%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU802^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:53:16 AM UTC 2026 % Result : Theorem 0.36s 0.59s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU802^2 : TPTP v9.2.1. Released v3.7.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n011.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 17:52:05 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.49 %----Proving TH0 % 0.36/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.59 % SZS status Theorem % 0.36/0.59 % SZS output start Proof % 0.36/0.59 ( % 0.36/0.59 (declare-sort $$unsorted 0) % 0.36/0.59 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.funcSet (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.36/0.59 (declare-const tptp.dsetconstrER Bool) % 0.36/0.59 (define tptp.surjective () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xy" $$unsorted))) (let ((_let_3 (@var "Xf" $$unsorted))) (let ((_let_4 (@var "B" $$unsorted))) (let ((_let_5 (@var "A" $$unsorted))) (lambda (@list _let_5 _let_4 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.in _let_1) _let_4) (exists (@list _let_2) (and (_ (_ tptp.in _let_2) _let_5) (= (_ (_ (_ (_ tptp.ap _let_5) _let_4) _let_3) _let_2) _let_1)))))))))))) % 0.36/0.59 (define tptp.surjFuncSet () (let ((_let_1 (@var "Xf" $$unsorted))) (let ((_let_2 (@var "B" $$unsorted))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ (_ tptp.dsetconstr (_ (_ tptp.funcSet _let_3) _let_2)) (lambda (@list _let_1) (_ (_ (_ tptp.surjective _let_3) _let_2) _let_1)))))))) % 0.36/0.59 (define @t1 () (@var "Xx" $$unsorted)) % 0.36/0.59 (define @t2 () (@var "Xphi" (-> $$unsorted Bool))) % 0.36/0.59 (define @t3 () (_ @t2 @t1)) % 0.36/0.59 (define @t4 () (@var "Xy" $$unsorted)) % 0.36/0.59 (define @t5 () (_ @t2 @t4)) % 0.36/0.59 (define @t6 () (@list @t4)) % 0.36/0.59 (define @t7 () (lambda @t6 @t5)) % 0.36/0.59 (define @t8 () (@var "A" $$unsorted)) % 0.36/0.59 (define @t9 () (_ tptp.dsetconstr @t8)) % 0.36/0.59 (define @t10 () (_ @t9 @t7)) % 0.36/0.59 (define @t11 () (_ tptp.in @t1)) % 0.36/0.59 (define @t12 () (_ @t11 @t10)) % 0.36/0.59 (define @t13 () (@list @t8 @t2 @t1)) % 0.36/0.59 (define @t14 () (forall @t13 (=> @t12 @t3))) % 0.36/0.59 (define @t15 () (= tptp.dsetconstrER @t14)) % 0.36/0.59 (define @t16 () (@var "Xf" $$unsorted)) % 0.36/0.59 (define @t17 () (_ tptp.in @t16)) % 0.36/0.59 (define @t18 () (=> (_ @t17 (_ (_ tptp.surjFuncSet @t1) @t4)) (_ (_ (_ tptp.surjective @t1) @t4) @t16))) % 0.36/0.59 (define @t19 () (@list @t1 @t4 @t16)) % 0.36/0.59 (define @t20 () (forall @t19 @t18)) % 0.36/0.59 (define @t21 () (=> tptp.dsetconstrER @t20)) % 0.36/0.59 (define @t22 () (not @t21)) % 0.36/0.59 (define @t23 () (@var "B" $$unsorted)) % 0.36/0.59 (define @t24 () (_ (_ (_ (_ tptp.ap @t8) @t23) @t16) @t4)) % 0.36/0.59 (define @t25 () (_ (_ tptp.in @t4) @t8)) % 0.36/0.59 (define @t26 () (and @t25 (= @t24 @t1))) % 0.36/0.59 (define @t27 () (exists @t6 @t26)) % 0.36/0.59 (define @t28 () (_ @t11 @t23)) % 0.36/0.59 (define @t29 () (=> @t28 @t27)) % 0.36/0.59 (define @t30 () (@list @t1)) % 0.36/0.59 (define @t31 () (forall @t30 @t29)) % 0.36/0.59 (define @t32 () (@list @t8 @t23 @t16)) % 0.36/0.59 (define @t33 () (lambda @t32 @t31)) % 0.36/0.59 (define @t34 () (@list @t16)) % 0.36/0.59 (define @t35 () (lambda @t34 (_ (_ (_ tptp.surjective @t8) @t23) @t16))) % 0.36/0.59 (define @t36 () (_ tptp.dsetconstr (_ (_ tptp.funcSet @t8) @t23))) % 0.36/0.59 (define @t37 () (@list @t8 @t23)) % 0.36/0.59 (define @t38 () (lambda @t37 (_ @t36 @t35))) % 0.36/0.59 (define @t39 () (@var "BOUND_VARIABLE_7764" $$unsorted)) % 0.36/0.59 (define @t40 () (@var "BOUND_VARIABLE_7696" $$unsorted)) % 0.36/0.59 (define @t41 () (tptp.ap @t1 @t4 @t16 @t40)) % 0.36/0.59 (define @t42 () (not (tptp.in @t40 @t1))) % 0.36/0.59 (define @t43 () (@list @t40)) % 0.36/0.59 (define @t44 () (not (tptp.in @t39 @t4))) % 0.36/0.59 (define @t45 () (@var "BOUND_VARIABLE_7628" $$unsorted)) % 0.36/0.59 (define @t46 () (@var "BOUND_VARIABLE_7736" $$unsorted)) % 0.36/0.59 (define @t47 () (tptp.ap @t1 @t4 @t46 @t45)) % 0.36/0.59 (define @t48 () (@var "BOUND_VARIABLE_7572" $$unsorted)) % 0.36/0.59 (define @t49 () (= @t48 @t47)) % 0.36/0.59 (define @t50 () (not @t49)) % 0.36/0.59 (define @t51 () (tptp.in @t45 @t1)) % 0.36/0.59 (define @t52 () (not @t51)) % 0.36/0.59 (define @t53 () (or @t52 @t50)) % 0.36/0.59 (define @t54 () (@list @t45)) % 0.36/0.59 (define @t55 () (forall @t54 @t53)) % 0.36/0.59 (define @t56 () (not @t55)) % 0.36/0.59 (define @t57 () (tptp.in @t48 @t4)) % 0.36/0.59 (define @t58 () (not @t57)) % 0.36/0.59 (define @t59 () (or @t58 @t56)) % 0.36/0.59 (define @t60 () (@list @t48)) % 0.36/0.59 (define @t61 () (forall @t60 @t59)) % 0.36/0.59 (define @t62 () (@list @t46)) % 0.36/0.59 (define @t63 () (lambda @t62 @t61)) % 0.36/0.59 (define @t64 () (tptp.funcSet @t1 @t4)) % 0.36/0.59 (define @t65 () (tptp.dsetconstr @t64 @t63)) % 0.36/0.59 (define @t66 () (tptp.in @t16 @t65)) % 0.36/0.59 (define @t67 () (not @t66)) % 0.36/0.59 (define @t68 () (@list @t1 @t4 @t16 @t39)) % 0.36/0.59 (define @t69 () (forall @t68 (or @t67 @t44 (not (forall @t43 (or @t42 (not (= @t41 @t39)))))))) % 0.36/0.59 (define @t70 () (_ @t2 @t1)) % 0.36/0.59 (define @t71 () (_ @t2 @t4)) % 0.36/0.59 (define @t72 () (lambda @t6 @t71)) % 0.36/0.59 (define @t73 () (tptp.dsetconstr @t8 @t72)) % 0.36/0.59 (define @t74 () (tptp.in @t1 @t73)) % 0.36/0.59 (define @t75 () (not @t74)) % 0.36/0.59 (define @t76 () (or @t75 @t70)) % 0.36/0.59 (define @t77 () (not @t12)) % 0.36/0.59 (define @t78 () (or @t77 @t3)) % 0.36/0.59 (define @t79 () (=> tptp.dsetconstrER @t69)) % 0.36/0.59 (define @t80 () (not (= @t39 @t41))) % 0.36/0.59 (define @t81 () (or @t42 @t80)) % 0.36/0.59 (define @t82 () (forall @t43 @t81)) % 0.36/0.59 (define @t83 () (not @t82)) % 0.36/0.59 (define @t84 () (or @t67 @t44 @t83)) % 0.36/0.59 (define @t85 () (or @t44 @t83)) % 0.36/0.59 (define @t86 () (or @t67 @t85)) % 0.36/0.59 (define @t87 () (forall @t68 @t86)) % 0.36/0.59 (define @t88 () (@list @t39)) % 0.36/0.59 (define @t89 () (forall @t88 @t86)) % 0.36/0.59 (define @t90 () (forall @t88 @t85)) % 0.36/0.59 (define @t91 () (@var "BOUND_VARIABLE_7660" $$unsorted)) % 0.36/0.59 (define @t92 () (@list @t91)) % 0.36/0.59 (define @t93 () (or @t67 @t90)) % 0.36/0.59 (define @t94 () (@list @t91)) % 0.36/0.59 (define @t95 () (forall @t94 (or (not (tptp.in @t91 @t4)) (not (forall @t43 (or @t42 (not (= @t91 @t41)))))))) % 0.36/0.59 (define @t96 () (lambda @t62 (forall @t60 (or (not (_ (_ tptp.in @t48) @t4)) (not (forall @t54 (or (not (_ (_ tptp.in @t45) @t1)) (not (= @t48 (_ (_ (_ (_ tptp.ap @t1) @t4) @t46) @t45)))))))))) % 0.36/0.59 (define @t97 () (_ tptp.funcSet @t1)) % 0.36/0.59 (define @t98 () (_ @t97 @t4)) % 0.36/0.59 (define @t99 () (_ tptp.dsetconstr @t98)) % 0.36/0.59 (define @t100 () (_ @t99 @t96)) % 0.36/0.59 (define @t101 () (_ @t17 (_ @t99 @t63))) % 0.36/0.59 (define @t102 () (not @t101)) % 0.36/0.59 (define @t103 () (or @t102 @t95)) % 0.36/0.59 (define @t104 () (lambda @t34 (forall @t60 (or @t58 (not (forall @t54 (or @t52 (not (= @t48 (tptp.ap @t1 @t4 @t16 @t45)))))))))) % 0.36/0.59 (define @t105 () (_ @t99 @t104)) % 0.36/0.59 (define @t106 () (=> (_ @t17 @t105) @t95)) % 0.36/0.59 (define @t107 () (lambda @t34 @t95)) % 0.36/0.59 (define @t108 () (tptp.ap @t1 @t23 @t16 @t40)) % 0.36/0.59 (define @t109 () (not (tptp.in @t91 @t23))) % 0.36/0.59 (define @t110 () (@list @t23 @t16)) % 0.36/0.59 (define @t111 () (not (= @t108 @t91))) % 0.36/0.59 (define @t112 () (or @t42 @t111)) % 0.36/0.59 (define @t113 () (forall @t43 @t112)) % 0.36/0.59 (define @t114 () (not @t113)) % 0.36/0.59 (define @t115 () (or @t109 @t114)) % 0.36/0.59 (define @t116 () (forall @t94 @t115)) % 0.36/0.59 (define @t117 () (tptp.ap @t1 @t23 @t16 @t4)) % 0.36/0.59 (define @t118 () (not (tptp.in @t4 @t1))) % 0.36/0.59 (define @t119 () (forall @t6 (or @t118 (not (= @t117 @t91))))) % 0.36/0.59 (define @t120 () (@list @t4)) % 0.36/0.59 (define @t121 () (@list @t40)) % 0.36/0.59 (define @t122 () (not @t119)) % 0.36/0.59 (define @t123 () (or @t109 @t122)) % 0.36/0.59 (define @t124 () (forall @t94 @t123)) % 0.36/0.59 (define @t125 () (lambda @t110 @t124)) % 0.36/0.59 (define @t126 () (tptp.ap @t8 @t23 @t16 @t4)) % 0.36/0.59 (define @t127 () (tptp.in @t4 @t8)) % 0.36/0.59 (define @t128 () (not @t127)) % 0.36/0.59 (define @t129 () (not (= @t91 @t126))) % 0.36/0.59 (define @t130 () (or @t128 @t129)) % 0.36/0.59 (define @t131 () (forall @t6 @t130)) % 0.36/0.59 (define @t132 () (not @t131)) % 0.36/0.59 (define @t133 () (or @t109 @t132)) % 0.36/0.59 (define @t134 () (forall @t94 @t133)) % 0.36/0.59 (define @t135 () (not (forall @t6 (or @t128 (not (= @t1 @t126)))))) % 0.36/0.59 (define @t136 () (tptp.in @t1 @t23)) % 0.36/0.59 (define @t137 () (forall @t30 (or (not @t136) @t135))) % 0.36/0.59 (define @t138 () (@list @t1)) % 0.36/0.59 (define @t139 () (lambda @t32 @t137)) % 0.36/0.59 (define @t140 () (not (tptp.in @t48 @t23))) % 0.36/0.59 (define @t141 () (_ tptp.dsetconstr (_ @t97 @t23))) % 0.36/0.59 (define @t142 () (@list @t23)) % 0.36/0.59 (define @t143 () (forall @t6 (or @t118 (not (= @t48 @t117))))) % 0.36/0.59 (define @t144 () (@list @t45)) % 0.36/0.59 (define @t145 () (not @t143)) % 0.36/0.59 (define @t146 () (or @t140 @t145)) % 0.36/0.59 (define @t147 () (forall @t60 @t146)) % 0.36/0.59 (define @t148 () (lambda @t34 @t147)) % 0.36/0.59 (define @t149 () (not (= @t117 @t48))) % 0.36/0.59 (define @t150 () (or @t118 @t149)) % 0.36/0.59 (define @t151 () (forall @t6 @t150)) % 0.36/0.59 (define @t152 () (not @t151)) % 0.36/0.59 (define @t153 () (or @t140 @t152)) % 0.36/0.59 (define @t154 () (forall @t60 @t153)) % 0.36/0.59 (define @t155 () (lambda @t34 @t154)) % 0.36/0.59 (define @t156 () (lambda @t142 (_ @t141 @t155))) % 0.36/0.59 (define @t157 () (not (= @t48 @t126))) % 0.36/0.59 (define @t158 () (or @t128 @t157)) % 0.36/0.59 (define @t159 () (forall @t6 @t158)) % 0.36/0.59 (define @t160 () (not @t159)) % 0.36/0.59 (define @t161 () (or @t140 @t160)) % 0.36/0.59 (define @t162 () (forall @t60 @t161)) % 0.36/0.59 (define @t163 () (lambda @t34 @t162)) % 0.36/0.59 (define @t164 () (lambda @t34 @t137)) % 0.36/0.59 (define @t165 () (lambda @t37 (_ @t36 @t164))) % 0.36/0.59 (define @t166 () (=> (_ @t17 (_ (_ @t165 @t1) @t4)) (_ (_ (_ @t139 @t1) @t4) @t16))) % 0.36/0.59 (define @t167 () (forall @t19 @t166)) % 0.36/0.59 (define @t168 () (=> tptp.dsetconstrER @t167)) % 0.36/0.59 (define @t169 () (not @t28)) % 0.36/0.59 (define @t170 () (or @t169 @t135)) % 0.36/0.59 (define @t171 () (= @t1 @t24)) % 0.36/0.59 (define @t172 () (not @t171)) % 0.36/0.59 (define @t173 () (not @t25)) % 0.36/0.59 (define @t174 () (or @t173 @t172)) % 0.36/0.59 (define @t175 () (and @t25 @t171)) % 0.36/0.59 (define @t176 () (forall @t6 (not @t175))) % 0.36/0.59 (define @t177 () (not @t176)) % 0.36/0.59 (define @t178 () (lambda @t110 @t137)) % 0.36/0.59 (define @t179 () (_ @t139 @t8)) % 0.36/0.59 (define @t180 () (@quantifiers_skolemize @t69 2)) % 0.36/0.59 (define @t181 () (@quantifiers_skolemize @t69 1)) % 0.36/0.59 (define @t182 () (@quantifiers_skolemize @t69 0)) % 0.36/0.59 (define @t183 () (tptp.ap @t182 @t181 @t180 @t40)) % 0.36/0.59 (define @t184 () (@quantifiers_skolemize @t69 3)) % 0.36/0.59 (define @t185 () (not (tptp.in @t40 @t182))) % 0.36/0.59 (define @t186 () (forall @t43 (or @t185 (not (= @t184 @t183))))) % 0.36/0.59 (define @t187 () (not @t186)) % 0.36/0.59 (define @t188 () (tptp.in @t184 @t181)) % 0.36/0.59 (define @t189 () (not @t188)) % 0.36/0.59 (define @t190 () (not (tptp.in @t45 @t182))) % 0.36/0.59 (define @t191 () (not (tptp.in @t48 @t181))) % 0.36/0.59 (define @t192 () (forall @t60 (or @t191 (not (forall @t54 (or @t190 (not (= @t48 (tptp.ap @t182 @t181 @t46 @t45))))))))) % 0.36/0.59 (define @t193 () (lambda @t62 @t192)) % 0.36/0.59 (define @t194 () (@purify @t193)) % 0.36/0.59 (define @t195 () (tptp.funcSet @t182 @t181)) % 0.36/0.59 (define @t196 () (tptp.in @t180 (tptp.dsetconstr @t195 @t194))) % 0.36/0.59 (define @t197 () (not @t196)) % 0.36/0.59 (define @t198 () (or @t197 @t189 @t187)) % 0.36/0.59 (define @t199 () (not @t198)) % 0.36/0.59 (define @t200 () (not @t69)) % 0.36/0.59 (define @t201 () (tptp.dsetconstr @t195 @t193)) % 0.36/0.59 (define @t202 () (tptp.in @t180 @t201)) % 0.36/0.59 (define @t203 () (not @t202)) % 0.36/0.59 (define @t204 () (or @t203 @t189 @t187)) % 0.36/0.59 (define @t205 () (not @t204)) % 0.36/0.59 (define @t206 () (not (= @t183 @t184))) % 0.36/0.59 (define @t207 () (or @t185 @t206)) % 0.36/0.59 (define @t208 () (forall @t43 @t207)) % 0.36/0.59 (define @t209 () (not @t208)) % 0.36/0.59 (define @t210 () (or @t203 @t189 @t209)) % 0.36/0.59 (define @t211 () (not @t210)) % 0.36/0.59 (define @t212 () (@list true)) % 0.36/0.59 (define @t213 () (@list @t198)) % 0.36/0.59 (define @t214 () (tptp.ap @t182 @t181 @t180 @t45)) % 0.36/0.59 (define @t215 () (forall @t54 (or @t190 (not (= @t184 @t214))))) % 0.36/0.59 (define @t216 () (@list false)) % 0.36/0.59 (define @t217 () (_ @t194 @t46)) % 0.36/0.59 (define @t218 () (_ @t193 @t46)) % 0.36/0.59 (define @t219 () (= @t217 @t218)) % 0.36/0.59 (define @t220 () (forall @t62 @t219)) % 0.36/0.59 (define @t221 () (forall @t60 (or @t191 (not (forall @t54 (or @t190 (not (= @t48 @t214)))))))) % 0.36/0.59 (define @t222 () (_ @t194 @t180)) % 0.36/0.59 (define @t223 () (forall @t62 (= @t192 @t217))) % 0.36/0.59 (define @t224 () (= @t221 @t222)) % 0.36/0.59 (define @t225 () (= @t222 @t221)) % 0.36/0.59 (define @t226 () (or @t197 @t222)) % 0.36/0.59 (define @t227 () (@list false false)) % 0.36/0.59 (define @t228 () (not @t215)) % 0.36/0.59 (define @t229 () (or @t189 @t228)) % 0.36/0.59 (assume @p1 @t15) % 0.36/0.59 (assume @p2 @t22) % 0.36/0.59 (assume @p3 true) % 0.36/0.59 (step @p4 (= tptp.surjective @t33) :rule refl :args (@t33)) % 0.36/0.59 (step @p5 (= tptp.surjFuncSet @t38) :rule refl :args (@t38)) % 0.36/0.59 (step @p6 :rule refl :args (@t69)) % 0.36/0.59 (step @p7 :rule refl :args (@t70)) % 0.36/0.59 (step @p8 :rule lambda-elim :args ((= @t72 @t2))) % 0.36/0.59 (step @p9 :rule refl :args (@t8)) % 0.36/0.59 (step @p10 :rule cong :premises (@p9 @p8) :args (@t73)) % 0.36/0.59 (step @p11 :rule refl :args (@t1)) % 0.36/0.59 (step @p12 :rule cong :premises (@p11 @p10) :args (@t74)) % 0.36/0.59 (step @p13 :rule cong :premises (@p12) :args (@t75)) % 0.36/0.59 (step @p14 :rule nary_cong :premises (@p13 @p7) :args (@t76)) % 0.36/0.59 (step @p15 :rule cong :premises (@p14) :args ((forall @t13 @t76))) % 0.36/0.60 (step @p16 :rule refl :args (@t70)) % 0.36/0.60 (step @p17 :rule refl :args (@t3)) % 0.36/0.60 (step @p18 :rule cong :premises (@p17 @p16) :args ((= @t3 @t70))) % 0.36/0.60 (step @p19 :rule symm :premises (@p18)) % 0.36/0.60 (step @p20 :rule eq_resolve :premises (@p17 @p19)) % 0.36/0.60 (step @p21 :rule refl :args ((tptp.in @t1 @t10))) % 0.36/0.60 (step @p22 :rule refl :args ((tptp.dsetconstr @t8 @t7))) % 0.36/0.60 (step @p23 :rule refl :args (@t71)) % 0.36/0.60 (step @p24 :rule cong :premises (@p23) :args (@t72)) % 0.36/0.60 (step @p25 :rule refl :args (@t8)) % 0.36/0.60 (step @p26 :rule cong :premises (@p25 @p24) :args (@t73)) % 0.36/0.60 (step @p27 :rule trans :premises (@p26 @p22)) % 0.36/0.60 (step @p28 :rule refl :args (@t1)) % 0.36/0.60 (step @p29 :rule cong :premises (@p28 @p27) :args (@t74)) % 0.36/0.60 (step @p30 :rule trans :premises (@p29 @p21)) % 0.36/0.60 (step @p31 :rule refl :args (@t11)) % 0.36/0.60 (step @p32 :rule ho_cong :premises (@p31 @p27)) % 0.36/0.60 (step @p33 :rule cong :premises 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(step @p81 :rule trans :premises (@p80 @p79)) % 0.36/0.60 (step @p82 :rule symm :premises (@p81)) % 0.36/0.60 (step @p83 :rule cong :premises (@p82) :args ((forall @t19 (or @t67 @t95)))) % 0.36/0.60 (step @p84 :rule trans :premises (@p83 @p76)) % 0.36/0.60 (step @p85 :rule trans :premises (@p84 @p75)) % 0.36/0.60 (step @p86 :rule refl :args (@t95)) % 0.36/0.60 (step @p87 :rule refl :args ((tptp.in @t16 @t100))) % 0.36/0.60 (step @p88 :rule refl :args ((tptp.dsetconstr @t98 @t96))) % 0.36/0.60 (step @p89 :rule refl :args (@t47)) % 0.36/0.60 (step @p90 :rule refl :args (@t48)) % 0.36/0.60 (step @p91 :rule cong :premises (@p90 @p89) :args (@t49)) % 0.36/0.60 (step @p92 :rule cong :premises (@p91) :args (@t50)) % 0.36/0.60 (step @p93 :rule refl :args (@t51)) % 0.36/0.60 (step @p94 :rule cong :premises (@p93) :args (@t52)) % 0.36/0.60 (step @p95 :rule nary_cong :premises (@p94 @p92) :args (@t53)) % 0.36/0.60 (step @p96 :rule cong :premises (@p95) :args (@t55)) % 0.36/0.60 (step @p97 :rule 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% 0.36/0.60 (step @p129 :rule trans :premises (@p128 @p121)) % 0.36/0.60 (step @p130 :rule ho_cong :premises (@p109 @p129)) % 0.36/0.60 (step @p131 :rule trans :premises (@p130 @p114)) % 0.36/0.60 (step @p132 :rule cong :premises (@p131) :args (@t102)) % 0.36/0.60 (step @p133 :rule nary_cong :premises (@p132 @p86) :args (@t103)) % 0.36/0.60 (step @p134 :rule cong :premises (@p133) :args ((forall @t19 @t103))) % 0.36/0.60 (step @p135 :rule trans :premises (@p134 @p85)) % 0.36/0.60 (step @p136 :rule bool-impl-elim :args (@t101 @t95)) % 0.36/0.60 (step @p137 :rule cong :premises (@p136) :args ((forall @t19 (=> @t101 @t95)))) % 0.36/0.60 (step @p138 :rule trans :premises (@p137 @p135)) % 0.36/0.60 (step @p139 :rule alpha_equiv :args (@t104 (@list @t16) (@list @t46))) % 0.36/0.60 (step @p140 :rule refl :args (@t99)) % 0.36/0.60 (step @p141 :rule ho_cong :premises (@p140 @p139)) % 0.36/0.60 (step @p142 :rule ho_cong :premises (@p109 @p141)) % 0.36/0.60 (step @p143 :rule cong :premises (@p142 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(step @p289 :rule trans :premises (@p4 @p288)) % 0.36/0.60 (step @p290 :rule ho_cong :premises (@p289 @p11)) % 0.36/0.60 (step @p291 :rule ho_cong :premises (@p290 @p149)) % 0.36/0.60 (step @p292 :rule ho_cong :premises (@p291 @p147)) % 0.36/0.60 (step @p293 :rule beta-reduce :args ((= (_ @t164 @t16) @t137))) % 0.36/0.60 (step @p294 :rule beta-reduce :args ((= (_ @t178 @t23) @t164))) % 0.36/0.60 (step @p295 :rule refl :args (@t23)) % 0.36/0.60 (step @p296 :rule beta-reduce :args ((= @t179 @t178))) % 0.36/0.60 (step @p297 :rule ho_cong :premises (@p296 @p295)) % 0.36/0.60 (step @p298 :rule trans :premises (@p297 @p294)) % 0.36/0.60 (step @p299 :rule ho_cong :premises (@p298 @p147)) % 0.36/0.60 (step @p300 :rule trans :premises (@p299 @p293)) % 0.36/0.60 (step @p301 :rule cong :premises (@p300) :args ((lambda @t34 (_ (_ @t179 @t23) @t16)))) % 0.36/0.60 (step @p302 :rule ho_cong :premises (@p225 @p301)) % 0.36/0.60 (step @p303 :rule ho_cong :premises (@p289 @p9)) % 0.36/0.60 (step @p304 :rule ho_cong :premises (@p303 @p295)) % 0.36/0.60 (step @p305 :rule ho_cong :premises (@p304 @p147)) % 0.36/0.60 (step @p306 :rule cong :premises (@p305) :args (@t35)) % 0.36/0.60 (step @p307 :rule ho_cong :premises (@p225 @p306)) % 0.36/0.60 (step @p308 :rule trans :premises (@p307 @p302)) % 0.36/0.60 (step @p309 :rule cong :premises (@p308) :args (@t38)) % 0.36/0.60 (step @p310 :rule trans :premises (@p5 @p309)) % 0.36/0.60 (step @p311 :rule ho_cong :premises (@p310 @p11)) % 0.36/0.60 (step @p312 :rule ho_cong :premises (@p311 @p149)) % 0.36/0.60 (step @p313 :rule ho_cong :premises (@p239 @p312)) % 0.36/0.60 (step @p314 :rule cong :premises (@p313 @p292) :args (@t18)) % 0.36/0.60 (step @p315 :rule cong :premises (@p314) :args (@t20)) % 0.36/0.60 (step @p316 :rule cong :premises (@p59 @p315) :args (@t21)) % 0.36/0.60 (step @p317 :rule cong :premises (@p316) :args (@t22)) % 0.36/0.60 (step @p318 :rule trans :premises (@p317 @p245)) % 0.36/0.60 (step @p319 :rule trans :premises (@p318 @p63)) % 0.36/0.60 (step @p320 :rule eq_resolve :premises (@p2 @p319)) % 0.36/0.60 (step @p321 :rule not_implies_elim2 :premises (@p320)) % 0.36/0.60 (step @p322 :rule refl :args (@t199)) % 0.36/0.60 (step @p323 :rule bool-double-not-elim :args (@t69)) % 0.36/0.60 (step @p324 :rule nary_cong :premises (@p323 @p322) :args ((or (not @t200) @t199))) % 0.36/0.60 (step @p325 :rule refl :args (@t187)) % 0.36/0.60 (step @p326 :rule refl :args (@t189)) % 0.36/0.60 (step @p327 :rule eq-refl :args (@t193)) % 0.36/0.60 (step @p328 :rule skolem_intro :args (@t194)) % 0.36/0.60 (step @p329 :rule refl :args (@t193)) % 0.36/0.60 (step @p330 :rule cong :premises (@p329 @p328) :args ((= @t193 @t194))) % 0.36/0.60 (step @p331 :rule trans :premises (@p330 @p327)) % 0.36/0.60 (step @p332 :rule true_elim :premises (@p331)) % 0.36/0.60 (step @p333 :rule refl :args (@t195)) % 0.36/0.60 (step @p334 :rule cong :premises (@p333 @p332) :args (@t201)) % 0.36/0.60 (step @p335 :rule refl :args (@t180)) % 0.36/0.60 (step @p336 :rule cong :premises (@p335 @p334) :args (@t202)) % 0.36/0.60 (step @p337 :rule cong :premises (@p336) :args (@t203)) % 0.36/0.60 (step @p338 :rule nary_cong :premises (@p337 @p326 @p325) :args (@t204)) % 0.36/0.60 (step @p339 :rule cong :premises (@p338) :args (@t205)) % 0.36/0.60 (step @p340 :rule refl :args (@t200)) % 0.36/0.60 (step @p341 :rule cong :premises (@p340 @p339) :args ((=> @t200 @t205))) % 0.36/0.60 (step @p342 :rule eq-symm :args (@t183 @t184)) % 0.36/0.60 (step @p343 :rule cong :premises (@p342) :args (@t206)) % 0.36/0.60 (step @p344 :rule refl :args (@t185)) % 0.36/0.60 (step @p345 :rule nary_cong :premises (@p344 @p343) :args (@t207)) % 0.36/0.60 (step @p346 :rule cong :premises (@p345) :args (@t208)) % 0.36/0.60 (step @p347 :rule cong :premises (@p346) :args (@t209)) % 0.36/0.60 (step @p348 :rule refl :args (@t203)) % 0.36/0.60 (step @p349 :rule nary_cong :premises (@p348 @p326 @p347) :args (@t210)) % 0.36/0.60 (step @p350 :rule cong :premises (@p349) 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(step @p378 :rule beta-reduce :args ((= @t218 @t192))) % 0.36/0.60 (step @p379 :rule refl :args (@t217)) % 0.36/0.60 (step @p380 :rule cong :premises (@p379 @p378) :args (@t219)) % 0.36/0.60 (step @p381 :rule trans :premises (@p380 @p377)) % 0.36/0.60 (step @p382 :rule cong :premises (@p381) :args (@t220)) % 0.36/0.60 (step @p383 :rule quant-unused-vars :args ((= (forall @t62 true) true))) % 0.36/0.60 (step @p384 :rule eq-refl :args (@t218)) % 0.36/0.60 (step @p385 :rule cong :premises (@p384) :args ((forall @t62 (= @t218 @t218)))) % 0.36/0.60 (step @p386 :rule trans :premises (@p385 @p383)) % 0.36/0.60 (step @p387 :rule refl :args (@t218)) % 0.36/0.60 (step @p388 :rule refl :args (@t46)) % 0.36/0.60 (step @p389 :rule ho_cong :premises (@p328 @p388)) % 0.36/0.60 (step @p390 :rule cong :premises (@p389 @p387) :args (@t219)) % 0.36/0.60 (step @p391 :rule cong :premises (@p390) :args (@t220)) % 0.36/0.60 (step @p392 :rule trans :premises (@p391 @p386)) % 0.36/0.60 (step @p393 :rule true_elim :premises (@p392)) % 0.36/0.60 (step @p394 :rule eq_resolve :premises (@p393 @p382)) % 0.36/0.60 (step @p395 :rule eq-symm :args (@t221 @t222)) % 0.36/0.60 (step @p396 :rule refl :args (@t223)) % 0.36/0.60 (step @p397 :rule cong :premises (@p396 @p395) :args ((=> @t223 @t224))) % 0.36/0.60 (assume-push @p425 @t223) % 0.36/0.60 (step @p399 :rule instantiate :premises (@p394) :args ((@list @t180))) % 0.36/0.60 (step-pop @p426 :rule scope :premises (@p399)) % 0.36/0.60 (step @p400 :rule process_scope :premises (@p426) :args (@t224)) % 0.36/0.60 (step @p402 :rule eq_resolve :premises (@p400 @p397)) % 0.36/0.60 (step @p403 :rule implies_elim :premises (@p402)) % 0.36/0.60 (step @p404 :rule chain_m_resolution :premises (@p403 @p394) :args (@t225 @t216 (@list @t223))) % 0.36/0.60 (step @p405 :rule not_implies_elim1 :premises (@p320)) % 0.36/0.60 (step @p406 :rule instantiate :premises (@p405) :args ((@list @t195 @t194 @t180))) % 0.36/0.60 (step @p407 :rule bool-double-not-elim :args (@t196)) % 0.36/0.60 (step @p408 :rule nary_cong :premises (@p362 @p407) :args ((or @t198 (not @t197)))) % 0.36/0.60 (step @p409 :rule cnf_or_neg :args (@t198 0)) % 0.36/0.60 (step @p410 :rule eq_resolve :premises (@p409 @p408)) % 0.36/0.60 (step @p411 :rule reordering :premises (@p410) :args ((or @t196 @t198))) % 0.36/0.60 (step @p412 :rule chain_m_resolution :premises (@p411 @p360) :args (@t196 @t212 @t213)) % 0.36/0.60 (step @p413 :rule cnf_or_pos :args (@t226)) % 0.36/0.60 (step @p414 :rule reordering :premises (@p413) :args ((or @t197 @t222 (not @t226)))) % 0.36/0.60 (step @p415 :rule chain_m_resolution :premises (@p414 @p412 @p406) :args (@t222 @t227 (@list @t196 @t226))) % 0.36/0.60 (step @p416 :rule cnf_equiv_pos1 :args (@t225)) % 0.36/0.60 (step @p417 :rule reordering :premises (@p416) :args ((or (not @t222) @t221 (not @t225)))) % 0.36/0.60 (step @p418 :rule chain_m_resolution :premises (@p417 @p415 @p404) :args (@t221 @t227 (@list @t222 @t225))) % 0.36/0.60 (step @p419 :rule instantiate :premises (@p418) :args ((@list @t184))) % 0.36/0.60 (step @p420 :rule cnf_or_pos :args (@t229)) % 0.36/0.60 (step @p421 :rule reordering :premises (@p420) :args ((or @t189 @t228 (not @t229)))) % 0.36/0.60 (step @p422 false :rule chain_m_resolution :premises (@p421 @p419 @p376 @p367) :args (false (@list false false false) (@list @t229 @t215 @t188))) % 0.36/0.60 ) % 0.36/0.60 % SZS output end Proof % 0.36/0.60 % cvc5 exiting %------------------------------------------------------------------------------