%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV406+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.12s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV406+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:46:46 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(pair_in_list_type, type, (
% 0.12/0.40 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_X3_3_type, type, (
% 0.12/0.40 tptp_fun_X3_3: $i)).
% 0.12/0.40 tff(tptp_fun_X2_4_type, type, (
% 0.12/0.40 tptp_fun_X2_4: $i)).
% 0.12/0.40 tff(insert_slb_type, type, (
% 0.12/0.40 insert_slb: ( $i * $i ) > $i)).
% 0.12/0.40 tff(pair_type, type, (
% 0.12/0.40 pair: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_U_0_type, type, (
% 0.12/0.40 tptp_fun_U_0: $i)).
% 0.12/0.40 tff(less_than_type, type, (
% 0.12/0.40 less_than: ( $i * $i ) > $o)).
% 0.12/0.40 tff(check_cpq_type, type, (
% 0.12/0.40 check_cpq: $i > $o)).
% 0.12/0.40 tff(triple_type, type, (
% 0.12/0.40 triple: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_X1_5_type, type, (
% 0.12/0.40 tptp_fun_X1_5: $i)).
% 0.12/0.40 tff(tptp_fun_Z_6_type, type, (
% 0.12/0.40 tptp_fun_Z_6: $i)).
% 0.12/0.40 tff(tptp_fun_X_2_type, type, (
% 0.12/0.40 tptp_fun_X_2: $i)).
% 0.12/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.40 tptp_fun_Y_1: $i)).
% 0.12/0.40 tff(tptp_fun_X4_8_type, type, (
% 0.12/0.40 tptp_fun_X4_8: $i)).
% 0.12/0.40 tff(tptp_fun_X5_7_type, type, (
% 0.12/0.40 tptp_fun_X5_7: $i)).
% 0.12/0.40 tff(strictly_less_than_type, type, (
% 0.12/0.40 strictly_less_than: ( $i * $i ) > $o)).
% 0.12/0.40 tff(1,assumption,((~(check_cpq(triple(Z!6, U!0, X1!5)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) | (~((~check_cpq(triple(Z!6, U!0, X1!5))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))))), introduced(assumption)).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (^[V: $i, W: $i] : rewrite((~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))))) <=> (~((~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) | (~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (![V: $i, W: $i] : (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))))) <=> ![V: $i, W: $i] : (~((~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) | (~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (^[V: $i, W: $i] : refl((~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))))) <=> (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![V: $i, W: $i] : (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))))) <=> ![V: $i, W: $i] : (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (^[V: $i, W: $i] : rewrite((~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))))) <=> (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![V: $i, W: $i] : (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))))) <=> ![V: $i, W: $i] : (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (![V: $i, W: $i] : (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))))) <=> ![V: $i, W: $i] : (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[7, 5])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (^[V: $i, W: $i] : trans(monotonicity(rewrite(((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) <=> ((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))), ((((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) <=> (((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))))), rewrite((((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) <=> (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)))))))), ((((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) <=> (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![V: $i, W: $i] : (((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) <=> ![V: $i, W: $i] : (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 ((![V: $i, W: $i] : (((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) & ((check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) & ((~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))) | (~((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8)))))) <=> (![V: $i, W: $i] : (((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) & (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) & ((~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))) | (~((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 ((check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) <=> (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (((check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) & ((~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))) | (~((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8))))) <=> ((check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) & ((~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))) | (~((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[12])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 ((![V: $i, W: $i] : (((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) & ((check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) & ((~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))) | (~((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8)))))) <=> (![V: $i, W: $i] : (((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) & ((check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) & ((~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))) | (~((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8))))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[13])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 ((![V: $i, W: $i] : (((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) & ((check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) & ((~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))) | (~((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8)))))) <=> (![V: $i, W: $i] : (((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) & (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) & ((~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))) | (~((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8)))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[14, 11])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 ((~![U: $i] : ((~![V: $i, W: $i] : (check_cpq(triple(V, U, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(U, X, Y)) | less_than(Y, X)))) | ![Z: $i, X1: $i, X2: $i, X3: $i] : (check_cpq(triple(Z, insert_slb(U, pair(X2, X3)), X1)) <=> ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U, pair(X2, X3)), X4, X5)) | less_than(X5, X4))))) <=> (~![U: $i] : ((~![V: $i, W: $i] : (check_cpq(triple(V, U, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(U, X, Y)) | less_than(Y, X)))) | ![Z: $i, X1: $i, X2: $i, X3: $i] : (check_cpq(triple(Z, insert_slb(U, pair(X2, X3)), X1)) <=> ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U, pair(X2, X3)), X4, X5)) | less_than(X5, X4)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 ((~![U: $i] : (![V: $i, W: $i] : (check_cpq(triple(V, U, W)) <=> ![X: $i, Y: $i] : (pair_in_list(U, X, Y) => less_than(Y, X))) => ![Z: $i, X1: $i, X2: $i, X3: $i] : (check_cpq(triple(Z, insert_slb(U, pair(X2, X3)), X1)) <=> ![X4: $i, X5: $i] : (pair_in_list(insert_slb(U, pair(X2, X3)), X4, X5) => less_than(X5, X4))))) <=> (~![U: $i] : ((~![V: $i, W: $i] : (check_cpq(triple(V, U, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(U, X, Y)) | less_than(Y, X)))) | ![Z: $i, X1: $i, X2: $i, X3: $i] : (check_cpq(triple(Z, insert_slb(U, pair(X2, X3)), X1)) <=> ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U, pair(X2, X3)), X4, X5)) | less_than(X5, X4)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(18,axiom,(~![U: $i] : (![V: $i, W: $i] : (check_cpq(triple(V, U, W)) <=> ![X: $i, Y: $i] : (pair_in_list(U, X, Y) => less_than(Y, X))) => ![Z: $i, X1: $i, X2: $i, X3: $i] : (check_cpq(triple(Z, insert_slb(U, pair(X2, X3)), X1)) <=> ![X4: $i, X5: $i] : (pair_in_list(insert_slb(U, pair(X2, X3)), X4, X5) => less_than(X5, X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l42_co')).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (~![U: $i] : ((~![V: $i, W: $i] : (check_cpq(triple(V, U, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(U, X, Y)) | less_than(Y, X)))) | ![Z: $i, X1: $i, X2: $i, X3: $i] : (check_cpq(triple(Z, insert_slb(U, pair(X2, X3)), X1)) <=> ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U, pair(X2, X3)), X4, X5)) | less_than(X5, X4))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (~![U: $i] : ((~![V: $i, W: $i] : (check_cpq(triple(V, U, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(U, X, Y)) | less_than(Y, X)))) | ![Z: $i, X1: $i, X2: $i, X3: $i] : (check_cpq(triple(Z, insert_slb(U, pair(X2, X3)), X1)) <=> ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U, pair(X2, X3)), X4, X5)) | less_than(X5, X4))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (~![U: $i] : ((~![V: $i, W: $i] : (check_cpq(triple(V, U, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(U, X, Y)) | less_than(Y, X)))) | ![Z: $i, X1: $i, X2: $i, X3: $i] : (check_cpq(triple(Z, insert_slb(U, pair(X2, X3)), X1)) <=> ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U, pair(X2, X3)), X4, X5)) | less_than(X5, X4))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (~![U: $i] : ((~![V: $i, W: $i] : (check_cpq(triple(V, U, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(U, X, Y)) | less_than(Y, X)))) | ![Z: $i, X1: $i, X2: $i, X3: $i] : (check_cpq(triple(Z, insert_slb(U, pair(X2, X3)), X1)) <=> ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U, pair(X2, X3)), X4, X5)) | less_than(X5, X4))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (![V: $i, W: $i] : (((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) & (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) & ((~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))) | (~((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (![V: $i, W: $i] : (((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) & (check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)))))),
% 0.21/0.41 inference(and_elim,[status(thm)],[23])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (![V: $i, W: $i] : (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[24, 10])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (![V: $i, W: $i] : (~((~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[25, 8])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (![V: $i, W: $i] : (~((~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) | (~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 3])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 ((~![V: $i, W: $i] : (~((~(check_cpq(triple(V, U!0, W)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) | (~((~check_cpq(triple(V, U!0, W))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))))))) | (~((~(check_cpq(triple(Z!6, U!0, X1!5)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) | (~((~check_cpq(triple(Z!6, U!0, X1!5))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[28, 27, 1])).
% 0.21/0.41 tff(30,plain,(~((~(check_cpq(triple(Z!6, U!0, X1!5)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) | (~((~check_cpq(triple(Z!6, U!0, X1!5))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (((~(check_cpq(triple(Z!6, U!0, X1!5)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) | (~((~check_cpq(triple(Z!6, U!0, X1!5))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))))) | (check_cpq(triple(Z!6, U!0, X1!5)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (check_cpq(triple(Z!6, U!0, X1!5)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.41 tff(33,assumption,(~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))), introduced(assumption)).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)) | (~less_than(Y!1, X!2))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (~less_than(Y!1, X!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.21/0.41 tff(36,assumption,(~(pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X!2, Y!1) <=> ((~((~(X2!4 = X!2)) | (~(X3!3 = Y!1)))) | pair_in_list(U!0, X!2, Y!1)))), introduced(assumption)).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.41 tff(44,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')).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.41 tff(47,plain,(
% 0.21/0.41 ![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)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[46])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X!2, Y!1) <=> ((~((~(X2!4 = X!2)) | (~(X3!3 = Y!1)))) | pair_in_list(U!0, X!2, Y!1)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[50, 49, 36])).
% 0.21/0.41 tff(52,plain,(pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X!2, Y!1) <=> ((~((~(X2!4 = X!2)) | (~(X3!3 = Y!1)))) | pair_in_list(U!0, X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)) | pair_in_list(U!0, X!2, Y!1)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (pair_in_list(U!0, X!2, Y!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[53, 33])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (((~((~(X2!4 = X!2)) | (~(X3!3 = Y!1)))) | pair_in_list(U!0, X!2, Y!1)) | (~pair_in_list(U!0, X!2, Y!1))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 ((~((~(X2!4 = X!2)) | (~(X3!3 = Y!1)))) | pair_in_list(U!0, X!2, Y!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 ((~(pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X!2, Y!1) <=> ((~((~(X2!4 = X!2)) | (~(X3!3 = Y!1)))) | pair_in_list(U!0, X!2, Y!1)))) | pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X!2, Y!1) | (~((~((~(X2!4 = X!2)) | (~(X3!3 = Y!1)))) | pair_in_list(U!0, X!2, Y!1)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X!2, Y!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[57, 56, 52])).
% 0.21/0.41 tff(59,assumption,(~((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8))), introduced(assumption)).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8)) | (~less_than(X5!7, X4!8))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (~less_than(X5!7, X4!8)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8)) | pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 (pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 ((~![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!4, X3!3)), X4!8, X5!7) <=> ((~((~(X2!4 = X4!8)) | (~(X3!3 = X5!7)))) | pair_in_list(U!0, X4!8, X5!7)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(65,plain,
% 0.21/0.42 (pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7) <=> ((~((~(X2!4 = X4!8)) | (~(X3!3 = X5!7)))) | pair_in_list(U!0, X4!8, X5!7))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[64, 49])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 ((~(pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7) <=> ((~((~(X2!4 = X4!8)) | (~(X3!3 = X5!7)))) | pair_in_list(U!0, X4!8, X5!7)))) | (~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | ((~((~(X2!4 = X4!8)) | (~(X3!3 = X5!7)))) | pair_in_list(U!0, X4!8, X5!7))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 ((~(pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7) <=> ((~((~(X2!4 = X4!8)) | (~(X3!3 = X5!7)))) | pair_in_list(U!0, X4!8, X5!7)))) | ((~((~(X2!4 = X4!8)) | (~(X3!3 = X5!7)))) | pair_in_list(U!0, X4!8, X5!7))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[66, 63])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 ((~((~(X2!4 = X4!8)) | (~(X3!3 = X5!7)))) | pair_in_list(U!0, X4!8, X5!7)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[67, 65])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (~((~(check_cpq(triple(Z!6, U!0, X1!5)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) | (~((~check_cpq(triple(Z!6, U!0, X1!5))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 (((~(check_cpq(triple(Z!6, U!0, X1!5)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) | (~((~check_cpq(triple(Z!6, U!0, X1!5))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))))) | ((~check_cpq(triple(Z!6, U!0, X1!5))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 ((~check_cpq(triple(Z!6, U!0, X1!5))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (^[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)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(77,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')).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.42 tff(79,plain,(
% 0.21/0.42 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[78])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(X2!4, X3!3)) | less_than(X3!3, X2!4)) <=> strictly_less_than(X2!4, X3!3)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (~(((~less_than(X2!4, X3!3)) | less_than(X3!3, X2!4)) <=> strictly_less_than(X2!4, X3!3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.42 tff(84,assumption,(check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))), introduced(assumption)).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : refl(((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)))) <=> ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : trans(monotonicity(rewrite((check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> $false) <=> (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)))), ((strictly_less_than(X, Y) => (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> $false)) <=> (strictly_less_than(X, Y) => (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)))))), rewrite((strictly_less_than(X, Y) => (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)))) <=> ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))), ((strictly_less_than(X, Y) => (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> $false)) <=> ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (strictly_less_than(X, Y) => (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> $false)) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.42 tff(90,axiom,(![U: $i, V: $i, W: $i, X: $i, Y: $i] : (strictly_less_than(X, Y) => (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> $false))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax38')).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.21/0.42 tff(93,plain,(
% 0.21/0.42 ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[92])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))) | ((~strictly_less_than(X2!4, X3!3)) | (~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))) | (~strictly_less_than(X2!4, X3!3)) | (~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))) | ((~strictly_less_than(X2!4, X3!3)) | (~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | (~check_cpq(triple(U, insert_slb(V, pair(X, Y)), W))))) | (~strictly_less_than(X2!4, X3!3)) | (~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (~strictly_less_than(X2!4, X3!3)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[97, 94, 84])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((((~less_than(X2!4, X3!3)) | less_than(X3!3, X2!4)) <=> strictly_less_than(X2!4, X3!3)) | ((~less_than(X2!4, X3!3)) | less_than(X3!3, X2!4)) | strictly_less_than(X2!4, X3!3)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 ((((~less_than(X2!4, X3!3)) | less_than(X3!3, X2!4)) <=> strictly_less_than(X2!4, X3!3)) | ((~less_than(X2!4, X3!3)) | less_than(X3!3, X2!4))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 ((~less_than(X2!4, X3!3)) | less_than(X3!3, X2!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[100, 83])).
% 0.21/0.42 tff(102,assumption,((~less_than(X2!4, X3!3)) | less_than(X3!3, X2!4)), introduced(assumption)).
% 0.21/0.42 tff(103,assumption,(~less_than(X3!3, X2!4)), introduced(assumption)).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 ((~((~less_than(X2!4, X3!3)) | less_than(X3!3, X2!4))) | (~less_than(X2!4, X3!3)) | less_than(X3!3, X2!4)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (~less_than(X2!4, X3!3)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[104, 103, 102])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.42 tff(111,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.21/0.42 tff(114,plain,(
% 0.21/0.42 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(skolemize,[status(sab)],[113])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X2!4, X3!3) | less_than(X3!3, X2!4))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X2!4, X3!3) | less_than(X3!3, X2!4))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X2!4, X3!3) | less_than(X3!3, X2!4))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X2!4, X3!3) | less_than(X3!3, X2!4)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[118, 115, 103, 105])).
% 0.21/0.42 tff(120,plain,(less_than(X3!3, X2!4) | (~((~less_than(X2!4, X3!3)) | less_than(X3!3, X2!4)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (less_than(X3!3, X2!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[120, 101])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : refl(((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W)))) <=> ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W)))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W)))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : rewrite((less_than(Y, X) => (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W)))) <=> ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (less_than(Y, X) => (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W)))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.42 tff(127,axiom,(![U: $i, V: $i, W: $i, X: $i, Y: $i] : (less_than(Y, X) => (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax37')).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.21/0.42 tff(130,plain,(
% 0.21/0.42 ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[129])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W))))) | ((~less_than(X3!3, X2!4)) | (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) <=> check_cpq(triple(Z!6, U!0, X1!5))))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W))))) | (~less_than(X3!3, X2!4)) | (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) <=> check_cpq(triple(Z!6, U!0, X1!5))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(133,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W))))) | ((~less_than(X3!3, X2!4)) | (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) <=> check_cpq(triple(Z!6, U!0, X1!5))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~less_than(Y, X)) | (check_cpq(triple(U, insert_slb(V, pair(X, Y)), W)) <=> check_cpq(triple(U, V, W))))) | (~less_than(X3!3, X2!4)) | (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) <=> check_cpq(triple(Z!6, U!0, X1!5)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 ((~less_than(X3!3, X2!4)) | (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) <=> check_cpq(triple(Z!6, U!0, X1!5)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[134, 131])).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) <=> check_cpq(triple(Z!6, U!0, X1!5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[135, 121])).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 ((~(check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) <=> check_cpq(triple(Z!6, U!0, X1!5)))) | (~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))) | check_cpq(triple(Z!6, U!0, X1!5))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 ((~(check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) <=> check_cpq(triple(Z!6, U!0, X1!5)))) | check_cpq(triple(Z!6, U!0, X1!5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[137, 84])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 (check_cpq(triple(Z!6, U!0, X1!5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[138, 136])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 ((~((~check_cpq(triple(Z!6, U!0, X1!5))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(Z!6, U!0, X1!5))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(141,plain,
% 0.21/0.43 ((~((~check_cpq(triple(Z!6, U!0, X1!5))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X)))) | ![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[141, 71])).
% 0.21/0.43 tff(143,assumption,((~((~(X2!4 = X4!8)) | (~(X3!3 = X5!7)))) | pair_in_list(U!0, X4!8, X5!7)), introduced(assumption)).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(X4!8, X5!7)) | less_than(X5!7, X4!8)) <=> strictly_less_than(X4!8, X5!7)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 (~(((~less_than(X4!8, X5!7)) | less_than(X5!7, X4!8)) <=> strictly_less_than(X4!8, X5!7))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[144, 81])).
% 0.21/0.43 tff(146,assumption,(~less_than(X5!7, X4!8)), introduced(assumption)).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X4!8, X5!7) | less_than(X5!7, X4!8))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X4!8, X5!7) | less_than(X5!7, X4!8))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X4!8, X5!7) | less_than(X5!7, X4!8))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X4!8, X5!7) | less_than(X5!7, X4!8)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.43 tff(150,plain,
% 0.21/0.43 (less_than(X4!8, X5!7)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[149, 115, 146])).
% 0.21/0.43 tff(151,plain,
% 0.21/0.43 ((~((~less_than(X4!8, X5!7)) | less_than(X5!7, X4!8))) | (~less_than(X4!8, X5!7)) | less_than(X5!7, X4!8)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(152,plain,
% 0.21/0.43 ((~((~less_than(X4!8, X5!7)) | less_than(X5!7, X4!8))) | (~less_than(X4!8, X5!7))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[151, 146])).
% 0.21/0.43 tff(153,plain,
% 0.21/0.43 (~((~less_than(X4!8, X5!7)) | less_than(X5!7, X4!8))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[152, 150])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 ((((~less_than(X4!8, X5!7)) | less_than(X5!7, X4!8)) <=> strictly_less_than(X4!8, X5!7)) | ((~less_than(X4!8, X5!7)) | less_than(X5!7, X4!8)) | strictly_less_than(X4!8, X5!7)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 (strictly_less_than(X4!8, X5!7)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[154, 153, 145])).
% 0.21/0.43 tff(156,assumption,(~((~(X2!4 = X4!8)) | (~(X3!3 = X5!7)))), introduced(assumption)).
% 0.21/0.43 tff(157,plain,
% 0.21/0.43 (((~(X2!4 = X4!8)) | (~(X3!3 = X5!7))) | (X3!3 = X5!7)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(158,plain,
% 0.21/0.43 (X3!3 = X5!7),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 (((~(X2!4 = X4!8)) | (~(X3!3 = X5!7))) | (X2!4 = X4!8)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(160,plain,
% 0.21/0.43 (X2!4 = X4!8),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[159, 156])).
% 0.21/0.43 tff(161,plain,
% 0.21/0.43 (strictly_less_than(X2!4, X3!3) <=> strictly_less_than(X4!8, X5!7)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[160, 158])).
% 0.21/0.43 tff(162,plain,
% 0.21/0.43 (strictly_less_than(X4!8, X5!7) <=> strictly_less_than(X2!4, X3!3)),
% 0.21/0.43 inference(symmetry,[status(thm)],[161])).
% 0.21/0.43 tff(163,assumption,(strictly_less_than(X4!8, X5!7)), introduced(assumption)).
% 0.21/0.43 tff(164,plain,
% 0.21/0.43 (strictly_less_than(X2!4, X3!3)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.21/0.43 tff(165,assumption,(~strictly_less_than(X2!4, X3!3)), introduced(assumption)).
% 0.21/0.43 tff(166,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.21/0.43 tff(167,plain,(((~(X2!4 = X4!8)) | (~(X3!3 = X5!7))) | strictly_less_than(X2!4, X3!3) | (~strictly_less_than(X4!8, X5!7))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(168,plain,
% 0.21/0.43 ((~(X2!4 = X4!8)) | (~(X3!3 = X5!7))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[167, 98, 155])).
% 0.21/0.43 tff(169,plain,
% 0.21/0.43 ((~((~((~(X2!4 = X4!8)) | (~(X3!3 = X5!7)))) | pair_in_list(U!0, X4!8, X5!7))) | (~((~(X2!4 = X4!8)) | (~(X3!3 = X5!7)))) | pair_in_list(U!0, X4!8, X5!7)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(170,plain,
% 0.21/0.43 (pair_in_list(U!0, X4!8, X5!7)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[169, 168, 143])).
% 0.21/0.43 tff(171,plain,
% 0.21/0.43 (((~![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) | ((~pair_in_list(U!0, X4!8, X5!7)) | less_than(X5!7, X4!8))) <=> ((~![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) | (~pair_in_list(U!0, X4!8, X5!7)) | less_than(X5!7, X4!8))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(172,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) | ((~pair_in_list(U!0, X4!8, X5!7)) | less_than(X5!7, X4!8))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(173,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~pair_in_list(U!0, X, Y)) | less_than(Y, X))) | (~pair_in_list(U!0, X4!8, X5!7)) | less_than(X5!7, X4!8)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.21/0.43 tff(174,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[173, 146, 170, 142])).
% 0.21/0.43 tff(175,plain,((~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))) | less_than(X5!7, X4!8) | (~((~((~(X2!4 = X4!8)) | (~(X3!3 = X5!7)))) | pair_in_list(U!0, X4!8, X5!7)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(176,plain,
% 0.21/0.43 (~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[175, 61, 68])).
% 0.21/0.43 tff(177,plain,
% 0.21/0.43 ((check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) <=> (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(178,plain,
% 0.21/0.43 (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))),
% 0.21/0.43 inference(and_elim,[status(thm)],[23])).
% 0.21/0.43 tff(179,plain,
% 0.21/0.43 (check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | ![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.43 tff(180,plain,
% 0.21/0.43 (![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[179, 176])).
% 0.21/0.43 tff(181,plain,
% 0.21/0.43 (((~![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) | ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8))) <=> ((~![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) | (~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(182,plain,
% 0.21/0.43 ((~![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) | ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(183,plain,
% 0.21/0.43 ((~![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) | (~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.21/0.43 tff(184,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[183, 180, 63, 61])).
% 0.21/0.43 tff(185,plain,((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(186,plain,
% 0.21/0.43 ((~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))) | (~((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4!8, X5!7)) | less_than(X5!7, X4!8)))),
% 0.21/0.43 inference(and_elim,[status(thm)],[23])).
% 0.21/0.43 tff(187,plain,
% 0.21/0.43 (~check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.21/0.43 tff(188,plain,
% 0.21/0.43 (![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[179, 187])).
% 0.21/0.43 tff(189,plain,
% 0.21/0.43 (((~![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) | ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X!2, Y!1)) | less_than(Y!1, X!2))) <=> ((~![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) | (~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X!2, Y!1)) | less_than(Y!1, X!2))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(190,plain,
% 0.21/0.43 ((~![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) | ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X!2, Y!1)) | less_than(Y!1, X!2))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(191,plain,
% 0.21/0.43 ((~![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) | (~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X!2, Y!1)) | less_than(Y!1, X!2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.21/0.43 tff(192,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[191, 188, 58, 35])).
% 0.21/0.43 tff(193,plain,((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(194,plain,
% 0.21/0.44 ((~(check_cpq(triple(Z!6, U!0, X1!5)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) | check_cpq(triple(Z!6, U!0, X1!5)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(195,plain,
% 0.21/0.44 ((~(check_cpq(triple(Z!6, U!0, X1!5)) | (~((~pair_in_list(U!0, X!2, Y!1)) | less_than(Y!1, X!2))))) | check_cpq(triple(Z!6, U!0, X1!5))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.21/0.44 tff(196,plain,
% 0.21/0.44 (check_cpq(triple(Z!6, U!0, X1!5))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[195, 32])).
% 0.21/0.44 tff(197,plain,
% 0.21/0.44 ((~(check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) <=> check_cpq(triple(Z!6, U!0, X1!5)))) | check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) | (~check_cpq(triple(Z!6, U!0, X1!5)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(198,plain,
% 0.21/0.44 ((~(check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) <=> check_cpq(triple(Z!6, U!0, X1!5)))) | (~check_cpq(triple(Z!6, U!0, X1!5)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[197, 187])).
% 0.21/0.44 tff(199,plain,
% 0.21/0.44 (~(check_cpq(triple(Z!6, insert_slb(U!0, pair(X2!4, X3!3)), X1!5)) <=> check_cpq(triple(Z!6, U!0, X1!5)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[198, 196])).
% 0.21/0.44 tff(200,plain,
% 0.21/0.44 (~less_than(X3!3, X2!4)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[135, 199])).
% 0.21/0.44 tff(201,plain,
% 0.21/0.44 (((~![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) | ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X2!4, X3!3)) | less_than(X3!3, X2!4))) <=> ((~![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) | (~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X2!4, X3!3)) | less_than(X3!3, X2!4))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(202,plain,
% 0.21/0.44 ((~![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) | ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X2!4, X3!3)) | less_than(X3!3, X2!4))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(203,plain,
% 0.21/0.44 ((~![X4: $i, X5: $i] : ((~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X4, X5)) | less_than(X5, X4))) | (~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X2!4, X3!3)) | less_than(X3!3, X2!4)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.21/0.44 tff(204,plain,
% 0.21/0.44 (~pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X2!4, X3!3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[203, 188, 200])).
% 0.21/0.44 tff(205,plain,
% 0.21/0.44 (((~![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!4, X3!3)), X2!4, X3!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(U!0, pair(X2!4, X3!3)), X2!4, X3!3))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(206,plain,
% 0.21/0.44 ((pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X2!4, X3!3) <=> $true) <=> pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X2!4, X3!3)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(207,plain,
% 0.21/0.44 (($true | pair_in_list(U!0, X2!4, X3!3)) <=> $true),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(208,plain,
% 0.21/0.44 ((~$false) <=> $true),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(209,plain,
% 0.21/0.44 (($false | $false) <=> $false),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(210,plain,
% 0.21/0.44 ((~$true) <=> $false),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(211,plain,
% 0.21/0.44 ((X3!3 = X3!3) <=> $true),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(212,plain,
% 0.21/0.44 ((~(X3!3 = X3!3)) <=> (~$true)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[211])).
% 0.21/0.44 tff(213,plain,
% 0.21/0.44 ((~(X3!3 = X3!3)) <=> $false),
% 0.21/0.44 inference(transitivity,[status(thm)],[212, 210])).
% 0.21/0.44 tff(214,plain,
% 0.21/0.44 ((X2!4 = X2!4) <=> $true),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(215,plain,
% 0.21/0.44 ((~(X2!4 = X2!4)) <=> (~$true)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[214])).
% 0.21/0.44 tff(216,plain,
% 0.21/0.44 ((~(X2!4 = X2!4)) <=> $false),
% 0.21/0.44 inference(transitivity,[status(thm)],[215, 210])).
% 0.21/0.44 tff(217,plain,
% 0.21/0.44 (((~(X2!4 = X2!4)) | (~(X3!3 = X3!3))) <=> ($false | $false)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[216, 213])).
% 0.21/0.44 tff(218,plain,
% 0.21/0.44 (((~(X2!4 = X2!4)) | (~(X3!3 = X3!3))) <=> $false),
% 0.21/0.44 inference(transitivity,[status(thm)],[217, 209])).
% 0.21/0.44 tff(219,plain,
% 0.21/0.44 ((~((~(X2!4 = X2!4)) | (~(X3!3 = X3!3)))) <=> (~$false)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[218])).
% 0.21/0.44 tff(220,plain,
% 0.21/0.44 ((~((~(X2!4 = X2!4)) | (~(X3!3 = X3!3)))) <=> $true),
% 0.21/0.44 inference(transitivity,[status(thm)],[219, 208])).
% 0.21/0.44 tff(221,plain,
% 0.21/0.44 (((~((~(X2!4 = X2!4)) | (~(X3!3 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3)) <=> ($true | pair_in_list(U!0, X2!4, X3!3))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[220])).
% 0.21/0.44 tff(222,plain,
% 0.21/0.44 (((~((~(X2!4 = X2!4)) | (~(X3!3 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3)) <=> $true),
% 0.21/0.44 inference(transitivity,[status(thm)],[221, 207])).
% 0.21/0.44 tff(223,plain,
% 0.21/0.44 ((pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X2!4, X3!3) <=> ((~((~(X2!4 = X2!4)) | (~(X3!3 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3))) <=> (pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X2!4, X3!3) <=> $true)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[222])).
% 0.21/0.44 tff(224,plain,
% 0.21/0.44 ((pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X2!4, X3!3) <=> ((~((~(X2!4 = X2!4)) | (~(X3!3 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3))) <=> pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X2!4, X3!3)),
% 0.21/0.44 inference(transitivity,[status(thm)],[223, 206])).
% 0.21/0.44 tff(225,plain,
% 0.21/0.44 (((~![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!4, X3!3)), X2!4, X3!3) <=> ((~((~(X2!4 = X2!4)) | (~(X3!3 = X3!3)))) | pair_in_list(U!0, X2!4, X3!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(U!0, pair(X2!4, X3!3)), X2!4, X3!3))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[224])).
% 0.21/0.44 tff(226,plain,
% 0.21/0.44 (((~![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!4, X3!3)), X2!4, X3!3) <=> ((~((~(X2!4 = X2!4)) | (~(X3!3 = X3!3)))) | pair_in_list(U!0, X2!4, X3!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(U!0, pair(X2!4, X3!3)), X2!4, X3!3))),
% 0.21/0.44 inference(transitivity,[status(thm)],[225, 205])).
% 0.21/0.44 tff(227,plain,
% 0.21/0.44 ((~![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!4, X3!3)), X2!4, X3!3) <=> ((~((~(X2!4 = X2!4)) | (~(X3!3 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(228,plain,
% 0.21/0.44 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | pair_in_list(insert_slb(U!0, pair(X2!4, X3!3)), X2!4, X3!3)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.21/0.44 tff(229,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[228, 49, 204])).
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44 % E exiting
%------------------------------------------------------------------------------