%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV416+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:32:24 AM UTC 2025
% Result : Theorem 0.24s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.15 % Problem : SWV416+2 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n015.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 09:45:56 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.24/0.49 % SZS status Theorem
% 0.24/0.49 % SZS output start Proof
% 0.24/0.49 tff(remove_pq_type, type, (
% 0.24/0.49 remove_pq: ( $i * $i ) > $i)).
% 0.24/0.49 tff(tptp_fun_X4_20_type, type, (
% 0.24/0.49 tptp_fun_X4_20: $i)).
% 0.24/0.49 tff(i_type, type, (
% 0.24/0.49 i: $i > $i)).
% 0.24/0.49 tff(triple_type, type, (
% 0.24/0.49 triple: ( $i * $i * $i ) > $i)).
% 0.24/0.49 tff(tptp_fun_X3_21_type, type, (
% 0.24/0.49 tptp_fun_X3_21: $i)).
% 0.24/0.49 tff(insert_slb_type, type, (
% 0.24/0.49 insert_slb: ( $i * $i ) > $i)).
% 0.24/0.49 tff(pair_type, type, (
% 0.24/0.49 pair: ( $i * $i ) > $i)).
% 0.24/0.49 tff(tptp_fun_X6_18_type, type, (
% 0.24/0.49 tptp_fun_X6_18: $i)).
% 0.24/0.49 tff(tptp_fun_X5_19_type, type, (
% 0.24/0.49 tptp_fun_X5_19: $i)).
% 0.24/0.49 tff(tptp_fun_X_17_type, type, (
% 0.24/0.49 tptp_fun_X_17: $i)).
% 0.24/0.49 tff(tptp_fun_X2_22_type, type, (
% 0.24/0.49 tptp_fun_X2_22: $i)).
% 0.24/0.49 tff(remove_cpq_type, type, (
% 0.24/0.49 remove_cpq: ( $i * $i ) > $i)).
% 0.24/0.49 tff(insert_pq_type, type, (
% 0.24/0.49 insert_pq: ( $i * $i ) > $i)).
% 0.24/0.49 tff(contains_pq_type, type, (
% 0.24/0.49 contains_pq: ( $i * $i ) > $o)).
% 0.24/0.49 tff(tptp_fun_X_32_type, type, (
% 0.24/0.49 tptp_fun_X_32: $i)).
% 0.24/0.49 tff(tptp_fun_W_33_type, type, (
% 0.24/0.49 tptp_fun_W_33: $i)).
% 0.24/0.49 tff(tptp_fun_V_34_type, type, (
% 0.24/0.49 tptp_fun_V_34: $i)).
% 0.24/0.49 tff(tptp_fun_U_35_type, type, (
% 0.24/0.49 tptp_fun_U_35: $i)).
% 0.24/0.49 tff(pi_sharp_remove_type, type, (
% 0.24/0.49 pi_sharp_remove: ( $i * $i ) > $o)).
% 0.24/0.49 tff(pi_remove_type, type, (
% 0.24/0.49 pi_remove: ( $i * $i ) > $o)).
% 0.24/0.49 tff(phi_type, type, (
% 0.24/0.49 phi: $i > $o)).
% 0.24/0.49 tff(tptp_fun_W_14_type, type, (
% 0.24/0.49 tptp_fun_W_14: $i)).
% 0.24/0.49 tff(tptp_fun_V_15_type, type, (
% 0.24/0.49 tptp_fun_V_15: $i)).
% 0.24/0.49 tff(create_slb_type, type, (
% 0.24/0.49 create_slb: $i)).
% 0.24/0.49 tff(tptp_fun_U_16_type, type, (
% 0.24/0.49 tptp_fun_U_16: $i)).
% 0.24/0.49 tff(create_pq_type, type, (
% 0.24/0.49 create_pq: $i)).
% 0.24/0.49 tff(remove_slb_type, type, (
% 0.24/0.49 remove_slb: ( $i * $i ) > $i)).
% 0.24/0.49 tff(remove_pqp_type, type, (
% 0.24/0.49 remove_pqp: ( $i * $i ) > $i)).
% 0.24/0.49 tff(less_than_type, type, (
% 0.24/0.49 less_than: ( $i * $i ) > $o)).
% 0.24/0.49 tff(lookup_slb_type, type, (
% 0.24/0.49 lookup_slb: ( $i * $i ) > $i)).
% 0.24/0.49 tff(contains_slb_type, type, (
% 0.24/0.49 contains_slb: ( $i * $i ) > $o)).
% 0.24/0.49 tff(contains_cpq_type, type, (
% 0.24/0.49 contains_cpq: ( $i * $i ) > $o)).
% 0.24/0.49 tff(tptp_fun_W_23_type, type, (
% 0.24/0.49 tptp_fun_W_23: $i)).
% 0.24/0.49 tff(tptp_fun_V_24_type, type, (
% 0.24/0.49 tptp_fun_V_24: $i)).
% 0.24/0.49 tff(tptp_fun_U_25_type, type, (
% 0.24/0.49 tptp_fun_U_25: $i)).
% 0.24/0.49 tff(tptp_fun_X6_27_type, type, (
% 0.24/0.49 tptp_fun_X6_27: $i)).
% 0.24/0.49 tff(tptp_fun_X3_30_type, type, (
% 0.24/0.49 tptp_fun_X3_30: $i)).
% 0.24/0.49 tff(tptp_fun_X5_28_type, type, (
% 0.24/0.49 tptp_fun_X5_28: $i)).
% 0.24/0.49 tff(tptp_fun_X4_29_type, type, (
% 0.24/0.49 tptp_fun_X4_29: $i)).
% 0.24/0.49 tff(tptp_fun_X_26_type, type, (
% 0.24/0.49 tptp_fun_X_26: $i)).
% 0.24/0.49 tff(tptp_fun_X2_31_type, type, (
% 0.24/0.49 tptp_fun_X2_31: $i)).
% 0.24/0.49 tff(strictly_less_than_type, type, (
% 0.24/0.49 strictly_less_than: ( $i * $i ) > $o)).
% 0.24/0.49 tff(bad_type, type, (
% 0.24/0.49 bad: $i)).
% 0.24/0.49 tff(tptp_fun_X_3_type, type, (
% 0.24/0.49 tptp_fun_X_3: $i)).
% 0.24/0.49 tff(tptp_fun_V_5_type, type, (
% 0.24/0.49 tptp_fun_V_5: $i)).
% 0.24/0.49 tff(tptp_fun_W_4_type, type, (
% 0.24/0.49 tptp_fun_W_4: $i)).
% 0.24/0.49 tff(tptp_fun_U_6_type, type, (
% 0.24/0.49 tptp_fun_U_6: $i)).
% 0.24/0.49 tff(tptp_fun_X7_10_type, type, (
% 0.24/0.49 tptp_fun_X7_10: $i)).
% 0.24/0.49 tff(tptp_fun_X9_8_type, type, (
% 0.24/0.49 tptp_fun_X9_8: $i)).
% 0.24/0.49 tff(tptp_fun_X8_9_type, type, (
% 0.24/0.49 tptp_fun_X8_9: $i)).
% 0.24/0.49 tff(tptp_fun_Y_7_type, type, (
% 0.24/0.49 tptp_fun_Y_7: $i)).
% 0.24/0.49 tff(tptp_fun_X5_12_type, type, (
% 0.24/0.49 tptp_fun_X5_12: $i)).
% 0.24/0.49 tff(tptp_fun_X6_11_type, type, (
% 0.24/0.49 tptp_fun_X6_11: $i)).
% 0.24/0.49 tff(tptp_fun_X4_13_type, type, (
% 0.24/0.49 tptp_fun_X4_13: $i)).
% 0.24/0.49 tff(1,plain,
% 0.24/0.49 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : refl((i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X)) <=> (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X)))),
% 0.24/0.49 inference(bind,[status(th)],[])).
% 0.24/0.49 tff(2,plain,
% 0.24/0.49 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X)) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))),
% 0.24/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.24/0.49 tff(3,plain,
% 0.24/0.49 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X)) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))),
% 0.24/0.49 inference(rewrite,[status(thm)],[])).
% 0.24/0.49 tff(4,axiom,(![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax','ax55')).
% 0.24/0.49 tff(5,plain,
% 0.24/0.49 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))),
% 0.24/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.24/0.49 tff(6,plain,(
% 0.24/0.49 ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))),
% 0.24/0.49 inference(skolemize,[status(sab)],[5])).
% 0.24/0.49 tff(7,plain,
% 0.24/0.49 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))),
% 0.24/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.24/0.49 tff(8,plain,
% 0.24/0.49 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))) | (i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)) = insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19))),
% 0.24/0.49 inference(quant_inst,[status(thm)],[])).
% 0.24/0.49 tff(9,plain,
% 0.24/0.49 (i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)) = insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19)),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.24/0.49 tff(10,plain,
% 0.24/0.49 (insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19) = i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21))),
% 0.24/0.49 inference(symmetry,[status(thm)],[9])).
% 0.24/0.49 tff(11,plain,
% 0.24/0.49 (remove_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)),
% 0.24/0.49 inference(monotonicity,[status(thm)],[10])).
% 0.24/0.49 tff(12,assumption,(~(X5!19 = X4!20)), introduced(assumption)).
% 0.24/0.49 tff(13,plain,
% 0.24/0.49 (^[U: $i, V: $i, W: $i] : refl((contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W))) <=> (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W))))),
% 0.24/0.49 inference(bind,[status(th)],[])).
% 0.24/0.49 tff(14,plain,
% 0.24/0.49 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W))) <=> ![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.24/0.49 inference(quant_intro,[status(thm)],[13])).
% 0.24/0.49 tff(15,plain,
% 0.24/0.49 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W))) <=> ![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.24/0.49 inference(rewrite,[status(thm)],[])).
% 0.24/0.49 tff(16,plain,
% 0.24/0.49 (^[U: $i, V: $i, W: $i] : rewrite((contains_pq(insert_pq(U, V), W) <=> (contains_pq(U, W) | (V = W))) <=> (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W))))),
% 0.24/0.49 inference(bind,[status(th)],[])).
% 0.24/0.49 tff(17,plain,
% 0.24/0.49 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> (contains_pq(U, W) | (V = W))) <=> ![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.24/0.49 inference(quant_intro,[status(thm)],[16])).
% 0.24/0.49 tff(18,axiom,(![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> (contains_pq(U, W) | (V = W)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax','ax9')).
% 0.24/0.49 tff(19,plain,
% 0.24/0.49 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.24/0.49 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.24/0.49 tff(20,plain,
% 0.24/0.49 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.24/0.49 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.24/0.49 tff(21,plain,(
% 0.24/0.49 ![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.24/0.49 inference(skolemize,[status(sab)],[20])).
% 0.24/0.49 tff(22,plain,
% 0.24/0.49 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.24/0.49 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.24/0.49 tff(23,plain,
% 0.24/0.49 ((~![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))) | (contains_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) <=> ((X5!19 = X4!20) | contains_pq(i(triple(X2!22, X!17, X3!21)), X4!20)))),
% 0.24/0.49 inference(quant_inst,[status(thm)],[])).
% 0.24/0.49 tff(24,plain,
% 0.24/0.49 (contains_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) <=> ((X5!19 = X4!20) | contains_pq(i(triple(X2!22, X!17, X3!21)), X4!20))),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.24/0.49 tff(25,plain,
% 0.24/0.49 (contains_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) <=> contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)),
% 0.24/0.49 inference(monotonicity,[status(thm)],[10])).
% 0.24/0.49 tff(26,plain,
% 0.24/0.49 (contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20) <=> contains_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20)),
% 0.24/0.49 inference(symmetry,[status(thm)],[25])).
% 0.24/0.49 tff(27,plain,
% 0.24/0.49 (^[U: $i, V: $i] : refl((pi_sharp_remove(U, V) <=> contains_pq(U, V)) <=> (pi_sharp_remove(U, V) <=> contains_pq(U, V)))),
% 0.24/0.49 inference(bind,[status(th)],[])).
% 0.24/0.49 tff(28,plain,
% 0.24/0.49 (![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V)) <=> ![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.24/0.49 inference(quant_intro,[status(thm)],[27])).
% 0.24/0.49 tff(29,plain,
% 0.24/0.49 (![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V)) <=> ![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.24/0.49 inference(rewrite,[status(thm)],[])).
% 0.24/0.49 tff(30,axiom,(![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax','ax56')).
% 0.24/0.49 tff(31,plain,
% 0.24/0.49 (![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.24/0.49 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.24/0.49 tff(32,plain,(
% 0.24/0.49 ![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.24/0.49 inference(skolemize,[status(sab)],[31])).
% 0.24/0.49 tff(33,plain,
% 0.24/0.49 (![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.24/0.49 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.24/0.49 tff(34,plain,
% 0.24/0.49 ((~![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))) | (pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) <=> contains_pq(i(triple(U!35, V!34, W!33)), X!32))),
% 0.24/0.49 inference(quant_inst,[status(thm)],[])).
% 0.24/0.49 tff(35,plain,
% 0.24/0.49 (pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) <=> contains_pq(i(triple(U!35, V!34, W!33)), X!32)),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.24/0.49 tff(36,plain,
% 0.24/0.49 (^[U: $i, V: $i] : refl((pi_remove(U, V) <=> pi_sharp_remove(i(U), V)) <=> (pi_remove(U, V) <=> pi_sharp_remove(i(U), V)))),
% 0.24/0.49 inference(bind,[status(th)],[])).
% 0.24/0.49 tff(37,plain,
% 0.24/0.49 (![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V)) <=> ![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.24/0.49 inference(quant_intro,[status(thm)],[36])).
% 0.24/0.49 tff(38,plain,
% 0.24/0.49 (![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V)) <=> ![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.24/0.49 inference(rewrite,[status(thm)],[])).
% 0.24/0.49 tff(39,axiom,(![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax','ax57')).
% 0.24/0.49 tff(40,plain,
% 0.24/0.49 (![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.24/0.49 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.24/0.49 tff(41,plain,(
% 0.24/0.49 ![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.24/0.49 inference(skolemize,[status(sab)],[40])).
% 0.24/0.49 tff(42,plain,
% 0.24/0.49 (![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.24/0.49 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.24/0.49 tff(43,plain,
% 0.24/0.49 ((~![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))) | (pi_remove(triple(U!35, V!34, W!33), X!32) <=> pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32))),
% 0.24/0.49 inference(quant_inst,[status(thm)],[])).
% 0.24/0.49 tff(44,plain,
% 0.24/0.49 (pi_remove(triple(U!35, V!34, W!33), X!32) <=> pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.24/0.49 tff(45,plain,
% 0.24/0.49 ((~((pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))) | (~phi(remove_cpq(triple(U!35, V!34, W!33), X!32))) | (~pi_remove(triple(U!35, V!34, W!33), X!32)))) <=> (~((pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))) | (~phi(remove_cpq(triple(U!35, V!34, W!33), X!32))) | (~pi_remove(triple(U!35, V!34, W!33), X!32))))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(46,plain,
% 0.24/0.50 ((~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))) <=> (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X))))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(47,plain,
% 0.24/0.50 ((~![U: $i, V: $i, W: $i, X: $i] : (pi_remove(triple(U, V, W), X) => (phi(remove_cpq(triple(U, V, W), X)) => (pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))))) <=> (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X))))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(48,axiom,(~![U: $i, V: $i, W: $i, X: $i] : (pi_remove(triple(U, V, W), X) => (phi(remove_cpq(triple(U, V, W), X)) => (pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co3')).
% 0.24/0.50 tff(49,plain,
% 0.24/0.50 (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.24/0.50 tff(50,plain,
% 0.24/0.50 (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.24/0.50 tff(51,plain,
% 0.24/0.50 (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.24/0.50 tff(52,plain,
% 0.24/0.50 (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[51, 46])).
% 0.24/0.50 tff(53,plain,(
% 0.24/0.50 ~((pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))) | (~phi(remove_cpq(triple(U!35, V!34, W!33), X!32))) | (~pi_remove(triple(U!35, V!34, W!33), X!32)))),
% 0.24/0.50 inference(skolemize,[status(sab)],[52])).
% 0.24/0.50 tff(54,plain,
% 0.24/0.50 (~((pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))) | (~phi(remove_cpq(triple(U!35, V!34, W!33), X!32))) | (~pi_remove(triple(U!35, V!34, W!33), X!32)))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[53, 45])).
% 0.24/0.50 tff(55,plain,
% 0.24/0.50 (pi_remove(triple(U!35, V!34, W!33), X!32)),
% 0.24/0.50 inference(or_elim,[status(thm)],[54])).
% 0.24/0.50 tff(56,plain,
% 0.24/0.50 ((~(pi_remove(triple(U!35, V!34, W!33), X!32) <=> pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32))) | (~pi_remove(triple(U!35, V!34, W!33), X!32)) | pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)),
% 0.24/0.50 inference(tautology,[status(thm)],[])).
% 0.24/0.50 tff(57,plain,
% 0.24/0.50 ((~(pi_remove(triple(U!35, V!34, W!33), X!32) <=> pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32))) | pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)),
% 0.24/0.50 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.24/0.50 tff(58,plain,
% 0.24/0.50 (pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)),
% 0.24/0.50 inference(unit_resolution,[status(thm)],[57, 44])).
% 0.24/0.50 tff(59,plain,
% 0.24/0.50 ((~(pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) <=> contains_pq(i(triple(U!35, V!34, W!33)), X!32))) | (~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | contains_pq(i(triple(U!35, V!34, W!33)), X!32)),
% 0.24/0.50 inference(tautology,[status(thm)],[])).
% 0.24/0.50 tff(60,plain,
% 0.24/0.50 ((~(pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) <=> contains_pq(i(triple(U!35, V!34, W!33)), X!32))) | contains_pq(i(triple(U!35, V!34, W!33)), X!32)),
% 0.24/0.50 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.24/0.50 tff(61,plain,
% 0.24/0.50 (contains_pq(i(triple(U!35, V!34, W!33)), X!32)),
% 0.24/0.50 inference(unit_resolution,[status(thm)],[60, 35])).
% 0.24/0.50 tff(62,plain,
% 0.24/0.50 ((~(~((~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))))) <=> ((~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(63,plain,
% 0.24/0.50 ((pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))) <=> (~((~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(64,plain,
% 0.24/0.50 ((~(pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))) <=> (~(~((~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))))))),
% 0.24/0.50 inference(monotonicity,[status(thm)],[63])).
% 0.24/0.50 tff(65,plain,
% 0.24/0.50 ((~(pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))) <=> ((~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))))),
% 0.24/0.50 inference(transitivity,[status(thm)],[64, 62])).
% 0.24/0.50 tff(66,plain,
% 0.24/0.50 (~(pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))),
% 0.24/0.50 inference(or_elim,[status(thm)],[54])).
% 0.24/0.50 tff(67,plain,
% 0.24/0.50 ((~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.24/0.50 tff(68,plain,
% 0.24/0.50 (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))),
% 0.24/0.50 inference(unit_resolution,[status(thm)],[67, 58])).
% 0.24/0.50 tff(69,assumption,(![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))), introduced(assumption)).
% 0.24/0.50 tff(70,plain,
% 0.24/0.50 (((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) | ((~contains_pq(i(triple(U!35, V!34, W!33)), X!32)) | (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))) <=> ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) | (~contains_pq(i(triple(U!35, V!34, W!33)), X!32)) | (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(71,plain,
% 0.24/0.50 ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) | ((~contains_pq(i(triple(U!35, V!34, W!33)), X!32)) | (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))),
% 0.24/0.50 inference(quant_inst,[status(thm)],[])).
% 0.24/0.50 tff(72,plain,
% 0.24/0.50 ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) | (~contains_pq(i(triple(U!35, V!34, W!33)), X!32)) | (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.24/0.50 tff(73,plain,
% 0.24/0.50 ($false),
% 0.24/0.50 inference(unit_resolution,[status(thm)],[72, 69, 68, 61])).
% 0.24/0.50 tff(74,plain,(~![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.50 tff(75,plain,
% 0.24/0.50 (^[U: $i, V: $i] : refl((i(triple(U, create_slb, V)) = create_pq) <=> (i(triple(U, create_slb, V)) = create_pq))),
% 0.24/0.50 inference(bind,[status(th)],[])).
% 0.24/0.50 tff(76,plain,
% 0.24/0.50 (![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq) <=> ![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.24/0.50 inference(quant_intro,[status(thm)],[75])).
% 0.24/0.50 tff(77,plain,
% 0.24/0.50 (![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq) <=> ![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(78,axiom,(![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax','ax54')).
% 0.24/0.50 tff(79,plain,
% 0.24/0.50 (![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.24/0.50 tff(80,plain,(
% 0.24/0.50 ![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.24/0.50 inference(skolemize,[status(sab)],[79])).
% 0.24/0.50 tff(81,plain,
% 0.24/0.50 (![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.24/0.50 tff(82,plain,
% 0.24/0.50 ((~![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)) | (i(triple(U!16, create_slb, V!15)) = create_pq)),
% 0.24/0.50 inference(quant_inst,[status(thm)],[])).
% 0.24/0.50 tff(83,plain,
% 0.24/0.50 (i(triple(U!16, create_slb, V!15)) = create_pq),
% 0.24/0.50 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.24/0.50 tff(84,plain,
% 0.24/0.50 (create_pq = i(triple(U!16, create_slb, V!15))),
% 0.24/0.50 inference(symmetry,[status(thm)],[83])).
% 0.24/0.50 tff(85,plain,
% 0.24/0.50 (contains_pq(create_pq, W!14) <=> contains_pq(i(triple(U!16, create_slb, V!15)), W!14)),
% 0.24/0.50 inference(monotonicity,[status(thm)],[84])).
% 0.24/0.50 tff(86,plain,
% 0.24/0.50 (contains_pq(i(triple(U!16, create_slb, V!15)), W!14) <=> contains_pq(create_pq, W!14)),
% 0.24/0.50 inference(symmetry,[status(thm)],[85])).
% 0.24/0.50 tff(87,assumption,(contains_pq(i(triple(U!16, create_slb, V!15)), W!14)), introduced(assumption)).
% 0.24/0.50 tff(88,plain,
% 0.24/0.50 (contains_pq(create_pq, W!14)),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.24/0.50 tff(89,plain,
% 0.24/0.50 (^[U: $i] : refl((~contains_pq(create_pq, U)) <=> (~contains_pq(create_pq, U)))),
% 0.24/0.50 inference(bind,[status(th)],[])).
% 0.24/0.50 tff(90,plain,
% 0.24/0.50 (![U: $i] : (~contains_pq(create_pq, U)) <=> ![U: $i] : (~contains_pq(create_pq, U))),
% 0.24/0.50 inference(quant_intro,[status(thm)],[89])).
% 0.24/0.50 tff(91,plain,
% 0.24/0.50 (![U: $i] : (~contains_pq(create_pq, U)) <=> ![U: $i] : (~contains_pq(create_pq, U))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(92,axiom,(![U: $i] : (~contains_pq(create_pq, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax','ax8')).
% 0.24/0.50 tff(93,plain,
% 0.24/0.50 (![U: $i] : (~contains_pq(create_pq, U))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.24/0.50 tff(94,plain,(
% 0.24/0.50 ![U: $i] : (~contains_pq(create_pq, U))),
% 0.24/0.50 inference(skolemize,[status(sab)],[93])).
% 0.24/0.50 tff(95,plain,
% 0.24/0.50 (![U: $i] : (~contains_pq(create_pq, U))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.24/0.50 tff(96,plain,
% 0.24/0.50 ((~![U: $i] : (~contains_pq(create_pq, U))) | (~contains_pq(create_pq, W!14))),
% 0.24/0.50 inference(quant_inst,[status(thm)],[])).
% 0.24/0.50 tff(97,plain,
% 0.24/0.50 (~contains_pq(create_pq, W!14)),
% 0.24/0.50 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.24/0.50 tff(98,plain,
% 0.24/0.50 ($false),
% 0.24/0.50 inference(unit_resolution,[status(thm)],[97, 88])).
% 0.24/0.50 tff(99,plain,(~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)), inference(lemma,lemma(discharge,[]))).
% 0.24/0.50 tff(100,plain,
% 0.24/0.51 (((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14))) | contains_pq(i(triple(U!16, create_slb, V!15)), W!14)),
% 0.24/0.51 inference(tautology,[status(thm)],[])).
% 0.24/0.51 tff(101,plain,
% 0.24/0.51 ((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14))),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.24/0.51 tff(102,plain,
% 0.24/0.51 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))))))) <=> ((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))))))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(103,plain,
% 0.24/0.51 ((~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))) <=> (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))))))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(104,plain,
% 0.24/0.51 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))))))),
% 0.24/0.51 inference(monotonicity,[status(thm)],[103])).
% 0.24/0.51 tff(105,plain,
% 0.24/0.51 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))) <=> ((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))))))),
% 0.24/0.51 inference(transitivity,[status(thm)],[104, 102])).
% 0.24/0.51 tff(106,plain,
% 0.24/0.51 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(107,plain,
% 0.24/0.51 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(108,plain,
% 0.24/0.52 ((![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))) <=> (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(109,plain,
% 0.24/0.52 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))),
% 0.24/0.52 inference(monotonicity,[status(thm)],[108])).
% 0.24/0.52 tff(110,plain,
% 0.24/0.52 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))),
% 0.24/0.52 inference(transitivity,[status(thm)],[109, 107])).
% 0.24/0.52 tff(111,plain,
% 0.24/0.52 ((((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(112,plain,
% 0.24/0.52 ((![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))) <=> (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(113,plain,
% 0.24/0.52 (((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) <=> ((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))))),
% 0.24/0.52 inference(monotonicity,[status(thm)],[112])).
% 0.24/0.52 tff(114,plain,
% 0.24/0.52 ((((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> (((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))))),
% 0.24/0.52 inference(monotonicity,[status(thm)],[113])).
% 0.24/0.52 tff(115,plain,
% 0.24/0.52 ((((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))))),
% 0.24/0.52 inference(transitivity,[status(thm)],[114, 111])).
% 0.24/0.52 tff(116,plain,
% 0.24/0.52 (((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))))),
% 0.24/0.53 inference(rewrite,[status(thm)],[])).
% 0.24/0.53 tff(117,plain,
% 0.24/0.53 (((![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4))))) => ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))))),
% 0.24/0.53 inference(rewrite,[status(thm)],[])).
% 0.24/0.53 tff(118,plain,
% 0.24/0.53 (^[X7: $i, X8: $i, X9: $i, X10: $i] : rewrite((contains_pq(i(triple(X7, X8, X9)), X10) => (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) <=> ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))))),
% 0.24/0.53 inference(bind,[status(th)],[])).
% 0.24/0.53 tff(119,plain,
% 0.24/0.53 (![X7: $i, X8: $i, X9: $i, X10: $i] : (contains_pq(i(triple(X7, X8, X9)), X10) => (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) <=> ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.24/0.53 inference(quant_intro,[status(thm)],[118])).
% 0.24/0.53 tff(120,plain,
% 0.24/0.53 ((![U: $i, V: $i, W: $i] : (contains_pq(i(triple(U, create_slb, V)), W) => (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : (![Y: $i, Z: $i, X1: $i] : (contains_pq(i(triple(Y, X, Z)), X1) => (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1))) => ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : (contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4) => (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4))))) <=> (![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))),
% 0.24/0.53 inference(rewrite,[status(thm)],[])).
% 0.24/0.53 tff(121,plain,
% 0.24/0.53 (((![U: $i, V: $i, W: $i] : (contains_pq(i(triple(U, create_slb, V)), W) => (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : (![Y: $i, Z: $i, X1: $i] : (contains_pq(i(triple(Y, X, Z)), X1) => (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1))) => ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : (contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4) => (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4))))) => ![X7: $i, X8: $i, X9: $i, X10: $i] : (contains_pq(i(triple(X7, X8, X9)), X10) => (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> ((![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4))))) => ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))))),
% 0.24/0.53 inference(monotonicity,[status(thm)],[120, 119])).
% 0.24/0.53 tff(122,plain,
% 0.24/0.53 (((![U: $i, V: $i, W: $i] : (contains_pq(i(triple(U, create_slb, V)), W) => (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : (![Y: $i, Z: $i, X1: $i] : (contains_pq(i(triple(Y, X, Z)), X1) => (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1))) => ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : (contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4) => (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4))))) => ![X7: $i, X8: $i, X9: $i, X10: $i] : (contains_pq(i(triple(X7, X8, X9)), X10) => (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))))),
% 0.24/0.53 inference(transitivity,[status(thm)],[121, 117])).
% 0.24/0.53 tff(123,axiom,((![U: $i, V: $i, W: $i] : (contains_pq(i(triple(U, create_slb, V)), W) => (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : (![Y: $i, Z: $i, X1: $i] : (contains_pq(i(triple(Y, X, Z)), X1) => (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1))) => ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : (contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4) => (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4))))) => ![X7: $i, X8: $i, X9: $i, X10: $i] : (contains_pq(i(triple(X7, X8, X9)), X10) => (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','big3_induction2')).
% 0.24/0.53 tff(124,plain,
% 0.24/0.53 ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.24/0.53 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.24/0.53 tff(125,plain,
% 0.24/0.53 ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.24/0.53 inference(modus_ponens,[status(thm)],[124, 116])).
% 0.24/0.53 tff(126,plain,
% 0.24/0.53 ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.24/0.53 inference(modus_ponens,[status(thm)],[125, 116])).
% 0.24/0.53 tff(127,plain,
% 0.24/0.53 ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.24/0.53 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.24/0.53 Proof display could not be completed: monotonicity rule is not handled
% 0.38/0.54 % E exiting
%------------------------------------------------------------------------------