67 tff(qr_type, type, (
% 163.43/163.67 qr: ( $i * $i ) > $i)).
% 163.43/163.67 tff(tptp_fun_K_0_type, type, (
% 163.43/163.67 tptp_fun_K_0: ( $i * $i ) > $i)).
% 163.43/163.67 tff(tptp_fun_J_3_type, type, (
% 163.43/163.67 tptp_fun_J_3: $i)).
% 163.43/163.67 tff(1,plain,
% 163.43/163.67 (^[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))))),
% 163.43/163.67 inference(bind,[status(th)],[])).
% 163.43/163.67 tff(2,plain,
% 163.43/163.67 (![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)))),
% 163.43/163.67 inference(quant_intro,[status(thm)],[1])).
% 163.43/163.67 tff(3,plain,
% 163.43/163.67 (![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)))),
% 163.43/163.67 inference(rewrite,[status(thm)],[])).
% 163.43/163.67 tff(4,plain,
% 163.43/163.67 (^[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))))),
% 163.43/163.67 inference(bind,[status(th)],[])).
% 163.43/163.67 tff(5,plain,
% 163.43/163.67 (![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)))),
% 163.43/163.67 inference(quant_intro,[status(thm)],[4])).
% 163.43/163.67 tff(6,axiom,(![I: $i, J: $i] : (int_leq(I, J) <=> (int_less(I, J) | (I = J)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','int_leq')).
% 163.43/163.67 tff(7,plain,
% 163.43/163.67 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 163.43/163.67 inference(modus_ponens,[status(thm)],[6, 5])).
% 163.43/163.67 tff(8,plain,
% 163.43/163.67 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 163.43/163.67 inference(modus_ponens,[status(thm)],[7, 3])).
% 163.43/163.67 tff(9,plain,(
% 163.43/163.67 ![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 163.43/163.67 inference(skolemize,[status(sab)],[8])).
% 163.43/163.67 tff(10,plain,
% 163.43/163.67 (![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))),
% 163.43/163.67 inference(modus_ponens,[status(thm)],[9, 2])).
% 163.43/163.67 tff(11,plain,
% 163.43/163.67 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(I!2, n) <=> ((I!2 = n) | int_less(I!2, n)))),
% 163.43/163.67 inference(quant_inst,[status(thm)],[])).
% 163.43/163.67 tff(12,plain,
% 163.43/163.67 (int_leq(I!2, n) <=> ((I!2 = n) | int_less(I!2, n))),
% 163.43/163.67 inference(unit_resolution,[status(thm)],[11, 10])).
% 163.43/163.67 tff(13,plain,
% 163.43/163.67 (^[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))))))))),
% 163.43/163.67 inference(bind,[status(th)],[])).
% 163.43/163.67 tff(14,plain,
% 163.43/163.67 (![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)))))))),
% 163.43/163.67 inference(quant_intro,[status(thm)],[13])).
% 163.43/163.67 tff(15,plain,
% 163.43/163.67 (^[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))))))))),
% 163.43/163.67 inference(bind,[status(th)],[])).
% 163.43/163.67 tff(16,plain,
% 163.43/163.67 (![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)))))))),
% 163.43/163.67 inference(quant_intro,[status(thm)],[15])).
% 163.43/163.67 tff(17,plain,
% 163.43/163.67 (![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)))))))),
% 163.43/163.67 inference(transitivity,[status(thm)],[16, 14])).
% 163.43/163.67 tff(18,plain,
% 163.43/163.67 (^[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)))))))))),
% 163.43/163.67 inference(bind,[status(th)],[])).
% 163.43/163.67 tff(19,plain,
% 163.43/163.67 (![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)))))))),
% 163.43/163.67 inference(quant_intro,[status(thm)],[18])).
% 163.43/163.67 tff(20,plain,
% 163.43/163.67 (![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)))),
% 163.43/163.67 inference(rewrite,[status(thm)],[])).
% 163.43/163.67 tff(21,axiom,(![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus_and_inverse')).
% 163.43/163.67 tff(22,plain,
% 163.43/163.67 (![I: $i, J: $i] : (int_less(I, J) <=> ?[K: $i] : ((plus(I, K) = J) & int_less(int_zero, K)))),
% 163.43/163.67 inference(modus_ponens,[status(thm)],[21, 20])).
% 163.43/163.67 tff(23,plain,(
% 163.43/163.67 ![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)))))),
% 163.43/163.67 inference(skolemize,[status(sab)],[22])).
% 163.43/163.67 tff(24,plain,
% 163.43/163.67 (![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)))))))),
% 163.43/163.67 inference(modus_ponens,[status(thm)],[23, 19])).
% 163.43/163.67 tff(25,plain,
% 163.43/163.67 (![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)))))))),
% 163.43/163.67 inference(modus_ponens,[status(thm)],[24, 17])).
% 163.43/163.67 tff(26,plain,
% 163.43/163.67 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))))))),
% 163.43/163.67 inference(rewrite,[status(thm)],[])).
% 163.43/163.67 tff(27,plain,
% 163.43/163.67 ((~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K))))))) <=> (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1)))))))),
% 163.43/163.67 inference(rewrite,[status(thm)],[])).
% 163.43/163.67 tff(28,plain,
% 163.43/163.67 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))))))),
% 163.43/163.67 inference(monotonicity,[status(thm)],[27])).
% 163.43/163.67 tff(29,plain,
% 163.43/163.67 (((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)) | (~int_less(int_zero, tptp_fun_K_0(J!1, I!2))))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~(plus(I!2, K) = J!1)) | (~int_less(int_zero, K)))))))) <=> ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))))))),
% 163.43/163.67 inference(transitivity,[status(thm)],[28, 26])).
% 163.43/163.67 tff(30,plain,
% 163.43/163.67 ((~![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)))))))),
% 163.43/163.67 inference(quant_inst,[status(thm)],[])).
% 163.43/163.67 tff(31,plain,
% 163.43/163.67 ((~![I: $i, J: $i] : (~((~((~int_less(I, J)) | (~((~(plus(I, tptp_fun_K_0(J, I)) = J)) | (~int_less(int_zero, tptp_fun_K_0(J, I))))))) | (~(int_less(I, J) | ![K: $i] : ((~(plus(I, K) = J)) | (~int_less(int_zero, K)))))))) | (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1)))))))),
% 163.43/163.67 inference(modus_ponens,[status(thm)],[30, 29])).
% 163.43/163.67 tff(32,plain,
% 163.43/163.67 (~((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1))))))),
% 163.43/163.67 inference(unit_resolution,[status(thm)],[31, 25])).
% 163.43/163.67 tff(33,plain,
% 163.43/163.67 (((~((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))) | (~(int_less(I!2, J!1) | ![K: $i] : ((~int_less(int_zero, K)) | (~(plus(I!2, K) = J!1)))))) | ((~int_less(I!2, J!1)) | (~((~int_less(int_zero, tptp_fun_K_0(J!1, I!2))) | (~(plus(I!2, tptp_fun_K_0(J!1, I!2)) = J!1)))))),
% 163.43/163.67 inference(tautology,[status(thm)],[])).
% 163.43/163.67 tff(34,plain,
% 163.43/163.67 ((~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))))),
% 163.43/163.67 inference(unit_resolution,[status(thm)],[33, 32])).
% 163.43/163.67 tff(35,assumption,(~((~int_leq(J!3, n)) | (~(a(J!3, J!3) = real_zero)) | (~int_leq(int_one, J!3)))), introduced(assumption)).
% 163.43/163.67 tff(36,plain,
% 163.43/163.67 (((~int_leq(J!3, n)) | (~(a(J!3, J!3) = real_zero)) | (~int_leq(int_one, J!3))) | int_leq(int_one, J!3)),
% 163.43/163.67 inference(tautology,[status(thm)],[])).
% 163.43/163.67 tff(37,plain,
% 163.43/163.67 (int_leq(int_one, J!3)),
% 163.43/163.67 inference(unit_resolution,[status(thm)],[36, 35])).
% 163.43/163.67 tff(38,plain,
% 163.43/163.67 (((~int_leq(J!3, n)) | (~(a(J!3, J!3) = real_zero)) | (~int_leq(int_one, J!3))) | int_leq(J!3, n)),
% 163.43/163.67 inference(tautology,[status(thm)],[])).
% 163.43/163.67 tff(39,plain,
% 163.43/163.67 (int_leq(J!3, n)),
% 163.43/163.67 inference(unit_resolution,[status(thm)],[38, 35])).
% 163.43/163.67 tff(40,plain,
% 163.43/163.67 (^[I: $i, J: $i] : refl(((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))),
% 163.43/163.67 inference(bind,[status(th)],[])).
% 163.43/163.67 tff(41,plain,
% 163.43/163.67 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 163.43/163.67 inference(quant_intro,[status(thm)],[40])).
% 163.43/163.67 tff(42,plain,
% 163.43/163.67 (^[I: $i, J: $i] : rewrite(((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))),
% 163.43/163.67 inference(bind,[status(th)],[])).
% 163.43/163.67 tff(43,plain,
% 163.43/163.67 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 163.43/163.67 inference(quant_intro,[status(thm)],[42])).
% 163.43/163.67 tff(44,plain,
% 163.43/163.67 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 163.43/163.67 inference(transitivity,[status(thm)],[43, 41])).
% 163.43/163.67 tff(45,plain,
% 163.43/163.67 (^[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(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, 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(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n))))))), rewrite((~(~((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n))))) <=> ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, 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(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, 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) = qr(plus(K, C), K))) <=> (((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K))))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K))) <=> ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J)))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K))) <=> ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K))) <=> ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) <=> (((~int_less(int_zero, C)) | (~(I = plus(J, C)))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), rewrite((((~int_less(int_zero, C)) | (~(I = plus(J, C)))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) <=> ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))))), (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) <=> ![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), quant_intro(proof_bind(^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, K) & int_leq(K, J)) <=> (~((~int_leq(int_one, K)) | (~int_leq(K, J))))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> (~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))))), rewrite((~(~((~int_leq(int_one, K)) | (~int_leq(K, J))))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J)))), ((~(int_leq(int_one, K) & int_leq(K, J))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, J))))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) <=> (((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(K, K) = real_one)))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, J))) | (a(K, K) = real_one)) <=> ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))), (((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) <=> ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) <=> ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_less(int_zero, C) & (J = plus(I, C))) <=> (~((~int_less(int_zero, C)) | (~(J = plus(I, C)))))), ((~(int_less(int_zero, C) & (J = plus(I, C)))) <=> (~(~((~int_less(int_zero, C)) | (~(J = plus(I, C)))))))), rewrite((~(~((~int_less(int_zero, C)) | (~(J = plus(I, C)))))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C))))), ((~(int_less(int_zero, C) & (J = plus(I, C)))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C)))))), quant_intro(proof_bind(^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((int_leq(int_one, K) & int_leq(K, I)) <=> (~((~int_leq(int_one, K)) | (~int_leq(K, I))))), ((~(int_leq(int_one, K) & int_leq(K, I))) <=> (~(~((~int_leq(int_one, K)) | (~int_leq(K, I))))))), rewrite((~(~((~int_leq(int_one, K)) | (~int_leq(K, I))))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, I)))), ((~(int_leq(int_one, K) & int_leq(K, I))) <=> ((~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> (((~int_leq(int_one, K)) | (~int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), rewrite((((~int_leq(int_one, K)) | (~int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))), (((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), (![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)) <=> ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> (((~int_less(int_zero, C)) | (~(J = plus(I, C)))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), rewrite((((~int_less(int_zero, C)) | (~(J = plus(I, C)))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))), (((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))), (![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> ![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))), ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))) <=> (![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) & ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J))) & ![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))), rewrite((![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) & ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J))) & ![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))), ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))), (((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> (((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n))) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))))), rewrite((((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n))) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I)))))))) <=> ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))), (((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))))),
% 163.43/163.68 inference(bind,[status(th)],[])).
% 163.43/163.68 tff(46,plain,
% 163.43/163.68 (![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) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 163.43/163.68 inference(quant_intro,[status(thm)],[45])).
% 163.43/163.68 tff(47,plain,
% 163.43/163.68 (![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) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 163.43/163.68 inference(rewrite,[status(thm)],[])).
% 163.43/163.68 tff(48,plain,
% 163.43/163.68 (^[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) = qr(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[K: $i] : rewrite(((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)) <=> ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), (![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)) <=> ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), (((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))) <=> ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))), rewrite(((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))) <=> ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))), (((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))) <=> ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), (![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))) <=> ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))), (((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))) <=> ((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one))) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), rewrite(((![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one))) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))), (((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))) <=> (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), (((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))))) <=> ((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) => (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))))), rewrite(((int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n)) => (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero))))) <=> ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))), (((((int_leq(int_one, I) & int_leq(I, n)) & int_leq(int_one, J)) & int_leq(J, n)) => ((![C: $i] : ((int_less(int_zero, C) & (I = plus(J, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))))) <=> ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))))),
% 163.43/163.68 inference(bind,[status(th)],[])).
% 163.43/163.68 tff(49,plain,
% 163.43/163.68 (![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) = qr(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero))))) <=> ![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_leq(I, n) & int_leq(int_one, J) & int_leq(J, n))) | (![C: $i] : ((~(int_less(int_zero, C) & (I = plus(J, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(plus(K, C), K) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 163.43/163.68 inference(quant_intro,[status(thm)],[48])).
% 163.43/163.68 tff(50,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) = qr(plus(K, C), K)))) & ![K: $i] : ((int_leq(int_one, K) & int_leq(K, J)) => (a(K, K) = real_one))) & ![C: $i] : ((int_less(int_zero, C) & (J = plus(I, C))) => ![K: $i] : ((int_leq(int_one, K) & int_leq(K, I)) => (a(K, plus(K, C)) = real_zero)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qih')).
% 163.43/163.68 tff(51,plain,
% 163.43/163.68 (![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) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 163.43/163.68 inference(modus_ponens,[status(thm)],[50, 49])).
% 163.43/163.68 tff(52,plain,
% 163.43/163.68 (![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) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 163.43/163.68 inference(modus_ponens,[status(thm)],[51, 47])).
% 163.43/163.68 tff(53,plain,(
% 163.43/163.68 ![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) = qr(plus(K, C), K)))) & ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, J))) | (a(K, K) = real_one)) & ![C: $i] : ((~(int_less(int_zero, C) & (J = plus(I, C)))) | ![K: $i] : ((~(int_leq(int_one, K) & int_leq(K, I))) | (a(K, plus(K, C)) = real_zero)))))),
% 163.43/163.68 inference(skolemize,[status(sab)],[52])).
% 163.43/163.68 tff(54,plain,
% 163.43/163.68 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 163.43/163.68 inference(modus_ponens,[status(thm)],[53, 46])).
% 163.43/163.68 tff(55,plain,
% 163.43/163.68 (![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))),
% 163.43/163.68 inference(modus_ponens,[status(thm)],[54, 44])).
% 163.43/163.68 tff(56,plain,
% 163.43/163.68 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))))))),
% 163.43/163.68 inference(rewrite,[status(thm)],[])).
% 163.43/163.68 tff(57,plain,
% 163.43/163.68 (((~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))))))) <=> ((~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))))))),
% 163.43/163.68 inference(rewrite,[status(thm)],[])).
% 163.43/163.68 tff(58,plain,
% 163.43/163.68 ((~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))))) <=> (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))))))),
% 163.43/163.68 inference(rewrite,[status(thm)],[])).
% 163.43/163.68 tff(59,plain,
% 163.43/163.68 (((~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))))))) <=> ((~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))))))),
% 163.43/163.68 inference(monotonicity,[status(thm)],[58])).
% 163.43/163.68 tff(60,plain,
% 163.43/163.68 (((~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))))))) <=> ((~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))))))),
% 163.43/163.69 inference(transitivity,[status(thm)],[59, 57])).
% 163.43/163.69 tff(61,plain,
% 163.43/163.69 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))))))))),
% 163.43/163.69 inference(monotonicity,[status(thm)],[60])).
% 163.43/163.69 tff(62,plain,
% 163.43/163.69 (((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))))))) <=> ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))))))),
% 163.43/163.69 inference(transitivity,[status(thm)],[61, 56])).
% 163.43/163.69 tff(63,plain,
% 163.43/163.69 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | ((~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~int_leq(J!3, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))))))),
% 163.43/163.69 inference(quant_inst,[status(thm)],[])).
% 163.43/163.69 tff(64,plain,
% 163.43/163.69 ((~![I: $i, J: $i] : ((~int_leq(int_one, I)) | (~int_leq(J, n)) | (~int_leq(int_one, J)) | (~int_leq(I, n)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(I = plus(J, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J = plus(I, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, I))))))))) | (~int_leq(J!3, n)) | (~int_leq(int_one, J!3)) | (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))))))),
% 163.43/163.69 inference(modus_ponens,[status(thm)],[63, 62])).
% 163.43/163.69 tff(65,plain,
% 163.43/163.69 (~((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))))),
% 163.43/163.69 inference(unit_resolution,[status(thm)],[64, 55, 39, 37])).
% 163.43/163.69 tff(66,plain,
% 163.43/163.69 (((~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(K, plus(K, C)) = real_zero) | (~int_leq(int_one, K)) | (~int_leq(K, J!3))))) | (~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~![C: $i] : ((~int_less(int_zero, C)) | (~(J!3 = plus(J!3, C))) | ![K: $i] : ((a(plus(K, C), K) = qr(plus(K, C), K)) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))))) | ![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))),
% 163.43/163.69 inference(tautology,[status(thm)],[])).
% 163.43/163.69 tff(67,plain,
% 163.43/163.69 (![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))),
% 163.43/163.69 inference(unit_resolution,[status(thm)],[66, 65])).
% 163.43/163.69 tff(68,assumption,(~int_leq(J!3, J!3)), introduced(assumption)).
% 163.43/163.69 tff(69,plain,
% 163.43/163.69 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!3, J!3)) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!3, J!3))),
% 163.43/163.69 inference(rewrite,[status(thm)],[])).
% 163.43/163.69 tff(70,plain,
% 163.43/163.69 ((int_leq(J!3, J!3) <=> $true) <=> int_leq(J!3, J!3)),
% 163.43/163.69 inference(rewrite,[status(thm)],[])).
% 163.43/163.69 tff(71,plain,
% 163.43/163.69 (($true | int_less(J!3, J!3)) <=> $true),
% 163.43/163.69 inference(rewrite,[status(thm)],[])).
% 163.43/163.69 tff(72,plain,
% 163.43/163.69 ((J!3 = J!3) <=> $true),
% 163.43/163.69 inference(rewrite,[status(thm)],[])).
% 163.43/163.69 tff(73,plain,
% 163.43/163.69 (((J!3 = J!3) | int_less(J!3, J!3)) <=> ($true | int_less(J!3, J!3))),
% 163.43/163.69 inference(monotonicity,[status(thm)],[72])).
% 163.43/163.69 tff(74,plain,
% 163.43/163.69 (((J!3 = J!3) | int_less(J!3, J!3)) <=> $true),
% 163.43/163.69 inference(transitivity,[status(thm)],[73, 71])).
% 163.43/163.69 tff(75,plain,
% 163.43/163.69 ((int_leq(J!3, J!3) <=> ((J!3 = J!3) | int_less(J!3, J!3))) <=> (int_leq(J!3, J!3) <=> $true)),
% 163.43/163.69 inference(monotonicity,[status(thm)],[74])).
% 163.43/163.69 tff(76,plain,
% 163.43/163.69 ((int_leq(J!3, J!3) <=> ((J!3 = J!3) | int_less(J!3, J!3))) <=> int_leq(J!3, J!3)),
% 163.43/163.69 inference(transitivity,[status(thm)],[75, 70])).
% 163.43/163.69 tff(77,plain,
% 163.43/163.69 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(J!3, J!3) <=> ((J!3 = J!3) | int_less(J!3, J!3)))) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!3, J!3))),
% 163.43/163.69 inference(monotonicity,[status(thm)],[76])).
% 163.43/163.69 tff(78,plain,
% 163.43/163.69 (((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(J!3, J!3) <=> ((J!3 = J!3) | int_less(J!3, J!3)))) <=> ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!3, J!3))),
% 163.43/163.69 inference(transitivity,[status(thm)],[77, 69])).
% 163.43/163.69 tff(79,plain,
% 163.43/163.69 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | (int_leq(J!3, J!3) <=> ((J!3 = J!3) | int_less(J!3, J!3)))),
% 163.43/163.69 inference(quant_inst,[status(thm)],[])).
% 163.43/163.69 tff(80,plain,
% 163.43/163.69 ((~![I: $i, J: $i] : (int_leq(I, J) <=> ((I = J) | int_less(I, J)))) | int_leq(J!3, J!3)),
% 163.43/163.69 inference(modus_ponens,[status(thm)],[79, 78])).
% 163.43/163.69 tff(81,plain,
% 163.43/163.69 ($false),
% 163.43/163.69 inference(unit_resolution,[status(thm)],[80, 10, 68])).
% 163.43/163.69 tff(82,plain,(int_leq(J!3, J!3)), inference(lemma,lemma(discharge,[]))).
% 163.43/163.69 tff(83,plain,
% 163.43/163.69 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | ((~int_leq(int_one, J!3)) | (a(J!3, J!3) = real_one) | (~int_leq(J!3, J!3)))) <=> ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~int_leq(int_one, J!3)) | (a(J!3, J!3) = real_one) | (~int_leq(J!3, J!3)))),
% 163.43/163.69 inference(rewrite,[status(thm)],[])).
% 163.43/163.69 tff(84,plain,
% 163.43/163.69 (((a(J!3, J!3) = real_one) | (~int_leq(int_one, J!3)) | (~int_leq(J!3, J!3))) <=> ((~int_leq(int_one, J!3)) | (a(J!3, J!3) = real_one) | (~int_leq(J!3, J!3)))),
% 163.43/163.69 inference(rewrite,[status(thm)],[])).
% 163.43/163.69 tff(85,plain,
% 163.43/163.69 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | ((a(J!3, J!3) = real_one) | (~int_leq(int_one, J!3)) | (~int_leq(J!3, J!3)))) <=> ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | ((~int_leq(int_one, J!3)) | (a(J!3, J!3) = real_one) | (~int_leq(J!3, J!3))))),
% 163.43/163.69 inference(monotonicity,[status(thm)],[84])).
% 163.43/163.69 tff(86,plain,
% 163.43/163.69 (((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | ((a(J!3, J!3) = real_one) | (~int_leq(int_one, J!3)) | (~int_leq(J!3, J!3)))) <=> ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~int_leq(int_one, J!3)) | (a(J!3, J!3) = real_one) | (~int_leq(J!3, J!3)))),
% 163.43/163.69 inference(transitivity,[status(thm)],[85, 83])).
% 163.43/163.69 tff(87,plain,
% 163.43/163.69 ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | ((a(J!3, J!3) = real_one) | (~int_leq(int_one, J!3)) | (~int_leq(J!3, J!3)))),
% 163.43/163.69 inference(quant_inst,[status(thm)],[])).
% 163.43/163.69 tff(88,plain,
% 163.43/163.69 ((~![K: $i] : ((a(K, K) = real_one) | (~int_leq(int_one, K)) | (~int_leq(K, J!3)))) | (~int_leq(int_one, J!3)) | (a(J!3, J!3) = real_one) | (~int_leq(J!3, J!3))),
% 163.43/163.69 inference(modus_ponens,[status(thm)],[87, 86])).
% 163.43/163.69 tff(89,plain,
% 163.43/163.69 (a(J!3, J!3) = real_one),
% 163.43/163.69 inference(unit_resolution,[status(thm)],[88, 37, 82, 67])).
% 163.43/163.69 tff(90,plain,
% 163.43/163.69 (((~int_leq(J!3, n)) | (~(a(J!3, J!3) = real_zero)) | (~int_leq(int_one, J!3))) | (a(J!3, J!3) = real_zero)),
% 163.43/163.69 inference(tautology,[status(thm)],[])).
% 163.43/163.69 tff(91,plain,
% 163.43/163.69 (a(J!3, J!3) = real_zero),
% 163.43/163.69 inference(unit_resolution,[status(thm)],[90, 35])).
% 163.43/163.69 tff(92,plain,
% 163.43/163.69 (real_zero = a(J!3, J!3)),
% 163.43/163.69 inference(symmetry,[status(thm)],[91])).
% 163.43/163.69 tff(93,plain,
% 163.43/163.69 (real_zero = real_one),
% 163.43/163.69 inference(transitivity,[status(thm)],[92, 89])).
% 163.43/163.69 tff(94,plain,
% 163.43/163.69 ((~(real_zero = real_one)) <=> (~(real_zero = real_one))),
% 163.43/163.69 inference(rewrite,[status(thm)],[])).
% 163.43/163.69 tff(95,axiom,(~(real_zero = real_one)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','real_constants')).
% 163.43/163.69 tff(96,plain,
% 163.43/163.69 (~(real_zero = real_one)),
% 163.43/163.69 inference(modus_ponens,[status(thm)],[95, 94])).
% 163.43/163.69 tff(97,plain,
% 163.43/163.69 ($false),
% 163.43/163.69 inference(unit_resolution,[status(thm)],[96, 93])).
% 163.43/163.69 tff(98,plain,((~int_leq(J!3, n)) | (~(a(J!3, J!3) = real_zero)) | (~int_leq(int_one, J!3))), inference(lemma,lemma(discharge,[]))).
% 163.43/163.69 tff(99,plain,
% 163.43/163.69 (((~((~(int_leq(int_one, I!2) & int_less(I!2, J!1) & int_leq(J!1, n))) | (a(I!2, J!1) = real_zero))) | (~((~int_leq(J!3, n)) | (~(a(J!3, J!3) = real_zero)) | (~int_leq(int_one, J!3))))) <=> ((~((a(I!2, J!1) = real_zero) | (~int_leq(int_one, I!2)) | (~int_less(I!2, J!1)) | (~int_leq(J!1, n)))) | (~((~int_leq(J!3, n)) | (~(a(J!3, J!3) = real_zero)) | (~int_leq(int_one, J!3)))))),
% 163.43/163.69 inference(rewrite,[status(thm)],[])).
% 163.43/163.69 tff(100,plain,
% 163.43/163.69 ((~((~int_leq(J!3, n)) | (~(a(J!3, J!3) = real_zero)) | (~int_leq(int_one, J!3)))) <=> (~((~int_leq(J!3, n)) | (~(a(J!3, J!3) = real_zero)) | (~int_leq(int_one, J!3))))),
% 163.43/163.69 inference(rewrite,[status(thm)],[])).
% 163.43/163.69 tff(101,plain,
% 163.43/163.69 (((~((~(int_leq(int_one, I!2) & int_less(I!2, J!1) & int_leq(J!1, n))) | (a(I!2, J!1) = real_zero))) | (~((~int_leq(J!3, n)) | (~(a(J!3, J!3) = real_zero)) | (~int_leq(int_one, J!3))))) <=> ((~((~(int_leq(int_one, I!2) & int_less(I!2, J!1) & int_leq(J!1, n))) | (a(I!2, J!1) = real_zero))) | (~((~int_leq(J!3, n)) | (~(a(J!3, J!3) = real_zero)) | (~int_leq(int_one, J!3)))))),
% 163.43/163.69 inference(monotonicity,[status(thm)],[100])).
% 163.43/163.69 tff(102,plain,
% 163.43/163.69 ((![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)) & ![J: $i] : ((~int_leq(J, n)) | (~(a(J, J) = real_zero)) | (~int_leq(int_one, J)))) <=> (![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)) & ![J: $i] : ((~int_leq(J, n)) | (~(a(J, J) = real_zero)) | (~int_leq(int_one, J))))),
% 163.43/163.69 inference(rewrite,[status(thm)],[])).
% 163.43/163.69 tff(103,plain,
% 163.43/163.69 ((~(![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)) & ![J: $i] : ((~int_leq(J, n)) | (~(a(J, J) = real_zero)) | (~int_leq(int_one, J))))) <=> (~(![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)) & ![J: $i] : ((~int_leq(J, n)) | (~(a(J, J) = real_zero)) | (~int_leq(int_one, J)))))),
% 163.43/163.69 inference(monotonicity,[status(thm)],[102])).
% 163.43/163.69 tff(104,plain,
% 163.43/163.69 ((~(![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)) & ![J: $i] : ((~int_leq(J, n)) | (~(a(J, J) = real_zero)) | (~int_leq(int_one, J))))) <=> (~(![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)) & ![J: $i] : ((~int_leq(J, n)) | (~(a(J, J) = real_zero)) | (~int_leq(int_one, J)))))),
% 163.43/163.69 inference(rewrite,[status(thm)],[])).
% 163.43/163.69 tff(105,plain,
% 163.43/163.69 ((~(![I: $i, J: $i] : (((int_leq(int_one, I) & int_less(I, J)) & int_leq(J, n)) => (a(I, J) = real_zero)) & ![I: $i, J: $i] : (((int_leq(int_one, I) & int_leq(J, n)) & (I = J)) => (~(a(I, J) = real_zero))))) <=> (~(![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)) & ![J: $i] : ((~int_leq(J, n)) | (~(a(J, J) = real_zero)) | (~int_leq(int_one, J)))))),
% 163.43/163.69 inference(rewrite,[status(thm)],[])).
% 163.43/163.69 tff(106,axiom,(~(![I: $i, J: $i] : (((int_leq(int_one, I) & int_less(I, J)) & int_leq(J, n)) => (a(I, J) = real_zero)) & ![I: $i, J: $i] : (((int_leq(int_one, I) & int_leq(J, n)) & (I = J)) => (~(a(I, J) = real_zero))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lti')).
% 163.43/163.69 tff(107,plain,
% 163.43/163.69 (~(![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)) & ![J: $i] : ((~int_leq(J, n)) | (~(a(J, J) = real_zero)) | (~int_leq(int_one, J))))),
% 163.43/163.69 inference(modus_ponens,[status(thm)],[106, 105])).
% 163.43/163.69 tff(108,plain,
% 163.43/163.69 (~(![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)) & ![J: $i] : ((~int_leq(J, n)) | (~(a(J, J) = real_zero)) | (~int_leq(int_one, J))))),
% 163.43/163.69 inference(modus_ponens,[status(thm)],[107, 103])).
% 163.43/163.69 tff(109,plain,
% 163.43/163.69 (~(![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)) & ![J: $i] : ((~int_leq(J, n)) | (~(a(J, J) = real_zero)) | (~int_leq(int_one, J))))),
% 163.43/163.69 inference(modus_ponens,[status(thm)],[108, 104])).
% 163.43/163.69 tff(110,plain,
% 163.43/163.69 (~(![I: $i, J: $i] : ((~(int_leq(int_one, I) & int_less(I, J) & int_leq(J, n))) | (a(I, J) = real_zero)) & ![J: $i] : ((~int_leq(J, n)) | (~(a(J, J) = real_zero)) | (~int_leq(int_one, J))))),
% 163.43/163.69 inference(modus_ponens,[status(thm)],[109, 103])).
% 163.43/163.69 unexpected number of arguments: (let ((a!1 (forall ((I $i) (J $i))
% 163.43/163.69 (or (not (and (int_leq int_one I) (int_less I J) (int_leq J n)))
% 163.43/163.69 (= (a I J) real_zero))))
% 163.43/163.69 (a!2 (or (not (and (int_leq int_one I!2)
% 163.43/163.69 (int_less I!2 J!1)
% 163.43/163.69 (int_leq J!1 n)))
% 163.43/163.69 (= (a I!2 J!1) real_zero)))
% 163.43/163.69 (a!3 (forall ((J $i))
% 163.43/163.69 (or (not (int_leq J n))
% 163.43/163.69 (not (= (a J J) real_zero))
% 163.43/163.69 (not (int_leq int_one J)))))
% 163.43/163.69 (a!4 (or (not (int_leq J!3 n))
% 163.43/163.69 (not (= (a J!3 J!3) real_zero))
% 163.43/163.69 (not (int_leq int_one J!3)))))
% 163.43/163.69 (nnf-neg (sk (~ (not a!1) (not a!2)))
% 163.43/163.69 (sk (~ (not a!3) (not a!4)))
% 163.43/163.69 (~ (not (and a!1 a!3)) (or (not a!2) (not a!4)))))
% 163.43/163.69 Proof display could not be completed: unexpected number of arguments
% 164.13/164.29 % E exiting
%------------------------------------------------------------------------------