%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU974^5 : 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 : n029.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 08:53:36 AM UTC 2026 % Result : Theorem 0.36s 0.61s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU974^5 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n029.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 18:04:02 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.49 %----Proving TH0 % 0.36/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.61 % SZS status Theorem % 0.36/0.61 % SZS output start Proof % 0.36/0.61 ( % 0.36/0.61 (declare-sort tptp.a 0) % 0.36/0.61 (declare-const tptp.cZ tptp.a) % 0.36/0.61 (declare-const tptp.cL (-> tptp.a tptp.a)) % 0.36/0.61 (declare-const tptp.cP (-> tptp.a tptp.a tptp.a)) % 0.36/0.61 (declare-const tptp.cR (-> tptp.a tptp.a)) % 0.36/0.61 (define @t1 () (@var "Xu" tptp.a)) % 0.36/0.61 (define @t2 () (_ tptp.cR @t1)) % 0.36/0.61 (define @t3 () (@var "Xt" tptp.a)) % 0.36/0.61 (define @t4 () (_ tptp.cR @t3)) % 0.36/0.61 (define @t5 () (_ (_ tptp.cP @t4) @t2)) % 0.36/0.61 (define @t6 () (@var "X" (-> tptp.a Bool))) % 0.36/0.61 (define @t7 () (_ @t6 @t5)) % 0.36/0.61 (define @t8 () (_ tptp.cL @t1)) % 0.36/0.61 (define @t9 () (_ tptp.cL @t3)) % 0.36/0.61 (define @t10 () (_ tptp.cP @t9)) % 0.36/0.61 (define @t11 () (_ @t10 @t8)) % 0.36/0.61 (define @t12 () (_ @t6 @t11)) % 0.36/0.61 (define @t13 () (= @t3 tptp.cZ)) % 0.36/0.61 (define @t14 () (= @t1 tptp.cZ)) % 0.36/0.61 (define @t15 () (=> @t14 @t13)) % 0.36/0.61 (define @t16 () (and @t15 @t12 @t7)) % 0.36/0.61 (define @t17 () (_ (_ tptp.cP @t3) @t1)) % 0.36/0.61 (define @t18 () (_ @t6 @t17)) % 0.36/0.61 (define @t19 () (=> @t18 @t16)) % 0.36/0.61 (define @t20 () (@list @t3 @t1)) % 0.36/0.61 (define @t21 () (forall @t20 @t19)) % 0.36/0.61 (define @t22 () (@var "Xy" tptp.a)) % 0.36/0.61 (define @t23 () (_ tptp.cR @t22)) % 0.36/0.61 (define @t24 () (@var "Xx" tptp.a)) % 0.36/0.61 (define @t25 () (_ tptp.cR @t24)) % 0.36/0.61 (define @t26 () (_ (_ tptp.cP @t25) @t23)) % 0.36/0.61 (define @t27 () (_ @t6 @t26)) % 0.36/0.61 (define @t28 () (and @t27 @t21)) % 0.36/0.61 (define @t29 () (@list @t6)) % 0.36/0.61 (define @t30 () (exists @t29 @t28)) % 0.36/0.61 (define @t31 () (_ (_ tptp.cP @t24) @t22)) % 0.36/0.61 (define @t32 () (_ @t6 @t31)) % 0.36/0.61 (define @t33 () (and @t32 @t21)) % 0.36/0.61 (define @t34 () (exists @t29 @t33)) % 0.36/0.61 (define @t35 () (=> @t34 @t30)) % 0.36/0.61 (define @t36 () (@list @t24 @t22)) % 0.36/0.61 (define @t37 () (forall @t36 @t35)) % 0.36/0.61 (define @t38 () (= @t3 @t1)) % 0.36/0.61 (define @t39 () (forall @t20 (=> @t18 @t38))) % 0.36/0.61 (define @t40 () (= @t13 @t14)) % 0.36/0.61 (define @t41 () (and @t40 @t12 @t7)) % 0.36/0.61 (define @t42 () (=> @t18 @t41)) % 0.36/0.61 (define @t43 () (forall @t20 @t42)) % 0.36/0.61 (define @t44 () (=> @t43 @t39)) % 0.36/0.61 (define @t45 () (forall @t29 @t44)) % 0.36/0.61 (define @t46 () (_ @t10 @t4)) % 0.36/0.61 (define @t47 () (= @t3 @t46)) % 0.36/0.61 (define @t48 () (not @t13)) % 0.36/0.61 (define @t49 () (= @t48 @t47)) % 0.36/0.61 (define @t50 () (@list @t3)) % 0.36/0.61 (define @t51 () (forall @t50 @t49)) % 0.36/0.61 (define @t52 () (_ tptp.cR @t31)) % 0.36/0.61 (define @t53 () (forall @t36 (= @t52 @t22))) % 0.36/0.61 (define @t54 () (_ tptp.cL @t31)) % 0.36/0.61 (define @t55 () (forall @t36 (= @t54 @t24))) % 0.36/0.61 (define @t56 () (_ tptp.cR tptp.cZ)) % 0.36/0.61 (define @t57 () (_ tptp.cL tptp.cZ)) % 0.36/0.61 (define @t58 () (and (= @t57 tptp.cZ) (= @t56 tptp.cZ) @t55 @t53 @t51 @t45)) % 0.36/0.61 (define @t59 () (=> @t58 @t37)) % 0.36/0.61 (define @t60 () (not @t59)) % 0.36/0.61 (define @t61 () (tptp.cR @t1)) % 0.36/0.61 (define @t62 () (tptp.cR @t3)) % 0.36/0.61 (define @t63 () (tptp.cP @t62 @t61)) % 0.36/0.61 (define @t64 () (@var "BOUND_VARIABLE_7613" (-> tptp.a Bool))) % 0.36/0.61 (define @t65 () (tptp.cL @t1)) % 0.36/0.61 (define @t66 () (tptp.cL @t3)) % 0.36/0.61 (define @t67 () (tptp.cP @t66 @t65)) % 0.36/0.61 (define @t68 () (= tptp.cZ @t3)) % 0.36/0.61 (define @t69 () (= tptp.cZ @t1)) % 0.36/0.61 (define @t70 () (or (not @t69) @t68)) % 0.36/0.61 (define @t71 () (tptp.cP @t3 @t1)) % 0.36/0.61 (define @t72 () (not (forall @t20 (or (not (_ @t64 @t71)) (and @t70 (_ @t64 @t67) (_ @t64 @t63)))))) % 0.36/0.61 (define @t73 () (tptp.cP @t24 @t22)) % 0.36/0.61 (define @t74 () (not (_ @t64 @t73))) % 0.36/0.61 (define @t75 () (_ @t6 @t63)) % 0.36/0.61 (define @t76 () (_ @t6 @t67)) % 0.36/0.61 (define @t77 () (_ @t6 @t71)) % 0.36/0.61 (define @t78 () (not @t77)) % 0.36/0.61 (define @t79 () (forall @t20 (or @t78 (and @t70 @t76 @t75)))) % 0.36/0.61 (define @t80 () (not @t79)) % 0.36/0.61 (define @t81 () (tptp.cR @t22)) % 0.36/0.61 (define @t82 () (tptp.cR @t24)) % 0.36/0.61 (define @t83 () (tptp.cP @t82 @t81)) % 0.36/0.61 (define @t84 () (_ @t6 @t83)) % 0.36/0.61 (define @t85 () (not (forall @t29 (or (not @t84) @t80)))) % 0.36/0.61 (define @t86 () (or @t85 @t74 @t72)) % 0.36/0.61 (define @t87 () (@list @t24 @t22 @t64)) % 0.36/0.61 (define @t88 () (forall @t87 @t86)) % 0.36/0.61 (define @t89 () (@var "BOUND_VARIABLE_7550" tptp.a)) % 0.36/0.61 (define @t90 () (@var "BOUND_VARIABLE_7548" tptp.a)) % 0.36/0.61 (define @t91 () (= @t90 @t89)) % 0.36/0.61 (define @t92 () (not (_ @t6 (tptp.cP @t90 @t89)))) % 0.36/0.61 (define @t93 () (= @t68 @t69)) % 0.36/0.61 (define @t94 () (forall @t20 (or @t78 (and @t93 @t76 @t75)))) % 0.36/0.61 (define @t95 () (not @t94)) % 0.36/0.61 (define @t96 () (or @t95 @t92 @t91)) % 0.36/0.61 (define @t97 () (@list @t6 @t90 @t89)) % 0.36/0.61 (define @t98 () (forall @t97 @t96)) % 0.36/0.61 (define @t99 () (tptp.cP @t66 @t62)) % 0.36/0.61 (define @t100 () (= @t3 @t99)) % 0.36/0.61 (define @t101 () (not @t68)) % 0.36/0.61 (define @t102 () (forall @t50 (= @t101 @t100))) % 0.36/0.61 (define @t103 () (tptp.cR @t73)) % 0.36/0.61 (define @t104 () (forall @t36 (= @t22 @t103))) % 0.36/0.61 (define @t105 () (tptp.cL @t73)) % 0.36/0.61 (define @t106 () (forall @t36 (= @t24 @t105))) % 0.36/0.61 (define @t107 () (tptp.cR tptp.cZ)) % 0.36/0.61 (define @t108 () (= tptp.cZ @t56)) % 0.36/0.61 (define @t109 () (tptp.cL tptp.cZ)) % 0.36/0.61 (define @t110 () (= tptp.cZ @t57)) % 0.36/0.61 (define @t111 () (and @t110 @t108 @t106 @t104 @t102 @t98)) % 0.36/0.61 (define @t112 () (=> @t111 @t88)) % 0.36/0.61 (define @t113 () (or @t74 @t72)) % 0.36/0.61 (define @t114 () (or @t113 @t85)) % 0.36/0.61 (define @t115 () (forall @t87 @t114)) % 0.36/0.61 (define @t116 () (@list @t64)) % 0.36/0.61 (define @t117 () (forall @t116 @t114)) % 0.36/0.61 (define @t118 () (forall @t116 @t113)) % 0.36/0.61 (define @t119 () (or @t118 @t85)) % 0.36/0.61 (define @t120 () (_ @t6 @t73)) % 0.36/0.61 (define @t121 () (forall @t29 (or (not @t120) @t80))) % 0.36/0.61 (define @t122 () (not @t121)) % 0.36/0.61 (define @t123 () (not @t27)) % 0.36/0.61 (define @t124 () (or @t123 @t80)) % 0.36/0.61 (define @t125 () (and @t27 @t79)) % 0.36/0.61 (define @t126 () (forall @t29 (not @t125))) % 0.36/0.61 (define @t127 () (not @t126)) % 0.36/0.61 (define @t128 () (_ tptp.cP @t66)) % 0.36/0.61 (define @t129 () (and @t70 @t12 @t7)) % 0.36/0.61 (define @t130 () (not @t18)) % 0.36/0.61 (define @t131 () (or @t130 @t129)) % 0.36/0.61 (define @t132 () (and (=> @t69 @t68) @t12 @t7)) % 0.36/0.61 (define @t133 () (not @t32)) % 0.36/0.61 (define @t134 () (or @t133 @t80)) % 0.36/0.61 (define @t135 () (and @t32 @t79)) % 0.36/0.61 (define @t136 () (forall @t29 (not @t135))) % 0.36/0.61 (define @t137 () (not @t136)) % 0.36/0.61 (define @t138 () (or @t92 @t91)) % 0.36/0.61 (define @t139 () (or @t95 @t138)) % 0.36/0.61 (define @t140 () (forall @t97 @t139)) % 0.36/0.61 (define @t141 () (@list @t90 @t89)) % 0.36/0.61 (define @t142 () (forall @t141 @t139)) % 0.36/0.61 (define @t143 () (forall @t141 @t138)) % 0.36/0.61 (define @t144 () (or @t95 @t143)) % 0.36/0.61 (define @t145 () (forall @t20 (or @t78 @t38))) % 0.36/0.61 (define @t146 () (or @t130 @t38)) % 0.36/0.61 (define @t147 () (and @t93 @t12 @t7)) % 0.36/0.61 (define @t148 () (or @t130 @t147)) % 0.36/0.61 (define @t149 () (= @t47 @t101)) % 0.36/0.61 (define @t150 () (= @t22 @t52)) % 0.36/0.61 (define @t151 () (= @t24 @t54)) % 0.36/0.61 (define @t152 () (@quantifiers_skolemize @t88 1)) % 0.36/0.61 (define @t153 () (@quantifiers_skolemize @t88 0)) % 0.36/0.61 (define @t154 () (tptp.cP (tptp.cR @t153) (tptp.cR @t152))) % 0.36/0.61 (define @t155 () (forall @t29 (or (not (_ @t6 @t154)) @t80))) % 0.36/0.61 (define @t156 () (@quantifiers_skolemize @t88 2)) % 0.36/0.61 (define @t157 () (forall @t20 (or (not (_ @t156 @t71)) (and @t70 (_ @t156 @t67) (_ @t156 @t63))))) % 0.36/0.61 (define @t158 () (not @t157)) % 0.36/0.61 (define @t159 () (_ @t156 (tptp.cP @t153 @t152))) % 0.36/0.61 (define @t160 () (not @t159)) % 0.36/0.61 (define @t161 () (not @t155)) % 0.36/0.61 (define @t162 () (or @t161 @t160 @t158)) % 0.36/0.61 (define @t163 () (@list true)) % 0.36/0.61 (define @t164 () (@list @t162)) % 0.36/0.61 (define @t165 () (_ @t156 @t154)) % 0.36/0.61 (define @t166 () (and (or (not (= tptp.cZ @t152)) (= tptp.cZ @t153)) (_ @t156 (tptp.cP (tptp.cL @t153) (tptp.cL @t152))) @t165)) % 0.36/0.61 (define @t167 () (or @t160 @t166)) % 0.36/0.61 (define @t168 () (@list false false)) % 0.36/0.61 (define @t169 () (not @t165)) % 0.36/0.61 (define @t170 () (or @t169 @t158)) % 0.36/0.61 (define @t171 () (not @t170)) % 0.36/0.61 (assume @p1 @t60) % 0.36/0.61 (assume @p2 true) % 0.36/0.61 (step @p3 :rule refl :args (@t88)) % 0.36/0.61 (step @p4 :rule refl :args (@t98)) % 0.36/0.61 (step @p5 :rule refl :args (@t102)) % 0.36/0.61 (step @p6 :rule refl :args (@t104)) % 0.36/0.61 (step @p7 :rule refl :args (@t106)) % 0.36/0.61 (step @p8 :rule refl :args (@t107)) % 0.36/0.61 (step @p9 :rule refl :args (@t56)) % 0.36/0.61 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t56 @t107))) % 0.36/0.61 (step @p11 :rule symm :premises (@p10)) % 0.36/0.61 (step @p12 :rule eq_resolve :premises (@p9 @p11)) % 0.36/0.61 (step @p13 :rule refl :args (tptp.cZ)) % 0.36/0.61 (step @p14 :rule cong :premises (@p13 @p12) :args (@t108)) % 0.36/0.61 (step @p15 :rule refl :args (@t109)) % 0.36/0.61 (step @p16 :rule refl :args (@t57)) % 0.36/0.61 (step @p17 :rule cong :premises (@p16 @p15) :args ((= @t57 @t109))) % 0.36/0.61 (step @p18 :rule symm :premises (@p17)) % 0.36/0.61 (step @p19 :rule eq_resolve :premises (@p16 @p18)) % 0.36/0.61 (step @p20 :rule cong :premises (@p13 @p19) :args (@t110)) % 0.36/0.61 (step @p21 :rule nary_cong :premises (@p20 @p14 @p7 @p6 @p5 @p4) :args (@t111)) % 0.36/0.61 (step @p22 :rule cong :premises (@p21 @p3) :args (@t112)) % 0.36/0.61 (step @p23 :rule cong :premises (@p22) :args ((not @t112))) % 0.36/0.61 (step @p24 :rule aci_norm :args ((= @t114 @t86))) % 0.36/0.61 (step @p25 :rule cong :premises (@p24) :args (@t115)) % 0.36/0.61 (step @p26 :rule quant-merge-prenex :args ((= (forall @t36 @t117) @t115))) % 0.36/0.61 (step @p27 :rule refl :args (@t85)) % 0.36/0.61 (step @p28 :rule alpha_equiv :args (@t118 (@list @t64) (@list @t6))) % 0.36/0.61 (step @p29 :rule nary_cong :premises (@p28 @p27) :args (@t119)) % 0.36/0.61 (step @p30 :rule quant-miniscope-or :args ((= @t117 @t119))) % 0.36/0.61 (step @p31 :rule trans :premises (@p30 @p29)) % 0.36/0.61 (step @p32 :rule symm :premises (@p31)) % 0.36/0.61 (step @p33 :rule cong :premises (@p32) :args ((forall @t36 (or @t121 @t85)))) % 0.36/0.61 (step @p34 :rule trans :premises (@p33 @p26)) % 0.36/0.61 (step @p35 :rule trans :premises (@p34 @p25)) % 0.36/0.61 (step @p36 :rule bool-double-not-elim :args (@t121)) % 0.36/0.61 (step @p37 :rule nary_cong :premises (@p36 @p27) :args ((or (not @t122) @t85))) % 0.36/0.61 (step @p38 :rule bool-impl-elim :args (@t122 @t85)) % 0.36/0.61 (step @p39 :rule trans :premises (@p38 @p37)) % 0.36/0.61 (step @p40 :rule cong :premises (@p39) :args ((forall @t36 (=> @t122 @t85)))) % 0.36/0.61 (step @p41 :rule trans :premises (@p40 @p35)) % 0.36/0.61 (step @p42 :rule refl :args (@t80)) % 0.36/0.61 (step @p43 :rule refl :args ((_ @t6 @t26))) % 0.36/0.61 (step @p44 :rule refl :args ((tptp.cP @t25 @t23))) % 0.36/0.61 (step @p45 :rule refl :args (@t81)) % 0.36/0.61 (step @p46 :rule refl :args (@t82)) % 0.36/0.61 (step @p47 :rule cong :premises (@p46 @p45) :args (@t83)) % 0.36/0.61 (step @p48 :rule trans :premises (@p47 @p44)) % 0.36/0.61 (step @p49 :rule cong :premises (@p48) :args (@t84)) % 0.36/0.61 (step @p50 :rule trans :premises (@p49 @p43)) % 0.36/0.61 (step @p51 :rule refl :args (@t6)) % 0.36/0.61 (step @p52 :rule ho_cong :premises (@p51 @p48)) % 0.36/0.61 (step @p53 :rule cong :premises (@p52 @p50) :args ((= (_ @t6 @t83) @t84))) % 0.36/0.61 (step @p54 :rule symm :premises (@p53)) % 0.36/0.61 (step @p55 :rule refl :args (@t27)) % 0.36/0.61 (step @p56 :rule eq_resolve :premises (@p55 @p54)) % 0.36/0.61 (step @p57 :rule refl :args (tptp.cP)) % 0.36/0.61 (step @p58 :rule ho_cong :premises (@p57 @p46)) % 0.36/0.61 (step @p59 :rule ho_cong :premises (@p58 @p45)) % 0.36/0.61 (step @p60 :rule cong :premises (@p59 @p48) :args ((= (_ (_ tptp.cP @t82) @t81) @t83))) % 0.36/0.61 (step @p61 :rule symm :premises (@p60)) % 0.36/0.61 (step @p62 :rule refl :args (@t26)) % 0.36/0.61 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 0.36/0.61 (step @p64 :rule refl :args (@t23)) % 0.36/0.61 (step @p65 :rule cong :premises (@p64 @p45) :args ((= @t23 @t81))) % 0.36/0.61 (step @p66 :rule symm :premises (@p65)) % 0.36/0.61 (step @p67 :rule eq_resolve :premises (@p64 @p66)) % 0.36/0.61 (step @p68 :rule refl :args (@t25)) % 0.36/0.61 (step @p69 :rule cong :premises (@p68 @p46) :args ((= @t25 @t82))) % 0.36/0.61 (step @p70 :rule symm :premises (@p69)) % 0.36/0.61 (step @p71 :rule eq_resolve :premises (@p68 @p70)) % 0.36/0.61 (step @p72 :rule ho_cong :premises (@p57 @p71)) % 0.36/0.61 (step @p73 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chain_m_resolution :premises (@p345 @p326) :args (@t159 @t163 @t164)) % 0.36/0.61 (step @p347 :rule cnf_or_pos :args (@t167)) % 0.36/0.61 (step @p348 :rule reordering :premises (@p347) :args ((or @t160 @t166 (not @t167)))) % 0.36/0.61 (step @p349 :rule chain_m_resolution :premises (@p348 @p346 @p340) :args (@t166 @t168 (@list @t159 @t167))) % 0.36/0.61 (step @p350 :rule cnf_and_pos :args (@t166 2)) % 0.36/0.61 (step @p351 :rule reordering :premises (@p350) :args ((or @t165 (not @t166)))) % 0.36/0.61 (step @p352 :rule chain_m_resolution :premises (@p351 @p349) :args (@t165 (@list false) (@list @t166))) % 0.36/0.61 (step @p353 :rule cnf_or_pos :args (@t170)) % 0.36/0.61 (step @p354 :rule reordering :premises (@p353) :args ((or @t158 @t169 @t171))) % 0.36/0.61 (step @p355 :rule chain_m_resolution :premises (@p354 @p339 @p352) :args (@t171 @t168 (@list @t157 @t165))) % 0.36/0.61 (assume-push @p362 @t155) % 0.36/0.61 (step @p357 :rule instantiate :premises (@p333) :args ((@list @t156))) % 0.36/0.61 (step-pop @p363 :rule scope :premises (@p357)) % 0.36/0.61 (step @p358 :rule process_scope :premises (@p363) :args (@t170)) % 0.36/0.61 (step @p360 :rule implies_elim :premises (@p358)) % 0.36/0.61 (step @p361 false :rule chain_m_resolution :premises (@p360 @p355 @p333) :args (false (@list true false) (@list @t170 @t155))) % 0.36/0.61 ) % 0.36/0.61 % SZS output end Proof % 0.36/0.61 % cvc5 exiting %------------------------------------------------------------------------------