%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC042+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:30:00 AM UTC 2025
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC042+1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n003.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 08:06:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(app_type, type, (
% 0.20/0.48 app: ( $i * $i ) > $i)).
% 0.20/0.48 tff(tptp_fun_Y_46_type, type, (
% 0.20/0.48 tptp_fun_Y_46: $i)).
% 0.20/0.48 tff(tptp_fun_U_45_type, type, (
% 0.20/0.48 tptp_fun_U_45: $i)).
% 0.20/0.48 tff(nil_type, type, (
% 0.20/0.48 nil: $i)).
% 0.20/0.48 tff(totalorderedP_type, type, (
% 0.20/0.48 totalorderedP: $i > $o)).
% 0.20/0.48 tff(leq_type, type, (
% 0.20/0.48 leq: ( $i * $i ) > $o)).
% 0.20/0.48 tff(cons_type, type, (
% 0.20/0.48 cons: ( $i * $i ) > $i)).
% 0.20/0.48 tff(ssList_type, type, (
% 0.20/0.48 ssList: $i > $o)).
% 0.20/0.48 tff(ssItem_type, type, (
% 0.20/0.48 ssItem: $i > $o)).
% 0.20/0.48 tff(1,plain,
% 0.20/0.48 (((~(nil = U!45)) & ssList(U!45) & ssList(nil) & (ssList(Y!46) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!46)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & totalorderedP(U!45) & (app(U!45, Y!46) = nil))) <=> ((~(nil = U!45)) & ssList(U!45) & ssList(nil) & ssList(Y!46) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!46)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & totalorderedP(U!45) & (app(U!45, Y!46) = nil))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 ((ssList(Y!46) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!46)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & totalorderedP(U!45) & (app(U!45, Y!46) = nil)) <=> (ssList(Y!46) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!46)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & totalorderedP(U!45) & (app(U!45, Y!46) = nil))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 (((~(nil = U!45)) & ssList(U!45) & ssList(nil) & (ssList(Y!46) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!46)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & totalorderedP(U!45) & (app(U!45, Y!46) = nil))) <=> ((~(nil = U!45)) & ssList(U!45) & ssList(nil) & (ssList(Y!46) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!46)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & totalorderedP(U!45) & (app(U!45, Y!46) = nil)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (((~(nil = U!45)) & ssList(U!45) & ssList(nil) & (ssList(Y!46) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!46)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & totalorderedP(U!45) & (app(U!45, Y!46) = nil))) <=> ((~(nil = U!45)) & ssList(U!45) & ssList(nil) & ssList(Y!46) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!46)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & totalorderedP(U!45) & (app(U!45, Y!46) = nil))),
% 0.20/0.48 inference(transitivity,[status(thm)],[3, 1])).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ![Y: $i] : ((~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z))))) | (~totalorderedP(U)) | (~(app(U, Y) = nil))))) <=> (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ![Y: $i] : ((~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z))))) | (~totalorderedP(U)) | (~(app(U, Y) = nil)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (nil = U)) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~totalorderedP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : ((ssList(X3) & (app(X3, cons(X2, nil)) = W)) & leq(X2, Z)))))))) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ![Y: $i] : ((~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z))))) | (~totalorderedP(U)) | (~(app(U, Y) = nil)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(7,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (nil = U)) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~totalorderedP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : ((ssList(X3) & (app(X3, cons(X2, nil)) = W)) & leq(X2, Z)))))))) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ![Y: $i] : ((~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z))))) | (~totalorderedP(U)) | (~(app(U, Y) = nil))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.49 tff(9,plain,
% 0.20/0.49 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ![Y: $i] : ((~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z))))) | (~totalorderedP(U)) | (~(app(U, Y) = nil))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ![Y: $i] : ((~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z))))) | (~totalorderedP(U)) | (~(app(U, Y) = nil))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ![Y: $i] : ((~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z))))) | (~totalorderedP(U)) | (~(app(U, Y) = nil))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.49 tff(12,plain,
% 0.20/0.49 ((~(nil = U!45)) & ssList(U!45) & ssList(nil) & ssList(Y!46) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!46)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & totalorderedP(U!45) & (app(U!45, Y!46) = nil)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.49 tff(13,plain,
% 0.20/0.49 (app(U!45, Y!46) = nil),
% 0.20/0.49 inference(and_elim,[status(thm)],[12])).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (nil = app(U!45, Y!46)),
% 0.20/0.49 inference(symmetry,[status(thm)],[13])).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 (~(nil = U!45)),
% 0.20/0.49 inference(and_elim,[status(thm)],[12])).
% 0.20/0.49 tff(16,plain,
% 0.20/0.49 (((~(nil = U!45)) | (~(nil = Y!46))) | (nil = U!45)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 ((~(nil = U!45)) | (~(nil = Y!46))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.20/0.49 tff(18,plain,
% 0.20/0.49 ((((~(nil = U!45)) | (~(nil = Y!46))) <=> (nil = app(U!45, Y!46))) | (~((~(nil = U!45)) | (~(nil = Y!46)))) | (~(nil = app(U!45, Y!46)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (((~(nil = U!45)) | (~(nil = Y!46))) <=> (nil = app(U!45, Y!46))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[18, 17, 14])).
% 0.20/0.49 tff(20,plain,
% 0.20/0.49 (ssList(U!45)),
% 0.20/0.49 inference(and_elim,[status(thm)],[12])).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(24,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[24, 22])).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(27,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(29,plain,
% 0.20/0.49 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), (![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(30,plain,
% 0.20/0.49 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.49 tff(31,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax83')).
% 0.20/0.49 tff(32,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.49 tff(33,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.49 tff(34,plain,(
% 0.20/0.49 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[33])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(38,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(39,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 (![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[39, 36, 20])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 (ssList(Y!46)),
% 0.20/0.49 inference(and_elim,[status(thm)],[12])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V)))))) | ((~ssList(Y!46)) | (~(((~(nil = U!45)) | (~(nil = Y!46))) <=> (nil = app(U!45, Y!46)))))) <=> ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V)))))) | (~ssList(Y!46)) | (~(((~(nil = U!45)) | (~(nil = Y!46))) <=> (nil = app(U!45, Y!46)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 (((~ssList(Y!46)) | (~(((~(nil = Y!46)) | (~(nil = U!45))) <=> (nil = app(U!45, Y!46))))) <=> ((~ssList(Y!46)) | (~(((~(nil = U!45)) | (~(nil = Y!46))) <=> (nil = app(U!45, Y!46)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V)))))) | ((~ssList(Y!46)) | (~(((~(nil = Y!46)) | (~(nil = U!45))) <=> (nil = app(U!45, Y!46)))))) <=> ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V)))))) | ((~ssList(Y!46)) | (~(((~(nil = U!45)) | (~(nil = Y!46))) <=> (nil = app(U!45, Y!46))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V)))))) | ((~ssList(Y!46)) | (~(((~(nil = Y!46)) | (~(nil = U!45))) <=> (nil = app(U!45, Y!46)))))) <=> ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V)))))) | (~ssList(Y!46)) | (~(((~(nil = U!45)) | (~(nil = Y!46))) <=> (nil = app(U!45, Y!46)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V)))))) | ((~ssList(Y!46)) | (~(((~(nil = Y!46)) | (~(nil = U!45))) <=> (nil = app(U!45, Y!46)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U!45))) <=> (nil = app(U!45, V)))))) | (~ssList(Y!46)) | (~(((~(nil = U!45)) | (~(nil = Y!46))) <=> (nil = app(U!45, Y!46))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[47, 41, 40, 19])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------