TSTP Solution File: SWC404+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC404+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 20:25:22 EDT 2023
% Result : Theorem 13.10s 13.34s
% Output : Proof 13.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC404+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n022.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 17:20:39 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 13.10/13.34 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Y2dtw8wJTm/cvc5---1.0.5_29784.p...
% 13.10/13.34 ------- get file name : TPTP file name is SWC404+1
% 13.10/13.34 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_29784.smt2...
% 13.10/13.34 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 13.10/13.34 --- Run --no-e-matching --full-saturate-quant at 5...
% 13.10/13.34 % SZS status Theorem for SWC404+1
% 13.10/13.34 % SZS output start Proof for SWC404+1
% 13.10/13.34 (
% 13.10/13.34 (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 $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (or (not (= (tptp.app (tptp.app Y W) Z) X)) (not (tptp.strictorderedP W)) (exists ((X1 $$unsorted)) (and (tptp.ssItem X1) (exists ((X2 $$unsorted)) (and (tptp.ssList X2) (= (tptp.app X2 (tptp.cons X1 tptp.nil)) Y) (exists ((X3 $$unsorted)) (and (tptp.ssItem X3) (exists ((X4 $$unsorted)) (and (tptp.ssList X4) (= (tptp.app (tptp.cons X3 tptp.nil) X4) W) (tptp.lt X1 X3))))))))) (exists ((X5 $$unsorted)) (and (tptp.ssItem X5) (exists ((X6 $$unsorted)) (and (tptp.ssList X6) (= (tptp.app (tptp.cons X5 tptp.nil) X6) Z) (exists ((X7 $$unsorted)) (and (tptp.ssItem X7) (exists ((X8 $$unsorted)) (and (tptp.ssList X8) (= (tptp.app X8 (tptp.cons X7 tptp.nil)) W) (tptp.lt X7 X5)))))))))))))) (forall ((X9 $$unsorted)) (=> (tptp.ssItem X9) (or (not (tptp.memberP U X9)) (tptp.memberP V X9)))) (and (not (= tptp.nil X)) (= tptp.nil W)))))))))))))) (let ((_let_2 (forall ((U $$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))))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_4 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_5 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_6 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_7 (tptp.ssList _let_6))) (let ((_let_8 (tptp.memberP _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_9 (or _let_8 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_10 (tptp.app _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_11 (tptp.memberP _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_12 (= _let_11 _let_9))) (let ((_let_13 (not _let_5))) (let ((_let_14 (not _let_7))) (let ((_let_15 (not _let_4))) (let ((_let_16 (or _let_15 _let_14 _let_13 _let_12))) (let ((_let_17 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_20 (not _let_19))) (let ((_let_21 (and (not (= tptp.nil _let_10)) (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_22 (not (tptp.ssList _let_10)))) (let ((_let_23 (not (tptp.strictorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_24 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_22 _let_21 _let_15 _let_20 _let_11 _let_18 (not (forall ((X1 $$unsorted) (BOUND_VARIABLE_5345 $$unsorted) (BOUND_VARIABLE_5332 $$unsorted) (BOUND_VARIABLE_5330 $$unsorted)) (or (not (tptp.ssItem X1)) (not (tptp.ssItem BOUND_VARIABLE_5330)) (not (tptp.lt X1 BOUND_VARIABLE_5330)) (not (tptp.ssList BOUND_VARIABLE_5332)) (not (= (tptp.app (tptp.cons BOUND_VARIABLE_5330 tptp.nil) BOUND_VARIABLE_5332) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.ssList BOUND_VARIABLE_5345)) (not (= (tptp.app BOUND_VARIABLE_5345 (tptp.cons X1 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) _let_13 (not (forall ((X5 $$unsorted) (BOUND_VARIABLE_5433 $$unsorted) (BOUND_VARIABLE_5420 $$unsorted) (BOUND_VARIABLE_5418 $$unsorted)) (or (not (tptp.ssItem X5)) (not (tptp.ssItem BOUND_VARIABLE_5418)) (not (tptp.lt BOUND_VARIABLE_5418 X5)) (not (tptp.ssList BOUND_VARIABLE_5420)) (not (= (tptp.app BOUND_VARIABLE_5420 (tptp.cons BOUND_VARIABLE_5418 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.ssList BOUND_VARIABLE_5433)) (not (= (tptp.app (tptp.cons X5 tptp.nil) BOUND_VARIABLE_5433) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))))))) (let ((_let_27 (forall ((U $$unsorted) (BOUND_VARIABLE_5688 $$unsorted) (BOUND_VARIABLE_5686 $$unsorted) (BOUND_VARIABLE_5684 $$unsorted)) (let ((_let_1 (tptp.app (tptp.app BOUND_VARIABLE_5686 U) BOUND_VARIABLE_5684))) (or (not (tptp.ssList U)) (not (tptp.strictorderedP U)) (not (tptp.ssList _let_1)) (and (not (= tptp.nil _let_1)) (= tptp.nil U)) (not (tptp.ssItem BOUND_VARIABLE_5688)) (not (tptp.memberP U BOUND_VARIABLE_5688)) (tptp.memberP _let_1 BOUND_VARIABLE_5688) (not (tptp.ssList BOUND_VARIABLE_5686)) (not (forall ((X1 $$unsorted) (BOUND_VARIABLE_5345 $$unsorted) (BOUND_VARIABLE_5332 $$unsorted) (BOUND_VARIABLE_5330 $$unsorted)) (or (not (tptp.ssItem X1)) (not (tptp.ssItem BOUND_VARIABLE_5330)) (not (tptp.lt X1 BOUND_VARIABLE_5330)) (not (tptp.ssList BOUND_VARIABLE_5332)) (not (= U (tptp.app (tptp.cons BOUND_VARIABLE_5330 tptp.nil) BOUND_VARIABLE_5332))) (not (tptp.ssList BOUND_VARIABLE_5345)) (not (= (tptp.app BOUND_VARIABLE_5345 (tptp.cons X1 tptp.nil)) BOUND_VARIABLE_5686))))) (not (tptp.ssList BOUND_VARIABLE_5684)) (not (forall ((X5 $$unsorted) (BOUND_VARIABLE_5433 $$unsorted) (BOUND_VARIABLE_5420 $$unsorted) (BOUND_VARIABLE_5418 $$unsorted)) (or (not (tptp.ssItem X5)) (not (tptp.ssItem BOUND_VARIABLE_5418)) (not (tptp.lt BOUND_VARIABLE_5418 X5)) (not (tptp.ssList BOUND_VARIABLE_5420)) (not (= U (tptp.app BOUND_VARIABLE_5420 (tptp.cons BOUND_VARIABLE_5418 tptp.nil)))) (not (tptp.ssList BOUND_VARIABLE_5433)) (not (= (tptp.app (tptp.cons X5 tptp.nil) BOUND_VARIABLE_5433) BOUND_VARIABLE_5684)))))))))) (let ((_let_28 (not _let_26))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (or))) (let ((_let_31 (not _let_27))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_29) :args (_let_31)) (REWRITE :args ((=> _let_31 (not (or _let_25 _let_23 _let_22 _let_21 _let_15 _let_20 _let_11 _let_18 (not (forall ((X1 $$unsorted) (BOUND_VARIABLE_5345 $$unsorted) (BOUND_VARIABLE_5332 $$unsorted) (BOUND_VARIABLE_5330 $$unsorted)) (or (not (tptp.ssItem X1)) (not (tptp.ssItem BOUND_VARIABLE_5330)) (not (tptp.lt X1 BOUND_VARIABLE_5330)) (not (tptp.ssList BOUND_VARIABLE_5332)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app (tptp.cons BOUND_VARIABLE_5330 tptp.nil) BOUND_VARIABLE_5332))) (not (tptp.ssList BOUND_VARIABLE_5345)) (not (= (tptp.app BOUND_VARIABLE_5345 (tptp.cons X1 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) _let_13 (not (forall ((X5 $$unsorted) (BOUND_VARIABLE_5433 $$unsorted) (BOUND_VARIABLE_5420 $$unsorted) (BOUND_VARIABLE_5418 $$unsorted)) (or (not (tptp.ssItem X5)) (not (tptp.ssItem BOUND_VARIABLE_5418)) (not (tptp.lt BOUND_VARIABLE_5418 X5)) (not (tptp.ssList BOUND_VARIABLE_5420)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app BOUND_VARIABLE_5420 (tptp.cons BOUND_VARIABLE_5418 tptp.nil)))) (not (tptp.ssList BOUND_VARIABLE_5433)) (not (= (tptp.app (tptp.cons X5 tptp.nil) BOUND_VARIABLE_5433) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_27))) (REFL :args (_let_28)) :args _let_30)) _let_29 :args (_let_28 true _let_27)))) (let ((_let_33 (REFL :args (_let_26)))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 4)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_4))) :args _let_30)) :args ((or _let_4 _let_26))) _let_32 :args (_let_4 true _let_26)))) (let ((_let_35 (or _let_18 _let_25 _let_7))) (let ((_let_36 (forall ((U $$unsorted) (BOUND_VARIABLE_3617 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3617)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3617)))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 7)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_30)) :args ((or _let_17 _let_26))) _let_32 :args (_let_17 true _let_26)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_30)) :args ((or _let_24 _let_26))) _let_32 :args (_let_24 true _let_26)))) (let ((_let_40 (forall ((U $$unsorted) (BOUND_VARIABLE_3924 $$unsorted) (BOUND_VARIABLE_3922 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList BOUND_VARIABLE_3922)) (not (tptp.ssList BOUND_VARIABLE_3924)) (= (tptp.memberP (tptp.app BOUND_VARIABLE_3922 BOUND_VARIABLE_3924) U) (or (tptp.memberP BOUND_VARIABLE_3922 U) (tptp.memberP BOUND_VARIABLE_3924 U))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (_let_40))) (let ((_let_43 (not _let_12))) (let ((_let_44 (or (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) _let_19))) (let ((_let_45 (= _let_8 _let_44))) (let ((_let_46 (or _let_15 _let_18 _let_25 _let_45))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_15 _let_13 _let_14 _let_12 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_12)) :args ((or _let_11 (not _let_9) _let_43))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 6)) _let_32 :args ((not _let_11) true _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_9 0)) :args ((or (not _let_8) _let_9))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_45)) :args ((or _let_8 (not _let_44) (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_44 1)) :args ((or _let_20 _let_44))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 5)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_30)) :args ((or _let_19 _let_26))) _let_32 :args (_let_19 true _let_26)) :args (_let_44 false _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_25 _let_15 _let_18 _let_45 (not _let_46)))) _let_39 _let_34 _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_42)) _let_41 :args (_let_46 false _let_40)) :args (_let_45 false _let_24 false _let_4 false _let_17 false _let_46)) :args (_let_8 false _let_44 false _let_45)) :args (_let_9 false _let_8)) :args (_let_43 true _let_11 false _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_42)) _let_41 :args (_let_16 false _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_25 _let_18 _let_7 (not _let_35)))) _let_39 _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_ENUM)) :args (_let_36))) _let_37 :args (_let_35 false _let_36)) :args (_let_7 false _let_24 false _let_17 false _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 9)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_5))) :args _let_30)) :args ((or _let_5 _let_26))) _let_32 :args (_let_5 true _let_26)) _let_34 :args (false true _let_12 false _let_16 false _let_7 false _let_5 false _let_4)) :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))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))) (tptp.ssList tptp.nil) (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 $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) _let_3 (forall ((U $$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)))))) _let_2 (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)))))))))))))))))))))))))))))))))))))))))))))))))
% 13.10/13.35 )
% 13.10/13.35 % SZS output end Proof for SWC404+1
% 13.10/13.35 % cvc5---1.0.5 exiting
% 13.10/13.35 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------