%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : COM023+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n016.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 : Wed Jun 3 08:10:27 AM UTC 2026 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM023+1 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n016.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Mon Jun 1 20:29:09 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort $$unsorted 0) % 0.38/0.57 (declare-const tptp.aNormalFormOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.isTerminating0 (-> $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.xR $$unsorted) % 0.38/0.57 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.isLocallyConfluent0 (-> $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.aReductOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.isConfluent0 (-> $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.sdtmndtasgtdt0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.sdtmndtplgtdt0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.aRewritingSystem0 (-> $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.38/0.57 (define @t1 () (@var "W0" $$unsorted)) % 0.38/0.57 (define @t2 () (tptp.aElement0 @t1)) % 0.38/0.57 (define @t3 () (@list @t1)) % 0.38/0.57 (define @t4 () (tptp.aRewritingSystem0 @t1)) % 0.38/0.57 (define @t5 () (@var "W2" $$unsorted)) % 0.38/0.57 (define @t6 () (tptp.aElement0 @t5)) % 0.38/0.57 (define @t7 () (@var "W1" $$unsorted)) % 0.38/0.57 (define @t8 () (tptp.aReductOfIn0 @t5 @t1 @t7)) % 0.38/0.57 (define @t9 () (@list @t5)) % 0.38/0.57 (define @t10 () (tptp.aRewritingSystem0 @t7)) % 0.38/0.57 (define @t11 () (and @t2 @t10)) % 0.38/0.57 (define @t12 () (@list @t1 @t7)) % 0.38/0.57 (define @t13 () (tptp.aElement0 @t7)) % 0.38/0.57 (define @t14 () (tptp.sdtmndtplgtdt0 @t1 @t7 @t5)) % 0.38/0.57 (define @t15 () (and @t2 @t10 @t6)) % 0.38/0.57 (define @t16 () (@list @t1 @t7 @t5)) % 0.38/0.57 (define @t17 () (@var "W3" $$unsorted)) % 0.38/0.57 (define @t18 () (tptp.aElement0 @t17)) % 0.38/0.57 (define @t19 () (@list @t17)) % 0.38/0.57 (define @t20 () (and @t2 @t10 @t6 @t18)) % 0.38/0.57 (define @t21 () (@list @t1 @t7 @t5 @t17)) % 0.38/0.57 (define @t22 () (tptp.sdtmndtasgtdt0 @t1 @t7 @t5)) % 0.38/0.57 (define @t23 () (@var "W4" $$unsorted)) % 0.38/0.57 (define @t24 () (tptp.sdtmndtasgtdt0 @t17 @t1 @t23)) % 0.38/0.57 (define @t25 () (tptp.sdtmndtasgtdt0 @t5 @t1 @t23)) % 0.38/0.57 (define @t26 () (tptp.aElement0 @t23)) % 0.38/0.57 (define @t27 () (and @t26 @t25 @t24)) % 0.38/0.57 (define @t28 () (@list @t23)) % 0.38/0.57 (define @t29 () (exists @t28 @t27)) % 0.38/0.57 (define @t30 () (tptp.sdtmndtasgtdt0 @t7 @t1 @t17)) % 0.38/0.57 (define @t31 () (tptp.sdtmndtasgtdt0 @t7 @t1 @t5)) % 0.38/0.57 (define @t32 () (and @t13 @t6 @t18 @t31 @t30)) % 0.38/0.57 (define @t33 () (=> @t32 @t29)) % 0.38/0.57 (define @t34 () (@list @t7 @t5 @t17)) % 0.38/0.57 (define @t35 () (forall @t34 @t33)) % 0.38/0.57 (define @t36 () (tptp.isConfluent0 @t1)) % 0.38/0.57 (define @t37 () (= @t36 @t35)) % 0.38/0.57 (define @t38 () (=> @t4 @t37)) % 0.38/0.57 (define @t39 () (forall @t3 @t38)) % 0.38/0.57 (define @t40 () (tptp.isTerminating0 @t1)) % 0.38/0.57 (define @t41 () (tptp.aRewritingSystem0 tptp.xR)) % 0.38/0.57 (define @t42 () (tptp.sdtmndtasgtdt0 @t5 tptp.xR @t17)) % 0.38/0.57 (define @t43 () (tptp.sdtmndtasgtdt0 @t7 tptp.xR @t17)) % 0.38/0.57 (define @t44 () (and @t18 @t43 @t42)) % 0.38/0.57 (define @t45 () (exists @t19 @t44)) % 0.38/0.57 (define @t46 () (tptp.sdtmndtasgtdt0 @t1 tptp.xR @t5)) % 0.38/0.57 (define @t47 () (tptp.sdtmndtasgtdt0 @t1 tptp.xR @t7)) % 0.38/0.57 (define @t48 () (and @t2 @t13 @t6 @t47 @t46)) % 0.38/0.57 (define @t49 () (=> @t48 @t45)) % 0.38/0.57 (define @t50 () (forall @t16 @t49)) % 0.38/0.57 (define @t51 () (tptp.isConfluent0 tptp.xR)) % 0.38/0.57 (define @t52 () (not @t24)) % 0.38/0.57 (define @t53 () (not @t25)) % 0.38/0.57 (define @t54 () (not @t26)) % 0.38/0.57 (define @t55 () (or @t54 @t53 @t52)) % 0.38/0.57 (define @t56 () (not (forall @t28 @t55))) % 0.38/0.57 (define @t57 () (not @t30)) % 0.38/0.57 (define @t58 () (not @t31)) % 0.38/0.57 (define @t59 () (not @t18)) % 0.38/0.57 (define @t60 () (not @t6)) % 0.38/0.57 (define @t61 () (not @t13)) % 0.38/0.57 (define @t62 () (or @t61 @t60 @t59 @t58 @t57 @t56)) % 0.38/0.57 (define @t63 () (= @t36 (forall @t34 @t62))) % 0.38/0.57 (define @t64 () (or @t61 @t60 @t59 @t58 @t57)) % 0.38/0.57 (define @t65 () (forall @t28 (not @t27))) % 0.38/0.57 (define @t66 () (not @t65)) % 0.38/0.57 (define @t67 () (not @t42)) % 0.38/0.57 (define @t68 () (not @t43)) % 0.38/0.57 (define @t69 () (or @t59 @t68 @t67)) % 0.38/0.57 (define @t70 () (not (forall @t19 @t69))) % 0.38/0.57 (define @t71 () (not @t46)) % 0.38/0.57 (define @t72 () (not @t47)) % 0.38/0.57 (define @t73 () (not @t2)) % 0.38/0.57 (define @t74 () (or @t73 @t61 @t60 @t72 @t71 @t70)) % 0.38/0.57 (define @t75 () (or @t73 @t61 @t60 @t72 @t71)) % 0.38/0.57 (define @t76 () (forall @t19 (not @t44))) % 0.38/0.57 (define @t77 () (not @t76)) % 0.38/0.57 (define @t78 () (@var "BOUND_VARIABLE_8204" $$unsorted)) % 0.38/0.57 (define @t79 () (@var "BOUND_VARIABLE_8203" $$unsorted)) % 0.38/0.57 (define @t80 () (@var "BOUND_VARIABLE_8202" $$unsorted)) % 0.38/0.57 (define @t81 () (@var "BOUND_VARIABLE_8201" $$unsorted)) % 0.38/0.57 (define @t82 () (@list @t81 @t80 @t79 @t78)) % 0.38/0.57 (define @t83 () (forall @t16 @t74)) % 0.38/0.57 (define @t84 () (forall @t34 (or @t61 @t60 @t59 (not (tptp.sdtmndtasgtdt0 @t7 tptp.xR @t5)) @t68 (not (forall @t28 (or @t54 (not (tptp.sdtmndtasgtdt0 @t5 tptp.xR @t23)) (not (tptp.sdtmndtasgtdt0 @t17 tptp.xR @t23)))))))) % 0.38/0.57 (define @t85 () (= @t51 @t84)) % 0.38/0.57 (define @t86 () (not @t85)) % 0.38/0.57 (define @t87 () (not @t41)) % 0.38/0.57 (define @t88 () (or @t87 @t85)) % 0.38/0.57 (assume @p1 (forall @t3 (=> @t2 true))) % 0.38/0.57 (assume @p2 (forall @t3 (=> @t4 true))) % 0.38/0.57 (assume @p3 (forall @t12 (=> @t11 (forall @t9 (=> @t8 @t6))))) % 0.38/0.57 (assume @p4 (forall @t12 (=> (and @t2 @t13) (=> (tptp.iLess0 @t1 @t7) true)))) % 0.38/0.57 (assume @p5 (forall @t16 (=> @t15 (=> @t14 true)))) % 0.38/0.57 (assume @p6 (forall @t16 (=> @t15 (= @t14 (or @t8 (exists @t19 (and @t18 (tptp.aReductOfIn0 @t17 @t1 @t7) (tptp.sdtmndtplgtdt0 @t17 @t7 @t5)))))))) % 0.38/0.57 (assume @p7 (forall @t21 (=> @t20 (=> (and @t14 (tptp.sdtmndtplgtdt0 @t5 @t7 @t17)) (tptp.sdtmndtplgtdt0 @t1 @t7 @t17))))) % 0.38/0.57 (assume @p8 (forall @t16 (=> @t15 (= @t22 (or (= @t1 @t5) @t14))))) % 0.38/0.57 (assume @p9 (forall @t21 (=> @t20 (=> (and @t22 (tptp.sdtmndtasgtdt0 @t5 @t7 @t17)) (tptp.sdtmndtasgtdt0 @t1 @t7 @t17))))) % 0.38/0.57 (assume @p10 @t39) % 0.38/0.57 (assume @p11 (forall @t3 (=> @t4 (= (tptp.isLocallyConfluent0 @t1) (forall @t34 (=> (and @t13 @t6 @t18 (tptp.aReductOfIn0 @t5 @t7 @t1) (tptp.aReductOfIn0 @t17 @t7 @t1)) @t29)))))) % 0.38/0.57 (assume @p12 (forall @t3 (=> @t4 (= @t40 (forall (@list @t7 @t5) (=> (and @t13 @t6) (=> (tptp.sdtmndtplgtdt0 @t7 @t1 @t5) (tptp.iLess0 @t5 @t7)))))))) % 0.38/0.57 (assume @p13 (forall @t12 (=> @t11 (forall @t9 (= (tptp.aNormalFormOfIn0 @t5 @t1 @t7) (and @t6 @t22 (not (exists @t19 (tptp.aReductOfIn0 @t17 @t5 @t7))))))))) % 0.38/0.57 (assume @p14 (forall @t3 (=> (and @t4 @t40) (forall (@list @t7) (=> @t13 (exists @t9 (tptp.aNormalFormOfIn0 @t5 @t7 @t1))))))) % 0.38/0.57 (assume @p15 @t41) % 0.38/0.57 (assume @p16 (and (tptp.isLocallyConfluent0 tptp.xR) (tptp.isTerminating0 tptp.xR))) % 0.38/0.57 (assume @p17 @t50) % 0.38/0.57 (assume @p18 (not @t51)) % 0.38/0.57 (assume @p19 true) % 0.38/0.57 (step @p20 :rule bool-impl-elim :args (@t4 @t63)) % 0.38/0.57 (step @p21 :rule cong :premises (@p20) :args ((forall @t3 (=> @t4 @t63)))) % 0.38/0.57 (step @p22 :rule aci_norm :args ((= (or @t64 @t56) @t62))) % 0.38/0.57 (step @p23 :rule refl :args (@t56)) % 0.38/0.57 (step @p24 :rule aci_norm :args ((= (or @t61 (or @t60 (or @t59 (or @t58 @t57)))) @t64))) % 0.38/0.57 (step @p25 :rule bool-and-de-morgan :args (@t31 @t30 true)) % 0.38/0.57 (step @p26 :rule refl :args (@t59)) % 0.38/0.57 (step @p27 :rule nary_cong :premises (@p26 @p25) :args ((or @t59 (not (and @t31 @t30))))) % 0.38/0.57 (step @p28 :rule bool-and-de-morgan :args (@t18 @t31 (and @t30))) % 0.38/0.57 (step @p29 :rule trans :premises (@p28 @p27)) % 0.38/0.57 (step @p30 :rule refl :args (@t60)) % 0.38/0.57 (step @p31 :rule nary_cong :premises (@p30 @p29) :args ((or @t60 (not (and @t18 @t31 @t30))))) % 0.38/0.57 (step @p32 :rule bool-and-de-morgan :args (@t6 @t18 (and @t31 @t30))) % 0.38/0.57 (step @p33 :rule trans :premises (@p32 @p31)) % 0.38/0.57 (step @p34 :rule refl :args (@t61)) % 0.38/0.57 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or @t61 (not (and @t6 @t18 @t31 @t30))))) % 0.38/0.57 (step @p36 :rule bool-and-de-morgan :args (@t13 @t6 (and @t18 @t31 @t30))) % 0.38/0.57 (step @p37 :rule trans :premises (@p36 @p35)) % 0.38/0.57 (step @p38 :rule trans :premises (@p37 @p24)) % 0.38/0.57 (step @p39 :rule nary_cong :premises (@p38 @p23) :args ((or (not @t32) @t56))) % 0.38/0.57 (step @p40 :rule trans :premises (@p39 @p22)) % 0.38/0.57 (step @p41 :rule bool-impl-elim :args (@t32 @t56)) % 0.38/0.57 (step @p42 :rule trans :premises (@p41 @p40)) % 0.38/0.57 (step @p43 :rule cong :premises (@p42) :args ((forall @t34 (=> @t32 @t56)))) % 0.38/0.57 (step @p44 :rule aci_norm :args ((= (or @t54 (or @t53 @t52)) @t55))) % 0.38/0.57 (step @p45 :rule bool-and-de-morgan :args (@t25 @t24 true)) % 0.38/0.57 (step @p46 :rule refl :args (@t54)) % 0.38/0.57 (step @p47 :rule nary_cong :premises (@p46 @p45) :args ((or @t54 (not (and @t25 @t24))))) % 0.38/0.57 (step @p48 :rule bool-and-de-morgan :args (@t26 @t25 (and @t24))) % 0.38/0.57 (step @p49 :rule trans :premises (@p48 @p47)) % 0.38/0.57 (step @p50 :rule trans :premises (@p49 @p44)) % 0.38/0.57 (step @p51 :rule cong :premises (@p50) :args (@t65)) % 0.38/0.57 (step @p52 :rule cong :premises (@p51) :args (@t66)) % 0.38/0.57 (step @p53 :rule exists-elim :args ((= @t29 @t66))) % 0.38/0.57 (step @p54 :rule trans :premises (@p53 @p52)) % 0.38/0.57 (step @p55 :rule refl :args (@t32)) % 0.38/0.57 (step @p56 :rule cong :premises (@p55 @p54) :args (@t33)) % 0.38/0.57 (step @p57 :rule cong :premises (@p56) :args (@t35)) % 0.38/0.57 (step @p58 :rule trans :premises (@p57 @p43)) % 0.38/0.57 (step @p59 :rule refl :args (@t36)) % 0.38/0.57 (step @p60 :rule cong :premises (@p59 @p58) :args (@t37)) % 0.38/0.57 (step @p61 :rule refl :args (@t4)) % 0.38/0.57 (step @p62 :rule cong :premises (@p61 @p60) :args (@t38)) % 0.38/0.57 (step @p63 :rule cong :premises (@p62) :args (@t39)) % 0.38/0.57 (step @p64 :rule trans :premises (@p63 @p21)) % 0.38/0.57 (step @p65 :rule eq_resolve :premises (@p10 @p64)) % 0.38/0.57 (step @p66 :rule instantiate :premises (@p65) :args ((@list tptp.xR))) % 0.38/0.57 (step @p67 :rule aci_norm :args ((= (or @t75 @t70) @t74))) % 0.38/0.57 (step @p68 :rule refl :args (@t70)) % 0.38/0.57 (step @p69 :rule aci_norm :args ((= (or @t73 (or @t61 (or @t60 (or @t72 @t71)))) @t75))) % 0.38/0.57 (step @p70 :rule bool-and-de-morgan :args (@t47 @t46 true)) % 0.38/0.57 (step @p71 :rule nary_cong :premises (@p30 @p70) :args ((or @t60 (not (and @t47 @t46))))) % 0.38/0.57 (step @p72 :rule bool-and-de-morgan :args (@t6 @t47 (and @t46))) % 0.38/0.57 (step @p73 :rule trans :premises (@p72 @p71)) % 0.38/0.57 (step @p74 :rule nary_cong :premises (@p34 @p73) :args ((or @t61 (not (and @t6 @t47 @t46))))) % 0.38/0.57 (step @p75 :rule bool-and-de-morgan :args (@t13 @t6 (and @t47 @t46))) % 0.38/0.57 (step @p76 :rule trans :premises (@p75 @p74)) % 0.38/0.57 (step @p77 :rule refl :args (@t73)) % 0.38/0.57 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((or @t73 (not (and @t13 @t6 @t47 @t46))))) % 0.38/0.57 (step @p79 :rule bool-and-de-morgan :args (@t2 @t13 (and @t6 @t47 @t46))) % 0.38/0.57 (step @p80 :rule trans :premises (@p79 @p78)) % 0.38/0.57 (step @p81 :rule trans :premises (@p80 @p69)) % 0.38/0.57 (step @p82 :rule nary_cong :premises (@p81 @p68) :args ((or (not @t48) @t70))) % 0.38/0.57 (step @p83 :rule trans :premises (@p82 @p67)) % 0.38/0.57 (step @p84 :rule bool-impl-elim :args (@t48 @t70)) % 0.38/0.57 (step @p85 :rule trans :premises (@p84 @p83)) % 0.38/0.57 (step @p86 :rule cong :premises (@p85) :args ((forall @t16 (=> @t48 @t70)))) % 0.38/0.57 (step @p87 :rule aci_norm :args ((= (or @t59 (or @t68 @t67)) @t69))) % 0.38/0.57 (step @p88 :rule bool-and-de-morgan :args (@t43 @t42 true)) % 0.38/0.57 (step @p89 :rule nary_cong :premises (@p26 @p88) :args ((or @t59 (not (and @t43 @t42))))) % 0.38/0.57 (step @p90 :rule bool-and-de-morgan :args (@t18 @t43 (and @t42))) % 0.38/0.57 (step @p91 :rule trans :premises (@p90 @p89)) % 0.38/0.57 (step @p92 :rule trans :premises (@p91 @p87)) % 0.38/0.57 (step @p93 :rule cong :premises (@p92) :args (@t76)) % 0.38/0.57 (step @p94 :rule cong :premises (@p93) :args (@t77)) % 0.38/0.57 (step @p95 :rule exists-elim :args ((= @t45 @t77))) % 0.38/0.57 (step @p96 :rule trans :premises (@p95 @p94)) % 0.38/0.57 (step @p97 :rule refl :args (@t48)) % 0.38/0.57 (step @p98 :rule cong :premises (@p97 @p96) :args (@t49)) % 0.38/0.57 (step @p99 :rule cong :premises (@p98) :args (@t50)) % 0.38/0.57 (step @p100 :rule trans :premises (@p99 @p86)) % 0.38/0.57 (step @p101 :rule eq_resolve :premises (@p17 @p100)) % 0.38/0.57 (step @p102 :rule alpha_equiv :args ((forall (@list @t81 @t80 @t79) (or (not (tptp.aElement0 @t81)) (not (tptp.aElement0 @t80)) (not (tptp.aElement0 @t79)) (not (tptp.sdtmndtasgtdt0 @t81 tptp.xR @t80)) (not (tptp.sdtmndtasgtdt0 @t81 tptp.xR @t79)) (not (forall (@list @t78) (or (not (tptp.aElement0 @t78)) (not (tptp.sdtmndtasgtdt0 @t80 tptp.xR @t78)) (not (tptp.sdtmndtasgtdt0 @t79 tptp.xR @t78))))))) @t82 (@list @t7 @t5 @t17 @t23))) % 0.38/0.57 (step @p103 :rule alpha_equiv :args (@t83 (@list @t1 @t7 @t5 @t17) @t82)) % 0.38/0.57 (step @p104 :rule trans :premises (@p103 @p102)) % 0.38/0.57 (step @p105 :rule equiv_elim1 :premises (@p104)) % 0.38/0.57 (step @p106 :rule chain_m_resolution :premises (@p105 @p101) :args (@t84 (@list false) (@list @t83))) % 0.38/0.57 (step @p107 :rule cnf_equiv_pos2 :args (@t85)) % 0.38/0.57 (step @p108 :rule reordering :premises (@p107) :args ((or @t51 (not @t84) @t86))) % 0.38/0.57 (step @p109 :rule chain_m_resolution :premises (@p108 @p18 @p106) :args (@t86 (@list true false) (@list @t51 @t84))) % 0.38/0.57 (step @p110 :rule cnf_or_pos :args (@t88)) % 0.38/0.57 (step @p111 :rule reordering :premises (@p110) :args ((or @t87 @t85 (not @t88)))) % 0.38/0.57 (step @p112 false :rule chain_m_resolution :premises (@p111 @p109 @p66 @p15) :args (false (@list true false false) (@list @t85 @t88 @t41))) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------