TSTP Solution File: SWC076+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC076+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 20:23:03 EDT 2023
% Result : Theorem 2.10s 2.34s
% Output : Proof 2.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWC076+1 : TPTP v8.1.2. Released v2.4.0.
% 0.09/0.12 % Command : do_cvc5 %s %d
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 15:42:16 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.45 %----Proving TF0_NAR, FOF, or CNF
% 2.10/2.34 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.k6XrBTVYGQ/cvc5---1.0.5_26986.p...
% 2.10/2.34 ------- get file name : TPTP file name is SWC076+1
% 2.10/2.34 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_26986.smt2...
% 2.10/2.34 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.10/2.34 % SZS status Theorem for SWC076+1
% 2.10/2.34 % SZS output start Proof for SWC076+1
% 2.10/2.34 (
% 2.10/2.34 (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)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq Y tptp.nil) (tptp.segmentP V Y) (tptp.segmentP U Y))) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (forall ((X1 $$unsorted)) (=> (tptp.ssList X1) (or (not (= (tptp.app (tptp.app Z W) X1) X)) (not (tptp.equalelemsP W)) (exists ((X2 $$unsorted)) (and (tptp.ssItem X2) (exists ((X3 $$unsorted)) (and (tptp.ssList X3) (= (tptp.app X3 (tptp.cons X2 tptp.nil)) Z) (exists ((X4 $$unsorted)) (and (tptp.ssList X4) (= (tptp.app (tptp.cons X2 tptp.nil) X4) W))))))) (exists ((X5 $$unsorted)) (and (tptp.ssItem X5) (exists ((X6 $$unsorted)) (and (tptp.ssList X6) (= (tptp.app (tptp.cons X5 tptp.nil) X6) X1) (exists ((X7 $$unsorted)) (and (tptp.ssList X7) (= (tptp.app X7 (tptp.cons X5 tptp.nil)) W)))))))))))) (and (not (= tptp.nil X)) (= tptp.nil W)) (and (= tptp.nil V) (= tptp.nil U)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP 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 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (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_6))) (let ((_let_12 (not _let_11))) (let ((_let_13 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_14 (not _let_13))) (let ((_let_15 (and _let_8 _let_6))) (let ((_let_16 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Y)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)))))) (let ((_let_17 (not _let_16))) (let ((_let_18 (not (tptp.ssList _let_7)))) (let ((_let_19 (not (tptp.equalelemsP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_20 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_18 _let_17 _let_15 _let_10 _let_14 (not (forall ((X2 $$unsorted) (BOUND_VARIABLE_5310 $$unsorted) (BOUND_VARIABLE_5302 $$unsorted)) (let ((_let_1 (tptp.cons X2 tptp.nil))) (or (not (tptp.ssItem X2)) (not (tptp.ssList BOUND_VARIABLE_5302)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5302) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.ssList BOUND_VARIABLE_5310)) (not (= (tptp.app BOUND_VARIABLE_5310 _let_1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) _let_12 (not (forall ((X5 $$unsorted) (BOUND_VARIABLE_5365 $$unsorted) (BOUND_VARIABLE_5357 $$unsorted)) (let ((_let_1 (tptp.cons X5 tptp.nil))) (or (not (tptp.ssItem X5)) (not (tptp.ssList BOUND_VARIABLE_5357)) (not (= (tptp.app BOUND_VARIABLE_5357 _let_1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.ssList BOUND_VARIABLE_5365)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5365) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))))))) (let ((_let_23 (forall ((U $$unsorted) (BOUND_VARIABLE_5610 $$unsorted) (BOUND_VARIABLE_5608 $$unsorted)) (let ((_let_1 (= tptp.nil U))) (let ((_let_2 (tptp.app (tptp.app BOUND_VARIABLE_5610 U) BOUND_VARIABLE_5608))) (let ((_let_3 (= tptp.nil _let_2))) (or (not (tptp.ssList U)) (not (tptp.equalelemsP U)) (not (tptp.ssList _let_2)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_5610 U) BOUND_VARIABLE_5608) Y)) (not (tptp.segmentP U Y))))) (and _let_3 _let_1) (and (not _let_3) _let_1) (not (tptp.ssList BOUND_VARIABLE_5610)) (not (forall ((X2 $$unsorted) (BOUND_VARIABLE_5310 $$unsorted) (BOUND_VARIABLE_5302 $$unsorted)) (let ((_let_1 (tptp.cons X2 tptp.nil))) (or (not (tptp.ssItem X2)) (not (tptp.ssList BOUND_VARIABLE_5302)) (not (= U (tptp.app _let_1 BOUND_VARIABLE_5302))) (not (tptp.ssList BOUND_VARIABLE_5310)) (not (= (tptp.app BOUND_VARIABLE_5310 _let_1) BOUND_VARIABLE_5610)))))) (not (tptp.ssList BOUND_VARIABLE_5608)) (not (forall ((X5 $$unsorted) (BOUND_VARIABLE_5365 $$unsorted) (BOUND_VARIABLE_5357 $$unsorted)) (let ((_let_1 (tptp.cons X5 tptp.nil))) (or (not (tptp.ssItem X5)) (not (tptp.ssList BOUND_VARIABLE_5357)) (not (= U (tptp.app BOUND_VARIABLE_5357 _let_1))) (not (tptp.ssList BOUND_VARIABLE_5365)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5365) BOUND_VARIABLE_5608))))))))))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (or))) (let ((_let_27 (not _let_23))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_25) :args (_let_27)) (REWRITE :args ((=> _let_27 (not (or _let_21 _let_19 _let_18 _let_17 _let_15 _let_10 _let_14 (not (forall ((X2 $$unsorted) (BOUND_VARIABLE_5310 $$unsorted) (BOUND_VARIABLE_5302 $$unsorted)) (let ((_let_1 (tptp.cons X2 tptp.nil))) (or (not (tptp.ssItem X2)) (not (tptp.ssList BOUND_VARIABLE_5302)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app _let_1 BOUND_VARIABLE_5302))) (not (tptp.ssList BOUND_VARIABLE_5310)) (not (= (tptp.app BOUND_VARIABLE_5310 _let_1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) _let_12 (not (forall ((X5 $$unsorted) (BOUND_VARIABLE_5365 $$unsorted) (BOUND_VARIABLE_5357 $$unsorted)) (let ((_let_1 (tptp.cons X5 tptp.nil))) (or (not (tptp.ssItem X5)) (not (tptp.ssList BOUND_VARIABLE_5357)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app BOUND_VARIABLE_5357 _let_1))) (not (tptp.ssList BOUND_VARIABLE_5365)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5365) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_23))) (REFL :args (_let_24)) :args _let_26)) _let_25 :args (_let_24 true _let_23)))) (let ((_let_29 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_30 (not _let_6))) (let ((_let_31 (= _let_30 _let_29))) (let ((_let_32 (not _let_4))) (let ((_let_33 (or _let_21 _let_32 _let_31))) (let ((_let_34 (forall ((U $$unsorted) (BOUND_VARIABLE_3324 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3324)) (= (tptp.neq U BOUND_VARIABLE_3324) (not (= U BOUND_VARIABLE_3324))))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (REFL :args (_let_22)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_26)) :args ((or _let_20 _let_22))) _let_28 :args (_let_20 true _let_22)))) (let ((_let_38 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.segmentP _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_41 (not _let_40))) (let ((_let_42 (not _let_29))) (let ((_let_43 (or _let_21 _let_42 _let_41 _let_39))) (let ((_let_44 (_let_16))) (let ((_let_45 (or _let_21 _let_21 _let_39 _let_14 _let_12 _let_40))) (let ((_let_46 (forall ((U $$unsorted) (BOUND_VARIABLE_4498 $$unsorted) (BOUND_VARIABLE_4496 $$unsorted) (BOUND_VARIABLE_4494 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4494)) (not (tptp.segmentP U BOUND_VARIABLE_4494)) (not (tptp.ssList BOUND_VARIABLE_4498)) (not (tptp.ssList BOUND_VARIABLE_4496)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4498 U) BOUND_VARIABLE_4496) BOUND_VARIABLE_4494))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (or _let_21 _let_38))) (let ((_let_49 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_21 _let_38 (not _let_48)))) _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_49))) _let_50 :args (_let_48 false _let_49)) :args (_let_38 false _let_20 false _let_48)))) (let ((_let_52 (not _let_31))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS1 :args (_let_31)) (CONG (REFL :args (_let_52)) (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_6))) (REFL :args (_let_29)) :args _let_26)) :args ((or _let_6 _let_29 _let_52))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_21 _let_39 _let_42 _let_41 (not _let_43)))) _let_37 _let_51 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_45))) :args ((or _let_21 _let_14 _let_12 _let_39 _let_40 (not _let_45)))) _let_37 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 6)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_26)) :args ((or _let_13 _let_22))) _let_28 :args (_let_13 true _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 8)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_26)) :args ((or _let_11 _let_22))) _let_28 :args (_let_11 true _let_22)) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4498 U) BOUND_VARIABLE_4496) BOUND_VARIABLE_4494) true))))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_40 false _let_20 false _let_13 false _let_11 false _let_38 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_44) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList Y) false))))) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 3)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_26)) :args ((or _let_16 _let_22))) _let_28 :args (_let_16 true _let_22)) :args (_let_43 false _let_16)) :args (_let_42 false _let_20 false _let_38 false _let_40 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_21 _let_31 (not _let_33)))) (ASSUME :args (_let_4)) _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.neq U BOUND_VARIABLE_3324)))) :args (_let_34)))) _let_35 :args (_let_33 false _let_34)) :args (_let_31 false _let_4 false _let_20 false _let_33)) :args (_let_6 true _let_29 false _let_31)))) (let ((_let_54 (_let_10))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_54) (CONG (REFL :args _let_54) (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) (REFL :args (_let_30)) :args _let_26)) :args ((or _let_8 _let_10 _let_30))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_15)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 4)) _let_28 :args ((not _let_15) true _let_22)) _let_53 :args (_let_9 true _let_15 false _let_6)) _let_53 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 5)) _let_28 :args ((not _let_10) true _let_22)) :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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_3 _let_2 (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 2.10/2.36 )
% 2.10/2.36 % SZS output end Proof for SWC076+1
% 2.10/2.36 % cvc5---1.0.5 exiting
% 2.10/2.36 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------