%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV399+1 : TPTP v9.0.0. Released v3.3.0.
% 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 05:32:22 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV399+1 : TPTP v9.0.0. Released v3.3.0.
% 0.10/0.11 % 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 09:45:24 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(less_than_type, type, (
% 0.11/0.37 less_than: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_V_2_type, type, (
% 0.11/0.37 tptp_fun_V_2: $i)).
% 0.11/0.37 tff(tptp_fun_X_3_type, type, (
% 0.11/0.37 tptp_fun_X_3: $i)).
% 0.11/0.37 tff(strictly_less_than_type, type, (
% 0.11/0.37 strictly_less_than: ( $i * $i ) > $o)).
% 0.11/0.37 tff(pair_in_list_type, type, (
% 0.11/0.37 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(update_slb_type, type, (
% 0.11/0.37 update_slb: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_U_0_type, type, (
% 0.11/0.37 tptp_fun_U_0: $i)).
% 0.11/0.37 tff(tptp_fun_W_1_type, type, (
% 0.11/0.37 tptp_fun_W_1: $i)).
% 0.11/0.37 tff(1,assumption,(~pair_in_list(update_slb(U!0, X!3), V!2, X!3)), introduced(assumption)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (^[U: $i, V: $i] : refl((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (^[U: $i, V: $i] : trans(trans(monotonicity(rewrite((less_than(U, V) & (~less_than(V, U))) <=> (~((~less_than(U, V)) | less_than(V, U)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))), rewrite((strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))), rewrite((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(7,axiom,(![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','stricly_smaller_definition')).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.11/0.37 tff(9,plain,(
% 0.11/0.37 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[8])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(W!1, X!3)) | less_than(X!3, W!1)) <=> strictly_less_than(W!1, X!3)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (~(((~less_than(W!1, X!3)) | less_than(X!3, W!1)) <=> strictly_less_than(W!1, X!3))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (^[Y: $i, Z: $i] : refl(((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z))) <=> ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z))) <=> ![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (^[Y: $i, Z: $i] : trans(monotonicity(rewrite((pair_in_list(update_slb(U!0, X!3), Y, Z) & strictly_less_than(Y, Z)) <=> (~((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z))))), ((~(pair_in_list(update_slb(U!0, X!3), Y, Z) & strictly_less_than(Y, Z))) <=> (~(~((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z))))))), rewrite((~(~((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z))))) <=> ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))), ((~(pair_in_list(update_slb(U!0, X!3), Y, Z) & strictly_less_than(Y, Z))) <=> ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![Y: $i, Z: $i] : (~(pair_in_list(update_slb(U!0, X!3), Y, Z) & strictly_less_than(Y, Z))) <=> ![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (((pair_in_list(U!0, V!2, W!1) & strictly_less_than(V!2, W!1)) & ![Y: $i, Z: $i] : (~(pair_in_list(update_slb(U!0, X!3), Y, Z) & strictly_less_than(Y, Z)))) <=> (pair_in_list(U!0, V!2, W!1) & strictly_less_than(V!2, W!1) & ![Y: $i, Z: $i] : (~(pair_in_list(update_slb(U!0, X!3), Y, Z) & strictly_less_than(Y, Z))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 ((~![U: $i] : ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z)))) <=> (~![U: $i] : ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((~![U: $i] : (?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W)) => ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z)))) <=> (~![U: $i] : ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(21,axiom,(~![U: $i] : (?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W)) => ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l35_co')).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (~![U: $i] : ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (~![U: $i] : ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (~![U: $i] : ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (~![U: $i] : ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (pair_in_list(U!0, V!2, W!1) & strictly_less_than(V!2, W!1) & ![Y: $i, Z: $i] : (~(pair_in_list(update_slb(U!0, X!3), Y, Z) & strictly_less_than(Y, Z)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (![Y: $i, Z: $i] : (~(pair_in_list(update_slb(U!0, X!3), Y, Z) & strictly_less_than(Y, Z)))),
% 0.11/0.37 inference(and_elim,[status(thm)],[26])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[28, 15])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (strictly_less_than(V!2, W!1)),
% 0.11/0.37 inference(and_elim,[status(thm)],[26])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (((~![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))) | ((~strictly_less_than(V!2, W!1)) | (~pair_in_list(update_slb(U!0, X!3), V!2, W!1)))) <=> ((~![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))) | (~strictly_less_than(V!2, W!1)) | (~pair_in_list(update_slb(U!0, X!3), V!2, W!1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 ((~![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))) | ((~strictly_less_than(V!2, W!1)) | (~pair_in_list(update_slb(U!0, X!3), V!2, W!1)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 ((~![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))) | (~strictly_less_than(V!2, W!1)) | (~pair_in_list(update_slb(U!0, X!3), V!2, W!1))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (~pair_in_list(update_slb(U!0, X!3), V!2, W!1)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[33, 30, 29])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (pair_in_list(U!0, V!2, W!1)),
% 0.11/0.37 inference(and_elim,[status(thm)],[26])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W))) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[36])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U, V, W) & less_than(X, W)) <=> (~((~less_than(X, W)) | (~pair_in_list(U, V, W))))), ((~(pair_in_list(U, V, W) & less_than(X, W))) <=> (~(~((~less_than(X, W)) | (~pair_in_list(U, V, W))))))), rewrite((~(~((~less_than(X, W)) | (~pair_in_list(U, V, W))))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W)))), ((~(pair_in_list(U, V, W) & less_than(X, W))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W))))), (((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> (((~less_than(X, W)) | (~pair_in_list(U, V, W))) | pair_in_list(update_slb(U, X), V, W)))), rewrite((((~less_than(X, W)) | (~pair_in_list(U, V, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))), (((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[38])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((pair_in_list(U, V, W) & less_than(X, W)) => pair_in_list(update_slb(U, X), V, W)) <=> ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & less_than(X, W)) => pair_in_list(update_slb(U, X), V, W)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[41])).
% 0.11/0.37 tff(43,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & less_than(X, W)) => pair_in_list(update_slb(U, X), V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l35_li3637')).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.11/0.37 tff(46,plain,(
% 0.11/0.37 ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.11/0.37 inference(skolemize,[status(sab)],[45])).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | (pair_in_list(update_slb(U!0, X!3), V!2, W!1) | (~less_than(X!3, W!1)) | (~pair_in_list(U!0, V!2, W!1)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | pair_in_list(update_slb(U!0, X!3), V!2, W!1) | (~less_than(X!3, W!1)) | (~pair_in_list(U!0, V!2, W!1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 (((~less_than(X!3, W!1)) | pair_in_list(update_slb(U!0, X!3), V!2, W!1) | (~pair_in_list(U!0, V!2, W!1))) <=> (pair_in_list(update_slb(U!0, X!3), V!2, W!1) | (~less_than(X!3, W!1)) | (~pair_in_list(U!0, V!2, W!1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~less_than(X!3, W!1)) | pair_in_list(update_slb(U!0, X!3), V!2, W!1) | (~pair_in_list(U!0, V!2, W!1)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | (pair_in_list(update_slb(U!0, X!3), V!2, W!1) | (~less_than(X!3, W!1)) | (~pair_in_list(U!0, V!2, W!1))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[50])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~less_than(X!3, W!1)) | pair_in_list(update_slb(U!0, X!3), V!2, W!1) | (~pair_in_list(U!0, V!2, W!1)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | pair_in_list(update_slb(U!0, X!3), V!2, W!1) | (~less_than(X!3, W!1)) | (~pair_in_list(U!0, V!2, W!1)))),
% 0.11/0.37 inference(transitivity,[status(thm)],[51, 49])).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~less_than(X!3, W!1)) | pair_in_list(update_slb(U!0, X!3), V!2, W!1) | (~pair_in_list(U!0, V!2, W!1)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(54,plain,
% 0.11/0.37 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | pair_in_list(update_slb(U!0, X!3), V!2, W!1) | (~less_than(X!3, W!1)) | (~pair_in_list(U!0, V!2, W!1))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.11/0.37 tff(55,plain,
% 0.11/0.38 (~less_than(X!3, W!1)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[54, 48, 35, 34])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[56])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[59])).
% 0.11/0.38 tff(61,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.11/0.38 tff(64,plain,(
% 0.11/0.38 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.38 inference(skolemize,[status(sab)],[63])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(W!1, X!3) | less_than(X!3, W!1))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(W!1, X!3) | less_than(X!3, W!1))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(W!1, X!3) | less_than(X!3, W!1))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(W!1, X!3) | less_than(X!3, W!1)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (less_than(W!1, X!3)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[68, 65, 55])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 ((~((~less_than(W!1, X!3)) | less_than(X!3, W!1))) | (~less_than(W!1, X!3)) | less_than(X!3, W!1)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 ((~((~less_than(W!1, X!3)) | less_than(X!3, W!1))) | (~less_than(W!1, X!3))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[70, 55])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 (~((~less_than(W!1, X!3)) | less_than(X!3, W!1))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[71, 69])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 ((((~less_than(W!1, X!3)) | less_than(X!3, W!1)) <=> strictly_less_than(W!1, X!3)) | ((~less_than(W!1, X!3)) | less_than(X!3, W!1)) | strictly_less_than(W!1, X!3)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(74,plain,
% 0.11/0.38 (strictly_less_than(W!1, X!3)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[73, 72, 13])).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 (^[U: $i, V: $i, W: $i, X: $i] : refl((pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))) <=> (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[75])).
% 0.11/0.38 tff(77,plain,
% 0.11/0.38 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U, V, W) & strictly_less_than(W, X)) <=> (~((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))), ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) <=> (~(~((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))))), rewrite((~(~((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))) <=> ((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))), ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) <=> ((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))), (((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))), rewrite((((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))), (((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(78,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[77])).
% 0.11/0.38 tff(79,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(80,plain,
% 0.11/0.38 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(81,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[80])).
% 0.11/0.38 tff(82,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l35_li3839')).
% 0.11/0.38 tff(83,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.11/0.38 tff(84,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.11/0.38 tff(85,plain,(
% 0.11/0.38 ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.11/0.38 inference(skolemize,[status(sab)],[84])).
% 0.11/0.38 tff(86,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.11/0.38 tff(87,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.11/0.38 tff(88,plain,
% 0.11/0.38 (((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | ((~pair_in_list(U!0, V!2, W!1)) | (~strictly_less_than(W!1, X!3)) | pair_in_list(update_slb(U!0, X!3), V!2, X!3))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | (~pair_in_list(U!0, V!2, W!1)) | (~strictly_less_than(W!1, X!3)) | pair_in_list(update_slb(U!0, X!3), V!2, X!3))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(89,plain,
% 0.11/0.38 ((pair_in_list(update_slb(U!0, X!3), V!2, X!3) | (~pair_in_list(U!0, V!2, W!1)) | (~strictly_less_than(W!1, X!3))) <=> ((~pair_in_list(U!0, V!2, W!1)) | (~strictly_less_than(W!1, X!3)) | pair_in_list(update_slb(U!0, X!3), V!2, X!3))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(90,plain,
% 0.11/0.38 (((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!0, X!3), V!2, X!3) | (~pair_in_list(U!0, V!2, W!1)) | (~strictly_less_than(W!1, X!3)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | ((~pair_in_list(U!0, V!2, W!1)) | (~strictly_less_than(W!1, X!3)) | pair_in_list(update_slb(U!0, X!3), V!2, X!3)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[89])).
% 0.11/0.38 tff(91,plain,
% 0.11/0.38 (((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!0, X!3), V!2, X!3) | (~pair_in_list(U!0, V!2, W!1)) | (~strictly_less_than(W!1, X!3)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | (~pair_in_list(U!0, V!2, W!1)) | (~strictly_less_than(W!1, X!3)) | pair_in_list(update_slb(U!0, X!3), V!2, X!3))),
% 0.11/0.38 inference(transitivity,[status(thm)],[90, 88])).
% 0.11/0.38 tff(92,plain,
% 0.11/0.38 ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!0, X!3), V!2, X!3) | (~pair_in_list(U!0, V!2, W!1)) | (~strictly_less_than(W!1, X!3)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(93,plain,
% 0.11/0.38 ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | (~pair_in_list(U!0, V!2, W!1)) | (~strictly_less_than(W!1, X!3)) | pair_in_list(update_slb(U!0, X!3), V!2, X!3)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.11/0.38 tff(94,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[93, 87, 35, 74, 1])).
% 0.11/0.38 tff(95,plain,(pair_in_list(update_slb(U!0, X!3), V!2, X!3)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(96,plain,
% 0.11/0.38 (((~![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))) | ((~strictly_less_than(V!2, X!3)) | (~pair_in_list(update_slb(U!0, X!3), V!2, X!3)))) <=> ((~![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))) | (~strictly_less_than(V!2, X!3)) | (~pair_in_list(update_slb(U!0, X!3), V!2, X!3)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(97,plain,
% 0.11/0.38 ((~![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))) | ((~strictly_less_than(V!2, X!3)) | (~pair_in_list(update_slb(U!0, X!3), V!2, X!3)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(98,plain,
% 0.11/0.38 ((~![Y: $i, Z: $i] : ((~strictly_less_than(Y, Z)) | (~pair_in_list(update_slb(U!0, X!3), Y, Z)))) | (~strictly_less_than(V!2, X!3)) | (~pair_in_list(update_slb(U!0, X!3), V!2, X!3))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.11/0.38 tff(99,plain,
% 0.11/0.38 ((~strictly_less_than(V!2, X!3)) | (~pair_in_list(update_slb(U!0, X!3), V!2, X!3))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[98, 29])).
% 0.11/0.38 tff(100,plain,
% 0.11/0.38 (~strictly_less_than(V!2, X!3)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.11/0.38 tff(101,plain,
% 0.11/0.38 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(V!2, X!3)) | less_than(X!3, V!2)) <=> strictly_less_than(V!2, X!3)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(102,plain,
% 0.11/0.38 (~(((~less_than(V!2, X!3)) | less_than(X!3, V!2)) <=> strictly_less_than(V!2, X!3))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[101, 11])).
% 0.11/0.38 tff(103,plain,
% 0.11/0.38 ((((~less_than(V!2, X!3)) | less_than(X!3, V!2)) <=> strictly_less_than(V!2, X!3)) | ((~less_than(V!2, X!3)) | less_than(X!3, V!2)) | strictly_less_than(V!2, X!3)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(104,plain,
% 0.11/0.38 (((~less_than(V!2, X!3)) | less_than(X!3, V!2)) | strictly_less_than(V!2, X!3)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.11/0.38 tff(105,plain,
% 0.11/0.38 ((~less_than(V!2, X!3)) | less_than(X!3, V!2)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[104, 100])).
% 0.11/0.38 tff(106,plain,
% 0.11/0.38 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(V!2, W!1)) | less_than(W!1, V!2)) <=> strictly_less_than(V!2, W!1)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(107,plain,
% 0.11/0.38 (~(((~less_than(V!2, W!1)) | less_than(W!1, V!2)) <=> strictly_less_than(V!2, W!1))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[106, 11])).
% 0.11/0.38 tff(108,plain,
% 0.11/0.38 ((((~less_than(V!2, W!1)) | less_than(W!1, V!2)) <=> strictly_less_than(V!2, W!1)) | (~((~less_than(V!2, W!1)) | less_than(W!1, V!2))) | (~strictly_less_than(V!2, W!1))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(109,plain,
% 0.11/0.38 ((((~less_than(V!2, W!1)) | less_than(W!1, V!2)) <=> strictly_less_than(V!2, W!1)) | (~((~less_than(V!2, W!1)) | less_than(W!1, V!2)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[108, 30])).
% 0.11/0.38 tff(110,plain,
% 0.11/0.38 (~((~less_than(V!2, W!1)) | less_than(W!1, V!2))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[109, 107])).
% 0.11/0.38 tff(111,plain,
% 0.11/0.38 (((~less_than(V!2, W!1)) | less_than(W!1, V!2)) | less_than(V!2, W!1)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(112,plain,
% 0.11/0.38 (less_than(V!2, W!1)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.11/0.38 tff(113,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V))) <=> ![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(114,plain,
% 0.11/0.38 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite((less_than(U, V) & less_than(V, W)) <=> (~((~less_than(V, W)) | (~less_than(U, V))))), ((~(less_than(U, V) & less_than(V, W))) <=> (~(~((~less_than(V, W)) | (~less_than(U, V))))))), rewrite((~(~((~less_than(V, W)) | (~less_than(U, V))))) <=> ((~less_than(V, W)) | (~less_than(U, V)))), ((~(less_than(U, V) & less_than(V, W))) <=> ((~less_than(V, W)) | (~less_than(U, V))))), (((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)) <=> (((~less_than(V, W)) | (~less_than(U, V))) | less_than(U, W)))), rewrite((((~less_than(V, W)) | (~less_than(U, V))) | less_than(U, W)) <=> (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))), (((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)) <=> (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(115,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)) <=> ![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[114])).
% 0.11/0.38 tff(116,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)) <=> ![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(117,plain,
% 0.11/0.38 (^[U: $i, V: $i, W: $i] : rewrite(((less_than(U, V) & less_than(V, W)) => less_than(U, W)) <=> ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(118,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i] : ((less_than(U, V) & less_than(V, W)) => less_than(U, W)) <=> ![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[117])).
% 0.11/0.38 tff(119,axiom,(![U: $i, V: $i, W: $i] : ((less_than(U, V) & less_than(V, W)) => less_than(U, W))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','transitivity')).
% 0.11/0.38 tff(120,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.11/0.38 tff(121,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.11/0.38 tff(122,plain,(
% 0.11/0.38 ![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.11/0.38 inference(skolemize,[status(sab)],[121])).
% 0.11/0.38 tff(123,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.11/0.39 tff(124,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[123, 113])).
% 0.11/0.39 tff(125,plain,
% 0.11/0.39 (((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | ((~less_than(V!2, W!1)) | (~less_than(W!1, X!3)) | less_than(V!2, X!3))) <=> ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (~less_than(V!2, W!1)) | (~less_than(W!1, X!3)) | less_than(V!2, X!3))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(126,plain,
% 0.11/0.39 ((less_than(V!2, X!3) | (~less_than(W!1, X!3)) | (~less_than(V!2, W!1))) <=> ((~less_than(V!2, W!1)) | (~less_than(W!1, X!3)) | less_than(V!2, X!3))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(127,plain,
% 0.11/0.39 (((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(V!2, X!3) | (~less_than(W!1, X!3)) | (~less_than(V!2, W!1)))) <=> ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | ((~less_than(V!2, W!1)) | (~less_than(W!1, X!3)) | less_than(V!2, X!3)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[126])).
% 0.11/0.39 tff(128,plain,
% 0.11/0.39 (((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(V!2, X!3) | (~less_than(W!1, X!3)) | (~less_than(V!2, W!1)))) <=> ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (~less_than(V!2, W!1)) | (~less_than(W!1, X!3)) | less_than(V!2, X!3))),
% 0.11/0.39 inference(transitivity,[status(thm)],[127, 125])).
% 0.11/0.39 tff(129,plain,
% 0.11/0.39 ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(V!2, X!3) | (~less_than(W!1, X!3)) | (~less_than(V!2, W!1)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(130,plain,
% 0.11/0.39 ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (~less_than(V!2, W!1)) | (~less_than(W!1, X!3)) | less_than(V!2, X!3)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.11/0.39 tff(131,plain,
% 0.11/0.39 (less_than(V!2, X!3)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[130, 124, 112, 69])).
% 0.11/0.39 tff(132,plain,
% 0.11/0.39 ((~((~less_than(V!2, X!3)) | less_than(X!3, V!2))) | (~less_than(V!2, X!3)) | less_than(X!3, V!2)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(133,plain,
% 0.11/0.39 ((~((~less_than(V!2, X!3)) | less_than(X!3, V!2))) | less_than(X!3, V!2)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.11/0.39 tff(134,plain,
% 0.11/0.39 (less_than(X!3, V!2)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[133, 105])).
% 0.11/0.39 tff(135,plain,
% 0.11/0.39 (((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | ((~less_than(V!2, W!1)) | less_than(X!3, W!1) | (~less_than(X!3, V!2)))) <=> ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (~less_than(V!2, W!1)) | less_than(X!3, W!1) | (~less_than(X!3, V!2)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(136,plain,
% 0.11/0.39 ((less_than(X!3, W!1) | (~less_than(V!2, W!1)) | (~less_than(X!3, V!2))) <=> ((~less_than(V!2, W!1)) | less_than(X!3, W!1) | (~less_than(X!3, V!2)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(137,plain,
% 0.11/0.39 (((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(X!3, W!1) | (~less_than(V!2, W!1)) | (~less_than(X!3, V!2)))) <=> ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | ((~less_than(V!2, W!1)) | less_than(X!3, W!1) | (~less_than(X!3, V!2))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[136])).
% 0.11/0.39 tff(138,plain,
% 0.11/0.39 (((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(X!3, W!1) | (~less_than(V!2, W!1)) | (~less_than(X!3, V!2)))) <=> ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (~less_than(V!2, W!1)) | less_than(X!3, W!1) | (~less_than(X!3, V!2)))),
% 0.11/0.39 inference(transitivity,[status(thm)],[137, 135])).
% 0.11/0.39 tff(139,plain,
% 0.11/0.39 ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(X!3, W!1) | (~less_than(V!2, W!1)) | (~less_than(X!3, V!2)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(140,plain,
% 0.11/0.39 ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (~less_than(V!2, W!1)) | less_than(X!3, W!1) | (~less_than(X!3, V!2))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.11/0.39 tff(141,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[140, 124, 112, 55, 134])).
% 0.11/0.39 % SZS output end Proof
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------