%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV378+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:32:20 AM UTC 2025
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWV378+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Jun 20 09:44:47 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41 % SZS output start Proof
% 0.22/0.41 tff(ok_type, type, (
% 0.22/0.41 ok: $i > $o)).
% 0.22/0.41 tff(remove_cpq_type, type, (
% 0.22/0.41 remove_cpq: ( $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_X_0_type, type, (
% 0.22/0.41 tptp_fun_X_0: $i)).
% 0.22/0.41 tff(triple_type, type, (
% 0.22/0.41 triple: ( $i * $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_W_1_type, type, (
% 0.22/0.41 tptp_fun_W_1: $i)).
% 0.22/0.41 tff(tptp_fun_V_2_type, type, (
% 0.22/0.41 tptp_fun_V_2: $i)).
% 0.22/0.41 tff(tptp_fun_U_3_type, type, (
% 0.22/0.41 tptp_fun_U_3: $i)).
% 0.22/0.41 tff(bad_type, type, (
% 0.22/0.41 bad: $i)).
% 0.22/0.41 tff(contains_slb_type, type, (
% 0.22/0.41 contains_slb: ( $i * $i ) > $o)).
% 0.22/0.41 tff(remove_slb_type, type, (
% 0.22/0.41 remove_slb: ( $i * $i ) > $i)).
% 0.22/0.41 tff(remove_pqp_type, type, (
% 0.22/0.41 remove_pqp: ( $i * $i ) > $i)).
% 0.22/0.41 tff(strictly_less_than_type, type, (
% 0.22/0.41 strictly_less_than: ( $i * $i ) > $o)).
% 0.22/0.41 tff(lookup_slb_type, type, (
% 0.22/0.41 lookup_slb: ( $i * $i ) > $i)).
% 0.22/0.41 tff(less_than_type, type, (
% 0.22/0.41 less_than: ( $i * $i ) > $o)).
% 0.22/0.41 tff(1,plain,
% 0.22/0.41 ((~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))) <=> (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X)))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(2,plain,
% 0.22/0.41 ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(triple(U, V, W))) => (~ok(remove_cpq(triple(U, V, W), X))))) <=> (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X)))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(3,axiom,(~![U: $i, V: $i, W: $i, X: $i] : ((~ok(triple(U, V, W))) => (~ok(remove_cpq(triple(U, V, W), X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l14_co')).
% 0.22/0.41 tff(4,plain,
% 0.22/0.41 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.22/0.41 tff(5,plain,
% 0.22/0.41 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.22/0.41 tff(6,plain,
% 0.22/0.41 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.22/0.41 tff(7,plain,
% 0.22/0.41 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.22/0.41 tff(8,plain,(
% 0.22/0.41 ~(ok(triple(U!3, V!2, W!1)) | (~ok(remove_cpq(triple(U!3, V!2, W!1), X!0))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[7])).
% 0.22/0.41 tff(9,plain,
% 0.22/0.41 (~ok(triple(U!3, V!2, W!1))),
% 0.22/0.41 inference(or_elim,[status(thm)],[8])).
% 0.22/0.41 tff(10,plain,
% 0.22/0.41 (^[U: $i, V: $i, W: $i] : refl((ok(triple(U, V, W)) | (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(11,plain,
% 0.22/0.41 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.22/0.41 tff(12,plain,
% 0.22/0.41 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(13,plain,
% 0.22/0.41 (^[U: $i, V: $i, W: $i] : rewrite(((~ok(triple(U, V, W))) => (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(14,plain,
% 0.22/0.41 (![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.22/0.41 tff(15,axiom,(![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax41')).
% 0.22/0.41 tff(16,plain,
% 0.22/0.41 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.22/0.41 tff(18,plain,(
% 0.22/0.41 ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.41 inference(skolemize,[status(sab)],[17])).
% 0.22/0.41 tff(19,plain,
% 0.22/0.41 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.22/0.41 tff(20,plain,
% 0.22/0.41 (((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(U!3, V!2, W!1)) | (W!1 = bad))) <=> ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(U!3, V!2, W!1)) | (W!1 = bad))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(21,plain,
% 0.22/0.42 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(U!3, V!2, W!1)) | (W!1 = bad))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(22,plain,
% 0.22/0.42 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(U!3, V!2, W!1)) | (W!1 = bad)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.22/0.42 tff(23,plain,
% 0.22/0.42 (W!1 = bad),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.22/0.42 tff(24,plain,
% 0.22/0.42 (triple(U!3, V!2, W!1) = triple(U!3, V!2, bad)),
% 0.22/0.42 inference(monotonicity,[status(thm)],[23])).
% 0.22/0.42 tff(25,plain,
% 0.22/0.42 (triple(U!3, V!2, bad) = triple(U!3, V!2, W!1)),
% 0.22/0.42 inference(symmetry,[status(thm)],[24])).
% 0.22/0.42 tff(26,assumption,(remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1)), introduced(assumption)).
% 0.22/0.42 tff(27,plain,
% 0.22/0.42 (triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1) = remove_cpq(triple(U!3, V!2, W!1), X!0)),
% 0.22/0.42 inference(symmetry,[status(thm)],[26])).
% 0.22/0.42 tff(28,plain,
% 0.22/0.42 (triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad)),
% 0.22/0.42 inference(monotonicity,[status(thm)],[23])).
% 0.22/0.42 tff(29,plain,
% 0.22/0.42 (triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1)),
% 0.22/0.42 inference(symmetry,[status(thm)],[28])).
% 0.22/0.42 tff(30,plain,
% 0.22/0.42 (triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad) = remove_cpq(triple(U!3, V!2, W!1), X!0)),
% 0.22/0.42 inference(transitivity,[status(thm)],[29, 27])).
% 0.22/0.42 tff(31,plain,
% 0.22/0.42 (ok(triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad)) <=> ok(remove_cpq(triple(U!3, V!2, W!1), X!0))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[30])).
% 0.22/0.42 tff(32,plain,
% 0.22/0.42 (ok(remove_cpq(triple(U!3, V!2, W!1), X!0)) <=> ok(triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad))),
% 0.22/0.42 inference(symmetry,[status(thm)],[31])).
% 0.22/0.42 tff(33,plain,
% 0.22/0.42 (ok(remove_cpq(triple(U!3, V!2, W!1), X!0))),
% 0.22/0.42 inference(or_elim,[status(thm)],[8])).
% 0.22/0.42 tff(34,plain,
% 0.22/0.42 (ok(triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 (^[U: $i, V: $i] : refl((~ok(triple(U, V, bad))) <=> (~ok(triple(U, V, bad))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(38,plain,
% 0.22/0.42 (^[U: $i, V: $i] : rewrite((ok(triple(U, V, bad)) <=> $false) <=> (~ok(triple(U, V, bad))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 (![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[38])).
% 0.22/0.42 tff(40,axiom,(![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false)), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax40')).
% 0.22/0.42 tff(41,plain,
% 0.22/0.42 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.22/0.42 tff(42,plain,
% 0.22/0.42 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.22/0.42 tff(43,plain,(
% 0.22/0.42 ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[42])).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.22/0.42 tff(45,plain,
% 0.22/0.42 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(46,plain,
% 0.22/0.42 (~ok(triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.22/0.42 tff(47,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[46, 34])).
% 0.22/0.42 tff(48,plain,(~(remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.42 tff(49,plain,
% 0.22/0.42 ((remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1)) <=> (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[28])).
% 0.22/0.42 tff(50,plain,
% 0.22/0.42 ((~(remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1))) <=> (~(remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad)))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[49])).
% 0.22/0.42 tff(51,assumption,(~(remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1))), introduced(assumption)).
% 0.22/0.42 tff(52,plain,
% 0.22/0.42 (~(remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.22/0.42 tff(53,assumption,(contains_slb(V!2, X!0)), introduced(assumption)).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 (^[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))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(55,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.22/0.42 tff(56,plain,
% 0.22/0.42 (^[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)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(57,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[56])).
% 0.22/0.42 tff(58,plain,
% 0.22/0.42 (![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))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(59,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')).
% 0.22/0.42 tff(60,plain,
% 0.22/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.22/0.42 tff(61,plain,(
% 0.22/0.42 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[60])).
% 0.22/0.42 tff(62,plain,
% 0.22/0.42 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.22/0.42 tff(63,plain,
% 0.22/0.42 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.22/0.42 tff(64,plain,
% 0.22/0.42 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(X!0, lookup_slb(V!2, X!0))) | less_than(lookup_slb(V!2, X!0), X!0)) <=> strictly_less_than(X!0, lookup_slb(V!2, X!0))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(65,plain,
% 0.22/0.42 (~(((~less_than(X!0, lookup_slb(V!2, X!0))) | less_than(lookup_slb(V!2, X!0), X!0)) <=> strictly_less_than(X!0, lookup_slb(V!2, X!0)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.22/0.42 tff(66,plain,
% 0.22/0.42 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X))) <=> ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(67,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[66])).
% 0.22/0.42 tff(68,plain,
% 0.22/0.42 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((contains_slb(V, X) & less_than(lookup_slb(V, X), X)) <=> (~((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X))))), ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) <=> (~(~((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X))))))), rewrite((~(~((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X))))) <=> ((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X)))), ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) <=> ((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X))))), (((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> (((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))))), rewrite((((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))), (((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(69,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[68])).
% 0.22/0.42 tff(70,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(71,plain,
% 0.22/0.42 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((contains_slb(V, X) & less_than(lookup_slb(V, X), X)) => (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(72,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((contains_slb(V, X) & less_than(lookup_slb(V, X), X)) => (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[71])).
% 0.22/0.42 tff(73,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((contains_slb(V, X) & less_than(lookup_slb(V, X), X)) => (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax44')).
% 0.22/0.42 tff(74,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.22/0.42 tff(75,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.22/0.42 tff(76,plain,(
% 0.22/0.42 ![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[75])).
% 0.22/0.42 tff(77,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.22/0.42 tff(78,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.22/0.42 tff(79,plain,
% 0.22/0.42 (((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))) | ((~contains_slb(V!2, X!0)) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1)) | (~less_than(lookup_slb(V!2, X!0), X!0)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))) | (~contains_slb(V!2, X!0)) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1)) | (~less_than(lookup_slb(V!2, X!0), X!0)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(80,plain,
% 0.22/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))) | ((~contains_slb(V!2, X!0)) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1)) | (~less_than(lookup_slb(V!2, X!0), X!0)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(81,plain,
% 0.22/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))) | (~contains_slb(V!2, X!0)) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1)) | (~less_than(lookup_slb(V!2, X!0), X!0))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.22/0.42 tff(82,plain,
% 0.22/0.42 ((~contains_slb(V!2, X!0)) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1)) | (~less_than(lookup_slb(V!2, X!0), X!0))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[81, 78])).
% 0.22/0.42 tff(83,plain,
% 0.22/0.42 (~less_than(lookup_slb(V!2, X!0), X!0)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[82, 51, 53])).
% 0.22/0.42 tff(84,plain,
% 0.22/0.42 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(85,plain,
% 0.22/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.22/0.42 tff(86,plain,
% 0.22/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(87,plain,
% 0.22/0.43 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(88,plain,
% 0.22/0.43 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[87])).
% 0.22/0.43 tff(89,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.22/0.43 tff(90,plain,
% 0.22/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.22/0.43 tff(91,plain,
% 0.22/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.22/0.43 tff(92,plain,(
% 0.22/0.43 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.22/0.43 inference(skolemize,[status(sab)],[91])).
% 0.22/0.43 tff(93,plain,
% 0.22/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.22/0.43 tff(94,plain,
% 0.22/0.43 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X!0, lookup_slb(V!2, X!0)) | less_than(lookup_slb(V!2, X!0), X!0))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X!0, lookup_slb(V!2, X!0)) | less_than(lookup_slb(V!2, X!0), X!0))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(95,plain,
% 0.22/0.43 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X!0, lookup_slb(V!2, X!0)) | less_than(lookup_slb(V!2, X!0), X!0))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(96,plain,
% 0.22/0.43 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X!0, lookup_slb(V!2, X!0)) | less_than(lookup_slb(V!2, X!0), X!0)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.22/0.43 tff(97,plain,
% 0.22/0.43 (less_than(X!0, lookup_slb(V!2, X!0))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[96, 93, 83])).
% 0.22/0.43 tff(98,plain,
% 0.22/0.43 ((~((~less_than(X!0, lookup_slb(V!2, X!0))) | less_than(lookup_slb(V!2, X!0), X!0))) | (~less_than(X!0, lookup_slb(V!2, X!0))) | less_than(lookup_slb(V!2, X!0), X!0)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(99,plain,
% 0.22/0.43 ((~((~less_than(X!0, lookup_slb(V!2, X!0))) | less_than(lookup_slb(V!2, X!0), X!0))) | (~less_than(X!0, lookup_slb(V!2, X!0)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[98, 83])).
% 0.22/0.43 tff(100,plain,
% 0.22/0.43 (~((~less_than(X!0, lookup_slb(V!2, X!0))) | less_than(lookup_slb(V!2, X!0), X!0))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[99, 97])).
% 0.22/0.43 tff(101,plain,
% 0.22/0.43 ((((~less_than(X!0, lookup_slb(V!2, X!0))) | less_than(lookup_slb(V!2, X!0), X!0)) <=> strictly_less_than(X!0, lookup_slb(V!2, X!0))) | ((~less_than(X!0, lookup_slb(V!2, X!0))) | less_than(lookup_slb(V!2, X!0), X!0)) | strictly_less_than(X!0, lookup_slb(V!2, X!0))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(102,plain,
% 0.22/0.43 (strictly_less_than(X!0, lookup_slb(V!2, X!0))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[101, 100, 65])).
% 0.22/0.43 tff(103,plain,
% 0.22/0.43 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X)))) <=> ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(104,plain,
% 0.22/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[103])).
% 0.22/0.43 tff(105,plain,
% 0.22/0.43 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X))) <=> (~((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X)))))), ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) <=> (~(~((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X)))))))), rewrite((~(~((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X)))))) <=> ((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X))))), ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) <=> ((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X)))))), (((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> (((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))))), rewrite((((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))), (((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(106,plain,
% 0.22/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[105])).
% 0.22/0.43 tff(107,plain,
% 0.22/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(108,plain,
% 0.22/0.43 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X))) => (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(109,plain,
% 0.22/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X))) => (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[108])).
% 0.22/0.43 tff(110,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X))) => (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax45')).
% 0.22/0.43 tff(111,plain,
% 0.22/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.22/0.43 tff(112,plain,
% 0.22/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.22/0.43 tff(113,plain,(
% 0.22/0.43 ![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[112])).
% 0.22/0.43 tff(114,plain,
% 0.22/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.22/0.43 tff(115,plain,
% 0.22/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[114, 104])).
% 0.22/0.43 tff(116,plain,
% 0.22/0.43 (((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))) | ((~contains_slb(V!2, X!0)) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad)) | (~strictly_less_than(X!0, lookup_slb(V!2, X!0))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))) | (~contains_slb(V!2, X!0)) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad)) | (~strictly_less_than(X!0, lookup_slb(V!2, X!0))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(117,plain,
% 0.22/0.43 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))) | ((~contains_slb(V!2, X!0)) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad)) | (~strictly_less_than(X!0, lookup_slb(V!2, X!0))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(118,plain,
% 0.22/0.43 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))) | (~contains_slb(V!2, X!0)) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad)) | (~strictly_less_than(X!0, lookup_slb(V!2, X!0)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.22/0.43 tff(119,plain,
% 0.22/0.43 ((~contains_slb(V!2, X!0)) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad)) | (~strictly_less_than(X!0, lookup_slb(V!2, X!0)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.22/0.43 tff(120,plain,
% 0.22/0.43 (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), bad)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[119, 102, 53])).
% 0.22/0.43 tff(121,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[120, 52])).
% 0.22/0.43 tff(122,plain,((remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(remove_pqp(U!3, X!0), remove_slb(V!2, X!0), W!1)) | (~contains_slb(V!2, X!0))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(123,plain,
% 0.22/0.43 (~contains_slb(V!2, X!0)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[122, 48])).
% 0.22/0.43 tff(124,plain,
% 0.22/0.43 (^[U: $i, V: $i, W: $i, X: $i] : refl((contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(125,plain,
% 0.22/0.43 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[124])).
% 0.22/0.43 tff(126,plain,
% 0.22/0.43 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(127,plain,
% 0.22/0.43 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((~contains_slb(V, X)) => (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(128,plain,
% 0.22/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) => (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[127])).
% 0.22/0.44 tff(129,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) => (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax43')).
% 0.22/0.44 tff(130,plain,
% 0.22/0.44 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.22/0.44 tff(131,plain,
% 0.22/0.44 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.22/0.44 tff(132,plain,(
% 0.22/0.44 ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[131])).
% 0.22/0.44 tff(133,plain,
% 0.22/0.44 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.22/0.44 tff(134,plain,
% 0.22/0.44 (((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | (contains_slb(V!2, X!0) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(U!3, V!2, bad)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | contains_slb(V!2, X!0) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(U!3, V!2, bad)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(135,plain,
% 0.22/0.44 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | (contains_slb(V!2, X!0) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(U!3, V!2, bad)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(136,plain,
% 0.22/0.44 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | contains_slb(V!2, X!0) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(U!3, V!2, bad))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.22/0.44 tff(137,plain,
% 0.22/0.44 (contains_slb(V!2, X!0) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(U!3, V!2, bad))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[136, 133])).
% 0.22/0.44 tff(138,plain,
% 0.22/0.44 (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(U!3, V!2, bad)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[137, 123])).
% 0.22/0.44 tff(139,plain,
% 0.22/0.44 (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(U!3, V!2, W!1)),
% 0.22/0.44 inference(transitivity,[status(thm)],[138, 25])).
% 0.22/0.44 tff(140,plain,
% 0.22/0.44 (ok(remove_cpq(triple(U!3, V!2, W!1), X!0)) <=> ok(triple(U!3, V!2, W!1))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[139])).
% 0.22/0.44 tff(141,plain,
% 0.22/0.44 (ok(triple(U!3, V!2, W!1)) <=> ok(remove_cpq(triple(U!3, V!2, W!1), X!0))),
% 0.22/0.44 inference(symmetry,[status(thm)],[140])).
% 0.22/0.44 tff(142,plain,
% 0.22/0.44 ((~ok(triple(U!3, V!2, W!1))) <=> (~ok(remove_cpq(triple(U!3, V!2, W!1), X!0)))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[141])).
% 0.22/0.44 tff(143,plain,
% 0.22/0.44 (~ok(remove_cpq(triple(U!3, V!2, W!1), X!0))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[9, 142])).
% 0.22/0.44 tff(144,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[33, 143])).
% 0.22/0.44 % SZS output end Proof
% 0.22/0.44 % E exiting
%------------------------------------------------------------------------------