%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC124+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n029.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 : Thu Aug 31 20:23:26 EDT 2023

% Result   : Theorem 0.85s 1.07s
% Output   : Proof 0.85s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SWC124+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n029.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon Aug 28 17:22:41 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.85/1.07  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.wIvUFZSaqV/cvc5---1.0.5_25687.p...
% 0.85/1.07  ------- get file name : TPTP file name is SWC124+1
% 0.85/1.07  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25687.smt2...
% 0.85/1.07  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.85/1.07  % SZS status Theorem for SWC124+1
% 0.85/1.07  % SZS output start Proof for SWC124+1
% 0.85/1.07  (
% 0.85/1.07  (let ((_let_1 (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (or (not (= (tptp.app W Y) X)) (not (tptp.totalorderedP W)) (exists ((Z $$unsorted)) (and (tptp.ssItem Z) (exists ((X1 $$unsorted)) (and (tptp.ssList X1) (= (tptp.app (tptp.cons Z tptp.nil) X1) Y) (exists ((X2 $$unsorted)) (and (tptp.ssItem X2) (exists ((X3 $$unsorted)) (and (tptp.ssList X3) (= (tptp.app X3 (tptp.cons X2 tptp.nil)) W) (tptp.leq X2 Z)))))))))))) (and (not (= tptp.nil X)) (= tptp.nil W)) (and (tptp.neq U tptp.nil) (tptp.segmentP V U)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_3 (tptp.ssList tptp.nil))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))))) (let ((_let_6 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_7 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_6))) (let ((_let_8 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_9 (= _let_8 (tptp.app _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_10 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_7))) (let ((_let_13 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_14 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_15 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (not _let_15))) (let ((_let_17 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_18 (= tptp.nil _let_8))) (let ((_let_19 (not _let_18))) (let ((_let_20 (and _let_19 _let_17))) (let ((_let_21 (tptp.segmentP _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_22 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_23 (and _let_22 _let_21))) (let ((_let_24 (tptp.neq _let_8 tptp.nil))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.ssList _let_8))) (let ((_let_27 (not _let_26))) (let ((_let_28 (not (tptp.totalorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_29 (or _let_11 _let_28 _let_27 _let_25 _let_23 _let_20 _let_16 (not (forall ((Z $$unsorted) (BOUND_VARIABLE_5308 $$unsorted) (BOUND_VARIABLE_5295 $$unsorted) (BOUND_VARIABLE_5293 $$unsorted)) (or (not (tptp.ssItem Z)) (not (tptp.ssItem BOUND_VARIABLE_5293)) (not (tptp.leq BOUND_VARIABLE_5293 Z)) (not (tptp.ssList BOUND_VARIABLE_5295)) (not (= (tptp.app BOUND_VARIABLE_5295 (tptp.cons BOUND_VARIABLE_5293 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.ssList BOUND_VARIABLE_5308)) (not (= (tptp.app (tptp.cons Z tptp.nil) BOUND_VARIABLE_5308) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))))) (let ((_let_30 (forall ((U $$unsorted) (BOUND_VARIABLE_5482 $$unsorted)) (let ((_let_1 (tptp.app U BOUND_VARIABLE_5482))) (or (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.ssList _let_1)) (not (tptp.neq _let_1 tptp.nil)) (and (tptp.neq U tptp.nil) (tptp.segmentP _let_1 U)) (and (not (= tptp.nil _let_1)) (= tptp.nil U)) (not (tptp.ssList BOUND_VARIABLE_5482)) (not (forall ((Z $$unsorted) (BOUND_VARIABLE_5308 $$unsorted) (BOUND_VARIABLE_5295 $$unsorted) (BOUND_VARIABLE_5293 $$unsorted)) (or (not (tptp.ssItem Z)) (not (tptp.ssItem BOUND_VARIABLE_5293)) (not (tptp.leq BOUND_VARIABLE_5293 Z)) (not (tptp.ssList BOUND_VARIABLE_5295)) (not (= U (tptp.app BOUND_VARIABLE_5295 (tptp.cons BOUND_VARIABLE_5293 tptp.nil)))) (not (tptp.ssList BOUND_VARIABLE_5308)) (not (= (tptp.app (tptp.cons Z tptp.nil) BOUND_VARIABLE_5308) BOUND_VARIABLE_5482)))))))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (or))) (let ((_let_34 (not _let_30))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_32) :args (_let_34)) (REWRITE :args ((=> _let_34 (not (or _let_11 _let_28 _let_27 _let_25 _let_23 _let_20 _let_16 (not (forall ((Z $$unsorted) (BOUND_VARIABLE_5308 $$unsorted) (BOUND_VARIABLE_5295 $$unsorted) (BOUND_VARIABLE_5293 $$unsorted)) (or (not (tptp.ssItem Z)) (not (tptp.ssItem BOUND_VARIABLE_5293)) (not (tptp.leq BOUND_VARIABLE_5293 Z)) (not (tptp.ssList BOUND_VARIABLE_5295)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app BOUND_VARIABLE_5295 (tptp.cons BOUND_VARIABLE_5293 tptp.nil)))) (not (tptp.ssList BOUND_VARIABLE_5308)) (not (= (tptp.app (tptp.cons Z tptp.nil) BOUND_VARIABLE_5308) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_30))) (REFL :args (_let_31)) :args _let_33)) _let_32 :args (_let_31 true _let_30)))) (let ((_let_36 (REFL :args (_let_29)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) :args _let_33)) :args ((or _let_10 _let_29))) _let_35 :args (_let_10 true _let_29)))) (let ((_let_38 (not _let_9))) (let ((_let_39 (not _let_3))) (let ((_let_40 (or _let_39 _let_16 _let_38))) (let ((_let_41 (forall ((W $$unsorted) (BOUND_VARIABLE_2329 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2329)) (not (= (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (tptp.app (tptp.app W SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) BOUND_VARIABLE_2329))))))) (let ((_let_42 (not _let_41))) (let ((_let_43 (= _let_21 _let_42))) (let ((_let_44 (or _let_27 _let_11 _let_43))) (let ((_let_45 (forall ((U $$unsorted) (BOUND_VARIABLE_2354 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_2354)) (= (tptp.segmentP U BOUND_VARIABLE_2354) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2329 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2329)) (not (= U (tptp.app (tptp.app W BOUND_VARIABLE_2354) BOUND_VARIABLE_2329))))))))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (not _let_17))) (let ((_let_48 (= _let_22 _let_47))) (let ((_let_49 (or _let_11 _let_39 _let_48))) (let ((_let_50 (forall ((U $$unsorted) (BOUND_VARIABLE_3299 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3299)) (= (tptp.neq U BOUND_VARIABLE_3299) (not (= U BOUND_VARIABLE_3299))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (ASSUME :args (_let_3)))) (let ((_let_53 (not _let_48))) (let ((_let_54 (REFL :args (_let_47)))) (let ((_let_55 (_let_20))) (let ((_let_56 (not _let_22))) (let ((_let_57 (not _let_43))) (let ((_let_58 (_let_41))) (let ((_let_59 (ASSUME :args (_let_38)))) (let ((_let_60 (_let_7))) (let ((_let_61 (ASSUME :args _let_60))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS _let_61 (SCOPE (CONG (SYMM (SYMM _let_61)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) :args (APPLY_UF tptp.app)) :args _let_60)) _let_59) :args (_let_7 _let_38)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (SYMM (SYMM (ASSUME :args (_let_9)))))) (FALSE_INTRO _let_59))) :args (_let_9 _let_38)) :args ((not (and _let_7 _let_38)) SB_LITERAL))) (CONG (REFL :args ((not _let_7))) (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_9))) :args _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_16 _let_38 (not _let_40)))) _let_52 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 6)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_33)) :args ((or _let_15 _let_29))) _let_35 :args (_let_15 true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_58) :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.app W SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) BOUND_VARIABLE_2329)))) :args _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_43)) (CONG (REFL :args (_let_57)) (REFL :args (_let_21)) (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_33)) :args ((or _let_21 _let_41 _let_57))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_23)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 4)) _let_35 :args ((not _let_23) true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_56)))) (CONG (TRANS (SYMM (ASSUME :args (_let_17))) (SYMM (SYMM (ASSUME :args (_let_18))))) (REFL :args (tptp.nil)) :args (APPLY_UF tptp.neq)) (TRUE_INTRO (ASSUME :args (_let_24))))) :args (_let_24 _let_18 _let_17 _let_56))) (CONG (REFL :args (_let_25)) (REFL :args (_let_19)) _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_22))) :args _let_33)) :args ((or _let_25 _let_22 _let_19 _let_47))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 3)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_33)) :args ((or _let_24 _let_29))) _let_35 :args (_let_24 true _let_29)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_55) (CONG (REFL :args _let_55) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) _let_54 :args _let_33)) :args ((or _let_18 _let_20 _let_47))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 5)) _let_35 :args ((not _let_20) true _let_29)) (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_48)) (CONG (REFL :args (_let_53)) (REFL :args (_let_22)) (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_17))) :args _let_33)) :args ((or _let_22 _let_17 _let_53))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_39 _let_11 _let_48 (not _let_49)))) _let_52 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.neq U BOUND_VARIABLE_3299)))) :args (_let_50)))) _let_51 :args (_let_49 false _let_50)) :args (_let_48 false _let_3 false _let_10 false _let_49)) :args (_let_22 false _let_24 false _let_18 true _let_20 false _let_17 false _let_48)) :args ((not _let_21) true _let_23 false _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_11 _let_27 _let_43 (not _let_44)))) _let_37 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 2)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_33)) :args ((or _let_26 _let_29))) _let_35 :args (_let_26 true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.segmentP U BOUND_VARIABLE_2354)))) :args (_let_45))) _let_46 :args (_let_44 false _let_45)) :args (_let_43 false _let_10 false _let_26 false _let_44)) :args (_let_41 true _let_21 false _let_43)) :args (_let_40 false _let_41)) :args (_let_38 false _let_3 false _let_15 false _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_12)) :args ((or _let_11 _let_7 (not _let_12)))) _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_14 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_13))) _let_14 :args (_let_12 false _let_13)) :args (_let_7 false _let_10 false _let_12)) :args (false true _let_9 false _let_7)) :args ((forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))) (exists ((U $$unsorted)) (and (tptp.ssItem U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (not (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.frontsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app V W) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.rearsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) _let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.cyclefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (and (tptp.leq V W) (tptp.leq W V))))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.duplicatefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (= V W)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.equalelemsP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) _let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))) _let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) _let_2 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) (not (tptp.singletonP tptp.nil)) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V W)) (tptp.frontsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V W)) (tptp.rearsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.rearsegP U V) (tptp.rearsegP (tptp.app W U) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.rearsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))) (tptp.cyclefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderP (tptp.cons U tptp.nil)))) (tptp.totalorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))) (tptp.totalorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))) (tptp.strictorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))) (tptp.duplicatefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))) (tptp.equalelemsP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.hd U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssList V) (= (tptp.tl U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app W V) (tptp.app U V)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.tl (tptp.app U V)) (tptp.app (tptp.tl U) V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.geq U V) (tptp.geq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.geq U V) (tptp.geq V W)) (tptp.geq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.leq U V) (or (= U V) (tptp.lt U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.gt U V) (not (tptp.gt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.gt U V) (tptp.gt V W)) (tptp.gt U W)))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.85/1.08  )
% 0.85/1.08  % SZS output end Proof for SWC124+1
% 0.85/1.08  % cvc5---1.0.5 exiting
% 0.85/1.08  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------