%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC380+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:31:04 AM UTC 2025
% Result : Theorem 0.81s 1.03s
% Output : Proof 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SWC380+1 : TPTP v9.0.0. Released v2.4.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:10:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.81/1.03 % SZS status Theorem
% 0.81/1.03 % SZS output start Proof
% 0.81/1.03 tff(memberP_type, type, (
% 0.81/1.03 memberP: ( $i * $i ) > $o)).
% 0.81/1.03 tff(tptp_fun_Z_47_type, type, (
% 0.81/1.03 tptp_fun_Z_47: $i)).
% 0.81/1.03 tff(cons_type, type, (
% 0.81/1.03 cons: ( $i * $i ) > $i)).
% 0.81/1.03 tff(tptp_fun_X1_48_type, type, (
% 0.81/1.03 tptp_fun_X1_48: $i)).
% 0.81/1.03 tff(tptp_fun_V_46_type, type, (
% 0.81/1.03 tptp_fun_V_46: $i)).
% 0.81/1.03 tff(app_type, type, (
% 0.81/1.03 app: ( $i * $i ) > $i)).
% 0.81/1.03 tff(nil_type, type, (
% 0.81/1.03 nil: $i)).
% 0.81/1.03 tff(tptp_fun_U_45_type, type, (
% 0.81/1.03 tptp_fun_U_45: $i)).
% 0.81/1.03 tff(ssList_type, type, (
% 0.81/1.03 ssList: $i > $o)).
% 0.81/1.03 tff(ssItem_type, type, (
% 0.81/1.03 ssItem: $i > $o)).
% 0.81/1.03 tff(neq_type, type, (
% 0.81/1.03 neq: ( $i * $i ) > $o)).
% 0.81/1.03 tff(1,plain,
% 0.81/1.03 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil) & ssItem(Z!47) & (~((~ssList(X1!48)) | (~(cons(Z!47, nil) = U!45)) | (~(app(cons(Z!47, nil), X1!48) = V!46)))))) <=> (ssList(U!45) & ssList(V!46) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil) & ssItem(Z!47) & (~((~ssList(X1!48)) | (~(cons(Z!47, nil) = U!45)) | (~(app(cons(Z!47, nil), X1!48) = V!46)))))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2,plain,
% 0.81/1.03 ((ssList(V!46) & ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil) & (ssItem(Z!47) & (~((~ssList(X1!48)) | (~(cons(Z!47, nil) = U!45)) | (~(app(cons(Z!47, nil), X1!48) = V!46)))))) <=> (ssList(V!46) & ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil) & ssItem(Z!47) & (~((~ssList(X1!48)) | (~(cons(Z!47, nil) = U!45)) | (~(app(cons(Z!47, nil), X1!48) = V!46)))))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(3,plain,
% 0.81/1.03 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil) & (ssItem(Z!47) & (~((~ssList(X1!48)) | (~(cons(Z!47, nil) = U!45)) | (~(app(cons(Z!47, nil), X1!48) = V!46))))))) <=> (ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil) & ssItem(Z!47) & (~((~ssList(X1!48)) | (~(cons(Z!47, nil) = U!45)) | (~(app(cons(Z!47, nil), X1!48) = V!46))))))),
% 0.81/1.03 inference(monotonicity,[status(thm)],[2])).
% 0.81/1.03 tff(4,plain,
% 0.81/1.03 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil) & (ssItem(Z!47) & (~((~ssList(X1!48)) | (~(cons(Z!47, nil) = U!45)) | (~(app(cons(Z!47, nil), X1!48) = V!46))))))) <=> (ssList(U!45) & ssList(V!46) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil) & ssItem(Z!47) & (~((~ssList(X1!48)) | (~(cons(Z!47, nil) = U!45)) | (~(app(cons(Z!47, nil), X1!48) = V!46)))))),
% 0.81/1.03 inference(transitivity,[status(thm)],[3, 1])).
% 0.81/1.03 tff(5,plain,
% 0.81/1.03 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(cons(Z, nil) = U)) | (~(app(cons(Z, nil), X1) = V))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(cons(Z, nil) = U)) | (~(app(cons(Z, nil), X1) = V)))))))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(6,plain,
% 0.81/1.03 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ?[Y: $i] : ((ssItem(Y) & (cons(Y, nil) = U)) & memberP(V, Y))) | ![Z: $i] : (ssItem(Z) => ![X1: $i] : (ssList(X1) => ((~(cons(Z, nil) = W)) | (~(app(cons(Z, nil), X1) = X)))))) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(cons(Z, nil) = U)) | (~(app(cons(Z, nil), X1) = V)))))))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(7,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ?[Y: $i] : ((ssItem(Y) & (cons(Y, nil) = U)) & memberP(V, Y))) | ![Z: $i] : (ssItem(Z) => ![X1: $i] : (ssList(X1) => ((~(cons(Z, nil) = W)) | (~(app(cons(Z, nil), X1) = X)))))) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.81/1.03 tff(8,plain,
% 0.81/1.03 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(cons(Z, nil) = U)) | (~(app(cons(Z, nil), X1) = V))))))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.81/1.03 tff(9,plain,
% 0.81/1.03 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(cons(Z, nil) = U)) | (~(app(cons(Z, nil), X1) = V))))))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.81/1.03 tff(10,plain,
% 0.81/1.03 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(cons(Z, nil) = U)) | (~(app(cons(Z, nil), X1) = V))))))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.81/1.03 tff(11,plain,
% 0.81/1.03 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(cons(Z, nil) = U)) | (~(app(cons(Z, nil), X1) = V))))))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.81/1.03 tff(12,plain,
% 0.81/1.03 (ssList(U!45) & ssList(V!46) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil) & ssItem(Z!47) & (~((~ssList(X1!48)) | (~(cons(Z!47, nil) = U!45)) | (~(app(cons(Z!47, nil), X1!48) = V!46))))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.81/1.03 tff(13,plain,
% 0.81/1.03 (~((~ssList(X1!48)) | (~(cons(Z!47, nil) = U!45)) | (~(app(cons(Z!47, nil), X1!48) = V!46)))),
% 0.81/1.03 inference(and_elim,[status(thm)],[12])).
% 0.81/1.03 tff(14,plain,
% 0.81/1.03 (app(cons(Z!47, nil), X1!48) = V!46),
% 0.81/1.03 inference(or_elim,[status(thm)],[13])).
% 0.81/1.03 tff(15,plain,
% 0.81/1.03 (ssList(X1!48)),
% 0.81/1.03 inference(or_elim,[status(thm)],[13])).
% 0.81/1.03 tff(16,plain,
% 0.81/1.03 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(17,plain,
% 0.81/1.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[16])).
% 0.81/1.03 tff(18,plain,
% 0.81/1.03 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(19,plain,
% 0.81/1.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[18])).
% 0.81/1.03 tff(20,plain,
% 0.81/1.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.81/1.03 inference(transitivity,[status(thm)],[19, 17])).
% 0.81/1.03 tff(21,plain,
% 0.81/1.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(22,plain,
% 0.81/1.03 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), (![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(23,plain,
% 0.81/1.03 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[22])).
% 0.81/1.03 tff(24,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax81')).
% 0.81/1.03 tff(25,plain,
% 0.81/1.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.81/1.03 tff(26,plain,
% 0.81/1.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.81/1.03 tff(27,plain,(
% 0.81/1.03 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.81/1.03 inference(skolemize,[status(sab)],[26])).
% 0.81/1.03 tff(28,plain,
% 0.81/1.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.81/1.03 tff(29,plain,
% 0.81/1.03 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(X1!48)) | ![V: $i] : ((~ssItem(V)) | (cons(V, X1!48) = app(cons(V, nil), X1!48))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(X1!48)) | ![V: $i] : ((~ssItem(V)) | (cons(V, X1!48) = app(cons(V, nil), X1!48))))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(30,plain,
% 0.81/1.03 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(X1!48)) | ![V: $i] : ((~ssItem(V)) | (cons(V, X1!48) = app(cons(V, nil), X1!48))))),
% 0.81/1.03 inference(quant_inst,[status(thm)],[])).
% 0.81/1.03 tff(31,plain,
% 0.81/1.03 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(X1!48)) | ![V: $i] : ((~ssItem(V)) | (cons(V, X1!48) = app(cons(V, nil), X1!48)))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.81/1.03 tff(32,plain,
% 0.81/1.03 (![V: $i] : ((~ssItem(V)) | (cons(V, X1!48) = app(cons(V, nil), X1!48)))),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[31, 28, 15])).
% 0.81/1.03 tff(33,plain,
% 0.81/1.03 (ssItem(Z!47)),
% 0.81/1.03 inference(and_elim,[status(thm)],[12])).
% 0.81/1.03 tff(34,plain,
% 0.81/1.03 (((~![V: $i] : ((~ssItem(V)) | (cons(V, X1!48) = app(cons(V, nil), X1!48)))) | ((~ssItem(Z!47)) | (cons(Z!47, X1!48) = app(cons(Z!47, nil), X1!48)))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, X1!48) = app(cons(V, nil), X1!48)))) | (~ssItem(Z!47)) | (cons(Z!47, X1!48) = app(cons(Z!47, nil), X1!48)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(35,plain,
% 0.81/1.03 ((~![V: $i] : ((~ssItem(V)) | (cons(V, X1!48) = app(cons(V, nil), X1!48)))) | ((~ssItem(Z!47)) | (cons(Z!47, X1!48) = app(cons(Z!47, nil), X1!48)))),
% 0.81/1.03 inference(quant_inst,[status(thm)],[])).
% 0.81/1.03 tff(36,plain,
% 0.81/1.03 ((~![V: $i] : ((~ssItem(V)) | (cons(V, X1!48) = app(cons(V, nil), X1!48)))) | (~ssItem(Z!47)) | (cons(Z!47, X1!48) = app(cons(Z!47, nil), X1!48))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.81/1.03 tff(37,plain,
% 0.81/1.03 (cons(Z!47, X1!48) = app(cons(Z!47, nil), X1!48)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[36, 33, 32])).
% 0.81/1.03 tff(38,plain,
% 0.81/1.03 (cons(Z!47, X1!48) = V!46),
% 0.81/1.03 inference(transitivity,[status(thm)],[37, 14])).
% 0.81/1.03 tff(39,plain,
% 0.81/1.03 (memberP(cons(Z!47, X1!48), Z!47) <=> memberP(V!46, Z!47)),
% 0.81/1.03 inference(monotonicity,[status(thm)],[38])).
% 0.81/1.03 tff(40,plain,
% 0.81/1.03 (memberP(V!46, Z!47) <=> memberP(cons(Z!47, X1!48), Z!47)),
% 0.81/1.03 inference(symmetry,[status(thm)],[39])).
% 0.81/1.03 tff(41,plain,
% 0.81/1.03 ((~memberP(V!46, Z!47)) <=> (~memberP(cons(Z!47, X1!48), Z!47))),
% 0.81/1.03 inference(monotonicity,[status(thm)],[40])).
% 0.81/1.03 tff(42,plain,
% 0.81/1.03 (cons(Z!47, nil) = U!45),
% 0.81/1.03 inference(or_elim,[status(thm)],[13])).
% 0.81/1.03 tff(43,plain,
% 0.81/1.03 (^[Y: $i] : refl(((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y))) <=> ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(44,plain,
% 0.81/1.03 (![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y))) <=> ![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[43])).
% 0.81/1.03 tff(45,plain,
% 0.81/1.03 (^[Y: $i] : trans(monotonicity(rewrite((ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y)) <=> (~((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y))))), ((~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) <=> (~(~((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y))))))), rewrite((~(~((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y))))) <=> ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))), ((~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) <=> ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(46,plain,
% 0.81/1.03 (![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) <=> ![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[45])).
% 0.81/1.03 tff(47,plain,
% 0.81/1.03 (![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y)))),
% 0.81/1.03 inference(and_elim,[status(thm)],[12])).
% 0.81/1.03 tff(48,plain,
% 0.81/1.03 (![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.81/1.03 tff(49,plain,
% 0.81/1.03 (![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.81/1.03 tff(50,plain,
% 0.81/1.03 (((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | ((~(cons(Z!47, nil) = U!45)) | (~ssItem(Z!47)) | (~memberP(V!46, Z!47)))) <=> ((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | (~(cons(Z!47, nil) = U!45)) | (~ssItem(Z!47)) | (~memberP(V!46, Z!47)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(51,plain,
% 0.81/1.03 (((~ssItem(Z!47)) | (~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47))) <=> ((~(cons(Z!47, nil) = U!45)) | (~ssItem(Z!47)) | (~memberP(V!46, Z!47)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(52,plain,
% 0.81/1.03 (((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | ((~ssItem(Z!47)) | (~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)))) <=> ((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | ((~(cons(Z!47, nil) = U!45)) | (~ssItem(Z!47)) | (~memberP(V!46, Z!47))))),
% 0.81/1.03 inference(monotonicity,[status(thm)],[51])).
% 0.81/1.03 tff(53,plain,
% 0.81/1.03 (((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | ((~ssItem(Z!47)) | (~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)))) <=> ((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | (~(cons(Z!47, nil) = U!45)) | (~ssItem(Z!47)) | (~memberP(V!46, Z!47)))),
% 0.81/1.03 inference(transitivity,[status(thm)],[52, 50])).
% 0.81/1.03 tff(54,plain,
% 0.81/1.03 ((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | ((~ssItem(Z!47)) | (~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)))),
% 0.81/1.03 inference(quant_inst,[status(thm)],[])).
% 0.81/1.03 tff(55,plain,
% 0.81/1.03 ((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | (~(cons(Z!47, nil) = U!45)) | (~ssItem(Z!47)) | (~memberP(V!46, Z!47))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.81/1.03 tff(56,plain,
% 0.81/1.03 (~memberP(V!46, Z!47)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[55, 49, 33, 42])).
% 0.81/1.03 tff(57,plain,
% 0.81/1.03 (~memberP(cons(Z!47, X1!48), Z!47)),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[56, 41])).
% 0.81/1.03 tff(58,plain,
% 0.81/1.03 (^[U: $i] : refl(((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(59,plain,
% 0.81/1.03 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[58])).
% 0.81/1.03 tff(60,plain,
% 0.81/1.03 (^[U: $i] : rewrite(((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(61,plain,
% 0.81/1.03 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[60])).
% 0.81/1.03 tff(62,plain,
% 0.81/1.03 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 0.81/1.03 inference(transitivity,[status(thm)],[61, 59])).
% 0.81/1.03 tff(63,plain,
% 0.81/1.03 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(64,plain,
% 0.81/1.03 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : rewrite((ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))) <=> ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))), (![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))) <=> ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))), ((ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))) <=> (ssItem(V) => ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))), rewrite((ssItem(V) => ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))) <=> ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))), ((ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))) <=> ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))))), (![V: $i] : (ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))) <=> ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))), ((ssItem(U) => ![V: $i] : (ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> (ssItem(U) => ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))))), rewrite((ssItem(U) => ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))), ((ssItem(U) => ![V: $i] : (ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))))),
% 0.81/1.04 inference(bind,[status(th)],[])).
% 0.81/1.04 tff(65,plain,
% 0.81/1.04 (![U: $i] : (ssItem(U) => ![V: $i] : (ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 0.81/1.04 inference(quant_intro,[status(thm)],[64])).
% 0.81/1.04 tff(66,axiom,(![U: $i] : (ssItem(U) => ![V: $i] : (ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax37')).
% 0.81/1.04 tff(67,plain,
% 0.81/1.04 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 0.81/1.04 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.81/1.04 tff(68,plain,
% 0.81/1.04 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 0.81/1.04 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.81/1.04 tff(69,plain,(
% 0.81/1.04 ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 0.81/1.04 inference(skolemize,[status(sab)],[68])).
% 0.81/1.04 tff(70,plain,
% 0.81/1.04 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 0.81/1.04 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.81/1.04 tff(71,plain,
% 0.81/1.04 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))) | ((~ssItem(Z!47)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47))))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))) | (~ssItem(Z!47)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47))))))),
% 0.81/1.04 inference(rewrite,[status(thm)],[])).
% 0.81/1.04 tff(72,plain,
% 0.81/1.04 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))) | ((~ssItem(Z!47)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47))))))),
% 0.81/1.04 inference(quant_inst,[status(thm)],[])).
% 0.81/1.04 tff(73,plain,
% 0.81/1.04 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))) | (~ssItem(Z!47)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47)))))),
% 0.81/1.04 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.81/1.04 tff(74,plain,
% 0.81/1.04 (![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47)))))),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[73, 70, 33])).
% 0.81/1.04 tff(75,plain,
% 0.81/1.04 (((~![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47)))))) | ((~ssItem(Z!47)) | ![W: $i] : ((~ssList(W)) | memberP(cons(Z!47, W), Z!47)))) <=> ((~![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47)))))) | (~ssItem(Z!47)) | ![W: $i] : ((~ssList(W)) | memberP(cons(Z!47, W), Z!47)))),
% 0.81/1.04 inference(rewrite,[status(thm)],[])).
% 0.81/1.04 tff(76,plain,
% 0.81/1.04 (((~ssItem(Z!47)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(Z!47, W), Z!47) <=> ((Z!47 = Z!47) | memberP(W, Z!47))))) <=> ((~ssItem(Z!47)) | ![W: $i] : ((~ssList(W)) | memberP(cons(Z!47, W), Z!47)))),
% 0.81/1.04 inference(rewrite,[status(thm)],[])).
% 0.81/1.04 tff(77,plain,
% 0.81/1.04 (((~![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47)))))) | ((~ssItem(Z!47)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(Z!47, W), Z!47) <=> ((Z!47 = Z!47) | memberP(W, Z!47)))))) <=> ((~![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47)))))) | ((~ssItem(Z!47)) | ![W: $i] : ((~ssList(W)) | memberP(cons(Z!47, W), Z!47))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[76])).
% 0.87/1.04 tff(78,plain,
% 0.87/1.04 (((~![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47)))))) | ((~ssItem(Z!47)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(Z!47, W), Z!47) <=> ((Z!47 = Z!47) | memberP(W, Z!47)))))) <=> ((~![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47)))))) | (~ssItem(Z!47)) | ![W: $i] : ((~ssList(W)) | memberP(cons(Z!47, W), Z!47)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[77, 75])).
% 0.87/1.04 tff(79,plain,
% 0.87/1.04 ((~![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47)))))) | ((~ssItem(Z!47)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(Z!47, W), Z!47) <=> ((Z!47 = Z!47) | memberP(W, Z!47)))))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(80,plain,
% 0.87/1.04 ((~![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), Z!47) <=> ((Z!47 = V) | memberP(W, Z!47)))))) | (~ssItem(Z!47)) | ![W: $i] : ((~ssList(W)) | memberP(cons(Z!47, W), Z!47))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.87/1.04 tff(81,plain,
% 0.87/1.04 (![W: $i] : ((~ssList(W)) | memberP(cons(Z!47, W), Z!47))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[80, 33, 74])).
% 0.87/1.04 tff(82,plain,
% 0.87/1.04 (((~![W: $i] : ((~ssList(W)) | memberP(cons(Z!47, W), Z!47))) | ((~ssList(X1!48)) | memberP(cons(Z!47, X1!48), Z!47))) <=> ((~![W: $i] : ((~ssList(W)) | memberP(cons(Z!47, W), Z!47))) | (~ssList(X1!48)) | memberP(cons(Z!47, X1!48), Z!47))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(83,plain,
% 0.87/1.04 ((~![W: $i] : ((~ssList(W)) | memberP(cons(Z!47, W), Z!47))) | ((~ssList(X1!48)) | memberP(cons(Z!47, X1!48), Z!47))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(84,plain,
% 0.87/1.04 ((~![W: $i] : ((~ssList(W)) | memberP(cons(Z!47, W), Z!47))) | (~ssList(X1!48)) | memberP(cons(Z!47, X1!48), Z!47)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.87/1.04 tff(85,plain,
% 0.87/1.04 (memberP(cons(Z!47, X1!48), Z!47)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[84, 15, 81])).
% 0.87/1.04 tff(86,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[85, 57])).
% 0.87/1.04 % SZS output end Proof
% 0.87/1.04 % E exiting
%------------------------------------------------------------------------------