%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC408+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:31:09 AM UTC 2025
% Result : Theorem 0.71s 0.88s
% Output : Proof 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC408+1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:14:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.71/0.88 % SZS status Theorem
% 0.71/0.88 % SZS output start Proof
% 0.71/0.88 tff(memberP_type, type, (
% 0.71/0.88 memberP: ( $i * $i ) > $o)).
% 0.71/0.88 tff(tptp_fun_Y_47_type, type, (
% 0.71/0.88 tptp_fun_Y_47: $i)).
% 0.71/0.88 tff(app_type, type, (
% 0.71/0.88 app: ( $i * $i ) > $i)).
% 0.71/0.88 tff(tptp_fun_V_46_type, type, (
% 0.71/0.88 tptp_fun_V_46: $i)).
% 0.71/0.88 tff(tptp_fun_U_45_type, type, (
% 0.71/0.88 tptp_fun_U_45: $i)).
% 0.71/0.88 tff(ssItem_type, type, (
% 0.71/0.88 ssItem: $i > $o)).
% 0.71/0.88 tff(ssList_type, type, (
% 0.71/0.88 ssList: $i > $o)).
% 0.71/0.88 tff(1,plain,
% 0.71/0.88 ((ssList(U!45) & ((app(V!46, V!46) = U!45) & ssList(V!46) & ssList(U!45) & (~((~ssItem(Y!47)) | memberP(U!45, Y!47) | (~memberP(V!46, Y!47)))))) <=> (ssList(U!45) & (app(V!46, V!46) = U!45) & ssList(V!46) & (~((~ssItem(Y!47)) | memberP(U!45, Y!47) | (~memberP(V!46, Y!47)))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(2,plain,
% 0.71/0.88 ((~((~ssItem(Y!47)) | memberP(U!45, Y!47) | (~memberP(V!46, Y!47)))) <=> (~((~ssItem(Y!47)) | memberP(U!45, Y!47) | (~memberP(V!46, Y!47))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(3,plain,
% 0.71/0.88 (((app(V!46, V!46) = U!45) & ssList(V!46) & ssList(U!45) & (~((~ssItem(Y!47)) | memberP(U!45, Y!47) | (~memberP(V!46, Y!47))))) <=> ((app(V!46, V!46) = U!45) & ssList(V!46) & ssList(U!45) & (~((~ssItem(Y!47)) | memberP(U!45, Y!47) | (~memberP(V!46, Y!47)))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2])).
% 0.71/0.88 tff(4,plain,
% 0.71/0.88 ((ssList(U!45) & ((app(V!46, V!46) = U!45) & ssList(V!46) & ssList(U!45) & (~((~ssItem(Y!47)) | memberP(U!45, Y!47) | (~memberP(V!46, Y!47)))))) <=> (ssList(U!45) & ((app(V!46, V!46) = U!45) & ssList(V!46) & ssList(U!45) & (~((~ssItem(Y!47)) | memberP(U!45, Y!47) | (~memberP(V!46, Y!47))))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3])).
% 0.71/0.88 tff(5,plain,
% 0.71/0.88 ((ssList(U!45) & ((app(V!46, V!46) = U!45) & ssList(V!46) & ssList(U!45) & (~((~ssItem(Y!47)) | memberP(U!45, Y!47) | (~memberP(V!46, Y!47)))))) <=> (ssList(U!45) & (app(V!46, V!46) = U!45) & ssList(V!46) & (~((~ssItem(Y!47)) | memberP(U!45, Y!47) | (~memberP(V!46, Y!47)))))),
% 0.71/0.88 inference(transitivity,[status(thm)],[4, 1])).
% 0.71/0.88 tff(6,plain,
% 0.71/0.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~(app(V, V) = U)) | (~ssList(V)) | (~ssList(U)) | ![Y: $i] : ((~ssItem(Y)) | memberP(U, Y) | (~memberP(V, Y)))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~(app(V, V) = U)) | (~ssList(V)) | (~ssList(U)) | ![Y: $i] : ((~ssItem(Y)) | memberP(U, Y) | (~memberP(V, Y))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(7,plain,
% 0.71/0.88 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(app(X, X) = W)) | (~(V = X))) | (~(U = W))) | ![Y: $i] : (ssItem(Y) => ((~memberP(V, Y)) | memberP(U, Y))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~(app(V, V) = U)) | (~ssList(V)) | (~ssList(U)) | ![Y: $i] : ((~ssItem(Y)) | memberP(U, Y) | (~memberP(V, Y))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(8,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(app(X, X) = W)) | (~(V = X))) | (~(U = W))) | ![Y: $i] : (ssItem(Y) => ((~memberP(V, Y)) | memberP(U, Y))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.71/0.88 tff(9,plain,
% 0.71/0.88 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~(app(V, V) = U)) | (~ssList(V)) | (~ssList(U)) | ![Y: $i] : ((~ssItem(Y)) | memberP(U, Y) | (~memberP(V, Y)))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.71/0.88 tff(10,plain,
% 0.71/0.88 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~(app(V, V) = U)) | (~ssList(V)) | (~ssList(U)) | ![Y: $i] : ((~ssItem(Y)) | memberP(U, Y) | (~memberP(V, Y)))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.71/0.88 tff(11,plain,
% 0.71/0.88 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~(app(V, V) = U)) | (~ssList(V)) | (~ssList(U)) | ![Y: $i] : ((~ssItem(Y)) | memberP(U, Y) | (~memberP(V, Y)))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.71/0.88 tff(12,plain,
% 0.71/0.88 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~(app(V, V) = U)) | (~ssList(V)) | (~ssList(U)) | ![Y: $i] : ((~ssItem(Y)) | memberP(U, Y) | (~memberP(V, Y)))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.71/0.88 tff(13,plain,
% 0.71/0.88 (ssList(U!45) & (app(V!46, V!46) = U!45) & ssList(V!46) & (~((~ssItem(Y!47)) | memberP(U!45, Y!47) | (~memberP(V!46, Y!47))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.71/0.88 tff(14,plain,
% 0.71/0.88 (app(V!46, V!46) = U!45),
% 0.71/0.88 inference(and_elim,[status(thm)],[13])).
% 0.71/0.88 tff(15,plain,
% 0.71/0.88 (memberP(app(V!46, V!46), Y!47) <=> memberP(U!45, Y!47)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[14])).
% 0.71/0.88 tff(16,plain,
% 0.71/0.88 (memberP(U!45, Y!47) <=> memberP(app(V!46, V!46), Y!47)),
% 0.71/0.88 inference(symmetry,[status(thm)],[15])).
% 0.71/0.88 tff(17,plain,
% 0.71/0.88 ((~memberP(U!45, Y!47)) <=> (~memberP(app(V!46, V!46), Y!47))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[16])).
% 0.71/0.88 tff(18,plain,
% 0.71/0.88 (~((~ssItem(Y!47)) | memberP(U!45, Y!47) | (~memberP(V!46, Y!47)))),
% 0.71/0.88 inference(and_elim,[status(thm)],[13])).
% 0.71/0.88 tff(19,plain,
% 0.71/0.88 (~memberP(U!45, Y!47)),
% 0.71/0.88 inference(or_elim,[status(thm)],[18])).
% 0.71/0.88 tff(20,plain,
% 0.71/0.88 (~memberP(app(V!46, V!46), Y!47)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.71/0.88 tff(21,plain,
% 0.71/0.88 (ssItem(Y!47)),
% 0.71/0.88 inference(or_elim,[status(thm)],[18])).
% 0.71/0.88 tff(22,plain,
% 0.71/0.88 (^[U: $i] : refl(((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(23,plain,
% 0.71/0.88 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[22])).
% 0.71/0.88 tff(24,plain,
% 0.71/0.88 (^[U: $i] : rewrite(((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(25,plain,
% 0.71/0.88 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[24])).
% 0.71/0.88 tff(26,plain,
% 0.71/0.88 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.71/0.88 inference(transitivity,[status(thm)],[25, 23])).
% 0.71/0.88 tff(27,plain,
% 0.71/0.88 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(28,plain,
% 0.71/0.88 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite((memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))) <=> (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))), ((ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> (ssList(W) => (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), rewrite((ssList(W) => (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))) <=> ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))), ((ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), (![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), ((ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> (ssItem(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))), rewrite((ssItem(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), ((ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(29,plain,
% 0.71/0.88 (![U: $i] : (ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[28])).
% 0.71/0.88 tff(30,axiom,(![U: $i] : (ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax36')).
% 0.71/0.88 tff(31,plain,
% 0.71/0.88 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.71/0.88 tff(32,plain,
% 0.71/0.88 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.71/0.88 tff(33,plain,(
% 0.71/0.88 ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.71/0.88 inference(skolemize,[status(sab)],[32])).
% 0.71/0.88 tff(34,plain,
% 0.71/0.88 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.71/0.88 tff(35,plain,
% 0.71/0.88 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | ((~ssItem(Y!47)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47))))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | (~ssItem(Y!47)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(36,plain,
% 0.71/0.88 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | ((~ssItem(Y!47)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47))))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(37,plain,
% 0.71/0.89 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | (~ssItem(Y!47)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47)))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.71/0.89 tff(38,plain,
% 0.71/0.89 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47)))))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[37, 34, 21])).
% 0.71/0.89 tff(39,plain,
% 0.71/0.89 (ssList(V!46)),
% 0.71/0.89 inference(and_elim,[status(thm)],[13])).
% 0.71/0.89 tff(40,plain,
% 0.71/0.89 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47)))))) | ((~ssList(V!46)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47)))))) | (~ssList(V!46)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47)))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(41,plain,
% 0.71/0.89 (((~ssList(V!46)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(W, Y!47) | memberP(V!46, Y!47))))) <=> ((~ssList(V!46)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47)))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(42,plain,
% 0.71/0.89 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47)))))) | ((~ssList(V!46)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(W, Y!47) | memberP(V!46, Y!47)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47)))))) | ((~ssList(V!46)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47))))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[41])).
% 0.71/0.89 tff(43,plain,
% 0.71/0.89 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47)))))) | ((~ssList(V!46)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(W, Y!47) | memberP(V!46, Y!47)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47)))))) | (~ssList(V!46)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47)))))),
% 0.71/0.89 inference(transitivity,[status(thm)],[42, 40])).
% 0.71/0.89 tff(44,plain,
% 0.71/0.89 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47)))))) | ((~ssList(V!46)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(W, Y!47) | memberP(V!46, Y!47)))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(45,plain,
% 0.71/0.89 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), Y!47) <=> (memberP(W, Y!47) | memberP(V, Y!47)))))) | (~ssList(V!46)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.71/0.89 tff(46,plain,
% 0.71/0.89 (![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47))))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[45, 39, 38])).
% 0.71/0.89 tff(47,plain,
% 0.71/0.89 (((~![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47))))) | ((~ssList(V!46)) | (memberP(app(V!46, V!46), Y!47) <=> memberP(V!46, Y!47)))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47))))) | (~ssList(V!46)) | (memberP(app(V!46, V!46), Y!47) <=> memberP(V!46, Y!47)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(48,plain,
% 0.71/0.89 (((~ssList(V!46)) | (memberP(app(V!46, V!46), Y!47) <=> (memberP(V!46, Y!47) | memberP(V!46, Y!47)))) <=> ((~ssList(V!46)) | (memberP(app(V!46, V!46), Y!47) <=> memberP(V!46, Y!47)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(49,plain,
% 0.71/0.89 (((~![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47))))) | ((~ssList(V!46)) | (memberP(app(V!46, V!46), Y!47) <=> (memberP(V!46, Y!47) | memberP(V!46, Y!47))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47))))) | ((~ssList(V!46)) | (memberP(app(V!46, V!46), Y!47) <=> memberP(V!46, Y!47))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[48])).
% 0.71/0.89 tff(50,plain,
% 0.71/0.89 (((~![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47))))) | ((~ssList(V!46)) | (memberP(app(V!46, V!46), Y!47) <=> (memberP(V!46, Y!47) | memberP(V!46, Y!47))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47))))) | (~ssList(V!46)) | (memberP(app(V!46, V!46), Y!47) <=> memberP(V!46, Y!47)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[49, 47])).
% 0.71/0.89 tff(51,plain,
% 0.71/0.89 ((~![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47))))) | ((~ssList(V!46)) | (memberP(app(V!46, V!46), Y!47) <=> (memberP(V!46, Y!47) | memberP(V!46, Y!47))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(52,plain,
% 0.71/0.89 ((~![W: $i] : ((~ssList(W)) | (memberP(app(V!46, W), Y!47) <=> (memberP(V!46, Y!47) | memberP(W, Y!47))))) | (~ssList(V!46)) | (memberP(app(V!46, V!46), Y!47) <=> memberP(V!46, Y!47))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.71/0.89 tff(53,plain,
% 0.71/0.89 (memberP(app(V!46, V!46), Y!47) <=> memberP(V!46, Y!47)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[52, 39, 46])).
% 0.71/0.89 tff(54,plain,
% 0.71/0.89 (memberP(V!46, Y!47)),
% 0.71/0.89 inference(or_elim,[status(thm)],[18])).
% 0.71/0.89 tff(55,plain,
% 0.71/0.89 ((~(memberP(app(V!46, V!46), Y!47) <=> memberP(V!46, Y!47))) | memberP(app(V!46, V!46), Y!47) | (~memberP(V!46, Y!47))),
% 0.71/0.89 inference(tautology,[status(thm)],[])).
% 0.71/0.89 tff(56,plain,
% 0.71/0.89 ((~(memberP(app(V!46, V!46), Y!47) <=> memberP(V!46, Y!47))) | memberP(app(V!46, V!46), Y!47)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.71/0.89 tff(57,plain,
% 0.71/0.89 (memberP(app(V!46, V!46), Y!47)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.71/0.89 tff(58,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[57, 20])).
% 0.71/0.89 % SZS output end Proof
% 0.71/0.89 % E exiting
%------------------------------------------------------------------------------