%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC351+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:30:58 AM UTC 2025
% Result : Theorem 0.80s 0.96s
% Output : Proof 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC351+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 09:07:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.80/0.96 % SZS status Theorem
% 0.80/0.96 % SZS output start Proof
% 0.80/0.96 tff(tptp_fun_V_46_type, type, (
% 0.80/0.96 tptp_fun_V_46: $i)).
% 0.80/0.96 tff(app_type, type, (
% 0.80/0.96 app: ( $i * $i ) > $i)).
% 0.80/0.96 tff(tptp_fun_U_45_type, type, (
% 0.80/0.96 tptp_fun_U_45: $i)).
% 0.80/0.96 tff(ssList_type, type, (
% 0.80/0.96 ssList: $i > $o)).
% 0.80/0.96 tff(frontsegP_type, type, (
% 0.80/0.96 frontsegP: ( $i * $i ) > $o)).
% 0.80/0.96 tff(tptp_fun_W_5_type, type, (
% 0.80/0.96 tptp_fun_W_5: ( $i * $i ) > $i)).
% 0.80/0.96 tff(neq_type, type, (
% 0.80/0.96 neq: ( $i * $i ) > $o)).
% 0.80/0.96 tff(nil_type, type, (
% 0.80/0.96 nil: $i)).
% 0.80/0.96 tff(lt_type, type, (
% 0.80/0.96 lt: ( $i * $i ) > $o)).
% 0.80/0.96 tff(cons_type, type, (
% 0.80/0.96 cons: ( $i * $i ) > $i)).
% 0.80/0.96 tff(ssItem_type, type, (
% 0.80/0.96 ssItem: $i > $o)).
% 0.80/0.96 tff(tptp_fun_Y_47_type, type, (
% 0.80/0.96 tptp_fun_Y_47: $i)).
% 0.80/0.96 tff(strictorderedP_type, type, (
% 0.80/0.96 strictorderedP: $i > $o)).
% 0.80/0.96 tff(1,plain,
% 0.80/0.96 ((ssList(U!45) & ((~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))) & ssList(U!45) & neq(V!46, nil))) <=> (ssList(U!45) & (~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))) & neq(V!46, nil))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(2,plain,
% 0.80/0.96 (((~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) & ssList(U!45) & neq(V!46, nil)) <=> ((~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))) & ssList(U!45) & neq(V!46, nil))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(3,plain,
% 0.80/0.96 ((strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) <=> (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(4,plain,
% 0.80/0.96 (((~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) & ssList(U!45) & neq(V!46, nil)) <=> ((~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) & ssList(U!45) & neq(V!46, nil))),
% 0.80/0.96 inference(monotonicity,[status(thm)],[3])).
% 0.80/0.96 tff(5,plain,
% 0.80/0.96 (((~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) & ssList(U!45) & neq(V!46, nil)) <=> ((~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))) & ssList(U!45) & neq(V!46, nil))),
% 0.80/0.96 inference(transitivity,[status(thm)],[4, 2])).
% 0.80/0.96 tff(6,plain,
% 0.80/0.96 ((ssList(U!45) & ((~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) & ssList(U!45) & neq(V!46, nil))) <=> (ssList(U!45) & ((~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))) & ssList(U!45) & neq(V!46, nil)))),
% 0.80/0.96 inference(monotonicity,[status(thm)],[5])).
% 0.80/0.96 tff(7,plain,
% 0.80/0.96 ((ssList(U!45) & ((~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) & ssList(U!45) & neq(V!46, nil))) <=> (ssList(U!45) & (~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))) & neq(V!46, nil))),
% 0.80/0.96 inference(transitivity,[status(thm)],[6, 1])).
% 0.80/0.96 tff(8,plain,
% 0.80/0.96 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~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) & lt(X2, Z)))))) | (~ssList(U)) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~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) & lt(X2, Z)))))) | (~ssList(U)) | (~neq(V, nil)))))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(9,plain,
% 0.80/0.96 ((~![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] : (ssList(Y) => (((~(app(W, Y) = X)) | (~strictorderedP(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)) & lt(X2, Z)))))))) | frontsegP(V, U)) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~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) & lt(X2, Z)))))) | (~ssList(U)) | (~neq(V, nil)))))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(10,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] : (ssList(Y) => (((~(app(W, Y) = X)) | (~strictorderedP(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)) & lt(X2, Z)))))))) | frontsegP(V, U)) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.80/0.96 tff(11,plain,
% 0.80/0.96 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~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) & lt(X2, Z)))))) | (~ssList(U)) | (~neq(V, nil))))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.80/0.96 tff(12,plain,
% 0.80/0.96 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~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) & lt(X2, Z)))))) | (~ssList(U)) | (~neq(V, nil))))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.80/0.96 tff(13,plain,
% 0.80/0.96 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~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) & lt(X2, Z)))))) | (~ssList(U)) | (~neq(V, nil))))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.80/0.96 tff(14,plain,
% 0.80/0.96 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~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) & lt(X2, Z)))))) | (~ssList(U)) | (~neq(V, nil))))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.80/0.97 tff(15,plain,
% 0.80/0.97 (ssList(U!45) & (~frontsegP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))) & neq(V!46, nil)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.80/0.97 tff(16,plain,
% 0.80/0.97 (ssList(V!46)),
% 0.80/0.97 inference(and_elim,[status(thm)],[15])).
% 0.80/0.97 tff(17,plain,
% 0.80/0.97 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 0.80/0.97 inference(bind,[status(th)],[])).
% 0.80/0.97 tff(18,plain,
% 0.80/0.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 0.80/0.97 inference(quant_intro,[status(thm)],[17])).
% 0.80/0.97 tff(19,plain,
% 0.80/0.97 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 0.80/0.97 inference(bind,[status(th)],[])).
% 0.80/0.97 tff(20,plain,
% 0.80/0.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 0.80/0.97 inference(quant_intro,[status(thm)],[19])).
% 0.80/0.97 tff(21,plain,
% 0.80/0.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 0.80/0.97 inference(transitivity,[status(thm)],[20, 18])).
% 0.80/0.97 tff(22,plain,
% 0.80/0.97 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 0.80/0.97 inference(bind,[status(th)],[])).
% 0.80/0.97 tff(23,plain,
% 0.80/0.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 0.80/0.97 inference(quant_intro,[status(thm)],[22])).
% 0.80/0.97 tff(24,plain,
% 0.80/0.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(25,plain,
% 0.80/0.97 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))) <=> (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))), ((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), rewrite((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))), ((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))))), (![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))))),
% 0.80/0.97 inference(bind,[status(th)],[])).
% 0.80/0.97 tff(26,plain,
% 0.80/0.97 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 0.80/0.97 inference(quant_intro,[status(thm)],[25])).
% 0.80/0.97 tff(27,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax5')).
% 0.80/0.97 tff(28,plain,
% 0.80/0.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.80/0.97 tff(29,plain,
% 0.80/0.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.80/0.97 tff(30,plain,(
% 0.80/0.97 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U)))))))),
% 0.80/0.97 inference(skolemize,[status(sab)],[29])).
% 0.80/0.97 tff(31,plain,
% 0.80/0.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.80/0.97 tff(32,plain,
% 0.80/0.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.80/0.97 tff(33,plain,
% 0.80/0.97 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46))))))))))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(34,plain,
% 0.80/0.97 (((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))) | (~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))))))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46))))))))))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(35,plain,
% 0.80/0.97 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))) | (~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))))),
% 0.80/0.97 inference(monotonicity,[status(thm)],[34])).
% 0.80/0.97 tff(36,plain,
% 0.80/0.97 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))) | (~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46))))))))))),
% 0.80/0.97 inference(transitivity,[status(thm)],[35, 33])).
% 0.80/0.97 tff(37,plain,
% 0.80/0.97 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))) | (~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46)))))))))),
% 0.80/0.97 inference(quant_inst,[status(thm)],[])).
% 0.80/0.97 tff(38,plain,
% 0.80/0.97 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.80/0.97 tff(39,plain,
% 0.80/0.97 (![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[38, 32, 16])).
% 0.80/0.97 tff(40,plain,
% 0.80/0.97 (ssList(U!45)),
% 0.80/0.97 inference(and_elim,[status(thm)],[15])).
% 0.80/0.97 tff(41,plain,
% 0.80/0.97 (((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))) | ((~ssList(U!45)) | (~((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | (~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))) | (~ssList(U!45)) | (~((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | (~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))))))))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(42,plain,
% 0.80/0.97 ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))) | ((~ssList(U!45)) | (~((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | (~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))))))))),
% 0.80/0.98 inference(quant_inst,[status(thm)],[])).
% 0.80/0.98 tff(43,plain,
% 0.80/0.98 ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))) | (~ssList(U!45)) | (~((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | (~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46))))))))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.80/0.98 tff(44,plain,
% 0.80/0.98 (~((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | (~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))))))),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[43, 40, 39])).
% 0.80/0.98 tff(45,plain,
% 0.80/0.98 (((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | (~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46))))))) | (frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))),
% 0.80/0.98 inference(tautology,[status(thm)],[])).
% 0.80/0.98 tff(46,plain,
% 0.80/0.98 (frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46)))),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.80/0.98 tff(47,plain,
% 0.80/0.98 (~frontsegP(V!46, U!45)),
% 0.80/0.98 inference(and_elim,[status(thm)],[15])).
% 0.80/0.98 tff(48,plain,
% 0.80/0.98 ((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46)))),
% 0.80/0.98 inference(tautology,[status(thm)],[])).
% 0.80/0.98 tff(49,plain,
% 0.80/0.98 ((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46)))),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.80/0.98 tff(50,plain,
% 0.80/0.98 (![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46)))),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.80/0.98 tff(51,plain,
% 0.80/0.98 (ssList(Y!47)),
% 0.80/0.98 inference(and_elim,[status(thm)],[15])).
% 0.80/0.98 tff(52,plain,
% 0.80/0.98 (app(U!45, Y!47) = V!46),
% 0.80/0.98 inference(and_elim,[status(thm)],[15])).
% 0.80/0.98 tff(53,plain,
% 0.80/0.98 (((~![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46)))) | ((~ssList(Y!47)) | (~(app(U!45, Y!47) = V!46)))) <=> ((~![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46)))) | (~ssList(Y!47)) | (~(app(U!45, Y!47) = V!46)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(54,plain,
% 0.80/0.98 ((~![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46)))) | ((~ssList(Y!47)) | (~(app(U!45, Y!47) = V!46)))),
% 0.80/0.98 inference(quant_inst,[status(thm)],[])).
% 0.80/0.98 tff(55,plain,
% 0.80/0.98 ((~![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46)))) | (~ssList(Y!47)) | (~(app(U!45, Y!47) = V!46))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.80/0.98 tff(56,plain,
% 0.80/0.98 ($false),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[55, 52, 51, 50])).
% 0.80/0.98 % SZS output end Proof
% 0.80/0.98 % E exiting
%------------------------------------------------------------------------------