0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : do_cvc5 %s %d 0.12/0.34 % Computer : n005.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Tue Aug 9 01:56:34 EDT 2022 0.12/0.34 % CPUTime : 0.20/0.47 %----Proving TF0_NAR, FOF, or CNF 0.39/0.60 ------- cvc5-fof casc J11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p... 0.39/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10... 0.39/0.60 % SZS status Theorem for theBenchmark 0.39/0.60 % SZS output start Proof for theBenchmark 0.39/0.60 (let ((_let_1 (not (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssList V) (forall ((W $$unsorted)) (=> (ssList W) (forall ((X $$unsorted)) (=> (ssList X) (or (and (forall ((Y $$unsorted)) (=> (ssList Y) (or (not (neq Y nil)) (not (segmentP W Y)) (not (segmentP X Y))))) (or (not (= nil W)) (not (= X nil)))) (= nil U) (not (= W U)) (not (= V X)) (not (= V nil)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (ssList U) (= (segmentP nil U) (= U nil)))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssList V) (= (not (= V U)) (neq U V)))))))) (let ((_let_4 (ssList nil))) (let ((_let_5 (segmentP nil skv_5))) (let ((_let_6 (= nil skv_5))) (let ((_let_7 (= _let_5 _let_6))) (let ((_let_8 (not _let_5))) (let ((_let_9 (neq skv_5 nil))) (let ((_let_10 (not _let_9))) (let ((_let_11 (ssList skv_5))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_10 (not (segmentP skv_4 skv_5)) _let_8))) (let ((_let_14 (= nil skv_4))) (let ((_let_15 (not _let_14))) (let ((_let_16 (and _let_13 _let_15))) (let ((_let_17 (not _let_13))) (let ((_let_18 (or (not (ssList skv_4)) _let_14 _let_16))) (let ((_let_19 (forall ((U $$unsorted) (BOUND_VARIABLE_5235 $$unsorted)) (let ((_let_1 (= nil U))) (or (not (ssList U)) _let_1 (and (or (not (ssList BOUND_VARIABLE_5235)) (not (neq BOUND_VARIABLE_5235 nil)) (not (segmentP U BOUND_VARIABLE_5235)) (not (segmentP nil BOUND_VARIABLE_5235))) (not _let_1))))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (OR))) (let ((_let_23 (not _let_19))) (let ((_let_24 (_let_23))) (let ((_let_25 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_24)) :args _let_24)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_19))) (REFL :args (_let_20)) :args _let_22)) (NOT_OR_ELIM _let_21 :args (1)) :args (_let_20 true _let_19)))) (let ((_let_26 (_let_16))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_26) (CONG (REFL :args _let_26) (REFL :args (_let_17)) (MACRO_SR_PRED_INTRO :args ((= (not 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(or _let_12 _let_35 _let_34))) (let ((_let_37 (forall ((U $$unsorted) (BOUND_VARIABLE_3148 $$unsorted)) (or (not (ssList U)) (not (ssList BOUND_VARIABLE_3148)) (= (neq U BOUND_VARIABLE_3148) (not (= U BOUND_VARIABLE_3148))))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_7)) :args ((or _let_8 _let_6 (not _let_7)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_34)) :args ((or _let_10 _let_33 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 1)) (CONG _let_28 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_22)) :args ((or _let_9 _let_13))) _let_27 :args (_let_9 true _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_12 _let_34 (not _let_36)))) (NOT_NOT_ELIM (NOT_OR_ELIM _let_21 :args (0))) _let_32 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_38 :args (skv_5 nil QUANTIFIERS_INST_E_MATCHING_SIMPLE ((neq U BOUND_VARIABLE_3148)))) :args (_let_37)))) _let_38 :args (_let_36 false _let_37)) :args (_let_34 false _let_4 false _let_11 false _let_36)) :args (_let_33 false _let_9 false _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_12 _let_7 (not _let_29)))) _let_32 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (skv_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ssList U) false))))) :args (_let_30))) _let_31 :args (_let_29 false _let_30)) :args (_let_7 false _let_11 false _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 3)) (CONG _let_28 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_5))) :args _let_22)) :args ((or _let_5 _let_13))) _let_27 :args (_let_5 true _let_13)) :args (false true _let_6 false _let_7 false _let_5)) :args ((forall ((U $$unsorted)) (=> (ssItem U) (forall ((V $$unsorted)) (=> (ssItem V) (forall ((W $$unsorted)) (=> (ssList W) (forall ((X $$unsorted)) (=> (ssList X) (= (frontsegP (cons U W) (cons V X)) (and (frontsegP W X) (= V U))))))))))) (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssList V) (forall ((W $$unsorted)) (=> (ssList W) (=> (frontsegP U V) (frontsegP (app U W) V)))))))) (forall ((U $$unsorted)) (=> (ssItem U) (not (memberP nil U)))) (equalelemsP nil) (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssList V) (=> (not (= U nil)) (= (hd (app U V)) (hd U))))))) (forall ((U $$unsorted)) (=> (ssList U) (rearsegP U nil))) (strictorderedP nil) (forall ((U $$unsorted)) (=> (ssList U) (= (app nil U) U))) (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssList V) (forall ((W $$unsorted)) (=> (ssList W) (=> (= (app W V) (app U V)) (= W U)))))))) (forall ((U $$unsorted)) (=> (ssItem U) (forall ((V $$unsorted)) (=> (ssItem V) (forall ((W $$unsorted)) (=> (ssItem 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(=> (ssList U) (forall ((V $$unsorted)) (=> (ssList V) (=> (and (not (= U nil)) (= (tl V) (tl U)) (= (hd U) (hd V)) (not (= nil V))) (= V U)))))) (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssList V) (forall ((W $$unsorted)) (=> (ssList W) (=> (rearsegP U V) (rearsegP (app W U) V)))))))) _let_2 (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssList V) (= (and (= nil V) (= U nil)) (= (app U V) nil)))))) (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssItem V) (= (tl (cons V U)) U))))) (forall ((U $$unsorted)) (=> (ssList U) (= U (app U nil)))) (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssList V) (forall ((W $$unsorted)) (=> (ssList W) (=> (= (app V W) (app V U)) (= U W)))))))) (forall ((U $$unsorted)) (=> (ssItem U) (leq U U))) (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssItem V) (not (= (cons V U) U)))))) (forall ((U $$unsorted)) (=> (ssList U) (forall ((V 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(lt V U)))))) (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssItem V) (= (memberP U V) (exists ((W $$unsorted)) (and (exists ((X $$unsorted)) (and (= U (app W (cons V X))) (ssList X))) (ssList W)))))))) (forall ((U $$unsorted)) (=> (ssList U) (segmentP U nil))) (forall ((U $$unsorted)) (=> (ssItem U) (forall ((V $$unsorted)) (=> (ssItem V) (forall ((W $$unsorted)) (=> (ssItem W) (=> (and (lt V W) (lt U V)) (lt U W)))))))) (forall ((U $$unsorted)) (=> (ssItem U) (forall ((V $$unsorted)) (=> (ssItem V) (=> (leq U V) (or (= V U) (lt U V))))))) (forall ((U $$unsorted)) (=> (ssList U) (= (exists ((V $$unsorted)) (and (ssItem V) (= U (cons V nil)))) (singletonP U)))) (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssList V) (forall ((W $$unsorted)) (=> (ssList W) (=> (and (segmentP V W) (segmentP U V)) (segmentP U W)))))))) (forall ((U $$unsorted)) (=> (ssList U) (forall ((V $$unsorted)) (=> (ssList V) (forall ((W $$unsorted)) (=> (ssList W) (= (app (app U V) W) (app U (app V W))))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))) 0.39/0.60 % SZS output end Proof for theBenchmark 0.39/0.60 EOF