TSTP Solution File: SWC412+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC412+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 20:25:26 EDT 2023
% Result : Theorem 1.45s 1.66s
% Output : Proof 1.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWC412+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 15:08:40 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 1.45/1.66 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.kbjLFAiUMb/cvc5---1.0.5_29609.p...
% 1.45/1.66 ------- get file name : TPTP file name is SWC412+1
% 1.45/1.66 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_29609.smt2...
% 1.45/1.66 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.45/1.66 % SZS status Theorem for SWC412+1
% 1.45/1.66 % SZS output start Proof for SWC412+1
% 1.45/1.66 (
% 1.45/1.66 (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)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (and (or (exists ((Y $$unsorted)) (and (tptp.ssItem Y) (exists ((Z $$unsorted)) (and (tptp.ssItem Z) (exists ((X1 $$unsorted)) (and (tptp.ssList X1) (= (tptp.app (tptp.app (tptp.cons Y tptp.nil) (tptp.cons Z tptp.nil)) X1) X))))))) (forall ((X2 $$unsorted)) (=> (tptp.ssItem X2) (forall ((X3 $$unsorted)) (=> (tptp.ssItem X3) (forall ((X4 $$unsorted)) (=> (tptp.ssList X4) (not (= (tptp.app (tptp.app (tptp.cons X2 tptp.nil) (tptp.cons X3 tptp.nil)) X4) V))))))))) (or (exists ((X5 $$unsorted)) (and (tptp.ssItem X5) (exists ((X6 $$unsorted)) (and (tptp.ssItem X6) (exists ((X7 $$unsorted)) (let ((_let_1 (tptp.cons X6 tptp.nil))) (let ((_let_2 (tptp.cons X5 tptp.nil))) (and (tptp.ssList X7) (not (= (tptp.app (tptp.app _let_1 X7) _let_2) W)) (= (tptp.app (tptp.app _let_2 X7) _let_1) X))))))))) (forall ((X8 $$unsorted)) (=> (tptp.ssItem X8) (forall ((X9 $$unsorted)) (=> (tptp.ssItem X9) (forall ((X10 $$unsorted)) (=> (tptp.ssList X10) (not (= (tptp.app (tptp.app (tptp.cons X8 tptp.nil) (tptp.cons X9 tptp.nil)) X10) V)))))))) (forall ((X11 $$unsorted)) (=> (tptp.ssItem X11) (forall ((X12 $$unsorted)) (=> (tptp.ssItem X12) (forall ((X13 $$unsorted)) (let ((_let_1 (tptp.cons X11 tptp.nil))) (let ((_let_2 (tptp.cons X12 tptp.nil))) (or (not (tptp.ssList X13)) (not (= (tptp.app (tptp.app _let_1 X13) _let_2) V)) (= (tptp.app (tptp.app _let_2 X13) _let_1) U)))))))))))))))))))))) (let ((_let_2 (forall ((Y $$unsorted) (BOUND_VARIABLE_5342 $$unsorted) (BOUND_VARIABLE_5340 $$unsorted)) (or (not (tptp.ssItem Y)) (not (tptp.ssItem BOUND_VARIABLE_5340)) (not (tptp.ssList BOUND_VARIABLE_5342)) (not (= (tptp.app (tptp.app (tptp.cons Y tptp.nil) (tptp.cons BOUND_VARIABLE_5340 tptp.nil)) BOUND_VARIABLE_5342) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))))) (let ((_let_3 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 (tptp.app (tptp.app (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_6 (not _let_5))) (let ((_let_7 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_8 (not _let_7))) (let ((_let_9 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_10 (not _let_9))) (let ((_let_11 (or _let_10 _let_8 _let_6 _let_4))) (let ((_let_12 (not _let_2))) (let ((_let_13 (or _let_12 _let_10 _let_6 _let_8 _let_4))) (let ((_let_14 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_15 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.nil))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app (tptp.app _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) _let_14)))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 (tptp.app (tptp.app _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) _let_15)))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_24 (not _let_23))) (let ((_let_25 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 (tptp.app (tptp.app (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 tptp.nil) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))))) (let ((_let_26 (not (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))) (let ((_let_27 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_28 (not (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)))) (let ((_let_29 (forall ((X5 $$unsorted) (BOUND_VARIABLE_5459 $$unsorted) (BOUND_VARIABLE_5457 $$unsorted)) (let ((_let_1 (tptp.cons BOUND_VARIABLE_5457 tptp.nil))) (let ((_let_2 (tptp.cons X5 tptp.nil))) (or (not (tptp.ssItem X5)) (not (tptp.ssItem BOUND_VARIABLE_5457)) (not (tptp.ssList BOUND_VARIABLE_5459)) (= (tptp.app (tptp.app _let_1 BOUND_VARIABLE_5459) _let_2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (not (= (tptp.app (tptp.app _let_2 BOUND_VARIABLE_5459) _let_1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))))))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_28 _let_27 _let_26 _let_25 _let_24 _let_22 _let_20 _let_18 _let_16))) (let ((_let_32 (and _let_13 _let_31))) (let ((_let_33 (or _let_24 _let_20 _let_22 _let_16 _let_18))) (let ((_let_34 (or))) (let ((_let_35 (REFL :args (_let_31)))) (let ((_let_36 (_let_29))) (let ((_let_37 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))) (let ((_let_38 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_39 (or _let_38 _let_37 _let_32))) (let ((_let_40 (forall ((U $$unsorted) (BOUND_VARIABLE_6074 $$unsorted) (BOUND_VARIABLE_6072 $$unsorted) (BOUND_VARIABLE_6070 $$unsorted) (BOUND_VARIABLE_6068 $$unsorted) (BOUND_VARIABLE_6066 $$unsorted) (BOUND_VARIABLE_6064 $$unsorted) (BOUND_VARIABLE_6062 $$unsorted) (BOUND_VARIABLE_6060 $$unsorted) (BOUND_VARIABLE_6058 $$unsorted) (BOUND_VARIABLE_6056 $$unsorted)) (let ((_let_1 (tptp.cons BOUND_VARIABLE_6072 tptp.nil))) (let ((_let_2 (tptp.cons BOUND_VARIABLE_6064 tptp.nil))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_6056)) (and (or (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5342 $$unsorted) (BOUND_VARIABLE_5340 $$unsorted)) (or (not (tptp.ssItem Y)) (not (tptp.ssItem BOUND_VARIABLE_5340)) (not (tptp.ssList BOUND_VARIABLE_5342)) (not (= (tptp.app (tptp.app (tptp.cons Y tptp.nil) (tptp.cons BOUND_VARIABLE_5340 tptp.nil)) BOUND_VARIABLE_5342) BOUND_VARIABLE_6056))))) (not (tptp.ssItem BOUND_VARIABLE_6074)) (not (tptp.ssList BOUND_VARIABLE_6070)) (not (tptp.ssItem BOUND_VARIABLE_6066)) (not (= BOUND_VARIABLE_6056 (tptp.app (tptp.app (tptp.cons BOUND_VARIABLE_6074 tptp.nil) (tptp.cons BOUND_VARIABLE_6066 tptp.nil)) BOUND_VARIABLE_6070)))) (or (not (forall ((X5 $$unsorted) (BOUND_VARIABLE_5459 $$unsorted) (BOUND_VARIABLE_5457 $$unsorted)) (let ((_let_1 (tptp.cons BOUND_VARIABLE_5457 tptp.nil))) (let ((_let_2 (tptp.cons X5 tptp.nil))) (or (not (tptp.ssItem X5)) (not (tptp.ssItem BOUND_VARIABLE_5457)) (not (tptp.ssList BOUND_VARIABLE_5459)) (= U (tptp.app (tptp.app _let_1 BOUND_VARIABLE_5459) _let_2)) (not (= (tptp.app (tptp.app _let_2 BOUND_VARIABLE_5459) _let_1) BOUND_VARIABLE_6056))))))) (not (tptp.ssItem BOUND_VARIABLE_6062)) (not (tptp.ssList BOUND_VARIABLE_6060)) (not (tptp.ssItem BOUND_VARIABLE_6058)) (not (= BOUND_VARIABLE_6056 (tptp.app (tptp.app (tptp.cons BOUND_VARIABLE_6062 tptp.nil) (tptp.cons BOUND_VARIABLE_6058 tptp.nil)) BOUND_VARIABLE_6060))) (not (tptp.ssItem BOUND_VARIABLE_6072)) (not (tptp.ssList BOUND_VARIABLE_6068)) (not (tptp.ssItem BOUND_VARIABLE_6064)) (not (= BOUND_VARIABLE_6056 (tptp.app (tptp.app _let_1 BOUND_VARIABLE_6068) _let_2))) (= U (tptp.app (tptp.app _let_2 BOUND_VARIABLE_6068) _let_1)))))))))) (let ((_let_41 (not _let_39))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (not _let_40))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_32)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 2)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_42) :args (_let_43)) (REWRITE :args ((=> _let_43 (not (or _let_38 _let_37 (and _let_13 (or (not (forall ((X5 $$unsorted) (BOUND_VARIABLE_5459 $$unsorted) (BOUND_VARIABLE_5457 $$unsorted)) (let ((_let_1 (tptp.cons BOUND_VARIABLE_5457 tptp.nil))) (let ((_let_2 (tptp.cons X5 tptp.nil))) (or (not (tptp.ssItem X5)) (not (tptp.ssItem BOUND_VARIABLE_5457)) (not (tptp.ssList BOUND_VARIABLE_5459)) (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app (tptp.app _let_1 BOUND_VARIABLE_5459) _let_2)) (not (= (tptp.app (tptp.app _let_2 BOUND_VARIABLE_5459) _let_1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))))))) _let_28 _let_27 _let_26 _let_25 _let_24 _let_22 _let_20 _let_18 _let_16))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_40))) (REFL :args (_let_41)) :args _let_34)) _let_42 :args (_let_41 true _let_40)) :args ((not _let_32) true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_24 _let_22 _let_20 _let_18 _let_16 (not _let_33)))) (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_36) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.app (tptp.app (tptp.cons BOUND_VARIABLE_5457 tptp.nil) BOUND_VARIABLE_5459) (tptp.cons X5 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) :args _let_36))) (CNF_OR_NEG :args (_let_31 9)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 8)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_34)) :args ((or _let_17 _let_31))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 7)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_34)) :args ((or _let_19 _let_31))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 6)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_34)) :args ((or _let_21 _let_31))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 5)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_34)) :args ((or _let_23 _let_31))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 0)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_34)) :args ((or _let_29 _let_31))) :args (_let_31 false _let_33 true _let_16 false _let_17 false _let_19 false _let_21 false _let_23 false _let_29)) :args ((not _let_13) true _let_32 false _let_31)))) (let ((_let_45 (REFL :args (_let_13)))) (let ((_let_46 (not _let_11))) (let ((_let_47 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_47) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.app (tptp.cons Y tptp.nil) (tptp.cons BOUND_VARIABLE_5340 tptp.nil)) BOUND_VARIABLE_5342)))) :args _let_47))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_11)) :args ((or _let_10 _let_6 _let_8 _let_4 _let_46))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 1)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_34)) :args ((or _let_9 _let_13))) _let_44 :args (_let_9 true _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 2)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_5))) :args _let_34)) :args ((or _let_5 _let_13))) _let_44 :args (_let_5 true _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 3)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_34)) :args ((or _let_7 _let_13))) _let_44 :args (_let_7 true _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 4)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_4) _let_3))) :args _let_34)) :args ((or _let_3 _let_13))) _let_44 :args (_let_3 true _let_13)) :args (_let_46 false _let_9 false _let_5 false _let_7 false _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 0)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_2))) :args _let_34)) :args ((or _let_2 _let_13))) _let_44 :args (_let_2 true _let_13)) :args (false true _let_11 false _let_2)) :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 $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) (forall ((U $$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)))))) (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))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.45/1.68 )
% 1.45/1.68 % SZS output end Proof for SWC412+1
% 1.45/1.68 % cvc5---1.0.5 exiting
% 1.45/1.68 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------