%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN550+1 : TPTP v9.2.1. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n008.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 09:09:22 AM UTC 2026 % Result : Theorem 0.47s 0.67s % Output : Proof 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN550+1 : TPTP v9.2.1. Released v2.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n008.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 23:32:03 EDT 2026 % 0.17/0.34 % CPUTime : % 0.32/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.47/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.47/0.67 % SZS status Theorem % 0.47/0.67 % SZS output start Proof % 0.47/0.67 ( % 0.47/0.67 (declare-sort $$unsorted 0) % 0.47/0.67 (declare-const tptp.initial_world $$unsorted) % 0.47/0.67 (declare-const tptp.p (-> $$unsorted Bool)) % 0.47/0.67 (declare-const tptp.reachable (-> $$unsorted $$unsorted Bool)) % 0.47/0.67 (define @t1 () (@var "X" $$unsorted)) % 0.47/0.67 (define @t2 () (@list @t1)) % 0.47/0.67 (define @t3 () (@var "Z" $$unsorted)) % 0.47/0.67 (define @t4 () (tptp.reachable @t1 @t3)) % 0.47/0.67 (define @t5 () (@var "Y" $$unsorted)) % 0.47/0.67 (define @t6 () (tptp.reachable @t5 @t3)) % 0.47/0.67 (define @t7 () (tptp.reachable @t1 @t5)) % 0.47/0.67 (define @t8 () (and @t7 @t6)) % 0.47/0.67 (define @t9 () (forall (@list @t1 @t5 @t3) (=> @t8 @t4))) % 0.47/0.67 (define @t10 () (@var "W" $$unsorted)) % 0.47/0.67 (define @t11 () (tptp.p @t10)) % 0.47/0.67 (define @t12 () (tptp.reachable @t3 @t10)) % 0.47/0.67 (define @t13 () (@list @t10)) % 0.47/0.67 (define @t14 () (forall @t13 (=> @t12 @t11))) % 0.47/0.67 (define @t15 () (and @t6 @t14)) % 0.47/0.67 (define @t16 () (@list @t3)) % 0.47/0.67 (define @t17 () (exists @t16 @t15)) % 0.47/0.67 (define @t18 () (=> @t7 @t17)) % 0.47/0.67 (define @t19 () (@list @t5)) % 0.47/0.67 (define @t20 () (forall @t19 @t18)) % 0.47/0.67 (define @t21 () (tptp.reachable tptp.initial_world @t1)) % 0.47/0.67 (define @t22 () (and @t21 @t20)) % 0.47/0.67 (define @t23 () (exists @t2 @t22)) % 0.47/0.67 (define @t24 () (tptp.p @t5)) % 0.47/0.67 (define @t25 () (forall @t19 (=> @t7 @t24))) % 0.47/0.67 (define @t26 () (and @t21 @t25)) % 0.47/0.67 (define @t27 () (exists @t2 @t26)) % 0.47/0.67 (define @t28 () (= @t27 @t23)) % 0.47/0.67 (define @t29 () (not @t28)) % 0.47/0.67 (define @t30 () (not @t6)) % 0.47/0.67 (define @t31 () (not @t7)) % 0.47/0.67 (define @t32 () (forall @t13 (or (not @t12) @t11))) % 0.47/0.67 (define @t33 () (not @t32)) % 0.47/0.67 (define @t34 () (not (forall @t16 (or @t30 @t33)))) % 0.47/0.67 (define @t35 () (forall @t19 (or @t31 @t34))) % 0.47/0.67 (define @t36 () (not @t21)) % 0.47/0.67 (define @t37 () (forall @t2 (or @t36 (not @t35)))) % 0.47/0.67 (define @t38 () (@quantifiers_skolemize @t37 0)) % 0.47/0.67 (define @t39 () (not (tptp.reachable @t38 @t5))) % 0.47/0.67 (define @t40 () (forall @t19 (or @t39 @t24))) % 0.47/0.67 (define @t41 () (@quantifiers_skolemize @t40 0)) % 0.47/0.67 (define @t42 () (forall @t16 (or (not (tptp.reachable @t41 @t3)) @t33))) % 0.47/0.67 (define @t43 () (@quantifiers_skolemize @t42 0)) % 0.47/0.67 (define @t44 () (forall @t19 (or @t31 @t24))) % 0.47/0.67 (define @t45 () (forall @t2 (or @t36 (not @t44)))) % 0.47/0.67 (define @t46 () (not @t37)) % 0.47/0.67 (define @t47 () (not @t46)) % 0.47/0.67 (define @t48 () (not @t45)) % 0.47/0.67 (define @t49 () (not @t48)) % 0.47/0.67 (define @t50 () (and @t21 @t35)) % 0.47/0.67 (define @t51 () (forall @t2 (not @t50))) % 0.47/0.67 (define @t52 () (not @t51)) % 0.47/0.67 (define @t53 () (and @t6 @t32)) % 0.47/0.67 (define @t54 () (forall @t16 (not @t53))) % 0.47/0.67 (define @t55 () (not @t54)) % 0.47/0.67 (define @t56 () (and @t21 @t44)) % 0.47/0.67 (define @t57 () (forall @t2 (not @t56))) % 0.47/0.67 (define @t58 () (not @t57)) % 0.47/0.67 (define @t59 () (@quantifiers_skolemize @t45 0)) % 0.47/0.67 (define @t60 () (not (tptp.reachable @t59 @t5))) % 0.47/0.67 (define @t61 () (forall @t19 (or @t60 @t24))) % 0.47/0.67 (define @t62 () (not @t61)) % 0.47/0.67 (define @t63 () (tptp.reachable tptp.initial_world @t59)) % 0.47/0.67 (define @t64 () (not @t63)) % 0.47/0.67 (define @t65 () (or @t64 @t62)) % 0.47/0.67 (define @t66 () (not @t65)) % 0.47/0.67 (define @t67 () (forall @t19 (or @t60 @t34))) % 0.47/0.67 (define @t68 () (not @t67)) % 0.47/0.67 (define @t69 () (or @t64 @t68)) % 0.47/0.67 (define @t70 () (@quantifiers_skolemize @t67 0)) % 0.47/0.67 (define @t71 () (forall @t19 (or (not (tptp.reachable @t70 @t5)) @t34))) % 0.47/0.68 (define @t72 () (not @t71)) % 0.47/0.68 (define @t73 () (tptp.reachable tptp.initial_world @t70)) % 0.47/0.68 (define @t74 () (not @t73)) % 0.47/0.68 (define @t75 () (or @t74 @t72)) % 0.47/0.68 (define @t76 () (@quantifiers_skolemize @t71 0)) % 0.47/0.68 (define @t77 () (forall @t13 (or (not (tptp.reachable @t76 @t10)) @t11))) % 0.47/0.68 (define @t78 () (@quantifiers_skolemize @t77 0)) % 0.47/0.68 (define @t79 () (tptp.p @t78)) % 0.47/0.68 (define @t80 () (tptp.reachable @t59 @t78)) % 0.47/0.68 (define @t81 () (not @t80)) % 0.47/0.68 (define @t82 () (or @t81 @t79)) % 0.47/0.68 (define @t83 () (forall @t16 (or (not (tptp.reachable @t70 @t3)) @t33))) % 0.47/0.68 (define @t84 () (not @t83)) % 0.47/0.68 (define @t85 () (tptp.reachable @t59 @t70)) % 0.47/0.68 (define @t86 () (not @t85)) % 0.47/0.68 (define @t87 () (or @t86 @t84)) % 0.47/0.68 (define @t88 () (not @t87)) % 0.47/0.68 (define @t89 () (or @t64 @t86 @t73)) % 0.47/0.68 (define @t90 () (not @t77)) % 0.47/0.68 (define @t91 () (tptp.reachable @t70 @t76)) % 0.47/0.68 (define @t92 () (not @t91)) % 0.47/0.68 (define @t93 () (or @t92 @t90)) % 0.47/0.68 (define @t94 () (or @t92 (not (forall @t16 (or (not (tptp.reachable @t76 @t3)) @t33))))) % 0.47/0.68 (define @t95 () (not @t94)) % 0.47/0.68 (define @t96 () (tptp.reachable @t76 @t78)) % 0.47/0.68 (define @t97 () (not @t96)) % 0.47/0.68 (define @t98 () (or @t97 @t79)) % 0.47/0.68 (define @t99 () (not @t98)) % 0.47/0.68 (define @t100 () (tptp.reachable @t70 @t78)) % 0.47/0.68 (define @t101 () (or @t92 @t97 @t100)) % 0.47/0.68 (define @t102 () (not @t100)) % 0.47/0.68 (define @t103 () (or @t86 @t102 @t80)) % 0.47/0.68 (define @t104 () (@list false)) % 0.47/0.68 (define @t105 () (@list @t45)) % 0.47/0.68 (define @t106 () (forall @t19 (or @t39 @t34))) % 0.47/0.68 (define @t107 () (not @t106)) % 0.47/0.68 (define @t108 () (tptp.reachable tptp.initial_world @t38)) % 0.47/0.68 (define @t109 () (not @t108)) % 0.47/0.68 (define @t110 () (or @t109 @t107)) % 0.47/0.68 (define @t111 () (not @t110)) % 0.47/0.68 (define @t112 () (@list true)) % 0.47/0.68 (define @t113 () (@list @t110)) % 0.47/0.68 (define @t114 () (not @t42)) % 0.47/0.68 (define @t115 () (tptp.reachable @t38 @t41)) % 0.47/0.68 (define @t116 () (not @t115)) % 0.47/0.68 (define @t117 () (or @t116 @t114)) % 0.47/0.68 (define @t118 () (not @t40)) % 0.47/0.68 (define @t119 () (or @t109 @t118)) % 0.47/0.68 (define @t120 () (@list false false)) % 0.47/0.68 (define @t121 () (or @t116 (tptp.p @t41))) % 0.47/0.68 (define @t122 () (not @t121)) % 0.47/0.68 (define @t123 () (forall @t13 (or (not (tptp.reachable @t43 @t10)) @t11))) % 0.47/0.68 (define @t124 () (not @t123)) % 0.47/0.68 (define @t125 () (tptp.reachable @t41 @t43)) % 0.47/0.68 (define @t126 () (not @t125)) % 0.47/0.68 (define @t127 () (or @t126 @t124)) % 0.47/0.68 (define @t128 () (not @t127)) % 0.47/0.68 (define @t129 () (@list @t127)) % 0.47/0.68 (define @t130 () (tptp.reachable @t38 @t43)) % 0.47/0.68 (define @t131 () (or @t116 @t126 @t130)) % 0.47/0.68 (define @t132 () (@list false false false)) % 0.47/0.68 (define @t133 () (tptp.reachable tptp.initial_world @t43)) % 0.47/0.68 (define @t134 () (not @t130)) % 0.47/0.68 (define @t135 () (or @t109 @t134 @t133)) % 0.47/0.68 (define @t136 () (forall @t19 (or (not (tptp.reachable @t43 @t5)) @t24))) % 0.47/0.68 (define @t137 () (not @t136)) % 0.47/0.68 (define @t138 () (not @t133)) % 0.47/0.68 (define @t139 () (or @t138 @t137)) % 0.47/0.68 (assume @p1 (forall @t2 (tptp.reachable @t1 @t1))) % 0.47/0.68 (assume @p2 @t9) % 0.47/0.68 (assume @p3 @t29) % 0.47/0.68 (assume @p4 true) % 0.47/0.68 (step @p5 :rule aci_norm :args ((= (or (or @t31 @t30) @t4) (or @t31 @t30 @t4)))) % 0.47/0.68 (step @p6 :rule refl :args (@t4)) % 0.47/0.68 (step @p7 :rule bool-and-de-morgan :args (@t7 @t6 true)) % 0.47/0.68 (step @p8 :rule nary_cong :premises (@p7 @p6) :args ((or (not @t8) @t4))) % 0.47/0.68 (step @p9 :rule trans :premises (@p8 @p5)) % 0.47/0.68 (step @p10 :rule bool-impl-elim :args (@t8 @t4)) % 0.47/0.68 (step @p11 :rule trans :premises (@p10 @p9)) % 0.47/0.68 (step @p12 :rule cong :premises (@p11) :args (@t9)) % 0.47/0.68 (step @p13 :rule eq_resolve :premises (@p2 @p12)) % 0.47/0.68 (step @p14 :rule instantiate :premises (@p13) :args ((@list tptp.initial_world @t38 @t43))) % 0.47/0.68 (step @p15 :rule instantiate :premises (@p13) :args ((@list @t38 @t41 @t43))) % 0.47/0.68 (step @p16 :rule bool-double-not-elim :args (@t37)) % 0.47/0.68 (step @p17 :rule bool-double-not-elim :args (@t45)) % 0.47/0.68 (step @p18 :rule nary_cong :premises (@p17 @p16) :args ((or @t49 @t47))) % 0.47/0.68 (step @p19 :rule bool-and-de-morgan :args (@t21 @t35 true)) % 0.47/0.68 (step @p20 :rule cong :premises (@p19) :args (@t51)) % 0.47/0.68 (step @p21 :rule cong :premises (@p20) :args (@t52)) % 0.47/0.68 (step @p22 :rule exists-elim :args ((= (exists @t2 @t50) @t52))) % 0.47/0.68 (step @p23 :rule trans :premises (@p22 @p21)) % 0.47/0.68 (step @p24 :rule bool-impl-elim :args (@t7 @t34)) % 0.47/0.68 (step @p25 :rule cong :premises (@p24) :args ((forall @t19 (=> @t7 @t34)))) % 0.47/0.68 (step @p26 :rule bool-and-de-morgan :args (@t6 @t32 true)) % 0.47/0.68 (step @p27 :rule cong :premises (@p26) :args (@t54)) % 0.47/0.68 (step @p28 :rule cong :premises (@p27) :args (@t55)) % 0.47/0.68 (step @p29 :rule exists-elim :args ((= (exists @t16 @t53) @t55))) % 0.47/0.68 (step @p30 :rule trans :premises (@p29 @p28)) % 0.47/0.68 (step @p31 :rule bool-impl-elim :args (@t12 @t11)) % 0.47/0.68 (step @p32 :rule cong :premises (@p31) :args (@t14)) % 0.47/0.68 (step @p33 :rule refl :args (@t6)) % 0.47/0.68 (step @p34 :rule nary_cong :premises (@p33 @p32) :args (@t15)) % 0.47/0.68 (step @p35 :rule cong :premises (@p34) :args (@t17)) % 0.47/0.68 (step @p36 :rule trans :premises (@p35 @p30)) % 0.47/0.68 (step @p37 :rule refl :args (@t7)) % 0.47/0.68 (step @p38 :rule cong :premises (@p37 @p36) :args (@t18)) % 0.47/0.68 (step @p39 :rule cong :premises (@p38) :args (@t20)) % 0.47/0.68 (step @p40 :rule trans :premises (@p39 @p25)) % 0.47/0.68 (step @p41 :rule refl :args (@t21)) % 0.47/0.68 (step @p42 :rule nary_cong :premises (@p41 @p40) :args (@t22)) % 0.47/0.68 (step @p43 :rule cong :premises (@p42) :args (@t23)) % 0.47/0.68 (step @p44 :rule trans :premises (@p43 @p23)) % 0.47/0.68 (step @p45 :rule bool-and-de-morgan :args (@t21 @t44 true)) % 0.47/0.68 (step @p46 :rule cong :premises (@p45) :args (@t57)) % 0.47/0.68 (step @p47 :rule cong :premises (@p46) :args (@t58)) % 0.47/0.68 (step @p48 :rule exists-elim :args ((= (exists @t2 @t56) @t58))) % 0.47/0.68 (step @p49 :rule trans :premises (@p48 @p47)) % 0.47/0.68 (step @p50 :rule bool-impl-elim :args (@t7 @t24)) % 0.47/0.68 (step @p51 :rule cong :premises (@p50) :args (@t25)) % 0.47/0.68 (step @p52 :rule nary_cong :premises (@p41 @p51) :args (@t26)) % 0.47/0.68 (step @p53 :rule cong :premises (@p52) :args (@t27)) % 0.47/0.68 (step @p54 :rule trans :premises (@p53 @p49)) % 0.47/0.68 (step @p55 :rule cong :premises (@p54 @p44) :args (@t28)) % 0.47/0.68 (step @p56 :rule cong :premises (@p55) :args (@t29)) % 0.47/0.68 (step @p57 :rule eq_resolve :premises (@p3 @p56)) % 0.47/0.68 (step @p58 :rule not_equiv_elim2 :premises (@p57)) % 0.47/0.68 (step @p59 :rule eq_resolve :premises (@p58 @p18)) % 0.47/0.68 (step @p60 :rule refl :args (@t66)) % 0.47/0.68 (step @p61 :rule nary_cong :premises (@p17 @p60) :args ((or @t49 @t66))) % 0.47/0.68 (assume-push @p268 @t48) % 0.47/0.68 (step @p63 :rule skolemize :premises (@p268)) % 0.47/0.68 (step-pop @p269 :rule scope :premises (@p63)) % 0.47/0.68 (step @p64 :rule process_scope :premises (@p269) :args (@t66)) % 0.47/0.68 (step @p66 :rule implies_elim :premises (@p64)) % 0.47/0.68 (step @p67 :rule eq_resolve :premises (@p66 @p61)) % 0.47/0.68 (assume-push @p270 @t37) % 0.47/0.68 (step @p69 :rule instantiate :premises (@p270) :args ((@list @t59))) % 0.47/0.68 (step-pop @p271 :rule scope :premises (@p69)) % 0.47/0.68 (step @p70 :rule process_scope :premises (@p271) :args (@t69)) % 0.47/0.68 (step @p72 :rule implies_elim :premises (@p70)) % 0.47/0.68 (assume-push @p272 @t37) % 0.47/0.68 (step @p74 :rule instantiate :premises (@p272) :args ((@list @t70))) % 0.47/0.68 (step-pop @p273 :rule scope :premises (@p74)) % 0.47/0.68 (step @p75 :rule process_scope :premises (@p273) :args (@t75)) % 0.47/0.68 (step @p77 :rule implies_elim :premises (@p75)) % 0.47/0.68 (step @p78 :rule bool-double-not-elim :args (@t63)) % 0.47/0.68 (step @p79 :rule refl :args (@t65)) % 0.47/0.68 (step @p80 :rule nary_cong :premises (@p79 @p78) :args ((or @t65 (not @t64)))) % 0.47/0.68 (step @p81 :rule cnf_or_neg :args (@t65 0)) % 0.47/0.68 (step @p82 :rule eq_resolve :premises (@p81 @p80)) % 0.47/0.68 (step @p83 :rule reordering :premises (@p82) :args ((or @t63 @t65))) % 0.47/0.68 (step @p84 :rule bool-double-not-elim :args (@t61)) % 0.47/0.68 (step @p85 :rule nary_cong :premises (@p79 @p84) :args ((or @t65 (not @t62)))) % 0.47/0.68 (step @p86 :rule cnf_or_neg :args (@t65 1)) % 0.47/0.68 (step @p87 :rule eq_resolve :premises (@p86 @p85)) % 0.47/0.68 (step @p88 :rule reordering :premises (@p87) :args ((or @t61 @t65))) % 0.47/0.68 (step @p89 :rule cnf_or_pos :args (@t69)) % 0.47/0.68 (step @p90 :rule reordering :premises (@p89) :args ((or @t64 @t68 (not @t69)))) % 0.47/0.68 (assume-push @p274 @t61) % 0.47/0.68 (step @p92 :rule instantiate :premises (@p274) :args ((@list @t78))) % 0.47/0.68 (step-pop @p275 :rule scope :premises (@p92)) % 0.47/0.68 (step @p93 :rule process_scope :premises (@p275) :args (@t82)) % 0.47/0.68 (step @p95 :rule implies_elim :premises (@p93)) % 0.47/0.68 (step @p96 :rule refl :args (@t88)) % 0.47/0.68 (step @p97 :rule bool-double-not-elim :args (@t67)) % 0.47/0.68 (step @p98 :rule nary_cong :premises (@p97 @p96) :args ((or (not @t68) @t88))) % 0.47/0.68 (assume-push @p276 @t68) % 0.47/0.68 (step @p100 :rule skolemize :premises (@p276)) % 0.47/0.68 (step-pop @p277 :rule scope :premises (@p100)) % 0.47/0.68 (step @p101 :rule process_scope :premises (@p277) :args (@t88)) % 0.47/0.68 (step @p103 :rule implies_elim :premises (@p101)) % 0.47/0.68 (step @p104 :rule eq_resolve :premises (@p103 @p98)) % 0.47/0.68 (step @p105 :rule bool-double-not-elim :args (@t85)) % 0.47/0.68 (step @p106 :rule refl :args (@t87)) % 0.47/0.68 (step @p107 :rule nary_cong :premises (@p106 @p105) :args ((or @t87 (not @t86)))) % 0.47/0.68 (step @p108 :rule cnf_or_neg :args (@t87 0)) % 0.47/0.68 (step @p109 :rule eq_resolve :premises (@p108 @p107)) % 0.47/0.68 (step @p110 :rule reordering :premises (@p109) :args ((or @t85 @t87))) % 0.47/0.68 (step @p111 :rule bool-double-not-elim :args (@t83)) % 0.47/0.68 (step @p112 :rule nary_cong :premises (@p106 @p111) :args ((or @t87 (not @t84)))) % 0.47/0.68 (step @p113 :rule cnf_or_neg :args (@t87 1)) % 0.47/0.68 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 0.47/0.68 (step @p115 :rule reordering :premises (@p114) :args ((or @t83 @t87))) % 0.47/0.68 (step @p116 :rule instantiate :premises (@p13) :args ((@list tptp.initial_world @t59 @t70))) % 0.47/0.68 (step @p117 :rule cnf_or_pos :args (@t89)) % 0.47/0.68 (step @p118 :rule reordering :premises (@p117) :args ((or @t64 @t86 @t73 (not @t89)))) % 0.47/0.68 (assume-push @p278 @t83) % 0.47/0.68 (step @p120 :rule instantiate :premises (@p278) :args ((@list @t76))) % 0.47/0.68 (step-pop @p279 :rule scope :premises (@p120)) % 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:rule reordering :premises (@p265) :args ((or @t138 @t137 (not @t139)))) % 0.47/0.68 (step @p267 false :rule chain_m_resolution :premises (@p266 @p264 @p258 @p249) :args (false @t132 (@list @t139 @t136 @t133))) % 0.47/0.68 ) % 0.47/0.68 % SZS output end Proof % 0.47/0.68 % cvc5 exiting %------------------------------------------------------------------------------