TSTP Solution File: SWC279+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC279+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 20:24:26 EDT 2023
% Result : Theorem 10.51s 10.75s
% Output : Proof 10.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC279+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n007.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 14:39:43 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 10.51/10.75 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.B7WhRW9Df6/cvc5---1.0.5_16004.p...
% 10.51/10.75 ------- get file name : TPTP file name is SWC279+1
% 10.51/10.75 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16004.smt2...
% 10.51/10.75 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.51/10.75 --- Run --no-e-matching --full-saturate-quant at 5...
% 10.51/10.75 % SZS status Theorem for SWC279+1
% 10.51/10.75 % SZS output start Proof for SWC279+1
% 10.51/10.75 (
% 10.51/10.75 (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 $$unsorted)) (and (tptp.ssItem Y) (exists ((Z $$unsorted)) (and (tptp.ssList Z) (exists ((X1 $$unsorted)) (and (tptp.ssList X1) (= (tptp.app (tptp.app Z (tptp.cons Y tptp.nil)) X1) W) (exists ((X2 $$unsorted)) (and (tptp.ssItem X2) (or (and (not (tptp.leq Y X2)) (tptp.memberP X1 X2)) (and (not (tptp.leq X2 Y)) (tptp.memberP Z X2))))))))))) (forall ((X3 $$unsorted)) (=> (tptp.ssItem X3) (forall ((X4 $$unsorted)) (=> (tptp.ssList X4) (forall ((X5 $$unsorted)) (=> (tptp.ssList X5) (or (not (= (tptp.app (tptp.app X4 (tptp.cons X3 tptp.nil)) X5) U)) (forall ((X6 $$unsorted)) (=> (tptp.ssItem X6) (and (or (not (tptp.memberP X4 X6)) (tptp.leq X6 X3)) (or (not (tptp.memberP X5 X6)) (tptp.leq X3 X6)))))))))))))))))))))))) (let ((_let_2 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_3 (not _let_2))) (let ((_let_4 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_5 (or _let_4 _let_3))) (let ((_let_6 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_9 (or _let_8 _let_7))) (let ((_let_10 (and _let_9 _let_5))) (let ((_let_11 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_12 (not _let_11))) (let ((_let_13 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16 _let_14 _let_12 _let_10))) (let ((_let_20 (forall ((Y $$unsorted) (BOUND_VARIABLE_5345 $$unsorted) (BOUND_VARIABLE_5343 $$unsorted) (BOUND_VARIABLE_5341 $$unsorted)) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5341)) (not (tptp.ssList BOUND_VARIABLE_5345)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5341 (tptp.cons Y tptp.nil)) BOUND_VARIABLE_5345) (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (not (tptp.ssItem BOUND_VARIABLE_5343)) (and (or (tptp.leq Y BOUND_VARIABLE_5343) (not (tptp.memberP BOUND_VARIABLE_5345 BOUND_VARIABLE_5343))) (or (tptp.leq BOUND_VARIABLE_5343 Y) (not (tptp.memberP BOUND_VARIABLE_5341 BOUND_VARIABLE_5343)))))))) (let ((_let_21 (or _let_7 _let_8))) (let ((_let_22 (or _let_3 _let_4))) (let ((_let_23 (and _let_22 _let_21))) (let ((_let_24 (not _let_20))) (let ((_let_25 (or (not (tptp.ssList (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) _let_24 _let_18 _let_16 _let_14 _let_12 _let_23))) (let ((_let_26 (forall ((BOUND_VARIABLE_5525 $$unsorted) (BOUND_VARIABLE_5523 $$unsorted) (BOUND_VARIABLE_5521 $$unsorted) (BOUND_VARIABLE_5519 $$unsorted)) (or (not (tptp.ssList (tptp.app (tptp.app BOUND_VARIABLE_5525 (tptp.cons BOUND_VARIABLE_5519 tptp.nil)) BOUND_VARIABLE_5521))) (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5345 $$unsorted) (BOUND_VARIABLE_5343 $$unsorted) (BOUND_VARIABLE_5341 $$unsorted)) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5341)) (not (tptp.ssList BOUND_VARIABLE_5345)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5341 (tptp.cons Y tptp.nil)) BOUND_VARIABLE_5345) (tptp.app (tptp.app BOUND_VARIABLE_5525 (tptp.cons BOUND_VARIABLE_5519 tptp.nil)) BOUND_VARIABLE_5521))) (not (tptp.ssItem BOUND_VARIABLE_5343)) (and (or (tptp.leq Y BOUND_VARIABLE_5343) (not (tptp.memberP BOUND_VARIABLE_5345 BOUND_VARIABLE_5343))) (or (tptp.leq BOUND_VARIABLE_5343 Y) (not (tptp.memberP BOUND_VARIABLE_5341 BOUND_VARIABLE_5343))))))) (not (tptp.ssItem BOUND_VARIABLE_5519)) (not (tptp.ssList BOUND_VARIABLE_5525)) (not (tptp.ssList BOUND_VARIABLE_5521)) (not (tptp.ssItem BOUND_VARIABLE_5523)) (and (or (not (tptp.memberP BOUND_VARIABLE_5525 BOUND_VARIABLE_5523)) (tptp.leq BOUND_VARIABLE_5523 BOUND_VARIABLE_5519)) (or (not (tptp.memberP BOUND_VARIABLE_5521 BOUND_VARIABLE_5523)) (tptp.leq BOUND_VARIABLE_5519 BOUND_VARIABLE_5523))))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (or))) (let ((_let_29 (not _let_26))) (let ((_let_30 (_let_29))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_30)) :args _let_30)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_26))) (REFL :args (_let_27)) :args _let_28)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_27 true _let_26)))) (let ((_let_32 (REFL :args (_let_25)))) (let ((_let_33 (_let_20))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_18 _let_16 _let_14 _let_12 _let_10 (not _let_19)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_28)) :args ((or _let_17 _let_25))) _let_31 :args (_let_17 true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 3)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_28)) :args ((or _let_15 _let_25))) _let_31 :args (_let_15 true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 4)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_28)) :args ((or _let_13 _let_25))) _let_31 :args (_let_13 true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 5)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_28)) :args ((or _let_11 _let_25))) _let_31 :args (_let_11 true _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_33) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_33))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_20))) :args _let_28)) :args ((or _let_20 _let_25))) _let_31 :args (_let_20 true _let_25)) :args (_let_19 false _let_20)) :args (_let_10 false _let_17 false _let_15 false _let_13 false _let_11 false _let_19)))) (let ((_let_35 (not _let_10))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_23)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 6)) _let_31 :args ((not _let_23) true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_9)) :args ((or _let_7 _let_8 (not _let_9)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_10 0)) :args ((or _let_9 _let_35))) _let_34 :args (_let_9 false _let_10)) (CNF_OR_NEG :args (_let_21 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 0)) (CONG (REFL :args (_let_21)) (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) :args _let_28)) :args ((or _let_6 _let_21))) :args (_let_21 false _let_9 true _let_8 false _let_6)) :args ((not _let_22) true _let_23 false _let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_5)) :args ((or _let_3 _let_4 (not _let_5)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 1)) _let_36 :args ((not _let_4) true _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 0)) (CONG (REFL :args (_let_22)) (MACRO_SR_PRED_INTRO :args ((= (not _let_3) _let_2))) :args _let_28)) :args ((or _let_2 _let_22))) _let_36 :args (_let_2 true _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_10 1)) :args ((or _let_5 _let_35))) _let_34 :args (_let_5 false _let_10)) :args (false true _let_4 false _let_2 false _let_5)) :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)))))))))))))))))))))))))))))))))))))))
% 10.51/10.75 )
% 10.51/10.75 % SZS output end Proof for SWC279+1
% 10.51/10.75 % cvc5---1.0.5 exiting
% 10.51/10.76 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------