%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV403+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:32:23 AM UTC 2025
% Result : Theorem 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV403+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 09:49:20 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(tptp_fun_Z_4_type, type, (
% 0.21/0.38 tptp_fun_Z_4: $i)).
% 0.21/0.38 tff(tptp_fun_X3_1_type, type, (
% 0.21/0.38 tptp_fun_X3_1: $i)).
% 0.21/0.38 tff(tptp_fun_Y_5_type, type, (
% 0.21/0.38 tptp_fun_Y_5: $i)).
% 0.21/0.38 tff(tptp_fun_X2_2_type, type, (
% 0.21/0.38 tptp_fun_X2_2: $i)).
% 0.21/0.38 tff(pair_in_list_type, type, (
% 0.21/0.38 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.21/0.38 tff(tptp_fun_X1_3_type, type, (
% 0.21/0.38 tptp_fun_X1_3: $i)).
% 0.21/0.38 tff(update_slb_type, type, (
% 0.21/0.38 update_slb: ( $i * $i ) > $i)).
% 0.21/0.38 tff(tptp_fun_U_0_type, type, (
% 0.21/0.38 tptp_fun_U_0: $i)).
% 0.21/0.38 tff(insert_slb_type, type, (
% 0.21/0.38 insert_slb: ( $i * $i ) > $i)).
% 0.21/0.38 tff(pair_type, type, (
% 0.21/0.38 pair: ( $i * $i ) > $i)).
% 0.21/0.38 tff(strictly_less_than_type, type, (
% 0.21/0.38 strictly_less_than: ( $i * $i ) > $o)).
% 0.21/0.38 tff(less_than_type, type, (
% 0.21/0.38 less_than: ( $i * $i ) > $o)).
% 0.21/0.38 tff(1,plain,
% 0.21/0.38 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : refl((pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y))) <=> (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : rewrite((pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y))) <=> (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.38 tff(5,plain,
% 0.21/0.38 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : rewrite((pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (pair_in_list(U, W, Y) | ((V = W) & (X = Y)))) <=> (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (pair_in_list(U, W, Y) | ((V = W) & (X = Y)))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.38 tff(8,axiom,(![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (pair_in_list(U, W, Y) | ((V = W) & (X = Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax23')).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.21/0.38 tff(11,plain,(
% 0.21/0.38 ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[10])).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> ((X2!2 = Y!5) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> ((X2!2 = Y!5) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 ((pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> ((~((~(X2!2 = Y!5)) | (~(X1!3 = X1!3)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))) <=> (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> ((X2!2 = Y!5) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(16,plain,
% 0.21/0.38 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> ((~((~(X2!2 = Y!5)) | (~(X1!3 = X1!3)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> ((X2!2 = Y!5) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[15])).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> ((~((~(X2!2 = Y!5)) | (~(X1!3 = X1!3)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> ((X2!2 = Y!5) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))))),
% 0.21/0.38 inference(transitivity,[status(thm)],[16, 14])).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> ((~((~(X2!2 = Y!5)) | (~(X1!3 = X1!3)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> ((X2!2 = Y!5) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> ((X2!2 = Y!5) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.21/0.38 tff(21,plain,
% 0.21/0.38 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, X1!3) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = X1!3)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, X1!3) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = X1!3)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[21, 13])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (^[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)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (![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))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(28,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')).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.39 tff(30,plain,(
% 0.21/0.39 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[29])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)) <=> strictly_less_than(X3!1, X1!3)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (~(((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)) <=> strictly_less_than(X3!1, X1!3))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.39 tff(35,assumption,(~strictly_less_than(X3!1, X1!3)), introduced(assumption)).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 ((((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)) <=> strictly_less_than(X3!1, X1!3)) | ((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)) | strictly_less_than(X3!1, X1!3)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 ((((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)) <=> strictly_less_than(X3!1, X1!3)) | ((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 ((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.21/0.39 tff(39,assumption,((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)), introduced(assumption)).
% 0.21/0.39 tff(40,assumption,(~less_than(X1!3, X3!1)), introduced(assumption)).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 ((~((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1))) | (~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (~less_than(X3!1, X1!3)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[41, 40, 39])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.39 tff(48,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.21/0.39 tff(51,plain,(
% 0.21/0.39 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(skolemize,[status(sab)],[50])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X1!3, X3!1) | less_than(X3!1, X1!3))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X1!3, X3!1) | less_than(X3!1, X1!3))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 ((less_than(X3!1, X1!3) | less_than(X1!3, X3!1)) <=> (less_than(X1!3, X3!1) | less_than(X3!1, X1!3))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X3!1, X1!3) | less_than(X1!3, X3!1))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X1!3, X3!1) | less_than(X3!1, X1!3)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[54])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X3!1, X1!3) | less_than(X1!3, X3!1))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X1!3, X3!1) | less_than(X3!1, X1!3))),
% 0.21/0.39 inference(transitivity,[status(thm)],[55, 53])).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X3!1, X1!3) | less_than(X1!3, X3!1))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(58,plain,
% 0.21/0.39 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X1!3, X3!1) | less_than(X3!1, X1!3)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.39 tff(59,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[58, 52, 40, 42])).
% 0.21/0.39 tff(60,plain,(less_than(X1!3, X3!1) | (~((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(61,plain,
% 0.21/0.39 (less_than(X1!3, X3!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[60, 38])).
% 0.21/0.39 tff(62,plain,
% 0.21/0.39 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))) <=> ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.39 tff(64,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(65,plain,
% 0.21/0.39 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((less_than(W, X) => (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))) <=> ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(66,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i, X: $i] : (less_than(W, X) => (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.39 tff(67,axiom,(![U: $i, V: $i, W: $i, X: $i] : (less_than(W, X) => (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax30')).
% 0.21/0.39 tff(68,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.39 tff(69,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.21/0.39 tff(70,plain,(
% 0.21/0.39 ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[69])).
% 0.21/0.39 tff(71,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.21/0.39 tff(72,plain,
% 0.21/0.39 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))) | ((~less_than(X1!3, X3!1)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))) | (~less_than(X1!3, X3!1)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(73,plain,
% 0.21/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))) | ((~less_than(X1!3, X3!1)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(74,plain,
% 0.21/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))) | (~less_than(X1!3, X3!1)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.39 tff(75,plain,
% 0.21/0.39 ((~less_than(X1!3, X3!1)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.21/0.39 tff(76,plain,
% 0.21/0.39 (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[75, 61])).
% 0.21/0.39 tff(77,plain,
% 0.21/0.39 (insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)) = update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3)),
% 0.21/0.39 inference(symmetry,[status(thm)],[76])).
% 0.21/0.39 tff(78,plain,
% 0.21/0.39 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, X1!3) <=> pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, X1!3)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[77])).
% 0.21/0.39 tff(79,plain,
% 0.21/0.39 (pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, X1!3) <=> pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, X1!3)),
% 0.21/0.39 inference(symmetry,[status(thm)],[78])).
% 0.21/0.39 tff(80,plain,
% 0.21/0.39 ((~pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, X1!3)) <=> (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, X1!3))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.39 tff(81,plain,
% 0.21/0.39 ((![V: $i, W: $i, X: $i] : ((~(pair_in_list(U!0, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U!0, X), V, X)) & (~((~(pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) & strictly_less_than(Z!4, X1!3))) | pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, X1!3)))) <=> (![V: $i, W: $i, X: $i] : ((~(pair_in_list(U!0, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U!0, X), V, X)) & (~((~(pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) & strictly_less_than(Z!4, X1!3))) | pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, X1!3))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(82,plain,
% 0.21/0.39 ((~![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))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & strictly_less_than(Z, X1))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, X1)))) <=> (~![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))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & strictly_less_than(Z, X1))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, X1))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(83,plain,
% 0.21/0.39 ((~![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)) => ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & strictly_less_than(Z, X1)) => pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, X1)))) <=> (~![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))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & strictly_less_than(Z, X1))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, X1))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(84,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)) => ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & strictly_less_than(Z, X1)) => pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l39_co')).
% 0.21/0.39 tff(85,plain,
% 0.21/0.39 (~![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))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & strictly_less_than(Z, X1))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, X1)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.39 tff(86,plain,
% 0.21/0.39 (~![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))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & strictly_less_than(Z, X1))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, X1)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (~![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))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & strictly_less_than(Z, X1))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, X1)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.21/0.40 tff(88,plain,
% 0.21/0.40 (~![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))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & strictly_less_than(Z, X1))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, X1)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[87, 82])).
% 0.21/0.40 tff(89,plain,
% 0.21/0.40 (![V: $i, W: $i, X: $i] : ((~(pair_in_list(U!0, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U!0, X), V, X)) & (~((~(pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) & strictly_less_than(Z!4, X1!3))) | pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, X1!3)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 (~((~(pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) & strictly_less_than(Z!4, X1!3))) | pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, X1!3))),
% 0.21/0.40 inference(and_elim,[status(thm)],[89])).
% 0.21/0.40 tff(91,plain,
% 0.21/0.40 (~pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, X1!3)),
% 0.21/0.40 inference(or_elim,[status(thm)],[90])).
% 0.21/0.40 tff(92,plain,
% 0.21/0.40 (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, X1!3)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[91, 80])).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 ((~(pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, X1!3) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = X1!3)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)))) | pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, X1!3) | (~((~((~(X2!2 = Y!5)) | (~(X3!1 = X1!3)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(94,plain,
% 0.21/0.40 (~((~((~(X2!2 = Y!5)) | (~(X3!1 = X1!3)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[93, 92, 22])).
% 0.21/0.40 tff(95,plain,
% 0.21/0.40 (((~((~(X2!2 = Y!5)) | (~(X3!1 = X1!3)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)) | (~pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (~pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.21/0.40 tff(97,assumption,(~pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)), introduced(assumption)).
% 0.21/0.40 tff(98,assumption,(pair_in_list(U!0, Y!5, Z!4)), introduced(assumption)).
% 0.21/0.40 tff(99,plain,
% 0.21/0.40 (pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) & strictly_less_than(Z!4, X1!3)),
% 0.21/0.40 inference(or_elim,[status(thm)],[90])).
% 0.21/0.40 tff(100,plain,
% 0.21/0.40 (strictly_less_than(Z!4, X1!3)),
% 0.21/0.40 inference(and_elim,[status(thm)],[99])).
% 0.21/0.40 tff(101,plain,
% 0.21/0.40 (^[V: $i, W: $i, X: $i] : refl((pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X))) <=> (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(102,plain,
% 0.21/0.40 (![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X))) <=> ![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[101])).
% 0.21/0.40 tff(103,plain,
% 0.21/0.40 (^[V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U!0, V, W) & strictly_less_than(W, X)) <=> (~((~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X))))), ((~(pair_in_list(U!0, V, W) & strictly_less_than(W, X))) <=> (~(~((~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X))))))), rewrite((~(~((~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X))))) <=> ((~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))), ((~(pair_in_list(U!0, V, W) & strictly_less_than(W, X))) <=> ((~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X))))), (((~(pair_in_list(U!0, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U!0, X), V, X)) <=> (((~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X))) | pair_in_list(update_slb(U!0, X), V, X)))), rewrite((((~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X))) | pair_in_list(update_slb(U!0, X), V, X)) <=> (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))), (((~(pair_in_list(U!0, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U!0, X), V, X)) <=> (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(104,plain,
% 0.21/0.40 (![V: $i, W: $i, X: $i] : ((~(pair_in_list(U!0, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U!0, X), V, X)) <=> ![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[103])).
% 0.21/0.40 tff(105,plain,
% 0.21/0.40 (![V: $i, W: $i, X: $i] : ((~(pair_in_list(U!0, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U!0, X), V, X))),
% 0.21/0.40 inference(and_elim,[status(thm)],[89])).
% 0.21/0.40 tff(106,plain,
% 0.21/0.40 (![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.40 tff(107,plain,
% 0.21/0.40 (![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.21/0.40 tff(108,plain,
% 0.21/0.40 (((~![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))) | ((~strictly_less_than(Z!4, X1!3)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))) <=> ((~![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))) | (~strictly_less_than(Z!4, X1!3)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(109,plain,
% 0.21/0.40 ((pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3) | (~pair_in_list(U!0, Y!5, Z!4)) | (~strictly_less_than(Z!4, X1!3))) <=> ((~strictly_less_than(Z!4, X1!3)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(110,plain,
% 0.21/0.40 (((~![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3) | (~pair_in_list(U!0, Y!5, Z!4)) | (~strictly_less_than(Z!4, X1!3)))) <=> ((~![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))) | ((~strictly_less_than(Z!4, X1!3)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.40 tff(111,plain,
% 0.21/0.40 (((~![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3) | (~pair_in_list(U!0, Y!5, Z!4)) | (~strictly_less_than(Z!4, X1!3)))) <=> ((~![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))) | (~strictly_less_than(Z!4, X1!3)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))),
% 0.21/0.40 inference(transitivity,[status(thm)],[110, 108])).
% 0.21/0.40 tff(112,plain,
% 0.21/0.40 ((~![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3) | (~pair_in_list(U!0, Y!5, Z!4)) | (~strictly_less_than(Z!4, X1!3)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(113,plain,
% 0.21/0.40 ((~![V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U!0, X), V, X) | (~pair_in_list(U!0, V, W)) | (~strictly_less_than(W, X)))) | (~strictly_less_than(Z!4, X1!3)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.40 tff(114,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[113, 107, 100, 98, 97])).
% 0.21/0.40 tff(115,plain,((~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(116,plain,
% 0.21/0.40 (~pair_in_list(U!0, Y!5, Z!4)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[115, 96])).
% 0.21/0.40 tff(117,plain,
% 0.21/0.40 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(118,plain,
% 0.21/0.40 (pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[117, 13])).
% 0.21/0.40 tff(119,plain,
% 0.21/0.40 (pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4)),
% 0.21/0.40 inference(and_elim,[status(thm)],[99])).
% 0.21/0.40 tff(120,plain,
% 0.21/0.40 ((~(pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)))) | (~pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4)) | ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(121,plain,
% 0.21/0.40 ((~(pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)))) | ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.21/0.40 tff(122,plain,
% 0.21/0.40 ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[121, 118])).
% 0.21/0.40 tff(123,plain,
% 0.21/0.40 ((~((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4))) | (~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(124,plain,
% 0.21/0.40 ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.21/0.40 tff(125,plain,
% 0.21/0.40 (~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[124, 116])).
% 0.21/0.40 tff(126,plain,
% 0.21/0.40 (((~(X2!2 = Y!5)) | (~(X3!1 = Z!4))) | (X3!1 = Z!4)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(127,plain,
% 0.21/0.40 (X3!1 = Z!4),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.21/0.40 tff(128,plain,
% 0.21/0.40 (Z!4 = X3!1),
% 0.21/0.40 inference(symmetry,[status(thm)],[127])).
% 0.21/0.40 tff(129,plain,
% 0.21/0.40 (strictly_less_than(Z!4, X1!3) <=> strictly_less_than(X3!1, X1!3)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[128])).
% 0.21/0.40 tff(130,plain,
% 0.21/0.40 (strictly_less_than(X3!1, X1!3) <=> strictly_less_than(Z!4, X1!3)),
% 0.21/0.40 inference(symmetry,[status(thm)],[129])).
% 0.21/0.40 tff(131,plain,
% 0.21/0.40 ((~strictly_less_than(X3!1, X1!3)) <=> (~strictly_less_than(Z!4, X1!3))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[130])).
% 0.21/0.40 tff(132,plain,
% 0.21/0.40 (~strictly_less_than(Z!4, X1!3)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[35, 131])).
% 0.21/0.40 tff(133,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[100, 132])).
% 0.21/0.40 tff(134,plain,(strictly_less_than(X3!1, X1!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(135,plain,
% 0.21/0.40 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))) <=> ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(136,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[135])).
% 0.21/0.41 tff(137,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(138,plain,
% 0.21/0.41 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((strictly_less_than(X, W) => (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))) <=> ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(139,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : (strictly_less_than(X, W) => (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[138])).
% 0.21/0.41 tff(140,axiom,(![U: $i, V: $i, W: $i, X: $i] : (strictly_less_than(X, W) => (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax29')).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.21/0.41 tff(142,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.21/0.41 tff(143,plain,(
% 0.21/0.41 ![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[142])).
% 0.21/0.41 tff(144,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.21/0.41 tff(145,plain,
% 0.21/0.41 (((~![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))) | ((~strictly_less_than(X3!1, X1!3)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))) | (~strictly_less_than(X3!1, X1!3)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(146,plain,
% 0.21/0.41 ((~![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))) | ((~strictly_less_than(X3!1, X1!3)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(147,plain,
% 0.21/0.41 ((~![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))) | (~strictly_less_than(X3!1, X1!3)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.21/0.41 tff(148,plain,
% 0.21/0.41 ((~strictly_less_than(X3!1, X1!3)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[147, 144])).
% 0.21/0.41 tff(149,plain,
% 0.21/0.41 (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[148, 134])).
% 0.21/0.41 tff(150,plain,
% 0.21/0.41 (insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)) = update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3)),
% 0.21/0.41 inference(symmetry,[status(thm)],[149])).
% 0.21/0.41 tff(151,plain,
% 0.21/0.41 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, X1!3)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[150])).
% 0.21/0.41 tff(152,plain,
% 0.21/0.41 (pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, X1!3) <=> pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3)),
% 0.21/0.41 inference(symmetry,[status(thm)],[151])).
% 0.21/0.41 tff(153,plain,
% 0.21/0.41 ((~pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, X1!3)) <=> (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[152])).
% 0.21/0.41 tff(154,plain,
% 0.21/0.41 (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[91, 153])).
% 0.21/0.41 tff(155,plain,
% 0.21/0.41 ((~(pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) <=> ((X2!2 = Y!5) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)))) | pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, X1!3) | (~((X2!2 = Y!5) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(156,plain,
% 0.21/0.41 (~((X2!2 = Y!5) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[155, 154, 20])).
% 0.21/0.41 tff(157,plain,
% 0.21/0.41 (((X2!2 = Y!5) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)) | (~(X2!2 = Y!5))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(158,plain,
% 0.21/0.41 (~(X2!2 = Y!5)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.21/0.41 tff(159,plain,
% 0.21/0.41 (((~(X2!2 = Y!5)) | (~(X3!1 = Z!4))) | (X2!2 = Y!5)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(160,plain,
% 0.21/0.41 ((~(X2!2 = Y!5)) | (~(X3!1 = Z!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.21/0.41 tff(161,plain,
% 0.21/0.41 (((X2!2 = Y!5) | pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)) | (~pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(162,plain,
% 0.21/0.41 (~pair_in_list(update_slb(U!0, X1!3), Y!5, X1!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[161, 156])).
% 0.21/0.41 tff(163,plain,
% 0.21/0.41 (~pair_in_list(U!0, Y!5, Z!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[115, 162])).
% 0.21/0.41 tff(164,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[124, 163, 160])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------