TSTP Solution File: SWC219+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC219+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 20:24:05 EDT 2023
% Result : Theorem 30.88s 31.14s
% Output : Proof 30.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWC219+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.37 % Computer : n019.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Mon Aug 28 14:47:28 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.23/0.57 %----Proving TF0_NAR, FOF, or CNF
% 30.88/31.14 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ZA9Jq92zFC/cvc5---1.0.5_21126.p...
% 30.88/31.14 ------- get file name : TPTP file name is SWC219+1
% 30.88/31.14 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21126.smt2...
% 30.88/31.14 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 30.88/31.14 --- Run --no-e-matching --full-saturate-quant at 5...
% 30.88/31.14 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 30.88/31.14 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 30.88/31.14 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.88/31.14 % SZS status Theorem for SWC219+1
% 30.88/31.14 % SZS output start Proof for SWC219+1
% 30.88/31.14 (
% 30.88/31.14 (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)) (= tptp.nil U) (exists ((Y $$unsorted)) (and (tptp.ssItem Y) (exists ((Z $$unsorted)) (and (tptp.ssList Z) (exists ((X1 $$unsorted)) (and (tptp.ssList X1) (= (tptp.app (tptp.app Z (tptp.cons Y tptp.nil)) X1) U) (forall ((X2 $$unsorted)) (=> (tptp.ssItem X2) (or (not (tptp.memberP Z X2)) (not (tptp.memberP X1 X2)) (not (tptp.leq Y X2)) (tptp.leq X2 Y)))))))))) (and (forall ((X3 $$unsorted)) (=> (tptp.ssItem X3) (or (not (= (tptp.cons X3 tptp.nil) W)) (not (tptp.memberP X X3)) (exists ((X4 $$unsorted)) (and (tptp.ssItem X4) (not (= X3 X4)) (tptp.memberP X X4) (tptp.leq X4 X3)))))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_5 (tptp.ssList tptp.nil))) (let ((_let_6 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.memberP tptp.nil U)))))) (let ((_let_7 (tptp.memberP tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62))) (let ((_let_8 (not _let_7))) (let ((_let_9 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62))) (let ((_let_10 (not _let_9))) (let ((_let_11 (or _let_10 _let_8))) (let ((_let_12 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_13 (not _let_11))) (let ((_let_14 (or _let_10 _let_8 (not (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62)) (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_15 (forall ((X2 $$unsorted)) (or (not (tptp.ssItem X2)) (not (tptp.memberP tptp.nil X2)) (not (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X2)) (tptp.leq X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_16 (not _let_14))) (let ((_let_17 (not _let_15))) (let ((_let_18 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_19 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app (tptp.app tptp.nil _let_18) tptp.nil)))) (let ((_let_20 (not _let_19))) (let ((_let_21 (not _let_5))) (let ((_let_22 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_21 _let_20 _let_17))) (let ((_let_25 (forall ((Y $$unsorted) (BOUND_VARIABLE_5296 $$unsorted) (BOUND_VARIABLE_5294 $$unsorted)) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5294)) (not (tptp.ssList BOUND_VARIABLE_5296)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5294 (tptp.cons Y tptp.nil)) BOUND_VARIABLE_5296) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (forall ((X2 $$unsorted)) (or (not (tptp.ssItem X2)) (not (tptp.memberP BOUND_VARIABLE_5294 X2)) (not (tptp.memberP BOUND_VARIABLE_5296 X2)) (not (tptp.leq Y X2)) (tptp.leq X2 Y)))))))) (let ((_let_26 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or (not (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) _let_27))) (let ((_let_29 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_18))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_23 _let_30 (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((X4 $$unsorted)) (or (not (tptp.ssItem X4)) (= X4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 X4)) (not (tptp.leq X4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))))) (let ((_let_32 (and _let_31 _let_28))) (let ((_let_33 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_34 (not _let_25))) (let ((_let_35 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_26 _let_34 _let_33 _let_32))) (let ((_let_38 (forall ((U $$unsorted) (BOUND_VARIABLE_5525 $$unsorted) (BOUND_VARIABLE_5523 $$unsorted)) (let ((_let_1 (= tptp.nil U))) (or (not (tptp.ssList U)) _let_1 (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5296 $$unsorted) (BOUND_VARIABLE_5294 $$unsorted)) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5294)) (not (tptp.ssList BOUND_VARIABLE_5296)) (not (= U (tptp.app (tptp.app BOUND_VARIABLE_5294 (tptp.cons Y tptp.nil)) BOUND_VARIABLE_5296))) (not (forall ((X2 $$unsorted)) (or (not (tptp.ssItem X2)) (not (tptp.memberP BOUND_VARIABLE_5294 X2)) (not (tptp.memberP BOUND_VARIABLE_5296 X2)) (not (tptp.leq Y X2)) (tptp.leq X2 Y))))))) (not (tptp.ssList BOUND_VARIABLE_5523)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5525)) (not (= U (tptp.cons BOUND_VARIABLE_5525 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5523 BOUND_VARIABLE_5525)) (not (forall ((X4 $$unsorted)) (or (not (tptp.ssItem X4)) (= X4 BOUND_VARIABLE_5525) (not (tptp.memberP BOUND_VARIABLE_5523 X4)) (not (tptp.leq X4 BOUND_VARIABLE_5525)))))) (or (not (= tptp.nil BOUND_VARIABLE_5523)) (not _let_1)))))))) (let ((_let_39 (not _let_37))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (or))) (let ((_let_42 (not _let_38))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_40) :args (_let_42)) (REWRITE :args ((=> _let_42 (not (or _let_36 _let_26 (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5296 $$unsorted) (BOUND_VARIABLE_5294 $$unsorted)) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5294)) (not (tptp.ssList BOUND_VARIABLE_5296)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app (tptp.app BOUND_VARIABLE_5294 (tptp.cons Y tptp.nil)) BOUND_VARIABLE_5296))) (not (forall ((X2 $$unsorted)) (or (not (tptp.ssItem X2)) (not (tptp.memberP BOUND_VARIABLE_5294 X2)) (not (tptp.memberP BOUND_VARIABLE_5296 X2)) (not (tptp.leq Y X2)) (tptp.leq X2 Y))))))) _let_33 _let_32))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_38))) (REFL :args (_let_39)) :args _let_41)) _let_40 :args (_let_39 true _let_38)))) (let ((_let_44 (REFL :args (_let_37)))) (let ((_let_45 (_let_25))) (let ((_let_46 (= _let_18 (tptp.app _let_18 tptp.nil)))) (let ((_let_47 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_48 (or _let_21 _let_23 _let_46))) (let ((_let_49 (forall ((U $$unsorted) (BOUND_VARIABLE_4822 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4822)) (= (tptp.cons BOUND_VARIABLE_4822 U) (tptp.app (tptp.cons BOUND_VARIABLE_4822 tptp.nil) U)))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_32)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 4)) _let_43 :args ((not _let_32) true _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 1)) (CONG (REFL :args (_let_28)) (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_41)) :args ((or _let_26 _let_28))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_37 1)) :args ((or _let_27 _let_37))) _let_43 :args (_let_27 true _let_37)) :args (_let_28 true _let_26)) :args ((not _let_31) true _let_32 false _let_28)))) (let ((_let_52 (REFL :args (_let_31)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 0)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_41)) :args ((or _let_22 _let_31))) _let_51 :args (_let_22 true _let_31)))) (let ((_let_54 (ASSUME :args (_let_5)))) (let ((_let_55 (or _let_36 _let_47))) (let ((_let_56 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (and _let_29 _let_47 _let_46))) (let ((_let_59 (APPLY_UF tptp.app))) (let ((_let_60 (REFL :args (tptp.nil)))) (let ((_let_61 (ASSUME :args (_let_29)))) (let ((_let_62 (SYMM _let_61))) (let ((_let_63 (SYMM _let_62))) (let ((_let_64 (ASSUME :args (_let_47)))) (let ((_let_65 (ASSUME :args (_let_46)))) (let ((_let_66 (_let_17))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_66)) :args _let_66)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_15))) (REFL :args (_let_16)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_24))) :args ((or _let_21 _let_23 _let_20 _let_17 (not _let_24)))) _let_54 _let_53 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_58)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_64 _let_65 _let_61) (SCOPE (TRANS _let_63 (SYMM (SYMM _let_65)) (CONG (TRANS _let_62 (TRANS (SYMM (SYMM _let_64)) (CONG _let_60 _let_63 :args _let_59))) _let_60 :args _let_59)) :args (_let_47 _let_46 _let_29))) :args (_let_29 _let_47 _let_46))) :args (true _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 1)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_41)) :args ((or _let_29 _let_31))) _let_51 :args (_let_29 true _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_36 _let_47 (not _let_55)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 0)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_41)) :args ((or _let_35 _let_37))) _let_43 :args (_let_35 true _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_56))) _let_57 :args (_let_55 false _let_56)) :args (_let_47 false _let_35 false _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_21 _let_23 _let_46 (not _let_48)))) _let_54 _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_4822 U)))) :args (_let_49))) _let_50 :args (_let_48 false _let_49)) :args (_let_46 false _let_5 false _let_22 false _let_48)) :args (_let_19 false _let_29 false _let_47 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_45) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil tptp.nil QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.app BOUND_VARIABLE_5294 (tptp.cons Y tptp.nil)) BOUND_VARIABLE_5296)))) :args _let_45))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 2)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_25))) :args _let_41)) :args ((or _let_25 _let_37))) _let_43 :args (_let_25 true _let_37)) :args (_let_24 false _let_25)) :args (_let_17 false _let_5 false _let_22 false _let_19 false _let_24)) :args (_let_16 true _let_15)))) (let ((_let_68 (REFL :args (_let_14)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_12 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_6))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_11)) :args ((or _let_10 _let_8 _let_13))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 0)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_41)) :args ((or _let_9 _let_14))) _let_67 :args (_let_9 true _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 1)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_41)) :args ((or _let_7 _let_14))) _let_67 :args (_let_7 true _let_14)) :args (_let_13 false _let_9 false _let_7)) _let_12 :args (false true _let_11 false _let_6)) :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 $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))) _let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) _let_4 (forall ((U $$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))))))))) _let_3 (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)))))))) _let_2 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 30.88/31.14 )
% 30.88/31.14 % SZS output end Proof for SWC219+1
% 30.88/31.14 % cvc5---1.0.5 exiting
% 30.88/31.14 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------