%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV186^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n020.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 08:55:34 AM UTC 2026 % Result : Theorem 0.38s 0.58s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV186^5 : TPTP v9.2.1. Released v4.0.0. % 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 : n020.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 18:17:55 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 0.38/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.58 % SZS status Theorem % 0.38/0.58 % SZS output start Proof % 0.38/0.58 ( % 0.38/0.58 (declare-sort tptp.b 0) % 0.38/0.58 (define @t1 () (@var "Xx" tptp.b)) % 0.38/0.58 (define @t2 () (@var "S0" (-> tptp.b Bool))) % 0.38/0.58 (define @t3 () (_ @t2 @t1)) % 0.38/0.58 (define @t4 () (@var "S" (-> (-> tptp.b Bool) Bool))) % 0.38/0.58 (define @t5 () (_ @t4 @t2)) % 0.38/0.58 (define @t6 () (@list @t2)) % 0.38/0.58 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.38/0.58 (define @t8 () (@var "Y" (-> tptp.b Bool))) % 0.38/0.58 (define @t9 () (_ @t8 @t1)) % 0.38/0.58 (define @t10 () (=> @t9 @t7)) % 0.38/0.58 (define @t11 () (@list @t1)) % 0.38/0.58 (define @t12 () (forall @t11 @t10)) % 0.38/0.58 (define @t13 () (@var "X" (-> tptp.b Bool))) % 0.38/0.58 (define @t14 () (@var "P" (-> (-> tptp.b Bool) (-> tptp.b Bool) Bool))) % 0.38/0.58 (define @t15 () (_ (_ @t14 @t13) @t8)) % 0.38/0.58 (define @t16 () (_ @t13 @t1)) % 0.38/0.58 (define @t17 () (=> @t16 @t7)) % 0.38/0.58 (define @t18 () (forall @t11 @t17)) % 0.38/0.58 (define @t19 () (and @t18 @t15)) % 0.38/0.58 (define @t20 () (=> @t19 @t12)) % 0.38/0.58 (define @t21 () (@list @t13 @t8)) % 0.38/0.58 (define @t22 () (forall @t21 @t20)) % 0.38/0.58 (define @t23 () (@var "Xx0" tptp.b)) % 0.38/0.58 (define @t24 () (@var "Xx" (-> tptp.b Bool))) % 0.38/0.58 (define @t25 () (_ @t24 @t23)) % 0.38/0.58 (define @t26 () (_ @t8 @t23)) % 0.38/0.58 (define @t27 () (@list @t23)) % 0.38/0.58 (define @t28 () (forall @t27 (=> @t26 @t25))) % 0.38/0.58 (define @t29 () (_ @t13 @t23)) % 0.38/0.58 (define @t30 () (forall @t27 (=> @t29 @t25))) % 0.38/0.58 (define @t31 () (and @t30 @t15)) % 0.38/0.58 (define @t32 () (=> @t31 @t28)) % 0.38/0.58 (define @t33 () (forall @t21 @t32)) % 0.38/0.58 (define @t34 () (_ @t4 @t24)) % 0.38/0.58 (define @t35 () (=> @t34 @t33)) % 0.38/0.58 (define @t36 () (@list @t24)) % 0.38/0.58 (define @t37 () (forall @t36 @t35)) % 0.38/0.58 (define @t38 () (=> @t37 @t22)) % 0.38/0.58 (define @t39 () (@list @t14 @t4)) % 0.38/0.58 (define @t40 () (forall @t39 @t38)) % 0.38/0.58 (define @t41 () (not @t40)) % 0.38/0.58 (define @t42 () (@var "BOUND_VARIABLE_7607" tptp.b)) % 0.38/0.58 (define @t43 () (@var "BOUND_VARIABLE_7609" (-> tptp.b Bool))) % 0.38/0.58 (define @t44 () (_ @t43 @t42)) % 0.38/0.58 (define @t45 () (not (_ @t4 @t43))) % 0.38/0.58 (define @t46 () (@var "BOUND_VARIABLE_7605" (-> tptp.b Bool))) % 0.38/0.58 (define @t47 () (not (_ @t46 @t42))) % 0.38/0.58 (define @t48 () (@var "BOUND_VARIABLE_7603" (-> tptp.b Bool))) % 0.38/0.58 (define @t49 () (not (_ @t14 @t48 @t46))) % 0.38/0.58 (define @t50 () (@var "BOUND_VARIABLE_7542" (-> tptp.b Bool))) % 0.38/0.58 (define @t51 () (_ @t50 @t1)) % 0.38/0.58 (define @t52 () (not (_ @t4 @t50))) % 0.38/0.58 (define @t53 () (@list @t1 @t50)) % 0.38/0.58 (define @t54 () (not (forall @t53 (or (not (_ @t48 @t1)) @t52 @t51)))) % 0.38/0.58 (define @t55 () (@var "BOUND_VARIABLE_7507" tptp.b)) % 0.38/0.58 (define @t56 () (_ @t24 @t55)) % 0.38/0.58 (define @t57 () (@var "BOUND_VARIABLE_7505" (-> tptp.b Bool))) % 0.38/0.58 (define @t58 () (not (_ @t57 @t55))) % 0.38/0.58 (define @t59 () (@var "BOUND_VARIABLE_7503" (-> tptp.b Bool))) % 0.38/0.58 (define @t60 () (not (_ @t14 @t59 @t57))) % 0.38/0.58 (define @t61 () (_ @t24 @t23)) % 0.38/0.58 (define @t62 () (not (forall @t27 (or (not (_ @t59 @t23)) @t61)))) % 0.38/0.58 (define @t63 () (_ @t4 @t24)) % 0.38/0.58 (define @t64 () (not @t63)) % 0.38/0.58 (define @t65 () (or @t64 @t62 @t60 @t58 @t56)) % 0.38/0.58 (define @t66 () (@list @t24 @t59 @t57 @t55)) % 0.38/0.58 (define @t67 () (forall @t66 @t65)) % 0.38/0.58 (define @t68 () (not @t67)) % 0.38/0.58 (define @t69 () (or @t68 @t54 @t49 @t47 @t45 @t44)) % 0.38/0.58 (define @t70 () (or @t54 @t49 @t47 @t45 @t44)) % 0.38/0.58 (define @t71 () (or @t68 @t70)) % 0.38/0.58 (define @t72 () (@list @t14 @t4 @t48 @t46 @t42 @t43)) % 0.38/0.58 (define @t73 () (forall @t72 @t71)) % 0.38/0.58 (define @t74 () (@list @t48 @t46 @t42 @t43)) % 0.38/0.58 (define @t75 () (forall @t74 @t71)) % 0.38/0.58 (define @t76 () (forall @t74 @t70)) % 0.38/0.58 (define @t77 () (@var "BOUND_VARIABLE_7585" (-> tptp.b Bool))) % 0.38/0.58 (define @t78 () (@var "BOUND_VARIABLE_7583" tptp.b)) % 0.38/0.58 (define @t79 () (or @t68 @t76)) % 0.38/0.58 (define @t80 () (_ @t77 @t78)) % 0.38/0.58 (define @t81 () (not (_ @t4 @t77))) % 0.38/0.58 (define @t82 () (not (_ @t8 @t78))) % 0.38/0.58 (define @t83 () (_ @t14 @t13 @t8)) % 0.38/0.58 (define @t84 () (not @t83)) % 0.38/0.58 (define @t85 () (_ @t13 @t1)) % 0.38/0.58 (define @t86 () (not @t85)) % 0.38/0.58 (define @t87 () (or @t86 @t52 @t51)) % 0.38/0.58 (define @t88 () (forall @t53 @t87)) % 0.38/0.58 (define @t89 () (not @t88)) % 0.38/0.58 (define @t90 () (or @t89 @t84 @t82 @t81 @t80)) % 0.38/0.58 (define @t91 () (@list @t13 @t8 @t78 @t77)) % 0.38/0.58 (define @t92 () (forall @t91 @t90)) % 0.38/0.58 (define @t93 () (or @t82 @t81 @t80)) % 0.38/0.58 (define @t94 () (or @t89 @t84 @t93)) % 0.38/0.58 (define @t95 () (forall @t91 @t94)) % 0.38/0.58 (define @t96 () (@list @t78 @t77)) % 0.38/0.58 (define @t97 () (forall @t96 @t94)) % 0.38/0.58 (define @t98 () (forall @t96 @t93)) % 0.38/0.58 (define @t99 () (@var "BOUND_VARIABLE_7563" (-> tptp.b Bool))) % 0.38/0.58 (define @t100 () (or @t89 @t84 @t98)) % 0.38/0.58 (define @t101 () (_ @t99 @t1)) % 0.38/0.58 (define @t102 () (not (_ @t4 @t99))) % 0.38/0.58 (define @t103 () (_ @t8 @t1)) % 0.38/0.58 (define @t104 () (not @t103)) % 0.38/0.58 (define @t105 () (or @t104 @t102 @t101)) % 0.38/0.58 (define @t106 () (@list @t1 @t99)) % 0.38/0.58 (define @t107 () (forall @t106 @t105)) % 0.38/0.58 (define @t108 () (not @t15)) % 0.38/0.58 (define @t109 () (or @t89 @t108 @t107)) % 0.38/0.58 (define @t110 () (and @t88 @t15)) % 0.38/0.58 (define @t111 () (or @t102 @t101)) % 0.38/0.58 (define @t112 () (or @t104 @t111)) % 0.38/0.58 (define @t113 () (forall @t106 @t112)) % 0.38/0.58 (define @t114 () (@list @t99)) % 0.38/0.58 (define @t115 () (forall @t114 @t112)) % 0.38/0.58 (define @t116 () (forall @t114 @t111)) % 0.38/0.58 (define @t117 () (@list @t2)) % 0.38/0.58 (define @t118 () (or @t104 @t116)) % 0.38/0.58 (define @t119 () (_ @t2 @t1)) % 0.38/0.58 (define @t120 () (_ @t4 @t2)) % 0.38/0.58 (define @t121 () (forall @t6 (or (not @t120) @t119))) % 0.38/0.58 (define @t122 () (not @t9)) % 0.38/0.58 (define @t123 () (or @t122 @t121)) % 0.38/0.58 (define @t124 () (not @t5)) % 0.38/0.58 (define @t125 () (or @t124 @t3)) % 0.38/0.58 (define @t126 () (or @t52 @t51)) % 0.38/0.58 (define @t127 () (or @t86 @t126)) % 0.38/0.58 (define @t128 () (forall @t53 @t127)) % 0.38/0.58 (define @t129 () (@list @t50)) % 0.38/0.58 (define @t130 () (forall @t129 @t127)) % 0.38/0.58 (define @t131 () (forall @t129 @t126)) % 0.38/0.58 (define @t132 () (or @t86 @t131)) % 0.38/0.58 (define @t133 () (not @t16)) % 0.38/0.58 (define @t134 () (or @t133 @t121)) % 0.38/0.58 (define @t135 () (or @t62 @t60 @t58 @t56)) % 0.38/0.58 (define @t136 () (or @t64 @t135)) % 0.38/0.58 (define @t137 () (forall @t66 @t136)) % 0.38/0.58 (define @t138 () (@list @t59 @t57 @t55)) % 0.38/0.58 (define @t139 () (forall @t138 @t136)) % 0.38/0.58 (define @t140 () (forall @t138 @t135)) % 0.38/0.58 (define @t141 () (@var "BOUND_VARIABLE_7483" tptp.b)) % 0.38/0.58 (define @t142 () (or @t64 @t140)) % 0.38/0.58 (define @t143 () (_ @t24 @t141)) % 0.38/0.58 (define @t144 () (not (_ @t8 @t141))) % 0.38/0.58 (define @t145 () (_ @t13 @t23)) % 0.38/0.58 (define @t146 () (forall @t27 (or (not @t145) @t61))) % 0.38/0.58 (define @t147 () (not @t146)) % 0.38/0.58 (define @t148 () (or @t147 @t84 @t144 @t143)) % 0.38/0.58 (define @t149 () (@list @t13 @t8 @t141)) % 0.38/0.58 (define @t150 () (forall @t149 @t148)) % 0.38/0.58 (define @t151 () (not @t34)) % 0.38/0.58 (define @t152 () (or @t151 @t150)) % 0.38/0.58 (define @t153 () (or @t144 @t143)) % 0.38/0.58 (define @t154 () (or @t147 @t84 @t153)) % 0.38/0.58 (define @t155 () (forall @t149 @t154)) % 0.38/0.58 (define @t156 () (@list @t141)) % 0.38/0.58 (define @t157 () (forall @t156 @t154)) % 0.38/0.58 (define @t158 () (forall @t156 @t153)) % 0.38/0.58 (define @t159 () (or @t147 @t84 @t158)) % 0.38/0.58 (define @t160 () (_ @t8 @t23)) % 0.38/0.58 (define @t161 () (forall @t27 (or (not @t160) @t61))) % 0.38/0.58 (define @t162 () (or @t147 @t108 @t161)) % 0.38/0.58 (define @t163 () (and @t146 @t15)) % 0.38/0.58 (define @t164 () (not @t26)) % 0.38/0.58 (define @t165 () (or @t164 @t25)) % 0.38/0.58 (define @t166 () (not @t29)) % 0.38/0.58 (define @t167 () (or @t166 @t25)) % 0.38/0.58 (define @t168 () (forall @t72 @t69)) % 0.38/0.58 (define @t169 () (@quantifiers_skolemize @t168 1)) % 0.38/0.58 (define @t170 () (@quantifiers_skolemize @t168 2)) % 0.38/0.58 (define @t171 () (forall @t53 (or (not (_ @t170 @t1)) (not (_ @t169 @t50)) @t51))) % 0.38/0.58 (define @t172 () (@quantifiers_skolemize @t168 4)) % 0.38/0.58 (define @t173 () (@quantifiers_skolemize @t168 5)) % 0.38/0.58 (define @t174 () (_ @t173 @t172)) % 0.38/0.58 (define @t175 () (_ @t169 @t173)) % 0.38/0.58 (define @t176 () (not @t175)) % 0.38/0.58 (define @t177 () (@quantifiers_skolemize @t168 3)) % 0.38/0.58 (define @t178 () (_ @t177 @t172)) % 0.38/0.58 (define @t179 () (not @t178)) % 0.38/0.58 (define @t180 () (@quantifiers_skolemize @t168 0)) % 0.38/0.58 (define @t181 () (_ @t180 @t170 @t177)) % 0.38/0.58 (define @t182 () (not @t181)) % 0.38/0.58 (define @t183 () (not @t171)) % 0.38/0.58 (define @t184 () (forall @t66 (or (not (_ @t169 @t24)) @t62 (not (_ @t180 @t59 @t57)) @t58 @t56))) % 0.38/0.58 (define @t185 () (not @t184)) % 0.38/0.58 (define @t186 () (or @t185 @t183 @t182 @t179 @t176 @t174)) % 0.38/0.58 (define @t187 () (@list true)) % 0.38/0.58 (define @t188 () (@list @t186)) % 0.38/0.58 (define @t189 () (forall @t27 (or (not (_ @t170 @t23)) (_ @t173 @t23)))) % 0.38/0.58 (define @t190 () (not @t189)) % 0.38/0.58 (define @t191 () (or @t176 @t190 @t182 @t179 @t174)) % 0.38/0.58 (define @t192 () (@quantifiers_skolemize @t189 0)) % 0.38/0.58 (define @t193 () (_ @t173 @t192)) % 0.38/0.58 (define @t194 () (_ @t170 @t192)) % 0.38/0.58 (define @t195 () (not @t194)) % 0.38/0.58 (define @t196 () (or @t195 @t193)) % 0.38/0.58 (define @t197 () (@list @t196)) % 0.38/0.58 (define @t198 () (or @t195 @t176 @t193)) % 0.38/0.58 (define @t199 () (not @t198)) % 0.38/0.58 (assume @p1 @t41) % 0.38/0.58 (assume @p2 true) % 0.38/0.58 (step @p3 :rule aci_norm :args ((= @t71 @t69))) % 0.38/0.58 (step @p4 :rule cong :premises (@p3) :args (@t73)) % 0.38/0.58 (step @p5 :rule quant-merge-prenex :args ((= (forall @t39 @t75) @t73))) % 0.38/0.58 (step @p6 :rule alpha_equiv :args (@t76 (@list @t48 @t46 @t42 @t43) (@list @t13 @t8 @t78 @t77))) % 0.38/0.58 (step @p7 :rule refl :args (@t68)) % 0.38/0.58 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t79)) % 0.38/0.58 (step @p9 :rule quant-miniscope-or :args ((= @t75 @t79))) % 0.38/0.58 (step @p10 :rule trans :premises (@p9 @p8)) % 0.38/0.58 (step @p11 :rule symm :premises (@p10)) % 0.38/0.58 (step @p12 :rule cong :premises (@p11) :args ((forall @t39 (or @t68 @t92)))) % 0.38/0.58 (step @p13 :rule trans :premises (@p12 @p5)) % 0.38/0.58 (step @p14 :rule trans :premises (@p13 @p4)) % 0.38/0.58 (step @p15 :rule bool-impl-elim :args (@t67 @t92)) % 0.38/0.58 (step @p16 :rule cong :premises (@p15) :args ((forall @t39 (=> @t67 @t92)))) % 0.38/0.58 (step @p17 :rule trans :premises (@p16 @p14)) % 0.38/0.58 (step @p18 :rule aci_norm :args ((= @t94 @t90))) % 0.38/0.58 (step @p19 :rule cong :premises (@p18) :args (@t95)) % 0.38/0.58 (step @p20 :rule quant-merge-prenex :args ((= (forall @t21 @t97) @t95))) % 0.38/0.58 (step @p21 :rule alpha_equiv :args (@t98 (@list @t78 @t77) (@list @t1 @t99))) % 0.38/0.58 (step @p22 :rule refl :args (@t84)) % 0.38/0.58 (step @p23 :rule refl :args (@t89)) % 0.38/0.58 (step @p24 :rule nary_cong :premises (@p23 @p22 @p21) :args (@t100)) % 0.38/0.58 (step @p25 :rule quant-miniscope-or :args ((= @t97 @t100))) % 0.38/0.58 (step @p26 :rule trans :premises (@p25 @p24)) % 0.38/0.58 (step @p27 :rule symm :premises (@p26)) % 0.38/0.58 (step @p28 :rule cong :premises (@p27) :args ((forall @t21 (or @t89 @t84 @t107)))) % 0.38/0.58 (step @p29 :rule trans :premises (@p28 @p20)) % 0.38/0.58 (step @p30 :rule trans :premises (@p29 @p19)) % 0.38/0.58 (step @p31 :rule refl :args (@t107)) % 0.38/0.58 (step @p32 :rule refl :args (@t83)) % 0.38/0.58 (step @p33 :rule refl :args (@t15)) % 0.38/0.58 (step @p34 :rule cong :premises (@p33 @p32) :args ((= @t15 @t83))) % 0.38/0.58 (step @p35 :rule symm :premises (@p34)) % 0.38/0.58 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 0.38/0.58 (step @p37 :rule cong :premises (@p36) :args (@t108)) % 0.38/0.58 (step @p38 :rule nary_cong :premises (@p23 @p37 @p31) :args (@t109)) % 0.38/0.58 (step @p39 :rule cong :premises (@p38) :args ((forall @t21 @t109))) % 0.38/0.58 (step @p40 :rule trans :premises (@p39 @p30)) % 0.38/0.58 (step @p41 :rule aci_norm :args ((= (or (or @t89 @t108) @t107) @t109))) % 0.38/0.58 (step @p42 :rule bool-and-de-morgan :args (@t88 @t15 true)) % 0.38/0.58 (step @p43 :rule nary_cong :premises (@p42 @p31) :args ((or (not @t110) @t107))) % 0.38/0.58 (step @p44 :rule trans :premises (@p43 @p41)) % 0.38/0.58 (step @p45 :rule bool-impl-elim :args (@t110 @t107)) % 0.38/0.58 (step @p46 :rule trans :premises (@p45 @p44)) % 0.38/0.58 (step @p47 :rule cong :premises (@p46) :args ((forall @t21 (=> @t110 @t107)))) % 0.38/0.58 (step @p48 :rule trans :premises (@p47 @p40)) % 0.38/0.58 (step @p49 :rule aci_norm :args ((= @t112 @t105))) % 0.38/0.58 (step @p50 :rule cong :premises (@p49) :args (@t113)) % 0.38/0.58 (step @p51 :rule quant-merge-prenex :args ((= (forall @t11 @t115) @t113))) % 0.38/0.58 (step @p52 :rule alpha_equiv :args (@t116 (@list @t99) @t117)) % 0.38/0.58 (step @p53 :rule refl :args (@t104)) % 0.38/0.58 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t118)) % 0.38/0.58 (step @p55 :rule quant-miniscope-or :args ((= @t115 @t118))) % 0.38/0.58 (step @p56 :rule trans :premises (@p55 @p54)) % 0.38/0.58 (step @p57 :rule symm :premises (@p56)) % 0.38/0.58 (step @p58 :rule cong :premises (@p57) :args ((forall @t11 (or @t104 @t121)))) % 0.38/0.58 (step @p59 :rule trans :premises (@p58 @p51)) % 0.38/0.58 (step @p60 :rule trans :premises (@p59 @p50)) % 0.38/0.58 (step @p61 :rule refl :args (@t121)) % 0.38/0.58 (step @p62 :rule refl :args (@t103)) % 0.38/0.58 (step @p63 :rule refl :args (@t9)) % 0.38/0.58 (step @p64 :rule cong :premises (@p63 @p62) :args ((= @t9 @t103))) % 0.38/0.58 (step @p65 :rule symm :premises (@p64)) % 0.38/0.58 (step @p66 :rule eq_resolve :premises (@p63 @p65)) % 0.38/0.58 (step @p67 :rule cong :premises (@p66) :args (@t122)) % 0.38/0.58 (step @p68 :rule nary_cong :premises (@p67 @p61) :args (@t123)) % 0.38/0.58 (step @p69 :rule cong :premises (@p68) :args ((forall @t11 @t123))) % 0.38/0.58 (step @p70 :rule trans :premises (@p69 @p60)) % 0.38/0.58 (step @p71 :rule bool-impl-elim :args (@t9 @t121)) % 0.38/0.58 (step @p72 :rule cong :premises (@p71) :args ((forall @t11 (=> @t9 @t121)))) % 0.38/0.58 (step @p73 :rule trans :premises (@p72 @p70)) % 0.38/0.58 (step @p74 :rule refl :args (@t119)) % 0.38/0.58 (step @p75 :rule refl :args (@t3)) % 0.38/0.58 (step @p76 :rule cong :premises (@p75 @p74) :args ((= @t3 @t119))) % 0.38/0.58 (step @p77 :rule symm 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(step @p109 :rule cong :premises (@p108 @p107) :args ((= @t16 @t85))) % 0.38/0.58 (step @p110 :rule symm :premises (@p109)) % 0.38/0.58 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 0.38/0.58 (step @p112 :rule cong :premises (@p111) :args (@t133)) % 0.38/0.58 (step @p113 :rule nary_cong :premises (@p112 @p61) :args (@t134)) % 0.38/0.58 (step @p114 :rule cong :premises (@p113) :args ((forall @t11 @t134))) % 0.38/0.58 (step @p115 :rule trans :premises (@p114 @p106)) % 0.38/0.58 (step @p116 :rule bool-impl-elim :args (@t16 @t121)) % 0.38/0.58 (step @p117 :rule cong :premises (@p116) :args ((forall @t11 (=> @t16 @t121)))) % 0.38/0.58 (step @p118 :rule trans :premises (@p117 @p115)) % 0.38/0.58 (step @p119 :rule refl :args (@t16)) % 0.38/0.58 (step @p120 :rule cong :premises (@p119 @p89) :args (@t17)) % 0.38/0.58 (step @p121 :rule cong :premises (@p120) :args (@t18)) % 0.38/0.58 (step @p122 :rule trans :premises (@p121 @p118)) % 0.38/0.58 (step @p123 :rule nary_cong :premises (@p122 @p94) :args (@t19)) % 0.38/0.58 (step @p124 :rule cong :premises (@p123 @p93) :args (@t20)) % 0.38/0.58 (step @p125 :rule cong :premises (@p124) :args (@t22)) % 0.38/0.58 (step @p126 :rule trans :premises (@p125 @p48)) % 0.38/0.58 (step @p127 :rule aci_norm :args ((= @t136 @t65))) % 0.38/0.58 (step @p128 :rule cong :premises (@p127) :args (@t137)) % 0.38/0.58 (step @p129 :rule quant-merge-prenex :args ((= (forall @t36 @t139) @t137))) % 0.38/0.58 (step @p130 :rule alpha_equiv :args (@t140 (@list @t59 @t57 @t55) (@list @t13 @t8 @t141))) % 0.38/0.58 (step @p131 :rule refl :args (@t64)) % 0.38/0.58 (step @p132 :rule nary_cong :premises (@p131 @p130) :args (@t142)) % 0.38/0.58 (step @p133 :rule quant-miniscope-or :args ((= @t139 @t142))) % 0.38/0.58 (step @p134 :rule trans :premises (@p133 @p132)) % 0.38/0.58 (step @p135 :rule symm :premises (@p134)) % 0.38/0.58 (step @p136 :rule cong :premises (@p135) :args ((forall @t36 (or @t64 @t150)))) % 0.38/0.58 (step @p137 :rule trans :premises (@p136 @p129)) % 0.38/0.58 (step @p138 :rule trans :premises (@p137 @p128)) % 0.38/0.58 (step @p139 :rule refl :args (@t150)) % 0.38/0.58 (step @p140 :rule refl :args (@t63)) % 0.38/0.58 (step @p141 :rule refl :args (@t34)) % 0.38/0.58 (step @p142 :rule cong :premises (@p141 @p140) :args ((= @t34 @t63))) % 0.38/0.58 (step @p143 :rule symm :premises (@p142)) % 0.38/0.58 (step @p144 :rule eq_resolve :premises (@p141 @p143)) % 0.38/0.58 (step @p145 :rule cong :premises (@p144) :args (@t151)) % 0.38/0.58 (step @p146 :rule nary_cong :premises (@p145 @p139) :args (@t152)) % 0.38/0.58 (step @p147 :rule cong :premises (@p146) :args ((forall @t36 @t152))) % 0.38/0.58 (step @p148 :rule trans :premises (@p147 @p138)) % 0.38/0.58 (step @p149 :rule bool-impl-elim :args (@t34 @t150)) % 0.38/0.58 (step @p150 :rule cong :premises (@p149) :args ((forall @t36 (=> @t34 @t150)))) % 0.38/0.58 (step @p151 :rule trans :premises (@p150 @p148)) % 0.38/0.58 (step @p152 :rule aci_norm :args ((= @t154 @t148))) % 0.38/0.58 (step @p153 :rule cong :premises (@p152) :args (@t155)) % 0.38/0.58 (step @p154 :rule quant-merge-prenex :args ((= (forall @t21 @t157) @t155))) % 0.38/0.58 (step @p155 :rule alpha_equiv :args (@t158 (@list @t141) (@list @t23))) % 0.38/0.58 (step @p156 :rule refl :args (@t147)) % 0.38/0.58 (step @p157 :rule nary_cong :premises (@p156 @p22 @p155) :args (@t159)) % 0.38/0.58 (step @p158 :rule quant-miniscope-or :args ((= @t157 @t159))) % 0.38/0.58 (step @p159 :rule trans :premises (@p158 @p157)) % 0.38/0.58 (step @p160 :rule symm :premises (@p159)) % 0.38/0.58 (step @p161 :rule cong :premises (@p160) :args ((forall @t21 (or @t147 @t84 @t161)))) % 0.38/0.58 (step @p162 :rule trans :premises (@p161 @p154)) % 0.38/0.58 (step @p163 :rule trans :premises (@p162 @p153)) % 0.38/0.58 (step @p164 :rule refl :args (@t161)) % 0.38/0.58 (step @p165 :rule nary_cong :premises (@p156 @p37 @p164) :args (@t162)) % 0.38/0.58 (step @p166 :rule cong :premises (@p165) :args ((forall @t21 @t162))) % 0.38/0.58 (step @p167 :rule trans :premises (@p166 @p163)) % 0.38/0.58 (step @p168 :rule aci_norm :args ((= (or (or @t147 @t108) @t161) @t162))) % 0.38/0.58 (step @p169 :rule bool-and-de-morgan :args (@t146 @t15 true)) % 0.38/0.58 (step @p170 :rule nary_cong :premises (@p169 @p164) :args ((or (not @t163) @t161))) % 0.38/0.58 (step @p171 :rule trans :premises (@p170 @p168)) % 0.38/0.58 (step @p172 :rule bool-impl-elim :args (@t163 @t161)) % 0.38/0.58 (step @p173 :rule trans :premises (@p172 @p171)) % 0.38/0.58 (step @p174 :rule cong :premises (@p173) :args ((forall @t21 (=> @t163 @t161)))) % 0.38/0.58 (step @p175 :rule trans :premises (@p174 @p167)) % 0.38/0.58 (step @p176 :rule refl :args (@t61)) % 0.38/0.58 (step @p177 :rule refl :args (@t25)) % 0.38/0.58 (step @p178 :rule cong :premises (@p177 @p176) :args ((= @t25 @t61))) % 0.38/0.58 (step @p179 :rule symm :premises (@p178)) % 0.38/0.58 (step @p180 :rule eq_resolve :premises (@p177 @p179)) % 0.38/0.58 (step @p181 :rule refl :args (@t160)) % 0.38/0.58 (step @p182 :rule refl :args (@t26)) % 0.38/0.58 (step @p183 :rule cong :premises (@p182 @p181) :args ((= @t26 @t160))) % 0.38/0.58 (step @p184 :rule symm :premises (@p183)) % 0.38/0.58 (step @p185 :rule eq_resolve :premises (@p182 @p184)) % 0.38/0.58 (step @p186 :rule cong :premises (@p185) :args (@t164)) % 0.38/0.58 (step @p187 :rule nary_cong :premises (@p186 @p180) :args (@t165)) % 0.38/0.58 (step @p188 :rule cong :premises (@p187) :args ((forall @t27 @t165))) % 0.38/0.58 (step @p189 :rule bool-impl-elim :args (@t26 @t25)) % 0.38/0.58 (step @p190 :rule cong :premises (@p189) :args (@t28)) % 0.38/0.58 (step @p191 :rule trans :premises (@p190 @p188)) % 0.38/0.58 (step @p192 :rule refl :args (@t145)) % 0.38/0.58 (step @p193 :rule refl :args (@t29)) % 0.38/0.58 (step @p194 :rule cong :premises (@p193 @p192) :args ((= @t29 @t145))) % 0.38/0.58 (step @p195 :rule symm :premises (@p194)) % 0.38/0.58 (step @p196 :rule eq_resolve :premises (@p193 @p195)) % 0.38/0.58 (step @p197 :rule cong :premises (@p196) :args (@t166)) % 0.38/0.58 (step @p198 :rule nary_cong :premises (@p197 @p180) :args (@t167)) % 0.38/0.58 (step @p199 :rule cong :premises (@p198) :args ((forall @t27 @t167))) % 0.38/0.58 (step @p200 :rule bool-impl-elim :args (@t29 @t25)) % 0.38/0.58 (step @p201 :rule cong :premises (@p200) :args (@t30)) % 0.38/0.58 (step @p202 :rule trans :premises (@p201 @p199)) % 0.38/0.58 (step @p203 :rule nary_cong :premises (@p202 @p94) :args (@t31)) % 0.38/0.58 (step @p204 :rule cong :premises (@p203 @p191) :args (@t32)) % 0.38/0.58 (step @p205 :rule cong :premises (@p204) :args (@t33)) % 0.38/0.58 (step @p206 :rule trans :premises (@p205 @p175)) % 0.38/0.58 (step @p207 :rule refl :args (@t34)) % 0.38/0.58 (step @p208 :rule cong :premises (@p207 @p206) :args (@t35)) % 0.38/0.58 (step @p209 :rule cong :premises (@p208) :args (@t37)) % 0.38/0.58 (step @p210 :rule trans :premises (@p209 @p151)) % 0.38/0.58 (step @p211 :rule cong :premises (@p210 @p126) :args (@t38)) % 0.38/0.58 (step @p212 :rule cong :premises (@p211) :args (@t40)) % 0.38/0.58 (step @p213 :rule trans :premises (@p212 @p17)) % 0.38/0.58 (step @p214 :rule cong :premises (@p213) :args (@t41)) % 0.38/0.58 (step @p215 :rule eq_resolve :premises (@p1 @p214)) % 0.38/0.58 (step @p216 :rule skolemize :premises (@p215)) % 0.38/0.58 (step @p217 :rule bool-double-not-elim :args (@t171)) % 0.38/0.58 (step @p218 :rule refl :args (@t186)) % 0.38/0.58 (step @p219 :rule nary_cong :premises (@p218 @p217) :args ((or @t186 (not @t183)))) % 0.38/0.58 (step @p220 :rule cnf_or_neg :args (@t186 1)) % 0.38/0.58 (step @p221 :rule eq_resolve :premises (@p220 @p219)) % 0.38/0.58 (step @p222 :rule reordering :premises (@p221) :args ((or @t171 @t186))) % 0.38/0.58 (step @p223 :rule chain_m_resolution :premises (@p222 @p216) :args (@t171 @t187 @t188)) % 0.38/0.58 (step @p224 :rule bool-double-not-elim :args (@t184)) % 0.38/0.58 (step @p225 :rule nary_cong :premises (@p218 @p224) :args ((or @t186 (not @t185)))) % 0.38/0.58 (step @p226 :rule cnf_or_neg :args (@t186 0)) % 0.38/0.58 (step @p227 :rule eq_resolve :premises (@p226 @p225)) % 0.38/0.58 (step @p228 :rule reordering :premises (@p227) :args ((or @t184 @t186))) % 0.38/0.58 (step @p229 :rule chain_m_resolution :premises (@p228 @p216) :args (@t184 @t187 @t188)) % 0.38/0.58 (step @p230 :rule instantiate :premises (@p229) :args ((@list @t173 @t170 @t177 @t172))) % 0.38/0.58 (step @p231 :rule cnf_or_neg :args (@t186 5)) % 0.38/0.58 (step @p232 :rule chain_m_resolution :premises (@p231 @p216) :args ((not @t174) @t187 @t188)) % 0.38/0.58 (step @p233 :rule bool-double-not-elim :args (@t175)) % 0.38/0.58 (step @p234 :rule nary_cong :premises (@p218 @p233) :args ((or @t186 (not @t176)))) % 0.38/0.58 (step @p235 :rule cnf_or_neg :args (@t186 4)) % 0.38/0.58 (step @p236 :rule eq_resolve :premises (@p235 @p234)) % 0.38/0.58 (step @p237 :rule reordering :premises (@p236) :args ((or @t175 @t186))) % 0.38/0.58 (step @p238 :rule chain_m_resolution :premises (@p237 @p216) :args (@t175 @t187 @t188)) % 0.38/0.58 (step @p239 :rule bool-double-not-elim :args (@t178)) % 0.38/0.58 (step @p240 :rule nary_cong :premises (@p218 @p239) :args ((or @t186 (not @t179)))) % 0.38/0.58 (step @p241 :rule cnf_or_neg :args (@t186 3)) % 0.38/0.58 (step @p242 :rule eq_resolve :premises (@p241 @p240)) % 0.38/0.58 (step @p243 :rule reordering :premises (@p242) :args ((or @t178 @t186))) % 0.38/0.58 (step @p244 :rule chain_m_resolution :premises (@p243 @p216) :args (@t178 @t187 @t188)) % 0.38/0.58 (step @p245 :rule bool-double-not-elim :args (@t181)) % 0.38/0.58 (step @p246 :rule nary_cong :premises (@p218 @p245) :args ((or @t186 (not @t182)))) % 0.38/0.58 (step @p247 :rule cnf_or_neg :args (@t186 2)) % 0.38/0.58 (step @p248 :rule eq_resolve :premises (@p247 @p246)) % 0.38/0.58 (step @p249 :rule reordering :premises (@p248) :args ((or @t181 @t186))) % 0.38/0.58 (step @p250 :rule chain_m_resolution :premises (@p249 @p216) :args (@t181 @t187 @t188)) % 0.38/0.58 (step @p251 :rule cnf_or_pos :args (@t191)) % 0.38/0.58 (step @p252 :rule reordering :premises (@p251) :args ((or @t182 @t179 @t176 @t174 @t190 (not @t191)))) % 0.38/0.58 (step @p253 :rule chain_m_resolution :premises (@p252 @p250 @p244 @p238 @p232 @p230) :args (@t190 (@list false false false true false) (@list @t181 @t178 @t175 @t174 @t191))) % 0.38/0.58 (step @p254 :rule skolemize :premises (@p253)) % 0.38/0.58 (step @p255 :rule cnf_or_neg :args (@t196 1)) % 0.38/0.58 (step @p256 :rule chain_m_resolution :premises (@p255 @p254) :args ((not @t193) @t187 @t197)) % 0.38/0.58 (step @p257 :rule bool-double-not-elim :args (@t194)) % 0.38/0.58 (step @p258 :rule refl :args (@t196)) % 0.38/0.58 (step @p259 :rule nary_cong :premises (@p258 @p257) :args ((or @t196 (not @t195)))) % 0.38/0.58 (step @p260 :rule cnf_or_neg :args (@t196 0)) % 0.38/0.58 (step @p261 :rule eq_resolve :premises (@p260 @p259)) % 0.38/0.58 (step @p262 :rule reordering :premises (@p261) :args ((or @t194 @t196))) % 0.38/0.58 (step @p263 :rule chain_m_resolution :premises (@p262 @p254) :args (@t194 @t187 @t197)) % 0.38/0.58 (step @p264 :rule cnf_or_pos :args (@t198)) % 0.38/0.58 (step @p265 :rule reordering :premises (@p264) :args ((or @t176 @t195 @t193 @t199))) % 0.38/0.58 (step @p266 :rule chain_m_resolution :premises (@p265 @p238 @p263 @p256) :args (@t199 (@list false false true) (@list @t175 @t194 @t193))) % 0.38/0.58 (assume-push @p273 @t171) % 0.38/0.58 (step @p268 :rule instantiate :premises (@p223) :args ((@list @t192 @t173))) % 0.38/0.58 (step-pop @p274 :rule scope :premises (@p268)) % 0.38/0.58 (step @p269 :rule process_scope :premises (@p274) :args (@t198)) % 0.38/0.58 (step @p271 :rule implies_elim :premises (@p269)) % 0.38/0.58 (step @p272 false :rule chain_m_resolution :premises (@p271 @p266 @p223) :args (false (@list true false) (@list @t198 @t171))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------