%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO038^1.003.003 : TPTP v9.2.1. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 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 : Wed Jun 3 09:11:50 AM UTC 2026 % Result : Theorem 0.45s 0.64s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO038^1.003.003 : TPTP v9.2.1. Released v5.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n007.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 23:51:26 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.48 %----Proving TH0 % 0.45/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.64 % SZS status Theorem % 0.45/0.64 % SZS output start Proof % 0.45/0.64 ( % 0.45/0.64 (declare-sort $$unsorted 0) % 0.45/0.64 (declare-const tptp.d (-> $$unsorted Bool)) % 0.45/0.64 (declare-const tptp.f (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.s (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.one $$unsorted) % 0.45/0.64 (define @t1 () (_ tptp.s tptp.one)) % 0.45/0.64 (define @t2 () (@var "N" $$unsorted)) % 0.45/0.64 (define @t3 () (_ tptp.f @t2)) % 0.45/0.64 (define @t4 () (_ @t3 tptp.one)) % 0.45/0.64 (define @t5 () (= @t4 @t1)) % 0.45/0.64 (define @t6 () (@list @t2)) % 0.45/0.64 (define @t7 () (forall @t6 @t5)) % 0.45/0.64 (define @t8 () (@var "X" $$unsorted)) % 0.45/0.64 (define @t9 () (_ tptp.f tptp.one)) % 0.45/0.64 (define @t10 () (_ @t9 @t8)) % 0.45/0.64 (define @t11 () (_ tptp.s @t10)) % 0.45/0.64 (define @t12 () (_ tptp.s @t11)) % 0.45/0.64 (define @t13 () (_ tptp.s @t8)) % 0.45/0.64 (define @t14 () (_ @t9 @t13)) % 0.45/0.64 (define @t15 () (= @t14 @t12)) % 0.45/0.64 (define @t16 () (@list @t8)) % 0.45/0.64 (define @t17 () (forall @t16 @t15)) % 0.45/0.64 (define @t18 () (_ tptp.s @t2)) % 0.45/0.64 (define @t19 () (_ tptp.f @t18)) % 0.45/0.64 (define @t20 () (_ @t19 @t8)) % 0.45/0.64 (define @t21 () (_ @t3 @t20)) % 0.45/0.64 (define @t22 () (_ @t19 @t13)) % 0.45/0.64 (define @t23 () (= @t22 @t21)) % 0.45/0.64 (define @t24 () (forall (@list @t2 @t8) @t23)) % 0.45/0.64 (define @t25 () (_ tptp.d tptp.one)) % 0.45/0.64 (define @t26 () (_ tptp.d @t13)) % 0.45/0.64 (define @t27 () (_ tptp.d @t8)) % 0.45/0.64 (define @t28 () (forall @t16 (=> @t27 @t26))) % 0.45/0.64 (define @t29 () (_ tptp.s @t1)) % 0.45/0.64 (define @t30 () (_ (_ tptp.f @t29) @t29)) % 0.45/0.64 (define @t31 () (_ tptp.d @t30)) % 0.45/0.64 (define @t32 () (not @t31)) % 0.45/0.64 (define @t33 () (tptp.s @t8)) % 0.45/0.64 (define @t34 () (tptp.d @t33)) % 0.45/0.64 (define @t35 () (tptp.d @t8)) % 0.45/0.64 (define @t36 () (not @t27)) % 0.45/0.64 (define @t37 () (or @t36 @t26)) % 0.45/0.64 (define @t38 () (tptp.s tptp.one)) % 0.45/0.64 (define @t39 () (tptp.f tptp.one @t38)) % 0.45/0.64 (define @t40 () (tptp.s @t39)) % 0.45/0.64 (define @t41 () (tptp.f tptp.one @t40)) % 0.45/0.64 (define @t42 () (tptp.s @t41)) % 0.45/0.64 (define @t43 () (tptp.f tptp.one tptp.one)) % 0.45/0.64 (define @t44 () (tptp.s @t43)) % 0.45/0.64 (define @t45 () (tptp.f tptp.one @t44)) % 0.45/0.64 (define @t46 () (tptp.f tptp.one @t45)) % 0.45/0.64 (define @t47 () (tptp.s @t46)) % 0.45/0.64 (define @t48 () (tptp.s @t45)) % 0.45/0.64 (define @t49 () (tptp.f tptp.one @t48)) % 0.45/0.64 (define @t50 () (tptp.s @t49)) % 0.45/0.64 (define @t51 () (tptp.s @t38)) % 0.45/0.64 (define @t52 () (tptp.f @t51 @t51)) % 0.45/0.64 (define @t53 () (tptp.d @t52)) % 0.45/0.64 (define @t54 () (tptp.s @t2)) % 0.45/0.64 (define @t55 () (tptp.f @t54 @t8)) % 0.45/0.64 (define @t56 () (tptp.f @t2 @t55)) % 0.45/0.64 (define @t57 () (_ tptp.f @t54)) % 0.45/0.64 (define @t58 () (tptp.f @t54 @t33)) % 0.45/0.64 (define @t59 () (tptp.f @t2 tptp.one)) % 0.45/0.64 (define @t60 () (tptp.f @t51 tptp.one)) % 0.45/0.64 (define @t61 () (forall @t6 (= @t59 @t38))) % 0.45/0.64 (define @t62 () (= @t60 @t38)) % 0.45/0.64 (define @t63 () (@list false)) % 0.45/0.64 (define @t64 () (@list @t61)) % 0.45/0.64 (define @t65 () (tptp.f @t38 @t38)) % 0.45/0.64 (define @t66 () (tptp.f @t38 tptp.one)) % 0.45/0.64 (define @t67 () (= @t66 @t38)) % 0.45/0.64 (define @t68 () (@list @t38)) % 0.45/0.64 (define @t69 () (tptp.f tptp.one @t8)) % 0.45/0.64 (define @t70 () (tptp.s @t69)) % 0.45/0.64 (define @t71 () (tptp.s @t70)) % 0.45/0.64 (define @t72 () (tptp.f tptp.one @t33)) % 0.45/0.64 (define @t73 () (@list tptp.one)) % 0.45/0.64 (define @t74 () (tptp.s @t44)) % 0.45/0.64 (define @t75 () (= @t43 @t38)) % 0.45/0.64 (define @t76 () (@list @t44)) % 0.45/0.64 (define @t77 () (tptp.s @t48)) % 0.45/0.64 (define @t78 () (@list @t48)) % 0.45/0.64 (define @t79 () (tptp.d (tptp.s @t50))) % 0.45/0.64 (define @t80 () (tptp.d @t50)) % 0.45/0.64 (define @t81 () (not @t80)) % 0.45/0.64 (define @t82 () (or @t81 @t79)) % 0.45/0.64 (define @t83 () (@list true false)) % 0.45/0.64 (define @t84 () (not (tptp.d @t49))) % 0.45/0.64 (define @t85 () (or @t84 @t80)) % 0.45/0.64 (define @t86 () (@list @t45)) % 0.45/0.64 (define @t87 () (tptp.d (tptp.s @t47))) % 0.45/0.64 (define @t88 () (tptp.d @t47)) % 0.45/0.64 (define @t89 () (not @t88)) % 0.45/0.64 (define @t90 () (or @t89 @t87)) % 0.45/0.64 (define @t91 () (not (tptp.d @t46))) % 0.45/0.64 (define @t92 () (or @t91 @t88)) % 0.45/0.64 (define @t93 () (tptp.s @t40)) % 0.45/0.64 (define @t94 () (@list @t40)) % 0.45/0.64 (define @t95 () (tptp.d (tptp.s @t42))) % 0.45/0.64 (define @t96 () (tptp.d @t42)) % 0.45/0.64 (define @t97 () (not @t96)) % 0.45/0.64 (define @t98 () (or @t97 @t95)) % 0.45/0.64 (define @t99 () (not (tptp.d @t41))) % 0.45/0.64 (define @t100 () (or @t99 @t96)) % 0.45/0.64 (define @t101 () (@list @t39)) % 0.45/0.64 (define @t102 () (tptp.f tptp.one @t39)) % 0.45/0.64 (define @t103 () (tptp.s @t102)) % 0.45/0.64 (define @t104 () (tptp.d (tptp.s @t103))) % 0.45/0.64 (define @t105 () (tptp.d tptp.one)) % 0.45/0.64 (define @t106 () (tptp.d @t38)) % 0.45/0.64 (define @t107 () (not @t105)) % 0.45/0.64 (define @t108 () (or @t107 @t106)) % 0.45/0.64 (define @t109 () (@list false false)) % 0.45/0.64 (define @t110 () (tptp.d @t51)) % 0.45/0.64 (define @t111 () (not @t106)) % 0.45/0.64 (define @t112 () (or @t111 @t110)) % 0.45/0.64 (define @t113 () (tptp.d @t44)) % 0.45/0.64 (define @t114 () (tptp.d @t74)) % 0.45/0.64 (define @t115 () (not @t113)) % 0.45/0.64 (define @t116 () (or @t115 @t114)) % 0.45/0.64 (define @t117 () (tptp.d @t39)) % 0.45/0.64 (define @t118 () (tptp.d @t40)) % 0.45/0.64 (define @t119 () (not @t117)) % 0.45/0.64 (define @t120 () (or @t119 @t118)) % 0.45/0.64 (define @t121 () (tptp.d @t93)) % 0.45/0.64 (define @t122 () (not @t118)) % 0.45/0.64 (define @t123 () (or @t122 @t121)) % 0.45/0.64 (define @t124 () (tptp.d @t45)) % 0.45/0.64 (define @t125 () (tptp.d @t48)) % 0.45/0.64 (define @t126 () (not @t124)) % 0.45/0.64 (define @t127 () (or @t126 @t125)) % 0.45/0.64 (define @t128 () (tptp.d @t77)) % 0.45/0.64 (define @t129 () (not @t125)) % 0.45/0.64 (define @t130 () (or @t129 @t128)) % 0.45/0.64 (define @t131 () (tptp.d @t102)) % 0.45/0.64 (define @t132 () (tptp.d @t103)) % 0.45/0.64 (define @t133 () (not @t131)) % 0.45/0.64 (define @t134 () (or @t133 @t132)) % 0.45/0.64 (define @t135 () (not @t132)) % 0.45/0.64 (define @t136 () (or @t135 @t104)) % 0.45/0.64 (assume @p1 @t7) % 0.45/0.64 (assume @p2 @t17) % 0.45/0.64 (assume @p3 @t24) % 0.45/0.64 (assume @p4 @t25) % 0.45/0.64 (assume @p5 @t28) % 0.45/0.64 (assume @p6 @t32) % 0.45/0.64 (assume @p7 true) % 0.45/0.64 (step @p8 :rule refl :args ((tptp.d @t13))) % 0.45/0.64 (step @p9 :rule refl :args (@t33)) % 0.45/0.64 (step @p10 :rule cong :premises (@p9) :args (@t34)) % 0.45/0.64 (step @p11 :rule trans :premises (@p10 @p8)) % 0.45/0.64 (step @p12 :rule refl :args (tptp.d)) % 0.45/0.64 (step @p13 :rule ho_cong :premises (@p12 @p9)) % 0.45/0.64 (step @p14 :rule cong :premises (@p13 @p11) :args ((= (_ tptp.d @t33) @t34))) % 0.45/0.64 (step @p15 :rule symm :premises (@p14)) % 0.45/0.64 (step @p16 :rule refl :args (@t26)) % 0.45/0.64 (step @p17 :rule eq_resolve :premises (@p16 @p15)) % 0.45/0.64 (step @p18 :rule refl :args (@t13)) % 0.45/0.64 (step @p19 :rule cong :premises (@p18 @p9) :args ((= @t13 @t33))) % 0.45/0.64 (step @p20 :rule symm :premises (@p19)) % 0.45/0.64 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.45/0.64 (step @p22 :rule ho_cong :premises (@p12 @p21)) % 0.45/0.64 (step @p23 :rule trans :premises (@p22 @p17)) % 0.45/0.64 (step @p24 :rule refl :args (@t35)) % 0.45/0.64 (step @p25 :rule refl :args (@t27)) % 0.45/0.64 (step @p26 :rule cong :premises (@p25 @p24) :args ((= @t27 @t35))) % 0.45/0.64 (step @p27 :rule symm :premises (@p26)) % 0.45/0.64 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.45/0.64 (step @p29 :rule cong :premises (@p28) :args (@t36)) % 0.45/0.64 (step @p30 :rule nary_cong :premises (@p29 @p23) :args (@t37)) % 0.45/0.64 (step @p31 :rule cong :premises (@p30) :args ((forall @t16 @t37))) % 0.45/0.64 (step @p32 :rule bool-impl-elim :args (@t27 @t26)) % 0.45/0.64 (step @p33 :rule cong :premises (@p32) :args (@t28)) % 0.45/0.64 (step @p34 :rule trans :premises (@p33 @p31)) % 0.45/0.64 (step @p35 :rule eq_resolve :premises (@p5 @p34)) % 0.45/0.64 (step @p36 :rule instantiate :premises (@p35) :args ((@list @t41))) % 0.45/0.64 (step @p37 :rule instantiate :premises (@p35) :args ((@list @t42))) % 0.45/0.64 (step @p38 :rule instantiate :premises (@p35) :args ((@list @t46))) % 0.45/0.64 (step @p39 :rule instantiate :premises (@p35) :args ((@list @t47))) % 0.45/0.64 (step @p40 :rule instantiate :premises (@p35) :args ((@list @t49))) % 0.45/0.64 (step @p41 :rule instantiate :premises (@p35) :args ((@list @t50))) % 0.45/0.64 (step @p42 :rule refl :args ((tptp.d @t30))) % 0.45/0.64 (step @p43 :rule refl :args ((tptp.f @t29 @t29))) % 0.45/0.64 (step @p44 :rule refl :args ((tptp.s @t1))) % 0.45/0.64 (step @p45 :rule refl :args (@t38)) % 0.45/0.64 (step @p46 :rule cong :premises (@p45) :args (@t51)) % 0.45/0.64 (step @p47 :rule trans :premises (@p46 @p44)) % 0.45/0.64 (step @p48 :rule cong :premises (@p47 @p47) :args (@t52)) % 0.45/0.64 (step @p49 :rule trans :premises (@p48 @p43)) % 0.45/0.64 (step @p50 :rule cong :premises (@p49) :args (@t53)) % 0.45/0.64 (step @p51 :rule trans :premises (@p50 @p42)) % 0.45/0.64 (step @p52 :rule ho_cong :premises (@p12 @p49)) % 0.45/0.64 (step @p53 :rule cong :premises (@p52 @p51) :args ((= (_ tptp.d @t52) @t53))) % 0.45/0.64 (step @p54 :rule symm :premises (@p53)) % 0.45/0.64 (step @p55 :rule refl :args (@t31)) % 0.45/0.64 (step @p56 :rule eq_resolve :premises (@p55 @p54)) % 0.45/0.64 (step @p57 :rule refl :args (tptp.f)) % 0.45/0.64 (step @p58 :rule ho_cong :premises (@p57 @p47)) % 0.45/0.64 (step @p59 :rule ho_cong :premises (@p58 @p47)) % 0.45/0.64 (step @p60 :rule cong :premises (@p59 @p49) :args ((= (_ (_ tptp.f @t51) @t51) @t52))) % 0.45/0.64 (step @p61 :rule symm :premises (@p60)) % 0.45/0.64 (step @p62 :rule refl :args (@t30)) % 0.45/0.64 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 0.45/0.64 (step @p64 :rule refl :args (tptp.s)) % 0.45/0.64 (step @p65 :rule ho_cong :premises (@p64 @p45)) % 0.45/0.64 (step @p66 :rule cong :premises (@p65 @p47) :args ((= (_ tptp.s @t38) @t51))) % 0.45/0.64 (step @p67 :rule symm :premises (@p66)) % 0.45/0.64 (step @p68 :rule refl :args (@t29)) % 0.45/0.64 (step @p69 :rule eq_resolve :premises (@p68 @p67)) % 0.45/0.64 (step @p70 :rule refl :args (@t1)) % 0.45/0.64 (step @p71 :rule cong :premises (@p70 @p45) :args ((= @t1 @t38))) % 0.45/0.64 (step @p72 :rule symm :premises (@p71)) % 0.45/0.64 (step @p73 :rule eq_resolve :premises (@p70 @p72)) % 0.45/0.64 (step @p74 :rule refl :args (tptp.s)) % 0.45/0.64 (step @p75 :rule ho_cong :premises (@p74 @p73)) % 0.45/0.64 (step @p76 :rule trans :premises (@p75 @p69)) % 0.45/0.64 (step @p77 :rule refl :args (tptp.f)) % 0.45/0.64 (step @p78 :rule ho_cong :premises (@p77 @p76)) % 0.45/0.64 (step @p79 :rule ho_cong :premises (@p78 @p76)) % 0.45/0.64 (step @p80 :rule trans :premises (@p79 @p63)) % 0.45/0.64 (step @p81 :rule refl :args (tptp.d)) % 0.45/0.64 (step @p82 :rule ho_cong :premises (@p81 @p80)) % 0.45/0.64 (step @p83 :rule trans :premises (@p82 @p56)) % 0.45/0.64 (step @p84 :rule cong :premises (@p83) :args (@t32)) % 0.45/0.64 (step @p85 :rule eq_resolve :premises (@p6 @p84)) % 0.45/0.64 (step @p86 :rule false_intro :premises (@p85)) % 0.45/0.64 (step @p87 :rule refl :args ((tptp.f @t2 @t20))) % 0.45/0.64 (step @p88 :rule refl :args ((tptp.f @t18 @t8))) % 0.45/0.64 (step @p89 :rule refl :args (@t8)) % 0.45/0.64 (step @p90 :rule refl :args (@t54)) % 0.45/0.64 (step @p91 :rule cong :premises (@p90 @p89) :args (@t55)) % 0.45/0.64 (step @p92 :rule trans :premises (@p91 @p88)) % 0.45/0.64 (step @p93 :rule refl :args (@t2)) % 0.45/0.64 (step @p94 :rule cong :premises (@p93 @p92) :args (@t56)) % 0.45/0.64 (step @p95 :rule trans :premises (@p94 @p87)) % 0.45/0.64 (step @p96 :rule refl :args (@t3)) % 0.45/0.64 (step @p97 :rule ho_cong :premises (@p96 @p92)) % 0.45/0.64 (step @p98 :rule cong :premises (@p97 @p95) :args ((= (_ @t3 @t55) @t56))) % 0.45/0.64 (step @p99 :rule symm :premises (@p98)) % 0.45/0.64 (step @p100 :rule refl :args (@t21)) % 0.45/0.64 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 0.45/0.64 (step @p102 :rule ho_cong :premises (@p57 @p90)) % 0.45/0.64 (step @p103 :rule ho_cong :premises (@p102 @p89)) % 0.45/0.64 (step @p104 :rule cong :premises (@p103 @p92) :args ((= (_ @t57 @t8) @t55))) % 0.45/0.64 (step @p105 :rule symm :premises (@p104)) % 0.45/0.64 (step @p106 :rule refl :args (@t20)) % 0.45/0.64 (step @p107 :rule eq_resolve :premises (@p106 @p105)) % 0.45/0.64 (step @p108 :rule refl :args (@t18)) % 0.45/0.64 (step @p109 :rule cong :premises (@p108 @p90) :args ((= @t18 @t54))) % 0.45/0.64 (step @p110 :rule symm :premises (@p109)) % 0.45/0.64 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 0.45/0.64 (step @p112 :rule ho_cong :premises (@p57 @p111)) % 0.45/0.64 (step @p113 :rule ho_cong :premises (@p112 @p89)) % 0.45/0.64 (step @p114 :rule trans :premises (@p113 @p107)) % 0.45/0.64 (step @p115 :rule ho_cong :premises (@p96 @p114)) % 0.45/0.64 (step @p116 :rule trans :premises (@p115 @p101)) % 0.45/0.64 (step @p117 :rule refl :args ((tptp.f @t18 @t13))) % 0.45/0.64 (step @p118 :rule cong :premises (@p90 @p9) :args (@t58)) % 0.45/0.64 (step @p119 :rule trans :premises (@p118 @p117)) % 0.45/0.64 (step @p120 :rule ho_cong :premises (@p102 @p9)) % 0.45/0.64 (step @p121 :rule cong :premises (@p120 @p119) :args ((= (_ @t57 @t33) @t58))) % 0.45/0.64 (step @p122 :rule symm :premises (@p121)) % 0.45/0.64 (step @p123 :rule refl :args (@t22)) % 0.45/0.64 (step @p124 :rule eq_resolve :premises (@p123 @p122)) % 0.45/0.64 (step @p125 :rule ho_cong :premises (@p112 @p21)) % 0.45/0.64 (step @p126 :rule trans :premises (@p125 @p124)) % 0.45/0.64 (step @p127 :rule cong :premises (@p126 @p116) :args (@t23)) % 0.45/0.64 (step @p128 :rule cong :premises (@p127) :args (@t24)) % 0.45/0.64 (step @p129 :rule eq_resolve :premises (@p3 @p128)) % 0.45/0.64 (step @p130 :rule instantiate :premises (@p129) :args ((@list @t38 @t38))) % 0.45/0.64 (step @p131 :rule symm :premises (@p130)) % 0.45/0.64 (step @p132 :rule instantiate :premises (@p129) :args ((@list @t38 tptp.one))) % 0.45/0.64 (step @p133 :rule symm :premises (@p132)) % 0.45/0.64 (step @p134 :rule eq_resolve :premises (@p70 @p72)) % 0.45/0.64 (step @p135 :rule refl :args (@t59)) % 0.45/0.64 (step @p136 :rule refl :args (@t4)) % 0.45/0.64 (step @p137 :rule cong :premises (@p136 @p135) :args ((= @t4 @t59))) % 0.45/0.64 (step @p138 :rule symm :premises (@p137)) % 0.45/0.64 (step @p139 :rule eq_resolve :premises (@p136 @p138)) % 0.45/0.64 (step @p140 :rule cong :premises (@p139 @p134) :args (@t5)) % 0.45/0.64 (step @p141 :rule cong :premises (@p140) :args (@t7)) % 0.45/0.64 (step @p142 :rule eq_resolve :premises (@p1 @p141)) % 0.45/0.64 (step @p143 :rule eq-symm :args (@t60 @t38)) % 0.45/0.64 (step @p144 :rule refl :args (@t61)) % 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