%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU927^5 : 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 : n011.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 08:53:32 AM UTC 2026 % Result : Theorem 0.37s 0.60s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU927^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n011.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 18:00:05 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.37/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.60 % SZS status Theorem % 0.37/0.60 % SZS output start Proof % 0.37/0.60 ( % 0.37/0.60 (declare-sort tptp.a 0) % 0.37/0.60 (define @t1 () (@var "Xx" tptp.a)) % 0.37/0.60 (define @t2 () (@var "Xf" (-> tptp.a tptp.a))) % 0.37/0.60 (define @t3 () (_ @t2 @t1)) % 0.37/0.60 (define @t4 () (_ @t2 @t3)) % 0.37/0.60 (define @t5 () (@list @t1)) % 0.37/0.60 (define @t6 () (lambda @t5 @t4)) % 0.37/0.60 (define @t7 () (@var "Xp" (-> (-> tptp.a tptp.a) Bool))) % 0.37/0.60 (define @t8 () (_ @t7 @t6)) % 0.37/0.60 (define @t9 () (@var "Xj" (-> tptp.a tptp.a))) % 0.37/0.60 (define @t10 () (_ @t9 @t1)) % 0.37/0.60 (define @t11 () (_ @t2 @t10)) % 0.37/0.60 (define @t12 () (lambda @t5 @t11)) % 0.37/0.60 (define @t13 () (_ @t7 @t12)) % 0.37/0.60 (define @t14 () (_ @t7 @t9)) % 0.37/0.60 (define @t15 () (@list @t9)) % 0.37/0.60 (define @t16 () (forall @t15 (=> @t14 @t13))) % 0.37/0.60 (define @t17 () (@var "Xu" tptp.a)) % 0.37/0.60 (define @t18 () (lambda (@list @t17) @t17)) % 0.37/0.60 (define @t19 () (_ @t7 @t18)) % 0.37/0.60 (define @t20 () (and @t19 @t16)) % 0.37/0.60 (define @t21 () (=> @t20 @t8)) % 0.37/0.60 (define @t22 () (@list @t2 @t7)) % 0.37/0.60 (define @t23 () (forall @t22 @t21)) % 0.37/0.60 (define @t24 () (not @t23)) % 0.37/0.60 (define @t25 () (_ @t2 @t1)) % 0.37/0.60 (define @t26 () (_ @t2 @t25)) % 0.37/0.60 (define @t27 () (lambda @t5 @t26)) % 0.37/0.60 (define @t28 () (_ @t7 @t27)) % 0.37/0.60 (define @t29 () (_ @t9 @t1)) % 0.37/0.60 (define @t30 () (_ @t2 @t29)) % 0.37/0.60 (define @t31 () (lambda @t5 @t30)) % 0.37/0.60 (define @t32 () (_ @t7 @t31)) % 0.37/0.60 (define @t33 () (_ @t7 @t9)) % 0.37/0.60 (define @t34 () (forall @t15 (or (not @t33) @t32))) % 0.37/0.60 (define @t35 () (not @t34)) % 0.37/0.60 (define @t36 () (_ @t7 @t18)) % 0.37/0.60 (define @t37 () (not @t19)) % 0.37/0.60 (define @t38 () (or @t37 @t35 @t8)) % 0.37/0.60 (define @t39 () (and @t19 @t34)) % 0.37/0.60 (define @t40 () (not @t14)) % 0.37/0.60 (define @t41 () (or @t40 @t13)) % 0.37/0.60 (define @t42 () (forall @t22 (or (not @t36) @t35 @t28))) % 0.37/0.60 (define @t43 () (@quantifiers_skolemize @t42 0)) % 0.37/0.60 (define @t44 () (_ @t43 (_ @t43 @t1))) % 0.37/0.60 (define @t45 () (lambda @t5 @t44)) % 0.37/0.60 (define @t46 () (@purify @t45)) % 0.37/0.60 (define @t47 () (@quantifiers_skolemize @t42 1)) % 0.37/0.60 (define @t48 () (_ @t47 @t46)) % 0.37/0.60 (define @t49 () (forall @t15 (or (not (_ @t47 @t9)) (_ @t47 (lambda @t5 (_ @t43 @t29)))))) % 0.37/0.60 (define @t50 () (not @t49)) % 0.37/0.60 (define @t51 () (@purify @t18)) % 0.37/0.60 (define @t52 () (_ @t47 @t51)) % 0.37/0.60 (define @t53 () (not @t52)) % 0.37/0.60 (define @t54 () (or @t53 @t50 @t48)) % 0.37/0.60 (define @t55 () (not @t54)) % 0.37/0.60 (define @t56 () (not @t42)) % 0.37/0.60 (define @t57 () (_ @t47 @t45)) % 0.37/0.60 (define @t58 () (_ @t47 @t18)) % 0.37/0.60 (define @t59 () (not @t58)) % 0.37/0.60 (define @t60 () (or @t59 @t50 @t57)) % 0.37/0.60 (define @t61 () (not @t60)) % 0.37/0.60 (define @t62 () (@list true)) % 0.37/0.60 (define @t63 () (@list @t54)) % 0.37/0.60 (define @t64 () (_ @t18 @t1)) % 0.37/0.60 (define @t65 () (_ @t43 @t64)) % 0.37/0.60 (define @t66 () (lambda @t5 @t65)) % 0.37/0.60 (define @t67 () (_ @t66 @t1)) % 0.37/0.60 (define @t68 () (_ @t43 @t67)) % 0.37/0.60 (define @t69 () (lambda @t5 @t68)) % 0.37/0.60 (define @t70 () (_ @t43 (_ @t51 @t1))) % 0.37/0.60 (define @t71 () (lambda @t5 @t70)) % 0.37/0.60 (define @t72 () (@purify @t71)) % 0.37/0.60 (define @t73 () (_ @t72 @t1)) % 0.37/0.60 (define @t74 () (_ @t43 @t73)) % 0.37/0.60 (define @t75 () (lambda @t5 @t74)) % 0.37/0.60 (define @t76 () (@purify @t75)) % 0.37/0.60 (define @t77 () (_ @t47 @t75)) % 0.37/0.60 (define @t78 () (_ @t47 @t72)) % 0.37/0.60 (define @t79 () (not @t78)) % 0.37/0.60 (define @t80 () (or @t79 @t77)) % 0.37/0.60 (define @t81 () (_ @t47 @t76)) % 0.37/0.60 (define @t82 () (or @t79 @t81)) % 0.37/0.60 (define @t83 () (@list false)) % 0.37/0.60 (define @t84 () (@list @t49)) % 0.37/0.60 (define @t85 () (_ @t47 @t71)) % 0.37/0.60 (define @t86 () (or @t53 @t85)) % 0.37/0.60 (define @t87 () (or @t53 @t78)) % 0.37/0.60 (define @t88 () (@list false false)) % 0.37/0.60 (define @t89 () (not @t48)) % 0.37/0.60 (define @t90 () (= @t46 @t76)) % 0.37/0.60 (define @t91 () (not @t90)) % 0.37/0.60 (define @t92 () (not @t81)) % 0.37/0.60 (define @t93 () (and @t89 @t90 @t81)) % 0.37/0.60 (define @t94 () (@const 0 tptp.a)) % 0.37/0.60 (define @t95 () (_ @t43 @t94)) % 0.37/0.60 (define @t96 () (_ @t43 @t95)) % 0.37/0.60 (define @t97 () (_ @t18 @t94)) % 0.37/0.60 (define @t98 () (_ @t43 @t97)) % 0.37/0.60 (define @t99 () (@var "BOUND_VARIABLE_8656" tptp.a)) % 0.37/0.60 (define @t100 () (lambda (@list @t99) (_ @t43 (_ @t18 @t99)))) % 0.37/0.60 (define @t101 () (_ @t100 @t94)) % 0.37/0.60 (define @t102 () (_ @t43 @t101)) % 0.37/0.60 (define @t103 () (_ @t45 @t94)) % 0.37/0.60 (define @t104 () (= @t103 (_ @t69 @t94))) % 0.37/0.60 (define @t105 () (not @t104)) % 0.37/0.60 (define @t106 () (= @t45 @t69)) % 0.37/0.60 (define @t107 () (_ @t76 @t94)) % 0.37/0.60 (define @t108 () (_ @t46 @t94)) % 0.37/0.60 (define @t109 () (= @t108 @t107)) % 0.37/0.60 (define @t110 () (not @t109)) % 0.37/0.60 (define @t111 () (_ @t76 @t1)) % 0.37/0.60 (define @t112 () (_ @t75 @t1)) % 0.37/0.60 (define @t113 () (= @t111 @t112)) % 0.37/0.60 (define @t114 () (forall @t5 @t113)) % 0.37/0.60 (define @t115 () (_ @t72 @t94)) % 0.37/0.60 (define @t116 () (_ @t43 @t115)) % 0.37/0.60 (define @t117 () (forall @t5 (= @t74 @t111))) % 0.37/0.60 (define @t118 () (= @t116 @t107)) % 0.37/0.60 (define @t119 () (@list @t94)) % 0.37/0.60 (define @t120 () (= @t107 @t116)) % 0.37/0.60 (define @t121 () (_ @t46 @t1)) % 0.37/0.60 (define @t122 () (_ @t45 @t1)) % 0.37/0.60 (define @t123 () (= @t121 @t122)) % 0.37/0.60 (define @t124 () (forall @t5 @t123)) % 0.37/0.60 (define @t125 () (forall @t5 (= @t44 @t121))) % 0.37/0.60 (define @t126 () (= @t96 @t108)) % 0.37/0.60 (define @t127 () (= @t108 @t96)) % 0.37/0.60 (define @t128 () (_ @t71 @t1)) % 0.37/0.60 (define @t129 () (= @t73 @t128)) % 0.37/0.60 (define @t130 () (forall @t5 @t129)) % 0.37/0.60 (define @t131 () (_ @t51 @t94)) % 0.37/0.60 (define @t132 () (_ @t43 @t131)) % 0.37/0.60 (define @t133 () (= @t115 @t132)) % 0.37/0.60 (define @t134 () (forall @t5 (= @t70 @t73))) % 0.37/0.60 (define @t135 () (= @t132 @t115)) % 0.37/0.60 (define @t136 () (= @t115 @t95)) % 0.37/0.60 (define @t137 () (and @t120 @t127 @t136)) % 0.37/0.60 (assume @p1 @t24) % 0.37/0.60 (assume @p2 true) % 0.37/0.60 (step @p3 :rule refl :args ((_ @t7 @t6))) % 0.37/0.60 (step @p4 :rule refl :args ((_ @t2 @t3))) % 0.37/0.60 (step @p5 :rule refl :args (@t25)) % 0.37/0.60 (step @p6 :rule cong :premises (@p5) :args (@t26)) % 0.37/0.60 (step @p7 :rule trans :premises (@p6 @p4)) % 0.37/0.60 (step @p8 :rule cong :premises (@p7) :args (@t27)) % 0.37/0.60 (step @p9 :rule cong :premises (@p8) :args (@t28)) % 0.37/0.60 (step @p10 :rule trans :premises (@p9 @p3)) % 0.37/0.60 (step @p11 :rule refl :args (@t7)) % 0.37/0.60 (step @p12 :rule ho_cong :premises (@p11 @p8)) % 0.37/0.60 (step @p13 :rule cong :premises (@p12 @p10) :args ((= (_ @t7 @t27) @t28))) % 0.37/0.60 (step @p14 :rule symm :premises (@p13)) % 0.37/0.60 (step @p15 :rule refl :args (@t8)) % 0.37/0.60 (step @p16 :rule eq_resolve :premises (@p15 @p14)) % 0.37/0.60 (step @p17 :rule refl :args (@t2)) % 0.37/0.60 (step @p18 :rule ho_cong :premises (@p17 @p5)) % 0.37/0.60 (step @p19 :rule cong :premises (@p18 @p7) :args ((= (_ @t2 @t25) @t26))) % 0.37/0.60 (step @p20 :rule symm :premises (@p19)) % 0.37/0.60 (step @p21 :rule refl :args (@t4)) % 0.37/0.60 (step @p22 :rule eq_resolve :premises (@p21 @p20)) % 0.37/0.60 (step @p23 :rule refl :args (@t3)) % 0.37/0.60 (step @p24 :rule cong :premises (@p23 @p5) :args ((= @t3 @t25))) % 0.37/0.60 (step @p25 :rule symm :premises (@p24)) % 0.37/0.60 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.37/0.60 (step @p27 :rule ho_cong :premises (@p17 @p26)) % 0.37/0.60 (step @p28 :rule trans :premises (@p27 @p22)) % 0.37/0.60 (step @p29 :rule cong :premises (@p28) :args (@t6)) % 0.37/0.60 (step @p30 :rule ho_cong :premises (@p11 @p29)) % 0.37/0.60 (step @p31 :rule trans :premises (@p30 @p16)) % 0.37/0.60 (step @p32 :rule refl :args (@t35)) % 0.37/0.60 (step @p33 :rule refl :args (@t36)) % 0.37/0.60 (step @p34 :rule refl :args (@t19)) % 0.37/0.60 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t19 @t36))) % 0.37/0.60 (step @p36 :rule symm :premises (@p35)) % 0.37/0.60 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 0.37/0.60 (step @p38 :rule cong :premises (@p37) :args (@t37)) % 0.37/0.60 (step @p39 :rule nary_cong :premises (@p38 @p32 @p31) :args (@t38)) % 0.37/0.60 (step @p40 :rule cong :premises (@p39) :args ((forall @t22 @t38))) % 0.37/0.60 (step @p41 :rule aci_norm :args ((= (or (or @t37 @t35) @t8) @t38))) % 0.37/0.60 (step @p42 :rule bool-and-de-morgan :args (@t19 @t34 true)) % 0.37/0.60 (step @p43 :rule nary_cong :premises (@p42 @p15) :args ((or (not @t39) @t8))) % 0.37/0.60 (step @p44 :rule trans :premises (@p43 @p41)) % 0.37/0.60 (step @p45 :rule bool-impl-elim :args (@t39 @t8)) % 0.37/0.60 (step @p46 :rule trans :premises (@p45 @p44)) % 0.37/0.60 (step @p47 :rule cong :premises (@p46) :args ((forall @t22 (=> @t39 @t8)))) % 0.37/0.60 (step @p48 :rule trans :premises (@p47 @p40)) % 0.37/0.60 (step @p49 :rule refl :args (@t8)) % 0.37/0.60 (step @p50 :rule refl :args ((_ @t7 @t12))) % 0.37/0.60 (step @p51 :rule refl :args ((_ @t2 @t10))) % 0.37/0.60 (step @p52 :rule refl :args (@t29)) % 0.37/0.60 (step @p53 :rule cong :premises (@p52) :args (@t30)) % 0.37/0.60 (step @p54 :rule trans :premises (@p53 @p51)) % 0.37/0.60 (step @p55 :rule cong :premises (@p54) :args (@t31)) % 0.37/0.60 (step @p56 :rule cong :premises (@p55) :args (@t32)) % 0.37/0.60 (step @p57 :rule trans :premises (@p56 @p50)) % 0.37/0.60 (step @p58 :rule ho_cong :premises (@p11 @p55)) % 0.37/0.60 (step @p59 :rule cong :premises (@p58 @p57) :args ((= (_ @t7 @t31) @t32))) % 0.37/0.60 (step @p60 :rule symm :premises (@p59)) % 0.37/0.60 (step @p61 :rule refl :args (@t13)) % 0.37/0.60 (step @p62 :rule eq_resolve :premises (@p61 @p60)) % 0.37/0.60 (step @p63 :rule ho_cong :premises (@p17 @p52)) % 0.37/0.60 (step @p64 :rule cong :premises (@p63 @p54) :args ((= (_ @t2 @t29) @t30))) % 0.37/0.60 (step @p65 :rule symm :premises (@p64)) % 0.37/0.60 (step @p66 :rule refl :args (@t11)) % 0.37/0.60 (step @p67 :rule eq_resolve :premises (@p66 @p65)) % 0.37/0.60 (step @p68 :rule refl :args (@t10)) % 0.37/0.60 (step @p69 :rule cong :premises (@p68 @p52) :args ((= @t10 @t29))) % 0.37/0.60 (step @p70 :rule symm :premises (@p69)) % 0.37/0.60 (step @p71 :rule eq_resolve :premises (@p68 @p70)) % 0.37/0.60 (step @p72 :rule ho_cong :premises (@p17 @p71)) % 0.37/0.60 (step @p73 :rule trans :premises (@p72 @p67)) % 0.37/0.60 (step @p74 :rule cong :premises (@p73) :args (@t12)) % 0.37/0.60 (step @p75 :rule ho_cong :premises (@p11 @p74)) % 0.37/0.60 (step @p76 :rule trans :premises (@p75 @p62)) % 0.37/0.60 (step @p77 :rule refl :args (@t33)) % 0.37/0.60 (step @p78 :rule refl :args (@t14)) % 0.37/0.60 (step @p79 :rule cong :premises (@p78 @p77) :args ((= @t14 @t33))) % 0.37/0.60 (step @p80 :rule symm :premises (@p79)) % 0.37/0.60 (step @p81 :rule eq_resolve :premises (@p78 @p80)) % 0.37/0.60 (step @p82 :rule cong :premises (@p81) :args (@t40)) % 0.37/0.60 (step @p83 :rule nary_cong :premises (@p82 @p76) :args (@t41)) % 0.37/0.60 (step @p84 :rule cong :premises (@p83) :args ((forall @t15 @t41))) % 0.37/0.60 (step @p85 :rule bool-impl-elim :args (@t14 @t13)) % 0.37/0.60 (step @p86 :rule cong :premises (@p85) :args (@t16)) % 0.37/0.60 (step @p87 :rule trans :premises (@p86 @p84)) % 0.37/0.60 (step @p88 :rule refl :args (@t19)) % 0.37/0.60 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t20)) % 0.37/0.60 (step @p90 :rule cong :premises (@p89 @p49) :args (@t21)) % 0.37/0.60 (step @p91 :rule cong :premises (@p90) :args (@t23)) % 0.37/0.60 (step @p92 :rule trans :premises (@p91 @p48)) % 0.37/0.60 (step @p93 :rule cong :premises (@p92) :args (@t24)) % 0.37/0.60 (step @p94 :rule eq_resolve :premises (@p1 @p93)) % 0.37/0.60 (step @p95 :rule refl :args (@t55)) % 0.37/0.60 (step @p96 :rule bool-double-not-elim :args (@t42)) % 0.37/0.60 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or (not @t56) @t55))) % 0.37/0.60 (step @p98 :rule eq-refl :args (@t45)) % 0.37/0.60 (step @p99 :rule skolem_intro :args (@t46)) % 0.37/0.60 (step @p100 :rule refl :args (@t45)) % 0.37/0.60 (step @p101 :rule cong :premises (@p100 @p99) :args ((= @t45 @t46))) % 0.37/0.60 (step @p102 :rule trans :premises (@p101 @p98)) % 0.37/0.60 (step @p103 :rule true_elim :premises (@p102)) % 0.37/0.60 (step @p104 :rule cong :premises (@p103) :args (@t57)) % 0.37/0.60 (step @p105 :rule refl :args (@t50)) % 0.37/0.60 (step @p106 :rule eq-refl :args (@t18)) % 0.37/0.60 (step @p107 :rule skolem_intro :args (@t51)) % 0.37/0.60 (step @p108 :rule refl :args (@t18)) % 0.37/0.60 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t18 @t51))) % 0.37/0.60 (step @p110 :rule trans :premises (@p109 @p106)) % 0.37/0.60 (step @p111 :rule true_elim :premises (@p110)) % 0.37/0.60 (step @p112 :rule cong :premises (@p111) :args (@t58)) % 0.37/0.60 (step @p113 :rule cong :premises (@p112) :args (@t59)) % 0.37/0.60 (step @p114 :rule nary_cong :premises (@p113 @p105 @p104) :args (@t60)) % 0.37/0.60 (step @p115 :rule cong :premises (@p114) :args (@t61)) % 0.37/0.60 (step @p116 :rule refl :args (@t56)) % 0.37/0.60 (step @p117 :rule cong :premises (@p116 @p115) :args ((=> @t56 @t61))) % 0.37/0.60 (assume-push @p371 @t56) % 0.37/0.60 (step @p119 :rule skolemize :premises (@p94)) % 0.37/0.60 (step-pop @p372 :rule scope :premises (@p119)) % 0.37/0.60 (step @p120 :rule process_scope :premises (@p372) :args (@t61)) % 0.37/0.60 (step @p122 :rule eq_resolve :premises (@p120 @p117)) % 0.37/0.60 (step @p123 :rule implies_elim :premises (@p122)) % 0.37/0.60 (step @p124 :rule eq_resolve :premises (@p123 @p97)) % 0.37/0.60 (step @p125 :rule chain_m_resolution :premises (@p124 @p94) :args (@t55 @t62 (@list @t42))) % 0.37/0.60 (step @p126 :rule bool-double-not-elim :args (@t49)) % 0.37/0.60 (step @p127 :rule refl :args (@t54)) % 0.37/0.60 (step @p128 :rule nary_cong :premises (@p127 @p126) :args ((or @t54 (not @t50)))) % 0.37/0.60 (step @p129 :rule cnf_or_neg :args (@t54 1)) % 0.37/0.60 (step @p130 :rule eq_resolve :premises (@p129 @p128)) % 0.37/0.60 (step @p131 :rule reordering :premises (@p130) :args ((or @t49 @t54))) % 0.37/0.60 (step @p132 :rule chain_m_resolution :premises (@p131 @p125) :args (@t49 @t62 @t63)) % 0.37/0.60 (step @p133 :rule eq-refl :args (@t69)) % 0.37/0.60 (step @p134 :rule refl :args (@t1)) % 0.37/0.60 (step @p135 :rule ho_cong :premises (@p107 @p134)) % 0.37/0.60 (step @p136 :rule cong :premises (@p135) :args (@t70)) % 0.37/0.60 (step @p137 :rule cong :premises (@p136) :args (@t71)) % 0.37/0.60 (step @p138 :rule skolem_intro :args (@t72)) % 0.37/0.60 (step @p139 :rule trans :premises (@p138 @p137)) % 0.37/0.60 (step @p140 :rule ho_cong :premises (@p139 @p134)) % 0.37/0.60 (step @p141 :rule cong :premises (@p140) :args (@t74)) % 0.37/0.60 (step @p142 :rule 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