%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV218^5 : 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 : n012.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 08:55:37 AM UTC 2026 % Result : Theorem 151.12s 151.45s % Output : Proof 151.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SEV218^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 18:20:33 EDT 2026 % 0.07/0.25 % CPUTime : % 0.07/0.33 %----Proving TH0 % 151.12/151.45 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 151.12/151.45 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 151.12/151.45 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 151.12/151.45 --- Run --ho-elim --full-saturate-quant at 18s... % 151.12/151.45 % SZS status Theorem % 151.12/151.45 % SZS output start Proof % 151.12/151.45 ( % 151.12/151.45 (declare-sort tptp.a 0) % 151.12/151.45 (declare-const tptp.cQ (-> tptp.a tptp.a Bool)) % 151.12/151.45 (define @t1 () (@var "Xz" tptp.a)) % 151.12/151.45 (define @t2 () (@var "Xx" tptp.a)) % 151.12/151.45 (define @t3 () (_ tptp.cQ @t2)) % 151.12/151.45 (define @t4 () (_ @t3 @t1)) % 151.12/151.45 (define @t5 () (@var "Xy" tptp.a)) % 151.12/151.45 (define @t6 () (_ tptp.cQ @t5)) % 151.12/151.45 (define @t7 () (_ @t6 @t1)) % 151.12/151.45 (define @t8 () (_ @t3 @t5)) % 151.12/151.45 (define @t9 () (and @t8 @t7)) % 151.12/151.45 (define @t10 () (@list @t2 @t5 @t1)) % 151.12/151.45 (define @t11 () (forall @t10 (=> @t9 @t4))) % 151.12/151.45 (define @t12 () (_ @t6 @t2)) % 151.12/151.45 (define @t13 () (@list @t2 @t5)) % 151.12/151.45 (define @t14 () (forall @t13 (=> @t8 @t12))) % 151.12/151.45 (define @t15 () (_ @t3 @t2)) % 151.12/151.45 (define @t16 () (@list @t2)) % 151.12/151.45 (define @t17 () (forall @t16 @t15)) % 151.12/151.45 (define @t18 () (and @t17 @t14 @t11)) % 151.12/151.45 (define @t19 () (@var "Xf" (-> tptp.a tptp.a Bool))) % 151.12/151.45 (define @t20 () (_ @t19 @t2)) % 151.12/151.45 (define @t21 () (_ @t20 @t2)) % 151.12/151.45 (define @t22 () (@var "Xx_0" tptp.a)) % 151.12/151.45 (define @t23 () (_ (_ tptp.cQ @t22) @t5)) % 151.12/151.45 (define @t24 () (_ @t20 @t5)) % 151.12/151.45 (define @t25 () (= @t24 @t23)) % 151.12/151.45 (define @t26 () (@list @t5)) % 151.12/151.45 (define @t27 () (forall @t26 @t25)) % 151.12/151.45 (define @t28 () (_ @t20 @t22)) % 151.12/151.45 (define @t29 () (=> @t28 @t27)) % 151.12/151.45 (define @t30 () (@list @t22)) % 151.12/151.45 (define @t31 () (forall @t30 @t29)) % 151.12/151.45 (define @t32 () (_ @t20 @t1)) % 151.12/151.45 (define @t33 () (@list @t1)) % 151.12/151.45 (define @t34 () (exists @t33 @t32)) % 151.12/151.45 (define @t35 () (and @t34 @t31 @t21)) % 151.12/151.45 (define @t36 () (forall @t16 @t35)) % 151.12/151.45 (define @t37 () (@list @t19)) % 151.12/151.45 (define @t38 () (exists @t37 @t36)) % 151.12/151.45 (define @t39 () (=> @t38 @t18)) % 151.12/151.45 (define @t40 () (not @t39)) % 151.12/151.45 (define @t41 () (@const 0 (@ho-elim-sort (-> tptp.a tptp.a Bool)))) % 151.12/151.45 (define @t42 () (@const 1 (-> (@ho-elim-sort (-> tptp.a tptp.a Bool)) tptp.a (@ho-elim-sort (-> tptp.a Bool))))) % 151.12/151.45 (define @t43 () (_ @t42 @t41 @t2)) % 151.12/151.45 (define @t44 () (@const 2 (-> (@ho-elim-sort (-> tptp.a Bool)) tptp.a Bool))) % 151.12/151.45 (define @t45 () (_ @t42 @t41 @t5)) % 151.12/151.45 (define @t46 () (not (_ @t44 @t43 @t5))) % 151.12/151.45 (define @t47 () (forall @t10 (or @t46 (not (_ @t44 @t45 @t1)) (_ @t44 @t43 @t1)))) % 151.12/151.45 (define @t48 () (forall @t13 (or @t46 (_ @t44 @t45 @t2)))) % 151.12/151.45 (define @t49 () (forall @t16 (_ @t44 @t43 @t2))) % 151.12/151.45 (define @t50 () (and @t49 @t48 @t47)) % 151.12/151.45 (define @t51 () (@var "BOUND_VARIABLE_7502" tptp.a)) % 151.12/151.45 (define @t52 () (@var "BOUND_VARIABLE_7577" (@ho-elim-sort (-> tptp.a tptp.a Bool)))) % 151.12/151.45 (define @t53 () (@list @t51)) % 151.12/151.45 (define @t54 () (not (forall @t53 (_ @t44 (_ @t42 @t52 @t51) @t51)))) % 151.12/151.45 (define @t55 () (@var "BOUND_VARIABLE_7474" tptp.a)) % 151.12/151.45 (define @t56 () (_ @t44 (_ @t42 @t41 @t22) @t55)) % 151.12/151.45 (define @t57 () (@var "BOUND_VARIABLE_7492" tptp.a)) % 151.12/151.45 (define @t58 () (_ @t42 @t52 @t57)) % 151.12/151.45 (define @t59 () (_ @t44 @t58 @t55)) % 151.12/151.45 (define @t60 () (not (_ @t44 @t58 @t22))) % 151.12/151.45 (define @t61 () (or @t60 (= @t56 @t59))) % 151.12/151.45 (define @t62 () (@list @t57 @t22 @t55)) % 151.12/151.45 (define @t63 () (forall @t62 @t61)) % 151.12/151.45 (define @t64 () (not @t63)) % 151.12/151.45 (define @t65 () (@var "BOUND_VARIABLE_7484" tptp.a)) % 151.12/151.45 (define @t66 () (@list @t65)) % 151.12/151.45 (define @t67 () (not (forall @t66 (not (forall @t33 (not (_ @t44 (_ @t42 @t52 @t65) @t1))))))) % 151.12/151.45 (define @t68 () (or @t67 @t64 @t54)) % 151.12/151.45 (define @t69 () (@list @t52)) % 151.12/151.45 (define @t70 () (forall @t69 @t68)) % 151.12/151.45 (define @t71 () (not @t70)) % 151.12/151.45 (define @t72 () (=> @t71 @t50)) % 151.12/151.45 (define @t73 () (not @t72)) % 151.12/151.45 (define @t74 () (tptp.cQ @t2 @t1)) % 151.12/151.45 (define @t75 () (tptp.cQ @t5 @t1)) % 151.12/151.45 (define @t76 () (tptp.cQ @t2 @t5)) % 151.12/151.45 (define @t77 () (not @t76)) % 151.12/151.45 (define @t78 () (tptp.cQ @t5 @t2)) % 151.12/151.45 (define @t79 () (tptp.cQ @t2 @t2)) % 151.12/151.45 (define @t80 () (_ @t19 @t51 @t51)) % 151.12/151.45 (define @t81 () (forall @t53 @t80)) % 151.12/151.45 (define @t82 () (not @t81)) % 151.12/151.45 (define @t83 () (_ @t19 @t57 @t55)) % 151.12/151.45 (define @t84 () (tptp.cQ @t22 @t55)) % 151.12/151.45 (define @t85 () (not (_ @t19 @t57 @t22))) % 151.12/151.45 (define @t86 () (forall @t62 (or @t85 (= @t84 @t83)))) % 151.12/151.45 (define @t87 () (not @t86)) % 151.12/151.45 (define @t88 () (forall @t66 (not (forall @t33 (not (_ @t19 @t65 @t1)))))) % 151.12/151.45 (define @t89 () (not @t88)) % 151.12/151.45 (define @t90 () (or @t89 @t87 @t82)) % 151.12/151.45 (define @t91 () (not @t7)) % 151.12/151.45 (define @t92 () (not @t8)) % 151.12/151.45 (define @t93 () (or @t92 @t91 @t4)) % 151.12/151.45 (define @t94 () (or @t92 @t12)) % 151.12/151.45 (define @t95 () (and @t88 @t86 @t81)) % 151.12/151.45 (define @t96 () (forall @t37 (not @t95))) % 151.12/151.45 (define @t97 () (not @t96)) % 151.12/151.45 (define @t98 () (_ (_ @t19 @t51) @t51)) % 151.12/151.45 (define @t99 () (forall @t53 @t98)) % 151.12/151.45 (define @t100 () (or @t85 (= @t83 @t84))) % 151.12/151.45 (define @t101 () (forall @t62 @t100)) % 151.12/151.45 (define @t102 () (@list @t22 @t55)) % 151.12/151.45 (define @t103 () (forall (@list @t57) (forall @t102 @t100))) % 151.12/151.45 (define @t104 () (forall @t16 @t21)) % 151.12/151.45 (define @t105 () (@list @t2)) % 151.12/151.45 (define @t106 () (= (_ @t19 @t2 @t55) @t84)) % 151.12/151.45 (define @t107 () (_ @t19 @t2 @t22)) % 151.12/151.45 (define @t108 () (not @t107)) % 151.12/151.45 (define @t109 () (or @t108 @t106)) % 151.12/151.45 (define @t110 () (forall @t102 @t109)) % 151.12/151.45 (define @t111 () (forall @t16 @t110)) % 151.12/151.45 (define @t112 () (_ @t19 @t2 @t1)) % 151.12/151.45 (define @t113 () (not (forall @t33 (not @t112)))) % 151.12/151.45 (define @t114 () (forall @t16 @t113)) % 151.12/151.45 (define @t115 () (and @t114 @t111 @t104)) % 151.12/151.45 (define @t116 () (@list @t55)) % 151.12/151.45 (define @t117 () (forall @t116 @t109)) % 151.12/151.45 (define @t118 () (forall @t116 @t106)) % 151.12/151.45 (define @t119 () (or @t108 @t118)) % 151.12/151.45 (define @t120 () (tptp.cQ @t22 @t5)) % 151.12/151.45 (define @t121 () (_ @t19 @t2 @t5)) % 151.12/151.45 (define @t122 () (forall @t26 (= @t121 @t120))) % 151.12/151.45 (define @t123 () (not @t28)) % 151.12/151.45 (define @t124 () (or @t123 @t122)) % 151.12/151.45 (define @t125 () (not @t32)) % 151.12/151.45 (define @t126 () (forall @t33 @t125)) % 151.12/151.45 (define @t127 () (not @t126)) % 151.12/151.45 (define @t128 () (forall @t69 (or @t67 (not (forall @t62 (or @t60 (= @t59 @t56)))) @t54))) % 151.12/151.45 (define @t129 () (@quantifiers_skolemize @t128 0)) % 151.12/151.45 (define @t130 () (forall @t53 (_ @t44 (_ @t42 @t129 @t51) @t51))) % 151.12/151.45 (define @t131 () (not @t130)) % 151.12/151.45 (define @t132 () (_ @t42 @t129 @t57)) % 151.12/151.45 (define @t133 () (_ @t44 @t132 @t55)) % 151.12/151.45 (define @t134 () (not (_ @t44 @t132 @t22))) % 151.12/151.45 (define @t135 () (forall @t62 (or @t134 (= @t56 @t133)))) % 151.12/151.45 (define @t136 () (not @t135)) % 151.12/151.45 (define @t137 () (not (forall @t66 (not (forall @t33 (not (_ @t44 (_ @t42 @t129 @t65) @t1))))))) % 151.12/151.45 (define @t138 () (or @t137 @t136 @t131)) % 151.12/151.45 (define @t139 () (not @t138)) % 151.12/151.45 (define @t140 () (not @t128)) % 151.12/151.45 (define @t141 () (or @t134 (= @t133 @t56))) % 151.12/151.45 (define @t142 () (forall @t62 @t141)) % 151.12/151.45 (define @t143 () (not @t142)) % 151.12/151.45 (define @t144 () (or @t137 @t143 @t131)) % 151.12/151.45 (define @t145 () (not @t144)) % 151.12/151.45 (define @t146 () (@list true)) % 151.12/151.45 (define @t147 () (@list @t138)) % 151.12/151.45 (define @t148 () (@quantifiers_skolemize @t47 0)) % 151.12/151.45 (define @t149 () (@quantifiers_skolemize @t47 2)) % 151.12/151.45 (define @t150 () (@quantifiers_skolemize @t47 1)) % 151.12/151.45 (define @t151 () (_ @t42 @t129 @t148)) % 151.12/151.45 (define @t152 () (_ @t44 @t151 @t150)) % 151.12/151.45 (define @t153 () (_ @t42 @t41 @t148)) % 151.12/151.45 (define @t154 () (_ @t44 @t153 @t150)) % 151.12/151.45 (define @t155 () (= @t154 @t152)) % 151.12/151.45 (define @t156 () (_ @t44 @t151 @t148)) % 151.12/151.45 (define @t157 () (not @t156)) % 151.12/151.45 (define @t158 () (or @t157 @t155)) % 151.12/151.45 (define @t159 () (@list false false)) % 151.12/151.45 (define @t160 () (@quantifiers_skolemize @t48 1)) % 151.12/151.45 (define @t161 () (@quantifiers_skolemize @t48 0)) % 151.12/151.45 (define @t162 () (_ @t44 (_ @t42 @t41 @t161) @t160)) % 151.12/151.45 (define @t163 () (_ @t44 (_ @t42 @t41 @t160) @t161)) % 151.12/151.45 (define @t164 () (not @t162)) % 151.12/151.45 (define @t165 () (or @t164 @t163)) % 151.12/151.45 (define @t166 () (_ @t42 @t129 @t161)) % 151.12/151.45 (define @t167 () (_ @t44 @t166 @t160)) % 151.12/151.45 (define @t168 () (= @t162 @t167)) % 151.12/151.45 (define @t169 () (_ @t44 @t166 @t161)) % 151.12/151.45 (define @t170 () (not @t169)) % 151.12/151.45 (define @t171 () (or @t170 @t168)) % 151.12/151.45 (define @t172 () (= @t163 @t169)) % 151.12/151.45 (define @t173 () (not @t167)) % 151.12/151.45 (define @t174 () (or @t173 @t172)) % 151.12/151.45 (define @t175 () (not @t165)) % 151.12/151.45 (define @t176 () (not @t48)) % 151.12/151.45 (define @t177 () (@list false)) % 151.12/151.45 (define @t178 () (@quantifiers_skolemize @t49 0)) % 151.12/151.45 (define @t179 () (_ @t44 (_ @t42 @t129 @t178) @t178)) % 151.12/151.45 (define @t180 () (_ @t44 (_ @t42 @t41 @t178) @t178)) % 151.12/151.45 (define @t181 () (= @t180 @t179)) % 151.12/151.45 (define @t182 () (not @t179)) % 151.12/151.45 (define @t183 () (or @t182 @t181)) % 151.12/151.45 (define @t184 () (not @t180)) % 151.12/151.45 (define @t185 () (not @t49)) % 151.12/151.45 (define @t186 () (not @t47)) % 151.12/151.45 (define @t187 () (_ @t44 @t153 @t149)) % 151.12/151.45 (define @t188 () (_ @t44 (_ @t42 @t41 @t150) @t149)) % 151.12/151.45 (define @t189 () (not @t188)) % 151.12/151.45 (define @t190 () (not @t154)) % 151.12/151.45 (define @t191 () (or @t190 @t189 @t187)) % 151.12/151.45 (define @t192 () (not @t191)) % 151.12/151.45 (define @t193 () (@list @t191)) % 151.12/151.45 (define @t194 () (_ @t44 @t151 @t149)) % 151.12/151.45 (define @t195 () (= @t188 @t194)) % 151.12/151.45 (define @t196 () (not @t152)) % 151.12/151.45 (define @t197 () (or @t196 @t195)) % 151.12/151.45 (define @t198 () (= @t187 @t194)) % 151.12/151.45 (define @t199 () (not @t198)) % 151.12/151.45 (define @t200 () (or @t157 @t198)) % 151.12/151.45 (assume @p1 @t40) % 151.12/151.45 (assume @p2 true) % 151.12/151.45 (step @p3 :rule refl :args (@t50)) % 151.12/151.45 (step @p4 :rule refl :args (@t54)) % 151.12/151.45 (step @p5 :rule eq-symm :args (@t56 @t59)) % 151.12/151.45 (step @p6 :rule refl :args (@t60)) % 151.12/151.45 (step @p7 :rule nary_cong :premises (@p6 @p5) :args (@t61)) % 151.12/151.45 (step @p8 :rule cong :premises (@p7) :args (@t63)) % 151.12/151.45 (step @p9 :rule cong :premises (@p8) :args (@t64)) % 151.12/151.45 (step @p10 :rule refl :args (@t67)) % 151.12/151.45 (step @p11 :rule nary_cong :premises (@p10 @p9 @p4) :args (@t68)) % 151.12/151.45 (step @p12 :rule cong :premises (@p11) :args (@t70)) % 151.12/151.45 (step @p13 :rule cong :premises (@p12) :args (@t71)) % 151.12/151.45 (step @p14 :rule cong :premises (@p13 @p3) :args (@t72)) % 151.12/151.45 (step @p15 :rule cong :premises (@p14) :args (@t73)) % 151.12/151.45 ; WARNING: add trust step for TRUST % 151.12/151.45 ; trust TRUST PREPROCESS_HO_ELIM % 151.12/151.45 (step @p16 :rule trust :premises () :args ((= (not (=> (not (forall @t37 @t90)) (and (forall @t16 @t79) (forall @t13 (or @t77 @t78)) (forall @t10 (or @t77 (not @t75) @t74))))) @t73))) % 151.12/151.45 (step @p17 :rule refl :args (@t74)) % 151.12/151.45 (step @p18 :rule refl :args (@t4)) % 151.12/151.45 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t4 @t74))) % 151.12/151.45 (step @p20 :rule symm :premises (@p19)) % 151.12/151.45 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 151.12/151.45 (step @p22 :rule refl :args (@t75)) % 151.12/151.45 (step @p23 :rule refl :args (@t7)) % 151.12/151.45 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t7 @t75))) % 151.12/151.45 (step @p25 :rule symm :premises (@p24)) % 151.12/151.45 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 151.12/151.45 (step @p27 :rule cong :premises (@p26) :args (@t91)) % 151.12/151.45 (step @p28 :rule refl :args (@t76)) % 151.12/151.45 (step @p29 :rule refl :args (@t8)) % 151.12/151.45 (step @p30 :rule cong :premises (@p29 @p28) :args ((= @t8 @t76))) % 151.12/151.45 (step @p31 :rule symm :premises (@p30)) % 151.12/151.45 (step @p32 :rule eq_resolve :premises (@p29 @p31)) % 151.12/151.45 (step @p33 :rule cong :premises (@p32) :args (@t92)) % 151.12/151.45 (step @p34 :rule nary_cong :premises (@p33 @p27 @p21) :args (@t93)) % 151.12/151.45 (step @p35 :rule cong :premises (@p34) :args ((forall @t10 @t93))) % 151.12/151.45 (step @p36 :rule aci_norm :args ((= (or (or @t92 @t91) @t4) @t93))) % 151.12/151.45 (step @p37 :rule bool-and-de-morgan :args (@t8 @t7 true)) % 151.12/151.45 (step @p38 :rule nary_cong :premises (@p37 @p18) :args ((or (not @t9) @t4))) % 151.12/151.45 (step @p39 :rule trans :premises (@p38 @p36)) % 151.12/151.45 (step @p40 :rule bool-impl-elim :args (@t9 @t4)) % 151.12/151.45 (step @p41 :rule trans :premises (@p40 @p39)) % 151.12/151.45 (step @p42 :rule cong :premises (@p41) :args (@t11)) % 151.12/151.45 (step @p43 :rule trans :premises (@p42 @p35)) % 151.12/151.45 (step @p44 :rule refl :args (@t78)) % 151.12/151.45 (step @p45 :rule refl :args (@t12)) % 151.12/151.45 (step @p46 :rule cong :premises (@p45 @p44) :args ((= @t12 @t78))) % 151.12/151.45 (step @p47 :rule symm :premises (@p46)) % 151.12/151.45 (step @p48 :rule eq_resolve :premises (@p45 @p47)) % 151.12/151.45 (step @p49 :rule nary_cong :premises (@p33 @p48) :args (@t94)) % 151.12/151.45 (step @p50 :rule cong :premises (@p49) :args ((forall @t13 @t94))) % 151.12/151.45 (step @p51 :rule bool-impl-elim :args (@t8 @t12)) % 151.12/151.45 (step @p52 :rule cong :premises (@p51) :args (@t14)) % 151.12/151.45 (step @p53 :rule trans :premises (@p52 @p50)) % 151.12/151.45 (step @p54 :rule refl :args (@t79)) % 151.12/151.45 (step @p55 :rule refl :args (@t15)) % 151.12/151.45 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t15 @t79))) % 151.12/151.45 (step @p57 :rule symm :premises (@p56)) % 151.12/151.45 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 151.12/151.45 (step @p59 :rule cong :premises (@p58) :args (@t17)) % 151.12/151.45 (step @p60 :rule nary_cong :premises (@p59 @p53 @p43) :args (@t18)) % 151.12/151.45 (step @p61 :rule aci_norm :args ((= (or @t89 (or @t87 @t82)) @t90))) % 151.12/151.45 (step @p62 :rule bool-and-de-morgan :args (@t86 @t81 true)) % 151.12/151.45 (step @p63 :rule refl :args (@t89)) % 151.12/151.45 (step @p64 :rule nary_cong :premises (@p63 @p62) :args ((or @t89 (not (and @t86 @t81))))) % 151.12/151.45 (step @p65 :rule bool-and-de-morgan :args (@t88 @t86 (and @t81))) % 151.12/151.45 (step @p66 :rule trans :premises (@p65 @p64)) % 151.12/151.45 (step @p67 :rule trans :premises (@p66 @p61)) % 151.12/151.45 (step @p68 :rule cong :premises (@p67) :args (@t96)) % 151.12/151.45 (step @p69 :rule cong :premises (@p68) :args (@t97)) % 151.12/151.45 (step @p70 :rule exists-elim :args ((= (exists @t37 @t95) @t97))) % 151.12/151.45 (step @p71 :rule trans :premises (@p70 @p69)) % 151.12/151.45 (step @p72 :rule refl :args (@t80)) % 151.12/151.45 (step @p73 :rule refl :args (@t98)) % 151.12/151.45 (step @p74 :rule cong :premises (@p73 @p72) :args ((= @t98 @t80))) % 151.12/151.45 (step @p75 :rule symm :premises (@p74)) % 151.12/151.45 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 151.12/151.45 (step @p77 :rule cong :premises (@p76) :args (@t99)) % 151.12/151.45 (step @p78 :rule eq-symm :args (@t83 @t84)) % 151.12/151.45 (step @p79 :rule refl :args (@t85)) % 151.12/151.45 (step @p80 :rule nary_cong :premises (@p79 @p78) :args (@t100)) % 151.12/151.45 (step @p81 :rule cong :premises (@p80) :args (@t101)) % 151.12/151.45 (step @p82 :rule quant-merge-prenex :args ((= @t103 @t101))) % 151.12/151.45 (step @p83 :rule trans :premises (@p82 @p81)) % 151.12/151.45 (step @p84 :rule refl :args (@t88)) % 151.12/151.45 (step @p85 :rule nary_cong :premises (@p84 @p83 @p77) :args ((and @t88 @t103 @t99))) % 151.12/151.45 (step @p86 :rule alpha_equiv :args (@t104 @t105 (@list @t51))) % 151.12/151.45 (step @p87 :rule alpha_equiv :args (@t111 @t105 (@list @t57))) % 151.12/151.45 (step @p88 :rule alpha_equiv :args (@t114 @t105 (@list @t65))) % 151.12/151.45 (step @p89 :rule nary_cong :premises (@p88 @p87 @p86) :args (@t115)) % 151.12/151.45 (step @p90 :rule quant-miniscope-and :args ((= (forall @t16 (and @t113 @t110 @t21)) @t115))) % 151.12/151.45 (step @p91 :rule trans :premises (@p90 @p89)) % 151.12/151.45 (step @p92 :rule trans :premises (@p91 @p85)) % 151.12/151.45 (step @p93 :rule refl :args (@t21)) % 151.12/151.45 (step @p94 :rule quant-merge-prenex :args ((= (forall @t30 @t117) @t110))) % 151.12/151.45 (step @p95 :rule alpha_equiv :args (@t118 (@list @t55) (@list @t5))) % 151.12/151.45 (step @p96 :rule refl :args (@t108)) % 151.12/151.45 (step @p97 :rule nary_cong :premises (@p96 @p95) :args (@t119)) % 151.12/151.45 (step @p98 :rule quant-miniscope-or :args ((= @t117 @t119))) % 151.12/151.45 (step @p99 :rule trans :premises (@p98 @p97)) % 151.12/151.45 (step @p100 :rule symm :premises (@p99)) % 151.12/151.45 (step @p101 :rule cong :premises (@p100) :args ((forall @t30 (or @t108 @t122)))) % 151.12/151.45 (step @p102 :rule trans :premises (@p101 @p94)) % 151.12/151.45 (step @p103 :rule refl :args (@t122)) % 151.12/151.45 (step @p104 :rule refl :args (@t107)) % 151.12/151.45 (step @p105 :rule refl :args (@t28)) % 151.12/151.45 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t28 @t107))) % 151.12/151.45 (step @p107 :rule symm :premises (@p106)) % 151.12/151.45 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 151.12/151.45 (step @p109 :rule cong :premises (@p108) :args (@t123)) % 151.12/151.45 (step @p110 :rule nary_cong :premises (@p109 @p103) :args (@t124)) % 151.12/151.45 (step @p111 :rule cong :premises (@p110) :args ((forall @t30 @t124))) % 151.12/151.45 (step @p112 :rule trans :premises (@p111 @p102)) % 151.12/151.45 (step @p113 :rule bool-impl-elim :args (@t28 @t122)) % 151.12/151.45 (step @p114 :rule cong :premises (@p113) :args ((forall @t30 (=> @t28 @t122)))) % 151.12/151.45 (step @p115 :rule trans :premises (@p114 @p112)) % 151.12/151.45 (step @p116 :rule refl :args (@t120)) % 151.12/151.45 (step @p117 :rule refl :args (@t23)) % 151.12/151.45 (step @p118 :rule cong :premises (@p117 @p116) :args ((= @t23 @t120))) % 151.12/151.45 (step @p119 :rule symm :premises (@p118)) % 151.12/151.45 (step @p120 :rule eq_resolve :premises (@p117 @p119)) % 151.12/151.45 (step @p121 :rule refl :args (@t121)) % 151.12/151.45 (step @p122 :rule refl :args (@t24)) % 151.12/151.45 (step @p123 :rule cong :premises (@p122 @p121) :args ((= @t24 @t121))) % 151.12/151.45 (step @p124 :rule symm :premises (@p123)) % 151.12/151.45 (step @p125 :rule eq_resolve :premises (@p122 @p124)) % 151.12/151.45 (step @p126 :rule cong :premises (@p125 @p120) :args (@t25)) % 151.12/151.45 (step @p127 :rule cong :premises (@p126) :args (@t27)) % 151.12/151.45 (step @p128 :rule refl :args (@t28)) % 151.12/151.45 (step @p129 :rule cong :premises (@p128 @p127) :args (@t29)) % 151.12/151.45 (step @p130 :rule cong :premises (@p129) :args (@t31)) % 151.12/151.45 (step @p131 :rule trans :premises (@p130 @p115)) % 151.12/151.45 (step @p132 :rule refl :args (@t112)) % 151.12/151.45 (step @p133 :rule refl :args (@t32)) % 151.12/151.45 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t32 @t112))) % 151.12/151.45 (step @p135 :rule symm :premises (@p134)) % 151.12/151.45 (step @p136 :rule eq_resolve :premises (@p133 @p135)) % 151.12/151.45 (step @p137 :rule cong :premises (@p136) :args (@t125)) % 151.12/151.45 (step @p138 :rule cong :premises (@p137) :args (@t126)) % 151.12/151.45 (step @p139 :rule cong :premises (@p138) :args (@t127)) % 151.12/151.45 (step @p140 :rule exists-elim :args ((= @t34 @t127))) % 151.12/151.45 (step @p141 :rule trans :premises (@p140 @p139)) % 151.12/151.45 (step @p142 :rule nary_cong :premises (@p141 @p131 @p93) :args (@t35)) % 151.12/151.45 (step @p143 :rule cong :premises (@p142) :args (@t36)) % 151.12/151.45 (step @p144 :rule trans :premises (@p143 @p92)) % 151.12/151.45 (step @p145 :rule cong :premises (@p144) :args (@t38)) % 151.12/151.45 (step @p146 :rule trans :premises (@p145 @p71)) % 151.12/151.45 (step @p147 :rule cong :premises (@p146 @p60) :args (@t39)) % 151.12/151.45 (step @p148 :rule cong :premises (@p147) :args (@t40)) % 151.12/151.45 (step @p149 :rule trans :premises (@p148 @p16 @p15)) % 151.12/151.45 (step @p150 :rule eq_resolve :premises (@p1 @p149)) % 151.12/151.45 (step @p151 :rule not_implies_elim1 :premises (@p150)) % 151.12/151.45 (step @p152 :rule refl :args (@t139)) % 151.12/151.45 (step @p153 :rule bool-double-not-elim :args (@t128)) % 151.12/151.45 (step @p154 :rule nary_cong :premises (@p153 @p152) :args ((or (not @t140) @t139))) % 151.12/151.45 (step @p155 :rule refl :args (@t131)) % 151.12/151.45 (step @p156 :rule eq-symm :args (@t133 @t56)) % 151.12/151.45 (step @p157 :rule refl :args (@t134)) % 151.12/151.45 (step @p158 :rule nary_cong :premises (@p157 @p156) :args (@t141)) % 151.12/151.45 (step @p159 :rule cong :premises (@p158) :args (@t142)) % 151.12/151.45 (step @p160 :rule cong :premises (@p159) :args (@t143)) % 151.12/151.45 (step @p161 :rule refl :args (@t137)) % 151.12/151.45 (step @p162 :rule nary_cong :premises (@p161 @p160 @p155) :args (@t144)) % 151.12/151.45 (step @p163 :rule cong :premises (@p162) :args (@t145)) % 151.12/151.45 (step @p164 :rule refl :args (@t140)) % 151.12/151.45 (step @p165 :rule cong :premises (@p164 @p163) :args ((=> @t140 @t145))) % 151.12/151.45 (assume-push @p285 @t140) % 151.12/151.45 (step @p167 :rule skolemize :premises (@p151)) % 151.12/151.45 (step-pop @p286 :rule scope :premises (@p167)) % 151.12/151.45 (step @p168 :rule process_scope :premises (@p286) :args (@t145)) % 151.12/151.45 (step @p170 :rule eq_resolve :premises (@p168 @p165)) % 151.12/151.45 (step @p171 :rule implies_elim :premises (@p170)) % 151.12/151.45 (step @p172 :rule eq_resolve :premises (@p171 @p154)) % 151.12/151.45 (step @p173 :rule chain_m_resolution :premises (@p172 @p151) :args (@t139 @t146 (@list @t128))) % 151.12/151.45 (step @p174 :rule bool-double-not-elim :args (@t130)) % 151.12/151.45 (step @p175 :rule refl :args (@t138)) % 151.12/151.45 (step @p176 :rule nary_cong :premises (@p175 @p174) :args ((or @t138 (not @t131)))) % 151.12/151.45 (step @p177 :rule cnf_or_neg :args (@t138 2)) % 151.12/151.45 (step @p178 :rule eq_resolve :premises (@p177 @p176)) % 151.12/151.45 (step @p179 :rule reordering :premises (@p178) :args ((or @t130 @t138))) % 151.12/151.45 (step @p180 :rule chain_m_resolution :premises (@p179 @p173) :args (@t130 @t146 @t147)) % 151.12/151.45 (step @p181 :rule instantiate :premises (@p180) :args ((@list @t148))) % 151.12/151.45 (step @p182 :rule bool-double-not-elim :args (@t135)) % 151.12/151.45 (step @p183 :rule nary_cong :premises (@p175 @p182) :args ((or @t138 (not @t136)))) % 151.12/151.45 (step @p184 :rule cnf_or_neg :args (@t138 1)) % 151.12/151.45 (step @p185 :rule eq_resolve :premises (@p184 @p183)) % 151.12/151.45 (step @p186 :rule reordering :premises (@p185) :args ((or @t135 @t138))) % 151.12/151.45 (step @p187 :rule chain_m_resolution :premises (@p186 @p173) :args (@t135 @t146 @t147)) % 151.12/151.45 (step @p188 :rule instantiate :premises (@p187) :args ((@list @t148 @t150 @t149))) % 151.12/151.45 (step @p189 :rule instantiate :premises (@p187) :args ((@list @t148 @t148 @t150))) % 151.12/151.45 (step @p190 :rule cnf_or_pos :args (@t158)) % 151.12/151.45 (step @p191 :rule reordering :premises (@p190) :args ((or @t155 @t157 (not @t158)))) % 151.12/151.45 (step @p192 :rule chain_m_resolution :premises (@p191 @p181 @p189) :args (@t155 @t159 (@list @t156 @t158))) % 151.12/151.45 (step @p193 :rule bool-double-not-elim :args (@t162)) % 151.12/151.45 (step @p194 :rule refl :args (@t165)) % 151.12/151.45 (step @p195 :rule nary_cong :premises (@p194 @p193) :args ((or @t165 (not @t164)))) % 151.12/151.45 (step @p196 :rule cnf_or_neg :args (@t165 0)) % 151.12/151.45 (step @p197 :rule eq_resolve :premises (@p196 @p195)) % 151.12/151.45 (step @p198 :rule reordering :premises (@p197) :args ((or @t162 @t165))) % 151.12/151.45 (step @p199 :rule cnf_or_neg :args (@t165 1)) % 151.12/151.45 (step @p200 :rule instantiate :premises (@p187) :args ((@list @t161 @t161 @t160))) % 151.12/151.45 (step @p201 :rule instantiate :premises (@p180) :args ((@list @t161))) % 151.12/151.45 (step @p202 :rule cnf_or_pos :args (@t171)) % 151.12/151.45 (step @p203 :rule reordering :premises (@p202) :args ((or @t170 @t168 (not @t171)))) % 151.12/151.45 (step @p204 :rule chain_m_resolution :premises (@p203 @p201 @p200) :args (@t168 @t159 (@list @t169 @t171))) % 151.12/151.45 (step @p205 :rule cnf_equiv_pos1 :args (@t168)) % 151.12/151.45 (step @p206 :rule reordering :premises (@p205) :args ((or @t164 @t167 (not @t168)))) % 151.12/151.45 (step @p207 :rule cnf_equiv_pos2 :args (@t172)) % 151.12/151.45 (step @p208 :rule reordering :premises (@p207) :args ((or @t163 @t170 (not @t172)))) % 151.12/151.45 (step @p209 :rule instantiate :premises (@p187) :args ((@list @t161 @t160 @t161))) % 151.12/151.45 (step @p210 :rule cnf_or_pos :args (@t174)) % 151.12/151.45 (step @p211 :rule reordering :premises (@p210) :args ((or @t173 @t172 (not @t174)))) % 151.12/151.45 (step @p212 :rule chain_m_resolution :premises (@p211 @p209 @p208 @p201 @p206 @p204 @p199 @p198) :args (@t165 (@list false true false false false true false) (@list @t174 @t172 @t169 @t167 @t168 @t163 @t162))) % 151.12/151.45 (step @p213 :rule refl :args (@t175)) % 151.12/151.45 (step @p214 :rule bool-double-not-elim :args (@t48)) % 151.12/151.45 (step @p215 :rule nary_cong :premises (@p214 @p213) :args ((or (not @t176) @t175))) % 151.12/151.45 (assume-push @p287 @t176) % 151.12/151.45 (step @p217 :rule skolemize :premises (@p287)) % 151.12/151.45 (step-pop @p288 :rule scope :premises (@p217)) % 151.12/151.45 (step @p218 :rule process_scope :premises (@p288) :args (@t175)) % 151.12/151.45 (step @p220 :rule implies_elim :premises (@p218)) % 151.12/151.45 (step @p221 :rule eq_resolve :premises (@p220 @p215)) % 151.12/151.45 (step @p222 :rule chain_m_resolution :premises (@p221 @p212) :args (@t48 @t177 (@list @t165))) % 151.12/151.45 (step @p223 :rule instantiate :premises (@p187) :args ((@list @t178 @t178 @t178))) % 151.12/151.45 (step @p224 :rule instantiate :premises (@p180) :args ((@list @t178))) % 151.12/151.45 (step @p225 :rule cnf_or_pos :args (@t183)) % 151.12/151.45 (step @p226 :rule reordering :premises (@p225) :args ((or @t182 @t181 (not @t183)))) % 151.12/151.45 (step @p227 :rule chain_m_resolution :premises (@p226 @p224 @p223) :args (@t181 @t159 (@list @t179 @t183))) % 151.12/151.45 (step @p228 :rule cnf_equiv_pos2 :args (@t181)) % 151.12/151.45 (step @p229 :rule reordering :premises (@p228) :args ((or @t180 @t182 (not @t181)))) % 151.12/151.45 (step @p230 :rule chain_m_resolution :premises (@p229 @p224 @p227) :args (@t180 @t159 (@list @t179 @t181))) % 151.12/151.45 (step @p231 :rule refl :args (@t184)) % 151.12/151.45 (step @p232 :rule bool-double-not-elim :args (@t49)) % 151.12/151.45 (step @p233 :rule nary_cong :premises (@p232 @p231) :args ((or (not @t185) @t184))) % 151.12/151.45 (assume-push @p289 @t185) % 151.12/151.45 (step @p235 :rule skolemize :premises (@p289)) % 151.12/151.45 (step-pop @p290 :rule scope :premises (@p235)) % 151.12/151.45 (step @p236 :rule process_scope :premises (@p290) :args (@t184)) % 151.12/151.45 (step @p238 :rule implies_elim :premises (@p236)) % 151.12/151.45 (step @p239 :rule eq_resolve :premises (@p238 @p233)) % 151.12/151.45 (step @p240 :rule chain_m_resolution :premises (@p239 @p230) :args (@t49 @t177 (@list @t180))) % 151.12/151.45 (step @p241 :rule not_implies_elim2 :premises (@p150)) % 151.12/151.45 (step @p242 :rule not_and :premises (@p241)) % 151.12/151.45 (step @p243 :rule chain_m_resolution :premises (@p242 @p240 @p222) :args (@t186 @t159 (@list @t49 @t48))) % 151.12/151.45 (step @p244 :rule refl :args (@t192)) % 151.12/151.45 (step @p245 :rule bool-double-not-elim :args (@t47)) % 151.12/151.45 (step @p246 :rule nary_cong :premises (@p245 @p244) :args ((or (not @t186) @t192))) % 151.12/151.45 (assume-push @p291 @t186) % 151.12/151.45 (step @p248 :rule skolemize :premises (@p291)) % 151.12/151.45 (step-pop @p292 :rule scope :premises (@p248)) % 151.12/151.45 (step @p249 :rule process_scope :premises (@p292) :args (@t192)) % 151.12/151.45 (step @p251 :rule implies_elim :premises (@p249)) % 151.12/151.45 (step @p252 :rule eq_resolve :premises (@p251 @p246)) % 151.12/151.45 (step @p253 :rule chain_m_resolution :premises (@p252 @p243) :args (@t192 @t146 (@list @t47))) % 151.12/151.45 (step @p254 :rule bool-double-not-elim :args (@t154)) % 151.12/151.45 (step @p255 :rule refl :args (@t191)) % 151.12/151.45 (step @p256 :rule nary_cong :premises (@p255 @p254) :args ((or @t191 (not @t190)))) % 151.12/151.45 (step @p257 :rule cnf_or_neg :args (@t191 0)) % 151.12/151.45 (step @p258 :rule eq_resolve :premises (@p257 @p256)) % 151.12/151.45 (step @p259 :rule reordering :premises (@p258) :args ((or @t154 @t191))) % 151.12/151.45 (step @p260 :rule chain_m_resolution :premises (@p259 @p253) :args (@t154 @t146 @t193)) % 151.12/151.45 (step @p261 :rule cnf_equiv_pos1 :args (@t155)) % 151.12/151.45 (step @p262 :rule reordering :premises (@p261) :args ((or @t190 @t152 (not @t155)))) % 151.12/151.45 (step @p263 :rule chain_m_resolution :premises (@p262 @p260 @p192) :args (@t152 @t159 (@list @t154 @t155))) % 151.12/151.45 (step @p264 :rule cnf_or_pos :args (@t197)) % 151.12/151.45 (step @p265 :rule reordering :premises (@p264) :args ((or @t196 @t195 (not @t197)))) % 151.12/151.45 (step @p266 :rule chain_m_resolution :premises (@p265 @p263 @p188) :args (@t195 @t159 (@list @t152 @t197))) % 151.12/151.45 (step @p267 :rule bool-double-not-elim :args (@t188)) % 151.12/151.45 (step @p268 :rule nary_cong :premises (@p255 @p267) :args ((or @t191 (not @t189)))) % 151.12/151.45 (step @p269 :rule cnf_or_neg :args (@t191 1)) % 151.12/151.45 (step @p270 :rule eq_resolve :premises (@p269 @p268)) % 151.12/151.45 (step @p271 :rule reordering :premises (@p270) :args ((or @t188 @t191))) % 151.12/151.45 (step @p272 :rule chain_m_resolution :premises (@p271 @p253) :args (@t188 @t146 @t193)) % 151.12/151.45 (step @p273 :rule cnf_equiv_pos1 :args (@t195)) % 151.12/151.45 (step @p274 :rule reordering :premises (@p273) :args ((or @t189 @t194 (not @t195)))) % 151.12/151.45 (step @p275 :rule chain_m_resolution :premises (@p274 @p272 @p266) :args (@t194 @t159 (@list @t188 @t195))) % 151.12/151.45 (step @p276 :rule cnf_or_neg :args (@t191 2)) % 151.12/151.45 (step @p277 :rule chain_m_resolution :premises (@p276 @p253) :args ((not @t187) @t146 @t193)) % 151.12/151.45 (step @p278 :rule cnf_equiv_pos2 :args (@t198)) % 151.12/151.45 (step @p279 :rule reordering :premises (@p278) :args ((or @t187 (not @t194) @t199))) % 151.12/151.45 (step @p280 :rule chain_m_resolution :premises (@p279 @p277 @p275) :args (@t199 (@list true false) (@list @t187 @t194))) % 151.12/151.45 (step @p281 :rule instantiate :premises (@p187) :args ((@list @t148 @t148 @t149))) % 151.12/151.45 (step @p282 :rule cnf_or_pos :args (@t200)) % 151.12/151.45 (step @p283 :rule reordering :premises (@p282) :args ((or @t198 @t157 (not @t200)))) % 151.12/151.45 (step @p284 false :rule chain_m_resolution :premises (@p283 @p281 @p280 @p181) :args (false (@list false true false) (@list @t200 @t198 @t156))) % 151.12/151.45 ) % 151.12/151.45 % SZS output end Proof % 151.12/151.45 % cvc5 exiting %------------------------------------------------------------------------------