%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG071+1 : TPTP v9.2.1. Released v2.7.0. % 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 08:05:09 AM UTC 2026 % Result : Theorem 0.37s 0.60s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG071+1 : TPTP v9.2.1. Released v2.7.0. % 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 : 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 : Wed Jun 3 01:39:25 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.60 % SZS status Theorem % 0.37/0.60 % SZS output start Proof % 0.37/0.60 ( % 0.37/0.60 (declare-sort $$unsorted 0) % 0.37/0.60 (declare-const tptp.j (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.h (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.sorti2 (-> $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.op2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.sorti1 (-> $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.op1 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.60 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.60 (define @t3 () (tptp.sorti1 (tptp.op1 @t2 @t1))) % 0.37/0.60 (define @t4 () (tptp.sorti1 @t1)) % 0.37/0.60 (define @t5 () (@list @t1)) % 0.37/0.60 (define @t6 () (forall @t5 (=> @t4 @t3))) % 0.37/0.60 (define @t7 () (tptp.sorti1 @t2)) % 0.37/0.60 (define @t8 () (=> @t7 @t6)) % 0.37/0.60 (define @t9 () (@list @t2)) % 0.37/0.60 (define @t10 () (forall @t9 @t8)) % 0.37/0.60 (define @t11 () (tptp.sorti2 @t1)) % 0.37/0.60 (define @t12 () (tptp.sorti2 @t2)) % 0.37/0.60 (define @t13 () (tptp.op1 @t1 @t2)) % 0.37/0.60 (define @t14 () (tptp.op1 @t2 @t13)) % 0.37/0.60 (define @t15 () (tptp.op1 @t1 @t13)) % 0.37/0.60 (define @t16 () (not (= @t15 @t2))) % 0.37/0.60 (define @t17 () (and @t4 @t16 (= @t14 @t1))) % 0.37/0.60 (define @t18 () (exists @t5 @t17)) % 0.37/0.60 (define @t19 () (=> @t7 @t18)) % 0.37/0.60 (define @t20 () (forall @t9 @t19)) % 0.37/0.60 (define @t21 () (tptp.op2 @t1 @t2)) % 0.37/0.60 (define @t22 () (tptp.op2 @t2 @t21)) % 0.37/0.60 (define @t23 () (tptp.op2 @t1 @t21)) % 0.37/0.60 (define @t24 () (not (= @t23 @t2))) % 0.37/0.60 (define @t25 () (and @t11 @t24 (= @t22 @t1))) % 0.37/0.60 (define @t26 () (exists @t5 @t25)) % 0.37/0.60 (define @t27 () (=> @t12 @t26)) % 0.37/0.60 (define @t28 () (forall @t9 @t27)) % 0.37/0.60 (define @t29 () (not @t28)) % 0.37/0.60 (define @t30 () (@var "X2" $$unsorted)) % 0.37/0.60 (define @t31 () (tptp.j (tptp.h @t30))) % 0.37/0.60 (define @t32 () (tptp.sorti1 @t30)) % 0.37/0.60 (define @t33 () (=> @t32 (= @t31 @t30))) % 0.37/0.60 (define @t34 () (@list @t30)) % 0.37/0.60 (define @t35 () (forall @t34 @t33)) % 0.37/0.60 (define @t36 () (@var "X1" $$unsorted)) % 0.37/0.60 (define @t37 () (tptp.h (tptp.j @t36))) % 0.37/0.60 (define @t38 () (tptp.sorti2 @t36)) % 0.37/0.60 (define @t39 () (=> @t38 (= @t37 @t36))) % 0.37/0.60 (define @t40 () (@list @t36)) % 0.37/0.60 (define @t41 () (forall @t40 @t39)) % 0.37/0.60 (define @t42 () (@var "Z" $$unsorted)) % 0.37/0.60 (define @t43 () (@var "Y" $$unsorted)) % 0.37/0.60 (define @t44 () (tptp.j @t43)) % 0.37/0.60 (define @t45 () (= (tptp.j (tptp.op2 @t43 @t42)) (tptp.op1 @t44 (tptp.j @t42)))) % 0.37/0.60 (define @t46 () (tptp.sorti2 @t42)) % 0.37/0.60 (define @t47 () (@list @t42)) % 0.37/0.60 (define @t48 () (forall @t47 (=> @t46 @t45))) % 0.37/0.60 (define @t49 () (tptp.sorti2 @t43)) % 0.37/0.60 (define @t50 () (=> @t49 @t48)) % 0.37/0.60 (define @t51 () (@list @t43)) % 0.37/0.60 (define @t52 () (forall @t51 @t50)) % 0.37/0.60 (define @t53 () (@var "X" $$unsorted)) % 0.37/0.60 (define @t54 () (@var "W" $$unsorted)) % 0.37/0.60 (define @t55 () (tptp.h @t54)) % 0.37/0.60 (define @t56 () (= (tptp.h (tptp.op1 @t54 @t53)) (tptp.op2 @t55 (tptp.h @t53)))) % 0.37/0.60 (define @t57 () (tptp.sorti1 @t53)) % 0.37/0.60 (define @t58 () (@list @t53)) % 0.37/0.60 (define @t59 () (forall @t58 (=> @t57 @t56))) % 0.37/0.60 (define @t60 () (tptp.sorti1 @t54)) % 0.37/0.60 (define @t61 () (=> @t60 @t59)) % 0.37/0.60 (define @t62 () (@list @t54)) % 0.37/0.60 (define @t63 () (forall @t62 @t61)) % 0.37/0.60 (define @t64 () (and @t63 @t52 @t41 @t35)) % 0.37/0.60 (define @t65 () (not @t64)) % 0.37/0.60 (define @t66 () (tptp.sorti1 (tptp.j @t1))) % 0.37/0.60 (define @t67 () (forall @t5 (=> @t11 @t66))) % 0.37/0.60 (define @t68 () (tptp.sorti2 (tptp.h @t2))) % 0.37/0.60 (define @t69 () (forall @t9 (=> @t7 @t68))) % 0.37/0.60 (define @t70 () (and @t69 @t67)) % 0.37/0.60 (define @t71 () (=> @t70 @t65)) % 0.37/0.60 (define @t72 () (not @t71)) % 0.37/0.60 (define @t73 () (= @t30 @t31)) % 0.37/0.60 (define @t74 () (= @t36 @t37)) % 0.37/0.60 (define @t75 () (@var "BOUND_VARIABLE_7631" $$unsorted)) % 0.37/0.60 (define @t76 () (= (tptp.j (tptp.op2 @t43 @t75)) (tptp.op1 @t44 (tptp.j @t75)))) % 0.37/0.60 (define @t77 () (not (tptp.sorti2 @t75))) % 0.37/0.60 (define @t78 () (not @t49)) % 0.37/0.60 (define @t79 () (or @t77 @t76)) % 0.37/0.60 (define @t80 () (or @t78 @t79)) % 0.37/0.60 (define @t81 () (forall (@list @t43 @t75) @t80)) % 0.37/0.60 (define @t82 () (@list @t75)) % 0.37/0.60 (define @t83 () (forall @t82 @t80)) % 0.37/0.60 (define @t84 () (forall @t82 @t79)) % 0.37/0.60 (define @t85 () (or @t78 @t84)) % 0.37/0.60 (define @t86 () (forall @t47 (or (not @t46) @t45))) % 0.37/0.60 (define @t87 () (@var "BOUND_VARIABLE_7608" $$unsorted)) % 0.37/0.60 (define @t88 () (= (tptp.h (tptp.op1 @t54 @t87)) (tptp.op2 @t55 (tptp.h @t87)))) % 0.37/0.60 (define @t89 () (not (tptp.sorti1 @t87))) % 0.37/0.60 (define @t90 () (not @t60)) % 0.37/0.60 (define @t91 () (or @t89 @t88)) % 0.37/0.60 (define @t92 () (or @t90 @t91)) % 0.37/0.60 (define @t93 () (forall (@list @t54 @t87) @t92)) % 0.37/0.60 (define @t94 () (@list @t87)) % 0.37/0.60 (define @t95 () (forall @t94 @t92)) % 0.37/0.60 (define @t96 () (forall @t94 @t91)) % 0.37/0.60 (define @t97 () (or @t90 @t96)) % 0.37/0.60 (define @t98 () (forall @t58 (or (not @t57) @t56))) % 0.37/0.60 (define @t99 () (= @t1 @t22)) % 0.37/0.60 (define @t100 () (not @t99)) % 0.37/0.60 (define @t101 () (= @t2 @t23)) % 0.37/0.60 (define @t102 () (not @t11)) % 0.37/0.60 (define @t103 () (not (forall @t5 (or @t102 @t101 @t100)))) % 0.37/0.60 (define @t104 () (@quantifiers_skolemize (forall @t9 (or (not @t12) @t103)) 0)) % 0.37/0.60 (define @t105 () (@list @t104)) % 0.37/0.60 (define @t106 () (not @t101)) % 0.37/0.60 (define @t107 () (not @t106)) % 0.37/0.60 (define @t108 () (or @t102 @t107 @t100)) % 0.37/0.60 (define @t109 () (and @t11 @t106 @t99)) % 0.37/0.60 (define @t110 () (forall @t5 (not @t109))) % 0.37/0.60 (define @t111 () (not @t110)) % 0.37/0.60 (define @t112 () (tptp.sorti2 @t104)) % 0.37/0.60 (define @t113 () (tptp.op2 @t1 @t104)) % 0.37/0.60 (define @t114 () (forall @t5 (or @t102 (= @t104 (tptp.op2 @t1 @t113)) (not (= @t1 (tptp.op2 @t104 @t113)))))) % 0.37/0.60 (define @t115 () (not @t114)) % 0.37/0.60 (define @t116 () (not @t112)) % 0.37/0.60 (define @t117 () (or @t116 @t115)) % 0.37/0.60 (define @t118 () (@list true)) % 0.37/0.60 (define @t119 () (@list @t117)) % 0.37/0.60 (define @t120 () (tptp.j @t104)) % 0.37/0.60 (define @t121 () (tptp.h @t120)) % 0.37/0.60 (define @t122 () (= @t104 @t121)) % 0.37/0.60 (define @t123 () (or @t116 @t122)) % 0.37/0.60 (define @t124 () (@list false false)) % 0.37/0.60 (define @t125 () (= @t1 @t14)) % 0.37/0.60 (define @t126 () (not @t125)) % 0.37/0.60 (define @t127 () (= @t2 @t15)) % 0.37/0.60 (define @t128 () (not @t4)) % 0.37/0.60 (define @t129 () (not (forall @t5 (or @t128 @t127 @t126)))) % 0.37/0.60 (define @t130 () (not @t127)) % 0.37/0.60 (define @t131 () (not @t130)) % 0.37/0.60 (define @t132 () (or @t128 @t131 @t126)) % 0.37/0.60 (define @t133 () (and @t4 @t130 @t125)) % 0.37/0.60 (define @t134 () (forall @t5 (not @t133))) % 0.37/0.60 (define @t135 () (not @t134)) % 0.37/0.60 (define @t136 () (tptp.sorti1 @t120)) % 0.37/0.60 (define @t137 () (or @t116 @t136)) % 0.37/0.60 (define @t138 () (tptp.op1 @t1 @t120)) % 0.37/0.60 (define @t139 () (forall @t5 (or @t128 (= @t120 (tptp.op1 @t1 @t138)) (not (= @t1 (tptp.op1 @t120 @t138)))))) % 0.37/0.60 (define @t140 () (not @t139)) % 0.37/0.60 (define @t141 () (not @t136)) % 0.37/0.60 (define @t142 () (or @t141 @t140)) % 0.37/0.60 (define @t143 () (@quantifiers_skolemize @t139 0)) % 0.37/0.60 (define @t144 () (tptp.op1 @t143 @t120)) % 0.37/0.60 (define @t145 () (tptp.op1 @t120 @t144)) % 0.37/0.60 (define @t146 () (= @t143 @t145)) % 0.37/0.60 (define @t147 () (not @t146)) % 0.37/0.60 (define @t148 () (tptp.op1 @t143 @t144)) % 0.37/0.60 (define @t149 () (= @t120 @t148)) % 0.37/0.60 (define @t150 () (tptp.sorti1 @t143)) % 0.37/0.60 (define @t151 () (not @t150)) % 0.37/0.60 (define @t152 () (or @t151 @t149 @t147)) % 0.37/0.60 (define @t153 () (@list @t152)) % 0.37/0.60 (define @t154 () (@list @t143 @t120)) % 0.37/0.60 (define @t155 () (tptp.h @t143)) % 0.37/0.60 (define @t156 () (tptp.op2 @t155 @t121)) % 0.37/0.60 (define @t157 () (tptp.h @t144)) % 0.37/0.60 (define @t158 () (= @t157 @t156)) % 0.37/0.60 (define @t159 () (or @t151 @t141 @t158)) % 0.37/0.60 (define @t160 () (@list false false false)) % 0.37/0.60 (define @t161 () (@list @t143 @t144)) % 0.37/0.60 (define @t162 () (@var "BOUND_VARIABLE_7526" $$unsorted)) % 0.37/0.60 (define @t163 () (tptp.sorti1 (tptp.op1 @t2 @t162))) % 0.37/0.60 (define @t164 () (not (tptp.sorti1 @t162))) % 0.37/0.60 (define @t165 () (not @t7)) % 0.37/0.60 (define @t166 () (or @t164 @t163)) % 0.37/0.60 (define @t167 () (or @t165 @t166)) % 0.37/0.60 (define @t168 () (forall (@list @t2 @t162) @t167)) % 0.37/0.60 (define @t169 () (@list @t162)) % 0.37/0.60 (define @t170 () (forall @t169 @t167)) % 0.37/0.60 (define @t171 () (forall @t169 @t166)) % 0.37/0.60 (define @t172 () (or @t165 @t171)) % 0.37/0.60 (define @t173 () (forall @t5 (or @t128 @t3))) % 0.37/0.60 (define @t174 () (tptp.sorti1 @t144)) % 0.37/0.60 (define @t175 () (or @t151 @t141 @t174)) % 0.37/0.60 (define @t176 () (tptp.h @t148)) % 0.37/0.60 (define @t177 () (= @t176 (tptp.op2 @t155 @t157))) % 0.37/0.60 (define @t178 () (not @t174)) % 0.37/0.60 (define @t179 () (or @t151 @t178 @t177)) % 0.37/0.60 (define @t180 () (tptp.sorti1 @t148)) % 0.37/0.60 (define @t181 () (or @t151 @t178 @t180)) % 0.37/0.60 (define @t182 () (= @t148 (tptp.j @t176))) % 0.37/0.60 (define @t183 () (not @t180)) % 0.37/0.60 (define @t184 () (or @t183 @t182)) % 0.37/0.60 (define @t185 () (tptp.op2 @t121 @t157)) % 0.37/0.60 (define @t186 () (= (tptp.h @t145) @t185)) % 0.37/0.60 (define @t187 () (or @t141 @t178 @t186)) % 0.37/0.60 (define @t188 () (tptp.sorti2 @t155)) % 0.37/0.60 (define @t189 () (or @t151 @t188)) % 0.37/0.60 (define @t190 () (tptp.op2 @t155 @t104)) % 0.37/0.60 (define @t191 () (= @t155 (tptp.op2 @t104 @t190))) % 0.37/0.60 (define @t192 () (not @t191)) % 0.37/0.60 (define @t193 () (tptp.op2 @t155 @t190)) % 0.37/0.60 (define @t194 () (= @t104 @t193)) % 0.37/0.60 (define @t195 () (not @t188)) % 0.37/0.60 (define @t196 () (or @t195 @t194 @t192)) % 0.37/0.60 (define @t197 () (and @t122 @t158 @t177 @t182 @t194)) % 0.37/0.60 (assume @p1 @t10) % 0.37/0.60 (assume @p2 (forall @t9 (=> @t12 (forall @t5 (=> @t11 (tptp.sorti2 (tptp.op2 @t2 @t1))))))) % 0.37/0.60 (assume @p3 @t20) % 0.37/0.60 (assume @p4 @t29) % 0.37/0.60 (assume @p5 @t72) % 0.37/0.60 (assume @p6 true) % 0.37/0.60 (step @p7 :rule bool-impl-elim :args (@t32 @t73)) % 0.37/0.60 (step @p8 :rule cong :premises (@p7) :args ((forall @t34 (=> @t32 @t73)))) % 0.37/0.60 (step @p9 :rule eq-symm :args (@t31 @t30)) % 0.37/0.60 (step @p10 :rule refl :args (@t32)) % 0.37/0.60 (step @p11 :rule cong :premises (@p10 @p9) :args (@t33)) % 0.37/0.60 (step @p12 :rule cong :premises (@p11) :args (@t35)) % 0.37/0.60 (step @p13 :rule trans :premises (@p12 @p8)) % 0.37/0.60 (step @p14 :rule bool-impl-elim :args (@t38 @t74)) % 0.37/0.60 (step @p15 :rule cong :premises (@p14) :args ((forall @t40 (=> @t38 @t74)))) % 0.37/0.60 (step @p16 :rule eq-symm :args (@t37 @t36)) % 0.37/0.60 (step @p17 :rule refl :args (@t38)) % 0.37/0.60 (step @p18 :rule cong :premises (@p17 @p16) :args (@t39)) % 0.37/0.60 (step @p19 :rule cong :premises (@p18) :args (@t41)) % 0.37/0.60 (step @p20 :rule trans :premises (@p19 @p15)) % 0.37/0.60 (step @p21 :rule aci_norm :args ((= @t80 (or @t78 @t77 @t76)))) % 0.37/0.60 (step @p22 :rule cong :premises (@p21) :args (@t81)) % 0.37/0.60 (step @p23 :rule quant-merge-prenex :args ((= (forall @t51 @t83) @t81))) % 0.37/0.60 (step @p24 :rule alpha_equiv :args (@t84 (@list @t75) (@list @t42))) % 0.37/0.60 (step @p25 :rule refl :args (@t78)) % 0.37/0.60 (step @p26 :rule nary_cong :premises (@p25 @p24) :args (@t85)) % 0.37/0.60 (step @p27 :rule quant-miniscope-or :args ((= @t83 @t85))) % 0.37/0.60 (step @p28 :rule trans :premises (@p27 @p26)) % 0.37/0.60 (step @p29 :rule symm :premises (@p28)) % 0.37/0.60 (step @p30 :rule cong :premises (@p29) :args ((forall @t51 (or @t78 @t86)))) % 0.37/0.60 (step @p31 :rule trans :premises (@p30 @p23)) % 0.37/0.60 (step @p32 :rule trans :premises (@p31 @p22)) % 0.37/0.60 (step @p33 :rule bool-impl-elim :args (@t49 @t86)) % 0.37/0.60 (step @p34 :rule cong :premises (@p33) :args ((forall @t51 (=> @t49 @t86)))) % 0.37/0.60 (step @p35 :rule trans :premises (@p34 @p32)) % 0.37/0.60 (step @p36 :rule bool-impl-elim :args (@t46 @t45)) % 0.37/0.60 (step @p37 :rule cong :premises (@p36) :args (@t48)) % 0.37/0.60 (step @p38 :rule refl :args (@t49)) % 0.37/0.60 (step @p39 :rule cong :premises (@p38 @p37) :args (@t50)) % 0.37/0.60 (step @p40 :rule cong :premises (@p39) :args (@t52)) % 0.37/0.60 (step @p41 :rule trans :premises (@p40 @p35)) % 0.37/0.60 (step @p42 :rule aci_norm :args ((= @t92 (or @t90 @t89 @t88)))) % 0.37/0.60 (step @p43 :rule cong :premises (@p42) :args (@t93)) % 0.37/0.60 (step @p44 :rule quant-merge-prenex :args ((= (forall @t62 @t95) @t93))) % 0.37/0.60 (step @p45 :rule alpha_equiv :args (@t96 (@list @t87) (@list @t53))) % 0.37/0.60 (step @p46 :rule refl :args (@t90)) % 0.37/0.60 (step @p47 :rule nary_cong :premises (@p46 @p45) :args (@t97)) % 0.37/0.60 (step @p48 :rule quant-miniscope-or :args ((= @t95 @t97))) % 0.37/0.60 (step @p49 :rule trans :premises (@p48 @p47)) % 0.37/0.60 (step @p50 :rule symm :premises (@p49)) % 0.37/0.60 (step @p51 :rule cong :premises (@p50) :args ((forall @t62 (or @t90 @t98)))) % 0.37/0.60 (step @p52 :rule trans :premises (@p51 @p44)) % 0.37/0.60 (step @p53 :rule trans :premises (@p52 @p43)) % 0.37/0.60 (step @p54 :rule bool-impl-elim :args (@t60 @t98)) % 0.37/0.60 (step @p55 :rule cong :premises (@p54) :args ((forall @t62 (=> @t60 @t98)))) % 0.37/0.60 (step @p56 :rule trans :premises (@p55 @p53)) % 0.37/0.60 (step @p57 :rule bool-impl-elim :args (@t57 @t56)) % 0.37/0.60 (step @p58 :rule cong :premises (@p57) :args (@t59)) % 0.37/0.60 (step @p59 :rule refl :args (@t60)) % 0.37/0.60 (step @p60 :rule cong :premises (@p59 @p58) :args (@t61)) % 0.37/0.60 (step @p61 :rule cong :premises (@p60) :args (@t63)) % 0.37/0.60 (step @p62 :rule trans :premises (@p61 @p56)) % 0.37/0.60 (step @p63 :rule nary_cong :premises (@p62 @p41 @p20 @p13) :args (@t64)) % 0.37/0.60 (step @p64 :rule cong :premises (@p63) :args (@t65)) % 0.37/0.60 (step @p65 :rule bool-impl-elim :args (@t11 @t66)) % 0.37/0.60 (step @p66 :rule cong :premises (@p65) :args (@t67)) % 0.37/0.60 (step @p67 :rule bool-impl-elim :args (@t7 @t68)) % 0.37/0.60 (step @p68 :rule cong :premises (@p67) :args (@t69)) % 0.37/0.60 (step @p69 :rule nary_cong :premises (@p68 @p66) :args (@t70)) % 0.37/0.60 (step @p70 :rule cong :premises (@p69 @p64) :args (@t71)) % 0.37/0.60 (step @p71 :rule cong :premises (@p70) :args (@t72)) % 0.37/0.60 (step @p72 :rule eq_resolve :premises (@p5 @p71)) % 0.37/0.60 (step @p73 :rule not_implies_elim2 :premises (@p72)) % 0.37/0.60 (step @p74 :rule not_not_elim :premises (@p73)) % 0.37/0.60 (step @p75 :rule and_elim :premises (@p74) :args (2)) % 0.37/0.60 (step @p76 :rule instantiate :premises (@p75) :args (@t105)) % 0.37/0.60 (step @p77 :rule bool-impl-elim :args (@t12 @t103)) % 0.37/0.60 (step @p78 :rule cong :premises (@p77) :args ((forall @t9 (=> @t12 @t103)))) % 0.37/0.60 (step @p79 :rule refl :args (@t100)) % 0.37/0.60 (step @p80 :rule bool-double-not-elim :args (@t101)) % 0.37/0.60 (step @p81 :rule refl :args (@t102)) % 0.37/0.60 (step @p82 :rule nary_cong :premises (@p81 @p80 @p79) :args (@t108)) % 0.37/0.60 (step @p83 :rule aci_norm :args ((= (or @t102 (or @t107 @t100)) @t108))) % 0.37/0.60 (step @p84 :rule trans :premises (@p83 @p82)) % 0.37/0.60 (step @p85 :rule bool-and-de-morgan :args (@t106 @t99 true)) % 0.37/0.60 (step @p86 :rule nary_cong :premises (@p81 @p85) :args ((or @t102 (not (and @t106 @t99))))) % 0.37/0.60 (step @p87 :rule bool-and-de-morgan :args (@t11 @t106 (and @t99))) % 0.37/0.60 (step @p88 :rule trans :premises (@p87 @p86)) % 0.37/0.60 (step @p89 :rule trans :premises (@p88 @p84)) % 0.37/0.60 (step @p90 :rule cong :premises (@p89) :args (@t110)) % 0.37/0.60 (step @p91 :rule cong :premises (@p90) :args (@t111)) % 0.37/0.60 (step @p92 :rule exists-elim :args ((= (exists @t5 @t109) @t111))) % 0.37/0.60 (step @p93 :rule trans :premises (@p92 @p91)) % 0.37/0.60 (step @p94 :rule eq-symm :args (@t22 @t1)) % 0.37/0.60 (step @p95 :rule eq-symm :args (@t23 @t2)) % 0.37/0.60 (step @p96 :rule cong :premises (@p95) :args (@t24)) % 0.37/0.60 (step @p97 :rule refl :args (@t11)) % 0.37/0.60 (step @p98 :rule nary_cong :premises (@p97 @p96 @p94) :args (@t25)) % 0.37/0.60 (step @p99 :rule cong :premises (@p98) :args (@t26)) % 0.37/0.60 (step @p100 :rule trans :premises (@p99 @p93)) % 0.37/0.60 (step @p101 :rule refl :args (@t12)) % 0.37/0.60 (step @p102 :rule cong :premises (@p101 @p100) :args (@t27)) % 0.37/0.60 (step @p103 :rule cong :premises (@p102) :args (@t28)) % 0.37/0.60 (step @p104 :rule trans :premises (@p103 @p78)) % 0.37/0.60 (step @p105 :rule cong :premises (@p104) :args (@t29)) % 0.37/0.60 (step @p106 :rule eq_resolve :premises (@p4 @p105)) % 0.37/0.60 (step @p107 :rule skolemize :premises (@p106)) % 0.37/0.60 (step @p108 :rule bool-double-not-elim :args (@t112)) % 0.37/0.60 (step @p109 :rule refl :args (@t117)) % 0.37/0.60 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((or @t117 (not @t116)))) % 0.37/0.60 (step @p111 :rule cnf_or_neg :args (@t117 0)) % 0.37/0.60 (step @p112 :rule eq_resolve :premises (@p111 @p110)) % 0.37/0.60 (step @p113 :rule reordering :premises (@p112) :args ((or @t112 @t117))) % 0.37/0.60 (step @p114 :rule chain_m_resolution :premises (@p113 @p107) :args (@t112 @t118 @t119)) % 0.37/0.60 (step @p115 :rule cnf_or_pos :args (@t123)) % 0.37/0.60 (step @p116 :rule reordering :premises (@p115) :args ((or @t116 @t122 (not @t123)))) % 0.37/0.60 (step @p117 :rule chain_m_resolution :premises (@p116 @p114 @p76) :args (@t122 @t124 (@list @t112 @t123))) % 0.37/0.60 (step @p118 :rule bool-impl-elim :args (@t7 @t129)) % 0.37/0.60 (step @p119 :rule cong :premises (@p118) :args ((forall @t9 (=> @t7 @t129)))) % 0.37/0.60 (step @p120 :rule refl :args (@t126)) % 0.37/0.60 (step @p121 :rule bool-double-not-elim :args (@t127)) % 0.37/0.60 (step @p122 :rule refl :args (@t128)) % 0.37/0.60 (step @p123 :rule nary_cong :premises (@p122 @p121 @p120) :args (@t132)) % 0.37/0.60 (step @p124 :rule aci_norm :args ((= (or @t128 (or @t131 @t126)) @t132))) % 0.37/0.60 (step @p125 :rule trans :premises (@p124 @p123)) % 0.37/0.60 (step @p126 :rule bool-and-de-morgan :args (@t130 @t125 true)) % 0.37/0.60 (step @p127 :rule nary_cong :premises (@p122 @p126) :args ((or @t128 (not (and @t130 @t125))))) % 0.37/0.60 (step @p128 :rule bool-and-de-morgan :args (@t4 @t130 (and @t125))) % 0.37/0.60 (step @p129 :rule trans :premises (@p128 @p127)) % 0.37/0.60 (step @p130 :rule trans :premises (@p129 @p125)) % 0.37/0.60 (step @p131 :rule cong :premises (@p130) :args (@t134)) % 0.37/0.60 (step @p132 :rule cong :premises (@p131) :args (@t135)) % 0.37/0.60 (step @p133 :rule exists-elim :args ((= (exists @t5 @t133) @t135))) % 0.37/0.60 (step @p134 :rule trans :premises (@p133 @p132)) % 0.37/0.60 (step @p135 :rule eq-symm :args (@t14 @t1)) % 0.37/0.60 (step @p136 :rule eq-symm :args (@t15 @t2)) % 0.37/0.60 (step @p137 :rule cong :premises (@p136) :args (@t16)) % 0.37/0.60 (step @p138 :rule refl :args (@t4)) % 0.37/0.60 (step @p139 :rule nary_cong :premises (@p138 @p137 @p135) :args (@t17)) % 0.37/0.60 (step @p140 :rule cong :premises (@p139) :args (@t18)) % 0.37/0.60 (step @p141 :rule trans :premises (@p140 @p134)) % 0.37/0.60 (step @p142 :rule refl :args (@t7)) % 0.37/0.60 (step @p143 :rule cong :premises (@p142 @p141) :args (@t19)) % 0.37/0.60 (step @p144 :rule cong :premises (@p143) :args (@t20)) % 0.37/0.60 (step @p145 :rule trans :premises (@p144 @p119)) % 0.37/0.60 (step @p146 :rule eq_resolve :premises (@p3 @p145)) % 0.37/0.60 (step @p147 :rule instantiate :premises (@p146) :args ((@list @t120))) % 0.37/0.60 (step @p148 :rule not_implies_elim1 :premises (@p72)) % 0.37/0.60 (step @p149 :rule and_elim :premises (@p148) :args (1)) % 0.37/0.60 (step @p150 :rule instantiate :premises (@p149) :args (@t105)) % 0.37/0.60 (step @p151 :rule cnf_or_pos :args (@t137)) % 0.37/0.60 (step @p152 :rule reordering :premises (@p151) :args ((or @t116 @t136 (not @t137)))) % 0.37/0.60 (step @p153 :rule chain_m_resolution :premises (@p152 @p114 @p150) :args (@t136 @t124 (@list @t112 @t137))) % 0.37/0.60 (step @p154 :rule cnf_or_pos :args (@t142)) % 0.37/0.60 (step @p155 :rule reordering :premises (@p154) :args ((or @t141 @t140 (not @t142)))) % 0.37/0.60 (step @p156 :rule chain_m_resolution :premises (@p155 @p153 @p147) :args (@t140 @t124 (@list @t136 @t142))) % 0.37/0.60 (step @p157 :rule skolemize :premises (@p156)) % 0.37/0.60 (step @p158 :rule cnf_or_neg :args (@t152 1)) % 0.37/0.60 (step @p159 :rule chain_m_resolution :premises (@p158 @p157) :args ((not @t149) @t118 @t153)) % 0.37/0.60 (step @p160 :rule and_elim :premises (@p74) :args (0)) % 0.37/0.60 (step @p161 :rule instantiate :premises (@p160) :args (@t154)) % 0.37/0.60 (step @p162 :rule bool-double-not-elim :args (@t150)) % 0.37/0.60 (step @p163 :rule refl :args (@t152)) % 0.37/0.60 (step @p164 :rule nary_cong :premises (@p163 @p162) :args ((or @t152 (not @t151)))) % 0.37/0.60 (step @p165 :rule cnf_or_neg :args (@t152 0)) % 0.37/0.60 (step @p166 :rule eq_resolve :premises (@p165 @p164)) % 0.37/0.60 (step @p167 :rule reordering :premises (@p166) :args ((or @t150 @t152))) % 0.37/0.60 (step @p168 :rule chain_m_resolution :premises (@p167 @p157) :args (@t150 @t118 @t153)) % 0.37/0.60 (step @p169 :rule cnf_or_pos :args (@t159)) % 0.37/0.60 (step @p170 :rule reordering :premises (@p169) :args ((or @t141 @t151 @t158 (not @t159)))) % 0.37/0.60 (step @p171 :rule chain_m_resolution :premises (@p170 @p153 @p168 @p161) :args (@t158 @t160 (@list @t136 @t150 @t159))) % 0.37/0.60 (step @p172 :rule instantiate :premises (@p160) :args (@t161)) % 0.37/0.60 (step @p173 :rule aci_norm :args ((= @t167 (or @t165 @t164 @t163)))) % 0.37/0.60 (step @p174 :rule cong :premises (@p173) :args (@t168)) % 0.37/0.60 (step @p175 :rule quant-merge-prenex :args ((= (forall @t9 @t170) @t168))) % 0.37/0.60 (step @p176 :rule alpha_equiv :args (@t171 (@list @t162) (@list @t1))) % 0.37/0.60 (step @p177 :rule refl :args (@t165)) % 0.37/0.60 (step @p178 :rule nary_cong :premises (@p177 @p176) :args (@t172)) % 0.37/0.60 (step @p179 :rule quant-miniscope-or :args ((= @t170 @t172))) % 0.37/0.60 (step @p180 :rule trans :premises (@p179 @p178)) % 0.37/0.60 (step @p181 :rule symm :premises (@p180)) % 0.37/0.60 (step @p182 :rule cong :premises (@p181) :args ((forall @t9 (or @t165 @t173)))) % 0.37/0.60 (step @p183 :rule trans :premises (@p182 @p175)) % 0.37/0.60 (step @p184 :rule trans :premises (@p183 @p174)) % 0.37/0.60 (step @p185 :rule bool-impl-elim :args (@t7 @t173)) % 0.37/0.60 (step @p186 :rule cong :premises (@p185) :args ((forall @t9 (=> @t7 @t173)))) % 0.37/0.60 (step @p187 :rule trans :premises (@p186 @p184)) % 0.37/0.60 (step @p188 :rule bool-impl-elim :args (@t4 @t3)) % 0.37/0.60 (step @p189 :rule cong :premises (@p188) :args (@t6)) % 0.37/0.60 (step @p190 :rule cong :premises (@p142 @p189) :args (@t8)) % 0.37/0.60 (step @p191 :rule cong :premises (@p190) :args (@t10)) % 0.37/0.60 (step @p192 :rule trans :premises (@p191 @p187)) % 0.37/0.60 (step @p193 :rule eq_resolve :premises (@p1 @p192)) % 0.37/0.60 (step @p194 :rule instantiate :premises (@p193) :args (@t154)) % 0.37/0.60 (step @p195 :rule cnf_or_pos :args (@t175)) % 0.37/0.60 (step @p196 :rule reordering :premises (@p195) :args ((or @t141 @t151 @t174 (not @t175)))) % 0.37/0.60 (step @p197 :rule chain_m_resolution :premises (@p196 @p153 @p168 @p194) :args (@t174 @t160 (@list @t136 @t150 @t175))) % 0.37/0.60 (step @p198 :rule cnf_or_pos :args (@t179)) % 0.37/0.60 (step @p199 :rule reordering :premises (@p198) :args ((or @t151 @t178 @t177 (not @t179)))) % 0.37/0.60 (step @p200 :rule chain_m_resolution :premises (@p199 @p168 @p197 @p172) :args (@t177 @t160 (@list @t150 @t174 @t179))) % 0.37/0.60 (step @p201 :rule and_elim :premises (@p74) :args (3)) % 0.37/0.60 (step @p202 :rule instantiate :premises (@p201) :args ((@list @t148))) % 0.37/0.60 (step @p203 :rule instantiate :premises (@p193) :args (@t161)) % 0.37/0.60 (step @p204 :rule cnf_or_pos :args (@t181)) % 0.37/0.60 (step @p205 :rule reordering :premises (@p204) :args ((or @t151 @t178 @t180 (not @t181)))) % 0.37/0.60 (step @p206 :rule chain_m_resolution :premises (@p205 @p168 @p197 @p203) :args (@t180 @t160 (@list @t150 @t174 @t181))) % 0.37/0.60 (step @p207 :rule cnf_or_pos :args (@t184)) % 0.37/0.60 (step @p208 :rule reordering :premises (@p207) :args ((or @t183 @t182 (not @t184)))) % 0.37/0.60 (step @p209 :rule chain_m_resolution :premises (@p208 @p206 @p202) :args (@t182 @t124 (@list @t180 @t184))) % 0.37/0.60 (step @p210 :rule bool-double-not-elim :args (@t114)) % 0.37/0.60 (step @p211 :rule nary_cong :premises (@p109 @p210) :args ((or @t117 (not @t115)))) % 0.37/0.60 (step @p212 :rule cnf_or_neg :args (@t117 1)) % 0.37/0.60 (step @p213 :rule eq_resolve :premises (@p212 @p211)) % 0.37/0.60 (step @p214 :rule reordering :premises (@p213) :args ((or @t114 @t117))) % 0.37/0.60 (step @p215 :rule chain_m_resolution :premises (@p214 @p107) :args (@t114 @t118 @t119)) % 0.37/0.60 (step @p216 :rule instantiate :premises (@p215) :args ((@list @t155))) % 0.37/0.60 (step @p217 :rule symm :premises (@p117)) % 0.37/0.60 (step @p218 :rule refl :args (@t155)) % 0.37/0.60 (step @p219 :rule cong :premises (@p218 @p217) :args (@t156)) % 0.37/0.60 (step @p220 :rule trans :premises (@p171 @p219)) % 0.37/0.60 (step @p221 :rule cong :premises (@p217 @p220) :args (@t185)) % 0.37/0.60 (step @p222 :rule instantiate :premises (@p160) :args ((@list @t120 @t144))) % 0.37/0.60 (step @p223 :rule cnf_or_pos :args (@t187)) % 0.37/0.60 (step @p224 :rule reordering :premises (@p223) :args ((or @t141 @t178 @t186 (not @t187)))) % 0.37/0.60 (step @p225 :rule chain_m_resolution :premises (@p224 @p153 @p197 @p222) :args (@t186 @t160 (@list @t136 @t174 @t187))) % 0.37/0.60 (step @p226 :rule bool-double-not-elim :args (@t146)) % 0.37/0.60 (step @p227 :rule nary_cong :premises (@p163 @p226) :args ((or @t152 (not @t147)))) % 0.37/0.60 (step @p228 :rule cnf_or_neg :args (@t152 2)) % 0.37/0.60 (step @p229 :rule eq_resolve :premises (@p228 @p227)) % 0.37/0.60 (step @p230 :rule reordering :premises (@p229) :args ((or @t146 @t152))) % 0.37/0.60 (step @p231 :rule chain_m_resolution :premises (@p230 @p157) :args (@t146 @t118 @t153)) % 0.37/0.60 (step @p232 :rule cong :premises (@p231) :args (@t155)) % 0.37/0.60 (step @p233 :rule trans :premises (@p232 @p225 @p221)) % 0.37/0.60 (step @p234 :rule and_elim :premises (@p148) :args (0)) % 0.37/0.60 (step @p235 :rule instantiate :premises (@p234) :args ((@list @t143))) % 0.37/0.60 (step @p236 :rule cnf_or_pos :args (@t189)) % 0.37/0.60 (step @p237 :rule reordering :premises (@p236) :args ((or @t151 @t188 (not @t189)))) % 0.37/0.60 (step @p238 :rule chain_m_resolution :premises (@p237 @p168 @p235) :args (@t188 @t124 (@list @t150 @t189))) % 0.37/0.60 (step @p239 :rule cnf_or_pos :args (@t196)) % 0.37/0.60 (step @p240 :rule reordering :premises (@p239) :args ((or @t195 @t194 @t192 (not @t196)))) % 0.37/0.60 (step @p241 :rule chain_m_resolution :premises (@p240 @p238 @p233 @p216) :args (@t194 @t160 (@list @t188 @t191 @t196))) % 0.37/0.60 (assume-push @p267 @t122) % 0.37/0.60 (assume-push @p268 @t158) % 0.37/0.60 (assume-push @p269 @t177) % 0.37/0.60 (assume-push @p270 @t182) % 0.37/0.60 (assume-push @p271 @t194) % 0.37/0.60 (step @p247 :rule symm :premises (@p209)) % 0.37/0.60 (step @p248 :rule symm :premises (@p200)) % 0.37/0.60 (step @p249 :rule symm :premises (@p171)) % 0.37/0.60 (step @p250 :rule cong :premises (@p218 @p117) :args (@t190)) % 0.37/0.60 (step @p251 :rule trans :premises (@p250 @p249)) % 0.37/0.60 (step @p252 :rule cong :premises (@p218 @p251) :args (@t193)) % 0.37/0.60 (step @p253 :rule trans :premises (@p241 @p252 @p248)) % 0.37/0.60 (step @p254 :rule cong :premises (@p253) :args (@t120)) % 0.37/0.60 (step @p255 :rule trans :premises (@p254 @p247)) % 0.37/0.60 (step-pop @p272 :rule scope :premises (@p255)) % 0.37/0.60 (step-pop @p273 :rule scope :premises (@p272)) % 0.37/0.60 (step-pop @p274 :rule scope :premises (@p273)) % 0.37/0.60 (step-pop @p275 :rule scope :premises (@p274)) % 0.37/0.60 (step-pop @p276 :rule scope :premises (@p275)) % 0.37/0.60 (step @p256 :rule process_scope :premises (@p276) :args (@t149)) % 0.37/0.60 (step @p262 :rule implies_elim :premises (@p256)) % 0.37/0.60 (step @p263 :rule cnf_and_neg :args (@t197)) % 0.37/0.60 (step @p264 :rule resolution :premises (@p263 @p262) :args (true @t197)) % 0.37/0.60 (step @p265 :rule reordering :premises (@p264) :args ((or (not @t122) @t149 (not @t158) (not @t177) (not @t182) (not @t194)))) % 0.37/0.60 (step @p266 false :rule chain_m_resolution :premises (@p265 @p241 @p209 @p200 @p171 @p159 @p117) :args (false (@list false false false false true false) (@list @t194 @t182 @t177 @t158 @t149 @t122))) % 0.37/0.60 ) % 0.37/0.60 % SZS output end Proof % 0.37/0.60 % cvc5 exiting %------------------------------------------------------------------------------