%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU220+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n005.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 08:51:00 AM UTC 2026 % Result : Theorem 0.72s 0.93s % Output : Proof 0.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU220+1 : TPTP v9.2.1. Released v3.3.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n005.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 16:43:03 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.72/0.93 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.72/0.93 % SZS status Theorem % 0.72/0.93 % SZS output start Proof % 0.72/0.93 ( % 0.72/0.93 (declare-sort $$unsorted 0) % 0.72/0.93 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.72/0.93 (declare-const tptp.function_inverse (-> $$unsorted $$unsorted)) % 0.72/0.93 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.72/0.93 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.72/0.93 (declare-const tptp.empty_set $$unsorted) % 0.72/0.93 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.72/0.93 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.72/0.93 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 0.72/0.93 (declare-const tptp.function (-> $$unsorted Bool)) % 0.72/0.93 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.72/0.93 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 0.72/0.93 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.72/0.93 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.72/0.93 (define @t1 () (@var "A" $$unsorted)) % 0.72/0.93 (define @t2 () (@var "B" $$unsorted)) % 0.72/0.93 (define @t3 () (tptp.in @t1 @t2)) % 0.72/0.93 (define @t4 () (@list @t1 @t2)) % 0.72/0.93 (define @t5 () (tptp.function @t1)) % 0.72/0.93 (define @t6 () (tptp.empty @t1)) % 0.72/0.93 (define @t7 () (@list @t1)) % 0.72/0.93 (define @t8 () (tptp.relation @t1)) % 0.72/0.93 (define @t9 () (tptp.one_to_one @t1)) % 0.72/0.93 (define @t10 () (and @t8 @t5 @t9)) % 0.72/0.93 (define @t11 () (and @t8 @t6 @t5)) % 0.72/0.93 (define @t12 () (tptp.function_inverse @t1)) % 0.72/0.93 (define @t13 () (and (tptp.relation @t12) (tptp.function @t12))) % 0.72/0.93 (define @t14 () (and @t8 @t5)) % 0.72/0.93 (define @t15 () (forall @t7 (=> @t14 @t13))) % 0.72/0.93 (define @t16 () (tptp.relation_composition @t1 @t2)) % 0.72/0.93 (define @t17 () (tptp.relation @t16)) % 0.72/0.93 (define @t18 () (tptp.relation @t2)) % 0.72/0.93 (define @t19 () (@list @t2)) % 0.72/0.93 (define @t20 () (tptp.relation_composition @t2 @t1)) % 0.72/0.93 (define @t21 () (and @t6 @t18)) % 0.72/0.93 (define @t22 () (tptp.relation tptp.empty_set)) % 0.72/0.93 (define @t23 () (tptp.empty tptp.empty_set)) % 0.72/0.93 (define @t24 () (tptp.function @t2)) % 0.72/0.93 (define @t25 () (tptp.relation_dom @t1)) % 0.72/0.93 (define @t26 () (tptp.empty @t25)) % 0.72/0.93 (define @t27 () (not @t6)) % 0.72/0.93 (define @t28 () (and @t27 @t8)) % 0.72/0.93 (define @t29 () (tptp.relation_rng @t1)) % 0.72/0.93 (define @t30 () (tptp.empty @t29)) % 0.72/0.93 (define @t31 () (tptp.element @t1 @t2)) % 0.72/0.93 (define @t32 () (tptp.apply @t2 @t1)) % 0.72/0.93 (define @t33 () (@var "C" $$unsorted)) % 0.72/0.93 (define @t34 () (= (tptp.apply (tptp.relation_composition @t2 @t33) @t1) (tptp.apply @t33 @t32))) % 0.72/0.93 (define @t35 () (tptp.relation_dom @t2)) % 0.72/0.93 (define @t36 () (tptp.in @t1 @t35)) % 0.72/0.93 (define @t37 () (=> @t36 @t34)) % 0.72/0.93 (define @t38 () (tptp.function @t33)) % 0.72/0.93 (define @t39 () (tptp.relation @t33)) % 0.72/0.93 (define @t40 () (and @t39 @t38)) % 0.72/0.93 (define @t41 () (@list @t33)) % 0.72/0.93 (define @t42 () (forall @t41 (=> @t40 @t37))) % 0.72/0.93 (define @t43 () (and @t18 @t24)) % 0.72/0.93 (define @t44 () (=> @t43 @t42)) % 0.72/0.93 (define @t45 () (forall @t4 @t44)) % 0.72/0.93 (define @t46 () (tptp.empty @t2)) % 0.72/0.93 (define @t47 () (@var "D" $$unsorted)) % 0.72/0.93 (define @t48 () (= @t47 (tptp.apply @t2 @t33))) % 0.72/0.93 (define @t49 () (tptp.in @t33 @t29)) % 0.72/0.93 (define @t50 () (and @t49 @t48)) % 0.72/0.93 (define @t51 () (= @t33 (tptp.apply @t1 @t47))) % 0.72/0.93 (define @t52 () (tptp.in @t47 @t25)) % 0.72/0.93 (define @t53 () (and @t52 @t51)) % 0.72/0.93 (define @t54 () (and (=> @t50 @t53) (=> @t53 @t50))) % 0.72/0.93 (define @t55 () (@list @t33 @t47)) % 0.72/0.93 (define @t56 () (forall @t55 @t54)) % 0.72/0.93 (define @t57 () (and (= @t35 @t29) @t56)) % 0.72/0.93 (define @t58 () (= @t2 @t12)) % 0.72/0.93 (define @t59 () (= @t58 @t57)) % 0.72/0.93 (define @t60 () (=> @t43 @t59)) % 0.72/0.93 (define @t61 () (forall @t19 @t60)) % 0.72/0.93 (define @t62 () (=> @t9 @t61)) % 0.72/0.93 (define @t63 () (=> @t14 @t62)) % 0.72/0.93 (define @t64 () (forall @t7 @t63)) % 0.72/0.93 (define @t65 () (and (= @t29 (tptp.relation_dom @t12)) (= @t25 (tptp.relation_rng @t12)))) % 0.72/0.93 (define @t66 () (=> @t9 @t65)) % 0.72/0.93 (define @t67 () (forall @t7 (=> @t14 @t66))) % 0.72/0.93 (define @t68 () (tptp.function_inverse @t2)) % 0.72/0.93 (define @t69 () (and (= @t1 (tptp.apply @t2 (tptp.apply @t68 @t1))) (= @t1 (tptp.apply (tptp.relation_composition @t68 @t2) @t1)))) % 0.72/0.93 (define @t70 () (tptp.in @t1 (tptp.relation_rng @t2))) % 0.72/0.93 (define @t71 () (tptp.one_to_one @t2)) % 0.72/0.93 (define @t72 () (and @t71 @t70)) % 0.72/0.93 (define @t73 () (=> @t72 @t69)) % 0.72/0.93 (define @t74 () (forall @t4 (=> @t43 @t73))) % 0.72/0.93 (define @t75 () (not @t74)) % 0.72/0.93 (define @t76 () (@var "BOUND_VARIABLE_7726" $$unsorted)) % 0.72/0.93 (define @t77 () (= (tptp.apply (tptp.relation_composition @t2 @t76) @t1) (tptp.apply @t76 @t32))) % 0.72/0.93 (define @t78 () (not (tptp.function @t76))) % 0.72/0.93 (define @t79 () (not (tptp.relation @t76))) % 0.72/0.93 (define @t80 () (not @t36)) % 0.72/0.93 (define @t81 () (not @t24)) % 0.72/0.93 (define @t82 () (not @t18)) % 0.72/0.93 (define @t83 () (or @t82 @t81 @t80 @t79 @t78 @t77)) % 0.72/0.93 (define @t84 () (or @t79 @t78 @t77)) % 0.72/0.93 (define @t85 () (or @t82 @t81 @t80 @t84)) % 0.72/0.93 (define @t86 () (@list @t1 @t2 @t76)) % 0.72/0.93 (define @t87 () (forall @t86 @t85)) % 0.72/0.93 (define @t88 () (@list @t76)) % 0.72/0.93 (define @t89 () (forall @t88 @t85)) % 0.72/0.93 (define @t90 () (forall @t88 @t84)) % 0.72/0.93 (define @t91 () (or @t82 @t81 @t80 @t90)) % 0.72/0.93 (define @t92 () (not @t38)) % 0.72/0.93 (define @t93 () (not @t39)) % 0.72/0.93 (define @t94 () (or @t93 @t92 @t34)) % 0.72/0.93 (define @t95 () (forall @t41 @t94)) % 0.72/0.93 (define @t96 () (or @t82 @t81 @t80 @t95)) % 0.72/0.93 (define @t97 () (or @t80 @t95)) % 0.72/0.93 (define @t98 () (or @t82 @t81)) % 0.72/0.93 (define @t99 () (not @t43)) % 0.72/0.93 (define @t100 () (or @t80 @t94)) % 0.72/0.93 (define @t101 () (or @t93 @t92 @t80 @t34)) % 0.72/0.93 (define @t102 () (not @t70)) % 0.72/0.93 (define @t103 () (not @t71)) % 0.72/0.93 (define @t104 () (or @t82 @t81 @t103 @t102 @t69)) % 0.72/0.93 (define @t105 () (forall @t4 @t104)) % 0.72/0.93 (define @t106 () (@quantifiers_skolemize @t105 0)) % 0.72/0.93 (define @t107 () (@quantifiers_skolemize @t105 1)) % 0.72/0.93 (define @t108 () (tptp.function_inverse @t107)) % 0.72/0.93 (define @t109 () (tptp.apply (tptp.relation_composition @t108 @t107) @t106)) % 0.72/0.93 (define @t110 () (tptp.apply @t108 @t106)) % 0.72/0.93 (define @t111 () (tptp.apply @t107 @t110)) % 0.72/0.93 (define @t112 () (tptp.function @t107)) % 0.72/0.93 (define @t113 () (not @t112)) % 0.72/0.93 (define @t114 () (tptp.relation @t107)) % 0.72/0.93 (define @t115 () (not @t114)) % 0.72/0.93 (define @t116 () (tptp.relation_dom @t108)) % 0.72/0.93 (define @t117 () (tptp.in @t106 @t116)) % 0.72/0.93 (define @t118 () (not @t117)) % 0.72/0.93 (define @t119 () (tptp.function @t108)) % 0.72/0.93 (define @t120 () (not @t119)) % 0.72/0.93 (define @t121 () (tptp.relation @t108)) % 0.72/0.93 (define @t122 () (not @t121)) % 0.72/0.93 (define @t123 () (or @t122 @t120 @t118 @t115 @t113 (= @t109 @t111))) % 0.72/0.93 (define @t124 () (forall @t86 @t83)) % 0.72/0.93 (define @t125 () (= @t111 @t109)) % 0.72/0.93 (define @t126 () (or @t122 @t120 @t118 @t115 @t113 @t125)) % 0.72/0.93 (define @t127 () (@list false)) % 0.72/0.93 (define @t128 () (or @t103 @t102 @t69)) % 0.72/0.93 (define @t129 () (tptp.relation_rng @t107)) % 0.72/0.93 (define @t130 () (tptp.in @t106 @t129)) % 0.72/0.93 (define @t131 () (= @t106 @t109)) % 0.72/0.93 (define @t132 () (= @t106 @t111)) % 0.72/0.93 (define @t133 () (and @t132 @t131)) % 0.72/0.93 (define @t134 () (not @t130)) % 0.72/0.93 (define @t135 () (tptp.one_to_one @t107)) % 0.72/0.93 (define @t136 () (not @t135)) % 0.72/0.93 (define @t137 () (or @t115 @t113 @t136 @t134 @t133)) % 0.72/0.93 (define @t138 () (@list true)) % 0.72/0.93 (define @t139 () (@list @t137)) % 0.72/0.93 (define @t140 () (not @t9)) % 0.72/0.93 (define @t141 () (not @t5)) % 0.72/0.93 (define @t142 () (not @t8)) % 0.72/0.93 (define @t143 () (or @t142 @t141)) % 0.72/0.93 (define @t144 () (not @t14)) % 0.72/0.93 (define @t145 () (@list @t107)) % 0.72/0.93 (define @t146 () (tptp.relation_dom @t107)) % 0.72/0.93 (define @t147 () (= @t129 @t116)) % 0.72/0.93 (define @t148 () (and @t147 (= @t146 (tptp.relation_rng @t108)))) % 0.72/0.93 (define @t149 () (or @t115 @t113 @t136 @t148)) % 0.72/0.93 (define @t150 () (and @t121 @t119)) % 0.72/0.93 (define @t151 () (or @t115 @t113 @t150)) % 0.72/0.93 (define @t152 () (not @t150)) % 0.72/0.93 (define @t153 () (@list @t150)) % 0.72/0.93 (define @t154 () (@list false false false false false false)) % 0.72/0.93 (define @t155 () (@var "BOUND_VARIABLE_7831" $$unsorted)) % 0.72/0.93 (define @t156 () (= @t12 @t155)) % 0.72/0.93 (define @t157 () (@var "BOUND_VARIABLE_7778" $$unsorted)) % 0.72/0.93 (define @t158 () (tptp.apply @t1 @t157)) % 0.72/0.93 (define @t159 () (tptp.in @t158 @t29)) % 0.72/0.93 (define @t160 () (not (tptp.in @t157 @t25))) % 0.72/0.93 (define @t161 () (@list @t157)) % 0.72/0.93 (define @t162 () (@var "BOUND_VARIABLE_7760" $$unsorted)) % 0.72/0.93 (define @t163 () (tptp.apply @t155 @t162)) % 0.72/0.93 (define @t164 () (not (tptp.in @t162 @t29))) % 0.72/0.93 (define @t165 () (@list @t162)) % 0.72/0.93 (define @t166 () (and (= @t29 (tptp.relation_dom @t155)) (forall @t165 (or @t164 (and (tptp.in @t163 @t25) (= @t162 (tptp.apply @t1 @t163))))) (forall @t161 (or @t160 (and @t159 (= @t157 (tptp.apply @t155 @t158))))))) % 0.72/0.93 (define @t167 () (= (= @t155 @t12) @t166)) % 0.72/0.93 (define @t168 () (not (tptp.function @t155))) % 0.72/0.93 (define @t169 () (not (tptp.relation @t155))) % 0.72/0.93 (define @t170 () (or @t142 @t141 @t140 @t169 @t168 @t167)) % 0.72/0.93 (define @t171 () (or @t169 @t168 @t167)) % 0.72/0.93 (define @t172 () (or @t142 @t141 @t140 @t171)) % 0.72/0.93 (define @t173 () (@list @t1 @t155)) % 0.72/0.93 (define @t174 () (forall @t173 @t172)) % 0.72/0.93 (define @t175 () (@list @t155)) % 0.72/0.93 (define @t176 () (forall @t175 @t172)) % 0.72/0.93 (define @t177 () (forall @t175 @t171)) % 0.72/0.93 (define @t178 () (or @t142 @t141 @t140 @t177)) % 0.72/0.93 (define @t179 () (and @t159 (= @t157 (tptp.apply @t2 @t158)))) % 0.72/0.93 (define @t180 () (or @t160 @t179)) % 0.72/0.93 (define @t181 () (forall @t161 @t180)) % 0.72/0.93 (define @t182 () (tptp.apply @t2 @t162)) % 0.72/0.93 (define @t183 () (and (tptp.in @t182 @t25) (= @t162 (tptp.apply @t1 @t182)))) % 0.72/0.93 (define @t184 () (or @t164 @t183)) % 0.72/0.93 (define @t185 () (forall @t165 @t184)) % 0.72/0.93 (define @t186 () (= @t29 @t35)) % 0.72/0.93 (define @t187 () (and @t186 @t185 @t181)) % 0.72/0.93 (define @t188 () (= @t58 @t187)) % 0.72/0.93 (define @t189 () (or @t82 @t81 @t188)) % 0.72/0.93 (define @t190 () (forall @t19 @t189)) % 0.72/0.93 (define @t191 () (or @t142 @t141 @t140 @t190)) % 0.72/0.93 (define @t192 () (=> @t9 @t190)) % 0.72/0.93 (define @t193 () (not (= @t158 @t158))) % 0.72/0.93 (define @t194 () (or @t160 @t193 @t179)) % 0.72/0.93 (define @t195 () (@var "BOUND_VARIABLE_7776" $$unsorted)) % 0.72/0.93 (define @t196 () (and (tptp.in @t195 @t29) (= @t157 (tptp.apply @t2 @t195)))) % 0.72/0.93 (define @t197 () (not (= @t195 @t158))) % 0.72/0.93 (define @t198 () (or @t197 @t160 @t197 @t196)) % 0.72/0.93 (define @t199 () (@list @t195)) % 0.72/0.93 (define @t200 () (or @t160 @t197 @t196)) % 0.72/0.93 (define @t201 () (forall @t199 @t200)) % 0.72/0.93 (define @t202 () (forall @t161 @t201)) % 0.72/0.93 (define @t203 () (forall (@list @t157 @t195) @t200)) % 0.72/0.93 (define @t204 () (forall (@list @t195 @t157) @t200)) % 0.72/0.93 (define @t205 () (not (= @t182 @t182))) % 0.72/0.93 (define @t206 () (or @t164 @t205 @t183)) % 0.72/0.93 (define @t207 () (@var "BOUND_VARIABLE_7762" $$unsorted)) % 0.72/0.93 (define @t208 () (and (tptp.in @t207 @t25) (= @t162 (tptp.apply @t1 @t207)))) % 0.72/0.93 (define @t209 () (not (= @t207 @t182))) % 0.72/0.93 (define @t210 () (or @t209 @t164 @t209 @t208)) % 0.72/0.93 (define @t211 () (@list @t207)) % 0.72/0.93 (define @t212 () (or @t164 @t209 @t208)) % 0.72/0.93 (define @t213 () (forall @t211 @t212)) % 0.72/0.93 (define @t214 () (forall @t165 @t213)) % 0.72/0.93 (define @t215 () (forall (@list @t162 @t207) @t212)) % 0.72/0.93 (define @t216 () (not @t51)) % 0.72/0.93 (define @t217 () (not @t52)) % 0.72/0.93 (define @t218 () (or @t217 @t216 @t50)) % 0.72/0.93 (define @t219 () (forall @t55 @t218)) % 0.72/0.93 (define @t220 () (@list @t33 @t47)) % 0.72/0.93 (define @t221 () (not @t48)) % 0.72/0.93 (define @t222 () (not @t49)) % 0.72/0.93 (define @t223 () (or @t222 @t221 @t53)) % 0.72/0.93 (define @t224 () (forall @t55 @t223)) % 0.72/0.93 (define @t225 () (and @t224 @t219)) % 0.72/0.93 (define @t226 () (tptp.apply @t107 @t157)) % 0.72/0.93 (define @t227 () (tptp.apply @t108 @t162)) % 0.72/0.93 (define @t228 () (forall @t165 (or (not (tptp.in @t162 @t129)) (and (tptp.in @t227 @t146) (= @t162 (tptp.apply @t107 @t227)))))) % 0.72/0.93 (define @t229 () (and @t147 @t228 (forall @t161 (or (not (tptp.in @t157 @t146)) (and (tptp.in @t226 @t129) (= @t157 (tptp.apply @t108 @t226))))))) % 0.72/0.93 (define @t230 () (= @t108 @t108)) % 0.72/0.93 (define @t231 () (or @t115 @t113 @t136 @t122 @t120 (= @t229 @t230))) % 0.72/0.93 (define @t232 () (forall @t173 (or @t142 @t141 @t140 @t169 @t168 (= @t166 @t156)))) % 0.72/0.93 (define @t233 () (or @t115 @t113 @t136 @t122 @t120 @t229)) % 0.72/0.93 (define @t234 () (and (tptp.in @t110 @t146) @t132)) % 0.72/0.93 (define @t235 () (or @t134 @t234)) % 0.72/0.93 (define @t236 () (and @t132 @t125)) % 0.72/0.93 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 0.72/0.93 (assume @p2 (forall @t7 (=> @t6 @t5))) % 0.72/0.93 (assume @p3 (forall @t7 (=> @t6 @t8))) % 0.72/0.93 (assume @p4 (forall @t7 (=> @t11 @t10))) % 0.72/0.93 (assume @p5 true) % 0.72/0.93 (assume @p6 @t15) % 0.72/0.93 (assume @p7 (forall @t4 (=> (and @t8 @t18) @t17))) % 0.72/0.93 (assume @p8 (forall @t7 (exists @t19 (tptp.element @t2 @t1)))) % 0.72/0.93 (assume @p9 (forall @t4 (=> @t21 (and (tptp.empty @t20) (tptp.relation @t20))))) % 0.72/0.93 (assume @p10 (and @t23 @t22 (tptp.relation_empty_yielding tptp.empty_set))) % 0.72/0.93 (assume @p11 (forall @t4 (=> (and @t8 @t5 @t18 @t24) (and @t17 (tptp.function @t16))))) % 0.72/0.93 (assume @p12 @t23) % 0.72/0.93 (assume @p13 (and @t23 @t22)) % 0.72/0.93 (assume @p14 (forall @t7 (=> @t28 (not @t26)))) % 0.72/0.93 (assume @p15 (forall @t7 (=> @t28 (not @t30)))) % 0.72/0.93 (assume @p16 (forall @t7 (=> @t6 (and @t26 (tptp.relation @t25))))) % 0.72/0.93 (assume @p17 (forall @t7 (=> @t6 (and @t30 (tptp.relation @t29))))) % 0.72/0.93 (assume @p18 (forall @t4 (=> @t21 (and (tptp.empty @t16) @t17)))) % 0.72/0.93 (assume @p19 (exists @t7 @t14)) % 0.72/0.93 (assume @p20 (exists @t7 (and @t6 @t8))) % 0.72/0.93 (assume @p21 (exists @t7 @t6)) % 0.72/0.93 (assume @p22 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cong :premises (@p208) :args ((forall @t7 (=> @t14 @t192)))) % 0.72/0.93 (step @p210 :rule trans :premises (@p209 @p202)) % 0.72/0.93 (step @p211 :rule aci_norm :args ((= (or @t98 @t188) @t189))) % 0.72/0.93 (step @p212 :rule refl :args (@t188)) % 0.72/0.93 (step @p213 :rule nary_cong :premises (@p52 @p212) :args ((or @t99 @t188))) % 0.72/0.93 (step @p214 :rule trans :premises (@p213 @p211)) % 0.72/0.93 (step @p215 :rule bool-impl-elim :args (@t43 @t188)) % 0.72/0.93 (step @p216 :rule trans :premises (@p215 @p214)) % 0.72/0.93 (step @p217 :rule cong :premises (@p216) :args ((forall @t19 (=> @t43 @t188)))) % 0.72/0.93 (step @p218 :rule aci_norm :args ((= (and @t186 (and @t185 @t181)) @t187))) % 0.72/0.93 (step @p219 :rule aci_norm :args ((= (or @t160 false @t179) @t180))) % 0.72/0.93 (step @p220 :rule refl :args (@t179)) % 0.72/0.93 (step @p221 :rule evaluate :args ((not true))) % 0.72/0.93 (step @p222 :rule eq-refl :args (@t158)) % 0.72/0.93 (step @p223 :rule cong :premises (@p222) :args (@t193)) % 0.72/0.93 (step @p224 :rule trans :premises (@p223 @p221)) % 0.72/0.93 (step @p225 :rule refl :args (@t160)) % 0.72/0.93 (step @p226 :rule nary_cong :premises (@p225 @p224 @p220) :args (@t194)) % 0.72/0.93 (step @p227 :rule trans :premises (@p226 @p219)) % 0.72/0.93 (step @p228 :rule cong :premises (@p227) :args ((forall @t161 @t194))) % 0.72/0.93 (step @p229 :rule quant-var-elim-eq :args ((= (forall @t199 @t198) @t194))) % 0.72/0.93 (step @p230 :rule aci_norm :args ((= @t200 @t198))) % 0.72/0.93 (step @p231 :rule cong :premises (@p230) :args (@t201)) % 0.72/0.93 (step @p232 :rule trans :premises (@p231 @p229)) % 0.72/0.93 (step @p233 :rule cong :premises (@p232) :args (@t202)) % 0.72/0.93 (step @p234 :rule quant-merge-prenex :args ((= @t202 @t203))) % 0.72/0.93 (step @p235 :rule symm :premises (@p234)) % 0.72/0.93 (step @p236 :rule quant_var_reordering :args ((= @t204 @t203))) % 0.72/0.93 (step @p237 :rule trans :premises (@p236 @p235 @p233)) % 0.72/0.93 (step @p238 :rule trans :premises (@p237 @p228)) % 0.72/0.93 (step @p239 :rule aci_norm :args ((= (or @t164 false @t183) @t184))) % 0.72/0.93 (step @p240 :rule refl :args (@t183)) % 0.72/0.93 (step @p241 :rule eq-refl :args (@t182)) % 0.72/0.93 (step @p242 :rule cong :premises (@p241) :args (@t205)) % 0.72/0.93 (step @p243 :rule trans :premises (@p242 @p221)) % 0.72/0.93 (step @p244 :rule refl :args (@t164)) % 0.72/0.93 (step @p245 :rule nary_cong :premises (@p244 @p243 @p240) :args (@t206)) % 0.72/0.93 (step @p246 :rule trans :premises (@p245 @p239)) % 0.72/0.93 (step @p247 :rule cong :premises (@p246) :args ((forall @t165 @t206))) % 0.72/0.93 (step @p248 :rule quant-var-elim-eq :args ((= (forall @t211 @t210) @t206))) % 0.72/0.93 (step @p249 :rule aci_norm :args ((= @t212 @t210))) % 0.72/0.93 (step @p250 :rule cong :premises (@p249) :args (@t213)) % 0.72/0.93 (step @p251 :rule trans :premises (@p250 @p248)) % 0.72/0.93 (step @p252 :rule cong :premises (@p251) :args (@t214)) % 0.72/0.93 (step @p253 :rule quant-merge-prenex :args ((= @t214 @t215))) % 0.72/0.93 (step @p254 :rule symm :premises (@p253)) % 0.72/0.93 (step @p255 :rule trans :premises (@p254 @p252)) % 0.72/0.93 (step @p256 :rule trans :premises (@p255 @p247)) % 0.72/0.93 (step @p257 :rule nary_cong :premises (@p256 @p238) :args ((and @t215 @t204))) % 0.72/0.93 (step @p258 :rule alpha_equiv :args (@t219 @t220 (@list @t195 @t157))) % 0.72/0.93 (step @p259 :rule alpha_equiv :args (@t224 @t220 (@list @t162 @t207))) % 0.72/0.93 (step @p260 :rule nary_cong :premises (@p259 @p258) :args (@t225)) % 0.72/0.93 (step @p261 :rule quant-miniscope-and :args ((= (forall @t55 (and @t223 @t218)) @t225))) % 0.72/0.93 (step @p262 :rule trans :premises (@p261 @p260)) % 0.72/0.93 (step @p263 :rule trans :premises (@p262 @p257)) % 0.72/0.93 (step @p264 :rule aci_norm :args ((= (or (or @t217 @t216) @t50) @t218))) % 0.72/0.93 (step @p265 :rule refl :args (@t50)) % 0.72/0.93 (step @p266 :rule bool-and-de-morgan :args (@t52 @t51 true)) % 0.72/0.93 (step @p267 :rule nary_cong :premises (@p266 @p265) :args ((or (not @t53) @t50))) % 0.72/0.93 (step @p268 :rule trans :premises (@p267 @p264)) % 0.72/0.93 (step @p269 :rule bool-impl-elim :args (@t53 @t50)) % 0.72/0.93 (step @p270 :rule trans :premises (@p269 @p268)) % 0.72/0.93 (step @p271 :rule aci_norm :args ((= (or (or @t222 @t221) @t53) @t223))) % 0.72/0.93 (step @p272 :rule refl :args (@t53)) % 0.72/0.93 (step @p273 :rule bool-and-de-morgan :args (@t49 @t48 true)) % 0.72/0.93 (step @p274 :rule nary_cong :premises (@p273 @p272) :args ((or (not @t50) @t53))) % 0.72/0.93 (step @p275 :rule trans :premises (@p274 @p271)) % 0.72/0.93 (step @p276 :rule bool-impl-elim :args (@t50 @t53)) % 0.72/0.93 (step @p277 :rule trans :premises (@p276 @p275)) % 0.72/0.93 (step @p278 :rule nary_cong :premises (@p277 @p270) :args (@t54)) % 0.72/0.93 (step @p279 :rule cong :premises (@p278) :args (@t56)) % 0.72/0.93 (step @p280 :rule trans :premises (@p279 @p263)) % 0.72/0.93 (step @p281 :rule eq-symm :args (@t35 @t29)) % 0.72/0.93 (step @p282 :rule nary_cong :premises (@p281 @p280) :args (@t57)) % 0.72/0.93 (step @p283 :rule trans :premises (@p282 @p218)) % 0.72/0.93 (step @p284 :rule refl :args (@t58)) % 0.72/0.93 (step @p285 :rule cong :premises (@p284 @p283) :args (@t59)) % 0.72/0.93 (step @p286 :rule cong :premises (@p72 @p285) :args (@t60)) % 0.72/0.93 (step @p287 :rule cong :premises (@p286) :args (@t61)) % 0.72/0.93 (step @p288 :rule trans :premises (@p287 @p217)) % 0.72/0.93 (step @p289 :rule refl :args (@t9)) % 0.72/0.93 (step @p290 :rule cong :premises (@p289 @p288) :args (@t62)) % 0.72/0.93 (step @p291 :rule refl :args (@t14)) % 0.72/0.93 (step @p292 :rule cong :premises (@p291 @p290) :args (@t63)) % 0.72/0.93 (step @p293 :rule cong :premises (@p292) :args (@t64)) % 0.72/0.93 (step @p294 :rule trans :premises (@p293 @p210)) % 0.72/0.93 (step @p295 :rule eq_resolve :premises (@p30 @p294)) % 0.72/0.93 (step @p296 :rule bool-eq-true :args (@t229)) % 0.72/0.93 (step @p297 :rule eq-symm :args (true @t229)) % 0.72/0.93 (step @p298 :rule trans :premises (@p297 @p296)) % 0.72/0.93 (step @p299 :rule refl :args (@t229)) % 0.72/0.93 (step @p300 :rule eq-refl :args (@t108)) % 0.72/0.93 (step @p301 :rule cong :premises (@p300 @p299) :args ((= @t230 @t229))) % 0.72/0.93 (step @p302 :rule trans :premises (@p301 @p298)) % 0.72/0.93 (step @p303 :rule eq-symm :args (@t229 @t230)) % 0.72/0.93 (step @p304 :rule trans :premises (@p303 @p302)) % 0.72/0.93 (step @p305 :rule refl :args (@t136)) % 0.72/0.93 (step @p306 :rule nary_cong :premises (@p79 @p78 @p305 @p82 @p81 @p304) :args (@t231)) % 0.72/0.93 (step @p307 :rule refl :args (@t232)) % 0.72/0.93 (step @p308 :rule cong :premises (@p307 @p306) :args ((=> @t232 @t231))) % 0.72/0.93 (assume-push @p346 @t232) % 0.72/0.93 (step @p310 :rule instantiate :premises (@p295) :args ((@list @t107 @t108))) % 0.72/0.93 (step-pop @p347 :rule scope :premises (@p310)) % 0.72/0.93 (step @p311 :rule process_scope :premises (@p347) :args (@t231)) % 0.72/0.93 (step @p313 :rule eq_resolve :premises (@p311 @p308)) % 0.72/0.93 (step @p314 :rule implies_elim :premises (@p313)) % 0.72/0.93 (step @p315 :rule chain_m_resolution :premises (@p314 @p295) :args (@t233 @t127 (@list @t232))) % 0.72/0.93 (step @p316 :rule cnf_or_pos :args (@t233)) % 0.72/0.93 (step @p317 :rule reordering :premises (@p316) :args ((or @t115 @t113 @t136 @t122 @t120 @t229 (not @t233)))) % 0.72/0.93 (step @p318 :rule chain_m_resolution :premises (@p317 @p144 @p138 @p132 @p173 @p170 @p315) :args (@t229 @t154 (@list @t114 @t112 @t135 @t121 @t119 @t233))) % 0.72/0.93 (step @p319 :rule cnf_and_pos :args (@t229 1)) % 0.72/0.93 (step @p320 :rule reordering :premises (@p319) :args ((or @t228 (not @t229)))) % 0.72/0.93 (step @p321 :rule chain_m_resolution :premises (@p320 @p318) :args (@t228 @t127 (@list @t229))) % 0.72/0.93 (step @p322 :rule instantiate :premises (@p321) :args ((@list @t106))) % 0.72/0.93 (step @p323 :rule cnf_or_pos :args (@t235)) % 0.72/0.93 (step @p324 :rule reordering :premises (@p323) :args ((or @t134 @t234 (not @t235)))) % 0.72/0.93 (step @p325 :rule chain_m_resolution :premises (@p324 @p115 @p322) :args (@t234 (@list false false) (@list @t130 @t235))) % 0.72/0.93 (step @p326 :rule cnf_and_pos :args (@t234 1)) % 0.72/0.93 (step @p327 :rule reordering :premises (@p326) :args ((or @t132 (not @t234)))) % 0.72/0.93 (step @p328 :rule chain_m_resolution :premises (@p327 @p325) :args (@t132 @t127 (@list @t234))) % 0.72/0.93 (step @p329 :rule cnf_or_neg :args (@t137 4)) % 0.72/0.93 (step @p330 :rule chain_m_resolution :premises (@p329 @p108) :args ((not @t133) @t138 @t139)) % 0.72/0.93 (step @p331 :rule cnf_and_neg :args (@t133)) % 0.72/0.93 (step @p332 :rule chain_m_resolution :premises (@p331 @p330 @p328) :args ((not @t131) (@list true false) (@list @t133 @t132))) % 0.72/0.93 (assume-push @p348 @t132) % 0.72/0.93 (assume-push @p349 @t125) % 0.72/0.93 (step @p335 :rule trans :premises (@p328 @p176)) % 0.72/0.93 (step-pop @p350 :rule scope :premises (@p335)) % 0.72/0.93 (step-pop @p351 :rule scope :premises (@p350)) % 0.72/0.93 (step @p336 :rule process_scope :premises (@p351) :args (@t131)) % 0.72/0.93 (step @p339 :rule implies_elim :premises (@p336)) % 0.72/0.93 (step @p340 :rule cnf_and_neg :args (@t236)) % 0.72/0.93 (step @p341 :rule resolution :premises (@p340 @p339) :args (true @t236)) % 0.72/0.93 (step @p342 :rule reordering :premises (@p341) :args ((or @t131 (not @t132) (not @t125)))) % 0.72/0.93 (step @p343 false :rule chain_m_resolution :premises (@p342 @p332 @p328 @p176) :args (false (@list true false false) (@list @t131 @t132 @t125))) % 0.72/0.93 ) % 0.72/0.93 % SZS output end Proof % 0.72/0.93 % cvc5 exiting %------------------------------------------------------------------------------