%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC101+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n027.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 20:23:15 EDT 2023

% Result   : Theorem 0.20s 0.64s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SWC101+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n027.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Aug 28 17:34:37 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.64  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.hT7k56HgLF/cvc5---1.0.5_1582.p...
% 0.20/0.64  ------- get file name : TPTP file name is SWC101+1
% 0.20/0.64  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1582.smt2...
% 0.20/0.64  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.64  % SZS status Theorem for SWC101+1
% 0.20/0.64  % SZS output start Proof for SWC101+1
% 0.20/0.64  (
% 0.20/0.64  (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)) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (or (not (= (tptp.app W Y) X)) (not (tptp.equalelemsP W)) (exists ((Z $$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.ssList X2) (= (tptp.app X2 (tptp.cons Z tptp.nil)) W)))))))))) (and (not (= tptp.nil X)) (= tptp.nil W)) (and (= tptp.nil V) (= tptp.nil U)) (and (tptp.neq U tptp.nil) (tptp.frontsegP V U)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))))) (let ((_let_4 (tptp.ssList tptp.nil))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_6 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_7 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_8 (= tptp.nil _let_7))) (let ((_let_9 (not _let_8))) (let ((_let_10 (and _let_9 _let_6))) (let ((_let_11 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_12 (not _let_11))) (let ((_let_13 (tptp.frontsegP _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_14 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_15 (and _let_14 _let_13))) (let ((_let_16 (and _let_8 _let_6))) (let ((_let_17 (not (tptp.ssList _let_7)))) (let ((_let_18 (not (tptp.equalelemsP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_19 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_18 _let_17 _let_16 _let_15 _let_10 _let_12 (not (forall ((Z $$unsorted) (BOUND_VARIABLE_5269 $$unsorted) (BOUND_VARIABLE_5261 $$unsorted)) (let ((_let_1 (tptp.cons Z tptp.nil))) (or (not (tptp.ssItem Z)) (not (tptp.ssList BOUND_VARIABLE_5261)) (not (= (tptp.app BOUND_VARIABLE_5261 _let_1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.ssList BOUND_VARIABLE_5269)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5269) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))))) (let ((_let_22 (forall ((U $$unsorted) (BOUND_VARIABLE_5440 $$unsorted)) (let ((_let_1 (= tptp.nil U))) (let ((_let_2 (tptp.app U BOUND_VARIABLE_5440))) (let ((_let_3 (= tptp.nil _let_2))) (or (not (tptp.ssList U)) (not (tptp.equalelemsP U)) (not (tptp.ssList _let_2)) (and _let_3 _let_1) (and (tptp.neq U tptp.nil) (tptp.frontsegP _let_2 U)) (and (not _let_3) _let_1) (not (tptp.ssList BOUND_VARIABLE_5440)) (not (forall ((Z $$unsorted) (BOUND_VARIABLE_5269 $$unsorted) (BOUND_VARIABLE_5261 $$unsorted)) (let ((_let_1 (tptp.cons Z tptp.nil))) (or (not (tptp.ssItem Z)) (not (tptp.ssList BOUND_VARIABLE_5261)) (not (= U (tptp.app BOUND_VARIABLE_5261 _let_1))) (not (tptp.ssList BOUND_VARIABLE_5269)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5269) BOUND_VARIABLE_5440))))))))))))) (let ((_let_23 (not _let_21))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (or))) (let ((_let_26 (not _let_22))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_24) :args (_let_26)) (REWRITE :args ((=> _let_26 (not (or _let_20 _let_18 _let_17 _let_16 _let_15 _let_10 _let_12 (not (forall ((Z $$unsorted) (BOUND_VARIABLE_5269 $$unsorted) (BOUND_VARIABLE_5261 $$unsorted)) (let ((_let_1 (tptp.cons Z tptp.nil))) (or (not (tptp.ssItem Z)) (not (tptp.ssList BOUND_VARIABLE_5261)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app BOUND_VARIABLE_5261 _let_1))) (not (tptp.ssList BOUND_VARIABLE_5269)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5269) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_22))) (REFL :args (_let_23)) :args _let_25)) _let_24 :args (_let_23 true _let_22)))) (let ((_let_28 (not _let_6))) (let ((_let_29 (= _let_14 _let_28))) (let ((_let_30 (not _let_4))) (let ((_let_31 (or _let_20 _let_30 _let_29))) (let ((_let_32 (forall ((U $$unsorted) (BOUND_VARIABLE_3293 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3293)) (= (tptp.neq U BOUND_VARIABLE_3293) (not (= U BOUND_VARIABLE_3293))))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (REFL :args (_let_21)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 0)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_25)) :args ((or _let_19 _let_21))) _let_27 :args (_let_19 true _let_21)))) (let ((_let_36 (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_20 _let_20 _let_37 _let_12 _let_13))) (let ((_let_39 (forall ((U $$unsorted) (BOUND_VARIABLE_4072 $$unsorted) (BOUND_VARIABLE_4070 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4070)) (not (tptp.frontsegP U BOUND_VARIABLE_4070)) (not (tptp.ssList BOUND_VARIABLE_4072)) (tptp.frontsegP (tptp.app U BOUND_VARIABLE_4072) BOUND_VARIABLE_4070))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (or _let_20 _let_36))) (let ((_let_42 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.frontsegP U U))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (not _let_29))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_29)) (CONG (REFL :args (_let_44)) (REFL :args (_let_14)) (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_6))) :args _let_25)) :args ((or _let_6 _let_14 _let_44))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_15)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_21 4)) _let_27 :args ((not _let_15) true _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_38))) :args ((or _let_20 _let_13 _let_12 _let_37 (not _let_38)))) _let_35 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 6)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_25)) :args ((or _let_11 _let_21))) _let_27 :args (_let_11 true _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_20 _let_36 (not _let_41)))) _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_36 false _let_19 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.frontsegP (tptp.app U BOUND_VARIABLE_4072) BOUND_VARIABLE_4070) true))))) :args (_let_39))) _let_40 :args (_let_38 false _let_39)) :args (_let_13 false _let_19 false _let_11 false _let_36 false _let_38)) :args ((not _let_14) true _let_15 false _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_20 _let_29 (not _let_31)))) (ASSUME :args (_let_4)) _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.neq U BOUND_VARIABLE_3293)))) :args (_let_32)))) _let_33 :args (_let_31 false _let_32)) :args (_let_29 false _let_4 false _let_19 false _let_31)) :args (_let_6 true _let_14 false _let_29)))) (let ((_let_46 (_let_10))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_46) (CONG (REFL :args _let_46) (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) (REFL :args (_let_28)) :args _let_25)) :args ((or _let_8 _let_10 _let_28))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_16)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_21 3)) _let_27 :args ((not _let_16) true _let_21)) _let_45 :args (_let_9 true _let_16 false _let_6)) _let_45 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_21 5)) _let_27 :args ((not _let_10) true _let_21)) :args (false true _let_8 false _let_6 true _let_10)) :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 $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))) (forall ((U $$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_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))) _let_4 (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)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))) (forall ((U $$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)))))) _let_3 _let_2 (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)))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.65  )
% 0.20/0.65  % SZS output end Proof for SWC101+1
% 0.20/0.65  % cvc5---1.0.5 exiting
% 0.20/0.65  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------