%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU546^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n014.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 08:52:08 AM UTC 2026 % Result : Theorem 0.40s 0.62s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU546^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n014.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 : Tue Jun 2 17:41:43 EDT 2026 % 0.16/0.34 % CPUTime : % 0.32/0.49 %----Proving TH0 % 0.40/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.62 % SZS status Theorem % 0.40/0.62 % SZS output start Proof % 0.40/0.62 ( % 0.40/0.62 (declare-sort $$unsorted 0) % 0.40/0.62 (declare-const tptp.exuI1 Bool) % 0.40/0.62 (define tptp.exu () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "Xphi" (-> $$unsorted Bool)))) (lambda (@list _let_3) (exists (@list _let_2) (and (_ _let_3 _let_2) (forall (@list _let_1) (=> (_ _let_3 _let_1) (= _let_2 _let_1)))))))))) % 0.40/0.62 (define @t1 () (@var "Xx" $$unsorted)) % 0.40/0.62 (define @t2 () (@var "Xphi" (-> $$unsorted Bool))) % 0.40/0.62 (define @t3 () (_ @t2 @t1)) % 0.40/0.62 (define @t4 () (@list @t1)) % 0.40/0.62 (define @t5 () (lambda @t4 @t3)) % 0.40/0.62 (define @t6 () (_ tptp.exu @t5)) % 0.40/0.62 (define @t7 () (@var "Xy" $$unsorted)) % 0.40/0.62 (define @t8 () (= @t1 @t7)) % 0.40/0.62 (define @t9 () (_ @t2 @t7)) % 0.40/0.62 (define @t10 () (@list @t7)) % 0.40/0.62 (define @t11 () (forall @t10 (=> @t9 @t8))) % 0.40/0.62 (define @t12 () (and @t3 @t11)) % 0.40/0.62 (define @t13 () (exists @t4 @t12)) % 0.40/0.62 (define @t14 () (=> @t13 @t6)) % 0.40/0.62 (define @t15 () (@list @t2)) % 0.40/0.62 (define @t16 () (forall @t15 @t14)) % 0.40/0.62 (define @t17 () (= tptp.exuI1 @t16)) % 0.40/0.62 (define @t18 () (= @t9 (= @t7 @t1))) % 0.40/0.62 (define @t19 () (forall @t10 @t18)) % 0.40/0.62 (define @t20 () (exists @t4 @t19)) % 0.40/0.62 (define @t21 () (=> @t20 @t6)) % 0.40/0.62 (define @t22 () (forall @t15 @t21)) % 0.40/0.62 (define @t23 () (=> tptp.exuI1 @t22)) % 0.40/0.62 (define @t24 () (not @t23)) % 0.40/0.62 (define @t25 () (lambda @t15 @t13)) % 0.40/0.62 (define @t26 () (_ @t2 @t7)) % 0.40/0.62 (define @t27 () (forall @t10 (or (not @t26) @t8))) % 0.40/0.62 (define @t28 () (not @t27)) % 0.40/0.62 (define @t29 () (_ @t2 @t1)) % 0.40/0.62 (define @t30 () (forall @t4 (or (not @t29) @t28))) % 0.40/0.62 (define @t31 () (not @t30)) % 0.40/0.62 (define @t32 () (@var "BOUND_VARIABLE_7506" $$unsorted)) % 0.40/0.62 (define @t33 () (@list @t2 @t32)) % 0.40/0.62 (define @t34 () (forall @t33 (or (not (forall @t10 (= @t26 (= @t7 @t32)))) @t31))) % 0.40/0.62 (define @t35 () (not @t3)) % 0.40/0.62 (define @t36 () (or @t35 @t28)) % 0.40/0.62 (define @t37 () (not @t9)) % 0.40/0.62 (define @t38 () (or @t37 @t8)) % 0.40/0.62 (define @t39 () (_ @t5 @t7)) % 0.40/0.62 (define @t40 () (not @t39)) % 0.40/0.62 (define @t41 () (or @t40 @t8)) % 0.40/0.62 (define @t42 () (forall @t10 @t41)) % 0.40/0.62 (define @t43 () (not @t42)) % 0.40/0.62 (define @t44 () (_ @t5 @t1)) % 0.40/0.62 (define @t45 () (not @t44)) % 0.40/0.62 (define @t46 () (or @t45 @t43)) % 0.40/0.62 (define @t47 () (forall @t4 @t46)) % 0.40/0.62 (define @t48 () (not @t47)) % 0.40/0.62 (define @t49 () (_ (lambda @t15 @t31) @t5)) % 0.40/0.62 (define @t50 () (and @t3 @t27)) % 0.40/0.62 (define @t51 () (forall @t4 (not @t50))) % 0.40/0.62 (define @t52 () (not @t51)) % 0.40/0.62 (define @t53 () (=> @t13 @t49)) % 0.40/0.62 (define @t54 () (forall @t15 @t53)) % 0.40/0.62 (define @t55 () (=> tptp.exuI1 @t34)) % 0.40/0.62 (define @t56 () (= @t32 @t7)) % 0.40/0.62 (define @t57 () (forall @t10 (= @t56 @t26))) % 0.40/0.62 (define @t58 () (not @t57)) % 0.40/0.62 (define @t59 () (or @t58 @t31)) % 0.40/0.62 (define @t60 () (forall @t33 @t59)) % 0.40/0.62 (define @t61 () (@list @t32)) % 0.40/0.62 (define @t62 () (forall @t61 @t59)) % 0.40/0.62 (define @t63 () (forall @t61 @t58)) % 0.40/0.62 (define @t64 () (or @t63 @t31)) % 0.40/0.62 (define @t65 () (forall @t10 (= @t8 @t26))) % 0.40/0.62 (define @t66 () (forall @t4 (not @t65))) % 0.40/0.62 (define @t67 () (not @t66)) % 0.40/0.62 (define @t68 () (= @t9 @t8)) % 0.40/0.62 (define @t69 () (=> @t20 @t49)) % 0.40/0.62 (define @t70 () (forall @t15 @t69)) % 0.40/0.62 (define @t71 () (=> tptp.exuI1 @t70)) % 0.40/0.62 (define @t72 () (@quantifiers_skolemize @t34 1)) % 0.40/0.62 (define @t73 () (@quantifiers_skolemize @t34 0)) % 0.40/0.62 (define @t74 () (_ @t73 @t7)) % 0.40/0.62 (define @t75 () (forall @t10 (= @t74 (= @t7 @t72)))) % 0.40/0.62 (define @t76 () (not @t74)) % 0.40/0.62 (define @t77 () (forall @t4 (or (not (_ @t73 @t1)) (not (forall @t10 (or @t76 @t8)))))) % 0.40/0.62 (define @t78 () (not @t77)) % 0.40/0.62 (define @t79 () (not @t75)) % 0.40/0.62 (define @t80 () (or @t79 @t78)) % 0.40/0.62 (define @t81 () (@list true)) % 0.40/0.62 (define @t82 () (@list @t80)) % 0.40/0.62 (define @t83 () (@const 0 $$unsorted)) % 0.40/0.62 (define @t84 () (forall @t10 (or @t76 (= @t7 @t83)))) % 0.40/0.62 (define @t85 () (@quantifiers_skolemize @t84 0)) % 0.40/0.62 (define @t86 () (or @t76 (= @t85 @t7))) % 0.40/0.62 (define @t87 () (forall @t10 @t86)) % 0.40/0.62 (define @t88 () (not @t87)) % 0.40/0.62 (define @t89 () (_ @t73 @t85)) % 0.40/0.62 (define @t90 () (not @t89)) % 0.40/0.62 (define @t91 () (or @t90 @t88)) % 0.40/0.62 (define @t92 () (@list @t85)) % 0.40/0.62 (define @t93 () (forall @t10 (or @t76 (= @t7 @t85)))) % 0.40/0.62 (define @t94 () (not @t93)) % 0.40/0.62 (define @t95 () (or @t90 @t94)) % 0.40/0.62 (define @t96 () (@list false)) % 0.40/0.62 (define @t97 () (@list @t77)) % 0.40/0.62 (define @t98 () (_ @t73 @t72)) % 0.40/0.62 (define @t99 () (= @t72 @t72)) % 0.40/0.62 (define @t100 () (= @t98 @t99)) % 0.40/0.62 (define @t101 () (@list @t72)) % 0.40/0.62 (define @t102 () (@list @t75)) % 0.40/0.62 (define @t103 () (_ @t73 @t83)) % 0.40/0.62 (define @t104 () (= @t103 (= @t83 @t72))) % 0.40/0.62 (define @t105 () (@list @t83)) % 0.40/0.62 (define @t106 () (= @t72 @t83)) % 0.40/0.62 (define @t107 () (= @t103 @t106)) % 0.40/0.62 (define @t108 () (not @t107)) % 0.40/0.62 (define @t109 () (not @t103)) % 0.40/0.62 (define @t110 () (or @t76 (= @t83 @t7))) % 0.40/0.62 (define @t111 () (forall @t10 @t110)) % 0.40/0.62 (define @t112 () (not @t111)) % 0.40/0.62 (define @t113 () (or @t109 @t112)) % 0.40/0.62 (define @t114 () (not @t84)) % 0.40/0.62 (define @t115 () (or @t109 @t114)) % 0.40/0.62 (define @t116 () (= @t83 @t85)) % 0.40/0.62 (define @t117 () (or @t90 @t116)) % 0.40/0.62 (define @t118 () (not @t117)) % 0.40/0.62 (define @t119 () (or @t90 (= @t85 @t83))) % 0.40/0.62 (define @t120 () (not @t119)) % 0.40/0.62 (define @t121 () (= @t89 (= @t85 @t72))) % 0.40/0.62 (define @t122 () (= @t72 @t85)) % 0.40/0.62 (define @t123 () (= @t89 @t122)) % 0.40/0.62 (define @t124 () (not @t122)) % 0.40/0.62 (define @t125 () (not @t106)) % 0.40/0.62 (define @t126 () (not @t116)) % 0.40/0.62 (define @t127 () (and @t106 @t126)) % 0.40/0.62 (define @t128 () (@list true false)) % 0.40/0.62 (define @t129 () (not @t98)) % 0.40/0.62 (define @t130 () (or @t129 @t106)) % 0.40/0.62 (define @t131 () (not @t130)) % 0.40/0.62 (define @t132 () (@list false false)) % 0.40/0.62 (define @t133 () (@quantifiers_skolemize @t93 0)) % 0.40/0.62 (define @t134 () (= @t85 @t133)) % 0.40/0.62 (define @t135 () (_ @t73 @t133)) % 0.40/0.62 (define @t136 () (not @t135)) % 0.40/0.62 (define @t137 () (or @t136 @t134)) % 0.40/0.62 (define @t138 () (not @t137)) % 0.40/0.62 (define @t139 () (or @t136 (= @t133 @t85))) % 0.40/0.62 (define @t140 () (not @t139)) % 0.40/0.62 (define @t141 () (not @t134)) % 0.40/0.62 (define @t142 () (@list @t137)) % 0.40/0.62 (define @t143 () (= @t72 @t133)) % 0.40/0.62 (define @t144 () (not @t143)) % 0.40/0.62 (define @t145 () (and @t122 @t141)) % 0.40/0.62 (define @t146 () (@list false true)) % 0.40/0.62 (define @t147 () (= @t135 @t143)) % 0.40/0.62 (define @t148 () (not @t147)) % 0.40/0.62 (define @t149 () (= @t135 (= @t133 @t72))) % 0.40/0.62 (assume @p1 @t17) % 0.40/0.62 (assume @p2 @t24) % 0.40/0.62 (assume @p3 true) % 0.40/0.62 (step @p4 (= tptp.exu @t25) :rule refl :args (@t25)) % 0.40/0.62 (step @p5 :rule bool-impl-true2 :args (@t34)) % 0.40/0.62 (step @p6 :rule cong :premises (@p5) :args ((not (=> true @t34)))) % 0.40/0.62 (step @p7 :rule refl :args (@t34)) % 0.40/0.62 (step @p8 :rule bool-eq-true :args (tptp.exuI1)) % 0.40/0.62 (step @p9 :rule symm :premises (@p8)) % 0.40/0.62 (step @p10 :rule quant-unused-vars :args ((= (forall @t15 true) true))) % 0.40/0.62 (step @p11 :rule bool-or-taut :args (false @t30 false false)) % 0.40/0.62 (step @p12 :rule refl :args (@t31)) % 0.40/0.62 (step @p13 :rule bool-double-not-elim :args (@t30)) % 0.40/0.62 (step @p14 :rule nary_cong :premises (@p13 @p12) :args ((or (not @t31) @t31))) % 0.40/0.62 (step @p15 :rule bool-impl-elim :args (@t31 @t31)) % 0.40/0.62 (step @p16 :rule trans :premises (@p15 @p14)) % 0.40/0.62 (step @p17 :rule trans :premises (@p16 @p11)) % 0.40/0.62 (step @p18 :rule cong :premises (@p17) :args ((forall @t15 (=> @t31 @t31)))) % 0.40/0.62 (step @p19 :rule trans :premises (@p18 @p10)) % 0.40/0.62 (step @p20 :rule refl :args (@t28)) % 0.40/0.62 (step @p21 :rule refl :args (@t29)) % 0.40/0.62 (step @p22 :rule refl :args (@t3)) % 0.40/0.62 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t3 @t29))) % 0.40/0.62 (step @p24 :rule symm :premises (@p23)) % 0.40/0.62 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.40/0.62 (step @p26 :rule cong :premises (@p25) :args (@t35)) % 0.40/0.62 (step @p27 :rule nary_cong :premises (@p26 @p20) :args (@t36)) % 0.40/0.62 (step @p28 :rule cong :premises (@p27) :args ((forall @t4 @t36))) % 0.40/0.62 (step @p29 :rule refl :args (@t8)) % 0.40/0.62 (step @p30 :rule refl :args (@t26)) % 0.40/0.62 (step @p31 :rule refl :args (@t9)) % 0.40/0.62 (step @p32 :rule cong :premises (@p31 @p30) :args ((= @t9 @t26))) % 0.40/0.62 (step @p33 :rule symm :premises (@p32)) % 0.40/0.62 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 0.40/0.62 (step @p35 :rule cong :premises (@p34) :args (@t37)) % 0.40/0.62 (step @p36 :rule nary_cong :premises (@p35 @p29) :args (@t38)) % 0.40/0.62 (step @p37 :rule cong :premises (@p36) :args ((forall @t10 @t38))) % 0.40/0.62 (step @p38 :rule refl :args (@t8)) % 0.40/0.62 (step @p39 :rule beta-reduce :args ((= @t39 @t9))) % 0.40/0.62 (step @p40 :rule cong :premises (@p39) :args (@t40)) % 0.40/0.62 (step @p41 :rule nary_cong :premises (@p40 @p38) :args (@t41)) % 0.40/0.62 (step @p42 :rule cong :premises (@p41) :args (@t42)) % 0.40/0.62 (step @p43 :rule trans :premises (@p42 @p37)) % 0.40/0.62 (step @p44 :rule cong :premises (@p43) :args (@t43)) % 0.40/0.62 (step @p45 :rule beta-reduce :args ((= @t44 @t3))) % 0.40/0.62 (step @p46 :rule cong :premises (@p45) :args (@t45)) % 0.40/0.62 (step @p47 :rule nary_cong :premises (@p46 @p44) :args (@t46)) % 0.40/0.62 (step @p48 :rule cong :premises (@p47) :args (@t47)) % 0.40/0.62 (step @p49 :rule trans :premises (@p48 @p28)) % 0.40/0.62 (step @p50 :rule cong :premises (@p49) :args (@t48)) % 0.40/0.62 (step @p51 :rule beta-reduce :args ((= @t49 @t48))) % 0.40/0.62 (step @p52 :rule trans :premises (@p51 @p50)) % 0.40/0.62 (step @p53 :rule bool-and-de-morgan :args (@t3 @t27 true)) % 0.40/0.62 (step @p54 :rule cong :premises (@p53) :args (@t51)) % 0.40/0.62 (step @p55 :rule trans :premises (@p54 @p28)) % 0.40/0.62 (step @p56 :rule cong :premises (@p55) :args (@t52)) % 0.40/0.62 (step @p57 :rule exists-elim :args ((= (exists @t4 @t50) @t52))) % 0.40/0.62 (step @p58 :rule trans :premises (@p57 @p56)) % 0.40/0.62 (step @p59 :rule bool-impl-elim :args (@t9 @t8)) % 0.40/0.62 (step @p60 :rule cong :premises (@p59) :args (@t11)) % 0.40/0.62 (step @p61 :rule trans :premises (@p60 @p37)) % 0.40/0.62 (step @p62 :rule refl :args (@t3)) % 0.40/0.62 (step @p63 :rule nary_cong :premises (@p62 @p61) :args (@t12)) % 0.40/0.62 (step @p64 :rule cong :premises (@p63) :args (@t13)) % 0.40/0.62 (step @p65 :rule trans :premises (@p64 @p58)) % 0.40/0.62 (step @p66 :rule cong :premises (@p65 @p52) :args (@t53)) % 0.40/0.62 (step @p67 :rule cong :premises (@p66) :args (@t54)) % 0.40/0.62 (step @p68 :rule trans :premises (@p67 @p19)) % 0.40/0.62 (step @p69 :rule refl :args (tptp.exuI1)) % 0.40/0.62 (step @p70 :rule cong :premises (@p69 @p68) :args ((= tptp.exuI1 @t54))) % 0.40/0.62 (step @p71 :rule trans :premises (@p70 @p8)) % 0.40/0.62 (step @p72 :rule refl :args (@t5)) % 0.40/0.62 (step @p73 :rule cong :premises (@p65) :args (@t25)) % 0.40/0.62 (step @p74 :rule trans :premises (@p4 @p73)) % 0.40/0.62 (step @p75 :rule ho_cong :premises (@p74 @p72)) % 0.40/0.62 (step @p76 :rule refl :args (@t13)) % 0.40/0.62 (step @p77 :rule cong :premises (@p76 @p75) :args (@t14)) % 0.40/0.62 (step @p78 :rule cong :premises (@p77) :args (@t16)) % 0.40/0.62 (step @p79 :rule cong :premises (@p69 @p78) :args (@t17)) % 0.40/0.62 (step @p80 :rule trans :premises (@p79 @p71)) % 0.40/0.62 (step @p81 :rule eq_resolve :premises (@p1 @p80)) % 0.40/0.62 (step @p82 :rule eq_resolve :premises (@p81 @p9)) % 0.40/0.62 (step @p83 :rule cong :premises (@p82 @p7) :args (@t55)) % 0.40/0.62 (step @p84 :rule cong :premises (@p83) :args ((not @t55))) % 0.40/0.62 (step @p85 :rule trans :premises (@p84 @p6)) % 0.40/0.62 (step @p86 :rule refl :args (@t31)) % 0.40/0.62 (step @p87 :rule eq-symm :args (@t32 @t7)) % 0.40/0.62 (step @p88 :rule refl :args (@t26)) % 0.40/0.62 (step @p89 :rule cong :premises (@p88 @p87) :args ((= @t26 @t56))) % 0.40/0.62 (step @p90 :rule eq-symm :args (@t56 @t26)) % 0.40/0.62 (step @p91 :rule trans :premises (@p90 @p89)) % 0.40/0.62 (step @p92 :rule cong :premises (@p91) :args (@t57)) % 0.40/0.62 (step @p93 :rule cong :premises (@p92) :args (@t58)) % 0.40/0.62 (step @p94 :rule nary_cong :premises (@p93 @p86) :args (@t59)) % 0.40/0.62 (step @p95 :rule cong :premises (@p94) :args (@t60)) % 0.40/0.62 (step @p96 :rule quant-merge-prenex :args ((= (forall @t15 @t62) @t60))) % 0.40/0.62 (step @p97 :rule alpha_equiv :args (@t63 (@list @t32) (@list @t1))) % 0.40/0.62 (step @p98 :rule nary_cong :premises (@p97 @p12) :args (@t64)) % 0.40/0.62 (step @p99 :rule quant-miniscope-or :args ((= @t62 @t64))) % 0.40/0.62 (step @p100 :rule trans :premises (@p99 @p98)) % 0.40/0.62 (step @p101 :rule symm :premises (@p100)) % 0.40/0.62 (step @p102 :rule cong :premises (@p101) :args ((forall @t15 (or @t66 @t31)))) % 0.40/0.62 (step @p103 :rule trans :premises (@p102 @p96)) % 0.40/0.62 (step @p104 :rule trans :premises (@p103 @p95)) % 0.40/0.62 (step @p105 :rule bool-double-not-elim :args (@t66)) % 0.40/0.62 (step @p106 :rule nary_cong :premises (@p105 @p12) :args ((or (not @t67) @t31))) % 0.40/0.62 (step @p107 :rule bool-impl-elim :args (@t67 @t31)) % 0.40/0.62 (step @p108 :rule trans :premises (@p107 @p106)) % 0.40/0.62 (step @p109 :rule cong :premises (@p108) :args ((forall @t15 (=> @t67 @t31)))) % 0.40/0.62 (step @p110 :rule trans :premises (@p109 @p104)) % 0.40/0.62 (step @p111 :rule exists-elim :args ((= (exists @t4 @t65) @t67))) % 0.40/0.62 (step @p112 :rule eq-symm :args (@t26 @t8)) % 0.40/0.62 (step @p113 :rule cong :premises (@p112) :args ((forall @t10 (= @t26 @t8)))) % 0.40/0.62 (step @p114 :rule cong :premises (@p34 @p29) :args (@t68)) % 0.40/0.62 (step @p115 :rule cong :premises (@p114) :args ((forall @t10 @t68))) % 0.40/0.62 (step @p116 :rule trans :premises (@p115 @p113)) % 0.40/0.62 (step @p117 :rule eq-symm :args (@t7 @t1)) % 0.40/0.62 (step @p118 :rule refl :args (@t9)) % 0.40/0.62 (step @p119 :rule cong :premises (@p118 @p117) :args (@t18)) % 0.40/0.62 (step @p120 :rule cong :premises (@p119) :args (@t19)) % 0.40/0.62 (step @p121 :rule trans :premises (@p120 @p116)) % 0.40/0.62 (step @p122 :rule cong :premises (@p121) :args (@t20)) % 0.40/0.62 (step @p123 :rule 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