%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU687^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n001.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 08:52:44 AM UTC 2026 % Result : Theorem 0.46s 0.66s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU687^2 : TPTP v9.2.1. Released v3.7.0. % 0.13/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n001.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 17:47:20 EDT 2026 % 0.16/0.35 % CPUTime : % 0.33/0.51 %----Proving TH0 % 0.46/0.66 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.46/0.66 % SZS status Theorem % 0.46/0.66 % SZS output start Proof % 0.46/0.66 ( % 0.46/0.66 (declare-sort $$unsorted 0) % 0.46/0.66 (declare-const tptp.emptyset $$unsorted) % 0.46/0.66 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.46/0.66 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.funcGraphProp1 Bool) % 0.46/0.66 (declare-const tptp.funcGraphProp2 Bool) % 0.46/0.66 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (define tptp.singleton () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_2) (= _let_2 (_ (_ tptp.setadjoin _let_1) tptp.emptyset)))))))) % 0.46/0.66 (define tptp.ex1 () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xphi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ tptp.singleton (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_1) (_ _let_2 _let_1))))))))) % 0.46/0.66 (define tptp.breln () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (let ((_let_3 (@var "C" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (_ (_ tptp.subset _let_3) (_ (_ tptp.cartprod _let_2) _let_1))))))) % 0.46/0.66 (define tptp.func () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "Xy" $$unsorted))) (let ((_let_3 (@var "Xx" $$unsorted))) (let ((_let_4 (@var "B" $$unsorted))) (let ((_let_5 (@var "A" $$unsorted))) (lambda (@list _let_5 _let_4 _let_1) (and (_ (_ (_ tptp.breln _let_5) _let_4) _let_1) (forall (@list _let_3) (=> (_ (_ tptp.in _let_3) _let_5) (_ (_ tptp.ex1 _let_4) (lambda (@list _let_2) (_ (_ tptp.in (_ (_ tptp.kpair _let_3) _let_2)) _let_1))))))))))))) % 0.46/0.66 (define @t1 () (@var "Xf" $$unsorted)) % 0.46/0.66 (define @t2 () (@var "Xx" $$unsorted)) % 0.46/0.66 (define @t3 () (@var "B" $$unsorted)) % 0.46/0.66 (define @t4 () (@var "A" $$unsorted)) % 0.46/0.66 (define @t5 () (_ (_ tptp.ap @t4) @t3)) % 0.46/0.66 (define @t6 () (_ (_ @t5 @t1) @t2)) % 0.46/0.66 (define @t7 () (_ tptp.kpair @t2)) % 0.46/0.66 (define @t8 () (_ @t7 @t6)) % 0.46/0.66 (define @t9 () (_ (_ tptp.in @t8) @t1)) % 0.46/0.66 (define @t10 () (_ (_ tptp.in @t2) @t4)) % 0.46/0.66 (define @t11 () (@list @t2)) % 0.46/0.66 (define @t12 () (forall @t11 (=> @t10 @t9))) % 0.46/0.66 (define @t13 () (_ (_ tptp.func @t4) @t3)) % 0.46/0.66 (define @t14 () (_ @t13 @t1)) % 0.46/0.66 (define @t15 () (=> @t14 @t12)) % 0.46/0.66 (define @t16 () (@list @t4 @t3 @t1)) % 0.46/0.66 (define @t17 () (forall @t16 @t15)) % 0.46/0.66 (define @t18 () (= tptp.funcGraphProp1 @t17)) % 0.46/0.66 (define @t19 () (@var "Xy" $$unsorted)) % 0.46/0.66 (define @t20 () (_ @t7 @t19)) % 0.46/0.66 (define @t21 () (_ tptp.in @t20)) % 0.46/0.66 (define @t22 () (_ @t21 @t1)) % 0.46/0.66 (define @t23 () (=> @t22 (= @t6 @t19))) % 0.46/0.66 (define @t24 () (_ (_ tptp.in @t19) @t3)) % 0.46/0.66 (define @t25 () (=> @t24 @t23)) % 0.46/0.66 (define @t26 () (@list @t19)) % 0.46/0.66 (define @t27 () (forall @t26 @t25)) % 0.46/0.66 (define @t28 () (=> @t10 @t27)) % 0.46/0.66 (define @t29 () (forall @t11 @t28)) % 0.46/0.66 (define @t30 () (=> @t14 @t29)) % 0.46/0.66 (define @t31 () (forall @t16 @t30)) % 0.46/0.66 (define @t32 () (= tptp.funcGraphProp2 @t31)) % 0.46/0.66 (define @t33 () (@var "Xg" $$unsorted)) % 0.46/0.66 (define @t34 () (_ @t21 @t33)) % 0.46/0.66 (define @t35 () (=> @t34 @t22)) % 0.46/0.66 (define @t36 () (forall @t26 (=> @t24 @t35))) % 0.46/0.66 (define @t37 () (=> @t10 @t36)) % 0.46/0.66 (define @t38 () (forall @t11 @t37)) % 0.46/0.66 (define @t39 () (_ (_ @t5 @t33) @t2)) % 0.46/0.66 (define @t40 () (= @t6 @t39)) % 0.46/0.66 (define @t41 () (forall @t11 (=> @t10 @t40))) % 0.46/0.66 (define @t42 () (=> @t41 @t38)) % 0.46/0.66 (define @t43 () (=> (_ @t13 @t33) @t42)) % 0.46/0.66 (define @t44 () (@list @t33)) % 0.46/0.66 (define @t45 () (forall @t44 @t43)) % 0.46/0.66 (define @t46 () (=> @t14 @t45)) % 0.46/0.66 (define @t47 () (forall @t16 @t46)) % 0.46/0.66 (define @t48 () (=> tptp.funcGraphProp2 @t47)) % 0.46/0.66 (define @t49 () (=> tptp.funcGraphProp1 @t48)) % 0.46/0.66 (define @t50 () (not @t49)) % 0.46/0.66 (define @t51 () (_ (_ tptp.setadjoin @t2) tptp.emptyset)) % 0.46/0.66 (define @t52 () (= @t4 @t51)) % 0.46/0.66 (define @t53 () (and @t10 @t52)) % 0.46/0.66 (define @t54 () (exists @t11 @t53)) % 0.46/0.66 (define @t55 () (@list @t4)) % 0.46/0.66 (define @t56 () (lambda @t55 @t54)) % 0.46/0.66 (define @t57 () (@var "Xphi" (-> $$unsorted Bool))) % 0.46/0.66 (define @t58 () (lambda @t11 (_ @t57 @t2))) % 0.46/0.66 (define @t59 () (_ tptp.dsetconstr @t4)) % 0.46/0.66 (define @t60 () (_ @t59 @t58)) % 0.46/0.66 (define @t61 () (@list @t4 @t57)) % 0.46/0.66 (define @t62 () (lambda @t61 (_ tptp.singleton @t60))) % 0.46/0.66 (define @t63 () (_ (_ tptp.cartprod @t4) @t3)) % 0.46/0.66 (define @t64 () (@var "C" $$unsorted)) % 0.46/0.66 (define @t65 () (_ (_ tptp.subset @t64) @t63)) % 0.46/0.66 (define @t66 () (lambda (@list @t4 @t3 @t64) @t65)) % 0.46/0.66 (define @t67 () (@var "R" $$unsorted)) % 0.46/0.66 (define @t68 () (_ @t21 @t67)) % 0.46/0.66 (define @t69 () (lambda @t26 @t68)) % 0.46/0.66 (define @t70 () (=> @t10 (_ (_ tptp.ex1 @t3) @t69))) % 0.46/0.66 (define @t71 () (forall @t11 @t70)) % 0.46/0.66 (define @t72 () (and (_ (_ (_ tptp.breln @t4) @t3) @t67) @t71)) % 0.46/0.66 (define @t73 () (@list @t4 @t3 @t67)) % 0.46/0.66 (define @t74 () (lambda @t73 @t72)) % 0.46/0.66 (define @t75 () (@var "BOUND_VARIABLE_7944" $$unsorted)) % 0.46/0.66 (define @t76 () (@var "BOUND_VARIABLE_7942" $$unsorted)) % 0.46/0.66 (define @t77 () (tptp.kpair @t76 @t75)) % 0.46/0.66 (define @t78 () (tptp.in @t77 @t1)) % 0.46/0.66 (define @t79 () (@var "BOUND_VARIABLE_7940" $$unsorted)) % 0.46/0.66 (define @t80 () (not (tptp.in @t77 @t79))) % 0.46/0.66 (define @t81 () (not (tptp.in @t75 @t3))) % 0.46/0.66 (define @t82 () (not (tptp.in @t76 @t4))) % 0.46/0.66 (define @t83 () (tptp.ap @t4 @t3 @t1 @t2)) % 0.46/0.66 (define @t84 () (tptp.in @t2 @t4)) % 0.46/0.66 (define @t85 () (not @t84)) % 0.46/0.66 (define @t86 () (not (forall @t11 (or @t85 (= @t83 (tptp.ap @t4 @t3 @t79 @t2)))))) % 0.46/0.66 (define @t87 () (tptp.kpair @t2 @t19)) % 0.46/0.66 (define @t88 () (tptp.dsetconstr @t3 (lambda @t26 (tptp.in @t87 @t79)))) % 0.46/0.66 (define @t89 () (@var "BOUND_VARIABLE_7577" $$unsorted)) % 0.46/0.66 (define @t90 () (tptp.setadjoin @t89 tptp.emptyset)) % 0.46/0.66 (define @t91 () (@list @t89)) % 0.46/0.66 (define @t92 () (not (forall @t11 (or @t85 (not (forall @t91 (or (not (tptp.in @t89 @t88)) (not (= @t90 @t88))))))))) % 0.46/0.66 (define @t93 () (tptp.cartprod @t4 @t3)) % 0.46/0.66 (define @t94 () (not (tptp.subset @t79 @t93))) % 0.46/0.66 (define @t95 () (tptp.in @t87 @t1)) % 0.46/0.66 (define @t96 () (tptp.dsetconstr @t3 (lambda @t26 @t95))) % 0.46/0.66 (define @t97 () (forall @t11 (or @t85 (not (forall @t91 (or (not (tptp.in @t89 @t96)) (not (= @t90 @t96)))))))) % 0.46/0.66 (define @t98 () (not @t97)) % 0.46/0.66 (define @t99 () (tptp.subset @t1 @t93)) % 0.46/0.66 (define @t100 () (not @t99)) % 0.46/0.66 (define @t101 () (or @t100 @t98 @t94 @t92 @t86 @t82 @t81 @t80 @t78)) % 0.46/0.66 (define @t102 () (@list @t4 @t3 @t1 @t79 @t76 @t75)) % 0.46/0.66 (define @t103 () (forall @t102 @t101)) % 0.46/0.66 (define @t104 () (@var "BOUND_VARIABLE_7819" $$unsorted)) % 0.46/0.66 (define @t105 () (tptp.ap @t4 @t3 @t1 @t104)) % 0.46/0.66 (define @t106 () (@var "BOUND_VARIABLE_7821" $$unsorted)) % 0.46/0.66 (define @t107 () (not (tptp.in (tptp.kpair @t104 @t106) @t1))) % 0.46/0.66 (define @t108 () (not (tptp.in @t106 @t3))) % 0.46/0.66 (define @t109 () (not (tptp.in @t104 @t4))) % 0.46/0.66 (define @t110 () (= @t105 @t106)) % 0.46/0.66 (define @t111 () (or @t100 @t98 @t109 @t108 @t107 @t110)) % 0.46/0.66 (define @t112 () (or @t109 @t108 @t107 @t110)) % 0.46/0.66 (define @t113 () (or @t100 @t98 @t112)) % 0.46/0.66 (define @t114 () (forall (@list @t4 @t3 @t1 @t104 @t106) @t113)) % 0.46/0.66 (define @t115 () (@list @t104 @t106)) % 0.46/0.66 (define @t116 () (forall @t115 @t113)) % 0.46/0.66 (define @t117 () (forall @t115 @t112)) % 0.46/0.66 (define @t118 () (@var "BOUND_VARIABLE_7797" $$unsorted)) % 0.46/0.66 (define @t119 () (or @t100 @t98 @t117)) % 0.46/0.66 (define @t120 () (not (tptp.in (tptp.kpair @t2 @t118) @t1))) % 0.46/0.66 (define @t121 () (not (tptp.in @t118 @t3))) % 0.46/0.66 (define @t122 () (@list @t2 @t118)) % 0.46/0.66 (define @t123 () (forall @t122 (or @t85 @t121 @t120 (= @t83 @t118)))) % 0.46/0.66 (define @t124 () (_ tptp.subset @t1)) % 0.46/0.66 (define @t125 () (_ @t124 @t63)) % 0.46/0.66 (define @t126 () (not @t125)) % 0.46/0.66 (define @t127 () (or @t126 @t98 @t123)) % 0.46/0.66 (define @t128 () (or @t126 @t98)) % 0.46/0.66 (define @t129 () (and @t125 @t97)) % 0.46/0.66 (define @t130 () (not @t129)) % 0.46/0.66 (define @t131 () (= @t118 @t83)) % 0.46/0.66 (define @t132 () (or @t85 @t121 @t120 @t131)) % 0.46/0.66 (define @t133 () (or @t121 @t120 @t131)) % 0.46/0.66 (define @t134 () (or @t85 @t133)) % 0.46/0.66 (define @t135 () (forall @t122 @t134)) % 0.46/0.66 (define @t136 () (@list @t118)) % 0.46/0.66 (define @t137 () (forall @t136 @t134)) % 0.46/0.66 (define @t138 () (forall @t136 @t133)) % 0.46/0.66 (define @t139 () (@list @t19)) % 0.46/0.66 (define @t140 () (or @t85 @t138)) % 0.46/0.66 (define @t141 () (tptp.in @t19 @t3)) % 0.46/0.66 (define @t142 () (not @t141)) % 0.46/0.66 (define @t143 () (forall @t26 (or @t142 (not @t95) (= @t19 @t83)))) % 0.46/0.66 (define @t144 () (not @t10)) % 0.46/0.66 (define @t145 () (or @t144 @t143)) % 0.46/0.66 (define @t146 () (= @t19 @t6)) % 0.46/0.66 (define @t147 () (_ tptp.in @t87)) % 0.46/0.66 (define @t148 () (not @t22)) % 0.46/0.66 (define @t149 () (not @t24)) % 0.46/0.66 (define @t150 () (or @t149 @t148 @t146)) % 0.46/0.66 (define @t151 () (=> @t22 @t146)) % 0.46/0.66 (define @t152 () (tptp.in @t87 @t67)) % 0.46/0.66 (define @t153 () (tptp.dsetconstr @t3 (lambda @t26 @t152))) % 0.46/0.66 (define @t154 () (not (forall @t91 (or (not (tptp.in @t89 @t153)) (not (= @t90 @t153)))))) % 0.46/0.66 (define @t155 () (_ (_ tptp.subset @t67) @t63)) % 0.46/0.66 (define @t156 () (and @t155 (forall @t11 (or @t85 @t154)))) % 0.46/0.66 (define @t157 () (lambda (@list @t67) @t156)) % 0.46/0.66 (define @t158 () (lambda (@list @t3 @t67) @t156)) % 0.46/0.66 (define @t159 () (_ (lambda @t73 @t156) @t4)) % 0.46/0.66 (define @t160 () (_ @t159 @t3)) % 0.46/0.66 (define @t161 () (_ @t160 @t1)) % 0.46/0.66 (define @t162 () (=> @t161 @t29)) % 0.46/0.66 (define @t163 () (forall @t16 @t162)) % 0.46/0.66 (define @t164 () (or @t144 @t154)) % 0.46/0.66 (define @t165 () (tptp.dsetconstr @t3 @t69)) % 0.46/0.66 (define @t166 () (= @t90 @t165)) % 0.46/0.66 (define @t167 () (not @t166)) % 0.46/0.66 (define @t168 () (tptp.in @t89 @t165)) % 0.46/0.66 (define @t169 () (not @t168)) % 0.46/0.66 (define @t170 () (or @t169 @t167)) % 0.46/0.66 (define @t171 () (not (= @t165 @t90))) % 0.46/0.66 (define @t172 () (or @t169 @t171)) % 0.46/0.66 (define @t173 () (forall @t91 @t172)) % 0.46/0.66 (define @t174 () (not @t173)) % 0.46/0.66 (define @t175 () (tptp.dsetconstr @t3 @t57)) % 0.46/0.66 (define @t176 () (not (tptp.in @t89 @t175))) % 0.46/0.66 (define @t177 () (@list @t57)) % 0.46/0.66 (define @t178 () (not (= @t90 @t175))) % 0.46/0.66 (define @t179 () (or @t176 @t178)) % 0.46/0.66 (define @t180 () (forall @t91 @t179)) % 0.46/0.66 (define @t181 () (not @t180)) % 0.46/0.66 (define @t182 () (tptp.setadjoin @t2 tptp.emptyset)) % 0.46/0.66 (define @t183 () (forall @t11 (or (not (tptp.in @t2 @t175)) (not (= @t182 @t175))))) % 0.46/0.66 (define @t184 () (@list @t2)) % 0.46/0.66 (define @t185 () (not @t183)) % 0.46/0.66 (define @t186 () (lambda @t177 @t185)) % 0.46/0.66 (define @t187 () (tptp.dsetconstr @t4 @t57)) % 0.46/0.66 (define @t188 () (_ (lambda @t61 (not (forall @t11 (or (not (tptp.in @t2 @t187)) (not (= @t182 @t187)))))) @t3)) % 0.46/0.66 (define @t189 () (=> @t10 (_ @t188 @t69))) % 0.46/0.66 (define @t190 () (forall @t11 @t189)) % 0.46/0.66 (define @t191 () (lambda (@list @t64) @t65)) % 0.46/0.66 (define @t192 () (lambda (@list @t3 @t64) @t65)) % 0.46/0.66 (define @t193 () (_ @t66 @t4)) % 0.46/0.66 (define @t194 () (@var "BOUND_VARIABLE_7478" $$unsorted)) % 0.46/0.66 (define @t195 () (_ @t57 @t194)) % 0.46/0.66 (define @t196 () (@list @t194)) % 0.46/0.66 (define @t197 () (lambda @t196 @t195)) % 0.46/0.66 (define @t198 () (tptp.dsetconstr @t4 @t197)) % 0.46/0.66 (define @t199 () (= @t182 @t198)) % 0.46/0.66 (define @t200 () (not @t199)) % 0.46/0.66 (define @t201 () (tptp.in @t2 @t198)) % 0.46/0.66 (define @t202 () (not @t201)) % 0.46/0.66 (define @t203 () (or @t202 @t200)) % 0.46/0.66 (define @t204 () (_ @t57 @t194)) % 0.46/0.66 (define @t205 () (lambda @t196 @t204)) % 0.46/0.66 (define @t206 () (_ @t59 @t205)) % 0.46/0.66 (define @t207 () (= @t182 @t206)) % 0.46/0.66 (define @t208 () (not @t207)) % 0.46/0.66 (define @t209 () (tptp.in @t2 @t206)) % 0.46/0.66 (define @t210 () (not @t209)) % 0.46/0.66 (define @t211 () (or @t210 @t208)) % 0.46/0.66 (define @t212 () (= @t182 @t60)) % 0.46/0.66 (define @t213 () (not @t212)) % 0.46/0.66 (define @t214 () (tptp.in @t2 @t60)) % 0.46/0.66 (define @t215 () (not @t214)) % 0.46/0.66 (define @t216 () (or @t215 @t213)) % 0.46/0.66 (define @t217 () (not (= @t60 @t182))) % 0.46/0.66 (define @t218 () (or @t215 @t217)) % 0.46/0.66 (define @t219 () (forall @t11 @t218)) % 0.46/0.66 (define @t220 () (not @t219)) % 0.46/0.66 (define @t221 () (not @t52)) % 0.46/0.66 (define @t222 () (or @t144 @t221)) % 0.46/0.66 (define @t223 () (forall @t11 (not @t53))) % 0.46/0.66 (define @t224 () (not @t223)) % 0.46/0.66 (define @t225 () (=> tptp.funcGraphProp2 @t103)) % 0.46/0.66 (define @t226 () (@var "BOUND_VARIABLE_7757" $$unsorted)) % 0.46/0.66 (define @t227 () (tptp.in (tptp.kpair @t226 (tptp.ap @t4 @t3 @t1 @t226)) @t1)) % 0.46/0.66 (define @t228 () (not (tptp.in @t226 @t4))) % 0.46/0.66 (define @t229 () (or @t228 @t227)) % 0.46/0.66 (define @t230 () (or @t100 @t98 @t229)) % 0.46/0.66 (define @t231 () (forall (@list @t4 @t3 @t1 @t226) @t230)) % 0.46/0.66 (define @t232 () (@list @t226)) % 0.46/0.66 (define @t233 () (forall @t232 @t230)) % 0.46/0.66 (define @t234 () (forall @t232 @t229)) % 0.46/0.66 (define @t235 () (or @t100 @t98 @t234)) % 0.46/0.66 (define @t236 () (tptp.kpair @t2 @t83)) % 0.46/0.66 (define @t237 () (tptp.in @t236 @t1)) % 0.46/0.66 (define @t238 () (forall @t11 (or @t85 @t237))) % 0.46/0.66 (define @t239 () (or @t126 @t98 @t238)) % 0.46/0.66 (define @t240 () (or @t144 @t9)) % 0.46/0.66 (define @t241 () (=> @t161 @t12)) % 0.46/0.66 (define @t242 () (forall @t16 @t241)) % 0.46/0.66 (define @t243 () (=> tptp.funcGraphProp1 @t225)) % 0.46/0.66 (define @t244 () (or @t94 @t92 @t86 @t82 @t81 @t80 @t78)) % 0.46/0.66 (define @t245 () (or @t100 @t98 @t244)) % 0.46/0.66 (define @t246 () (forall @t102 @t245)) % 0.46/0.66 (define @t247 () (@list @t79 @t76 @t75)) % 0.46/0.66 (define @t248 () (forall @t247 @t245)) % 0.46/0.66 (define @t249 () (forall @t247 @t244)) % 0.46/0.66 (define @t250 () (@var "BOUND_VARIABLE_7918" $$unsorted)) % 0.46/0.66 (define @t251 () (@var "BOUND_VARIABLE_7916" $$unsorted)) % 0.46/0.66 (define @t252 () (or @t100 @t98 @t249)) % 0.46/0.66 (define @t253 () (tptp.kpair @t251 @t250)) % 0.46/0.66 (define @t254 () (tptp.in @t253 @t1)) % 0.46/0.66 (define @t255 () (not (tptp.in @t253 @t33))) % 0.46/0.66 (define @t256 () (not (tptp.in @t250 @t3))) % 0.46/0.66 (define @t257 () (not (tptp.in @t251 @t4))) % 0.46/0.66 (define @t258 () (tptp.ap @t4 @t3 @t33 @t2)) % 0.46/0.66 (define @t259 () (forall @t11 (or @t85 (= @t83 @t258)))) % 0.46/0.66 (define @t260 () (not @t259)) % 0.46/0.66 (define @t261 () (tptp.in @t87 @t33)) % 0.46/0.66 (define @t262 () (tptp.dsetconstr @t3 (lambda @t26 @t261))) % 0.46/0.66 (define @t263 () (forall @t11 (or @t85 (not (forall @t91 (or (not (tptp.in @t89 @t262)) (not (= @t90 @t262)))))))) % 0.46/0.66 (define @t264 () (not @t263)) % 0.46/0.66 (define @t265 () (tptp.subset @t33 @t93)) % 0.46/0.66 (define @t266 () (not @t265)) % 0.46/0.66 (define @t267 () (or @t266 @t264 @t260 @t257 @t256 @t255 @t254)) % 0.46/0.66 (define @t268 () (@list @t33 @t251 @t250)) % 0.46/0.66 (define @t269 () (forall @t268 @t267)) % 0.46/0.66 (define @t270 () (or @t126 @t98 @t269)) % 0.46/0.66 (define @t271 () (or @t257 @t256 @t255 @t254)) % 0.46/0.66 (define @t272 () (or @t266 @t264 @t260 @t271)) % 0.46/0.66 (define @t273 () (forall @t268 @t272)) % 0.46/0.66 (define @t274 () (@list @t251 @t250)) % 0.46/0.66 (define @t275 () (forall @t274 @t272)) % 0.46/0.66 (define @t276 () (forall @t274 @t271)) % 0.46/0.66 (define @t277 () (@var "BOUND_VARIABLE_7886" $$unsorted)) % 0.46/0.66 (define @t278 () (or @t266 @t264 @t260 @t276)) % 0.46/0.66 (define @t279 () (tptp.kpair @t2 @t277)) % 0.46/0.66 (define @t280 () (tptp.in @t279 @t1)) % 0.46/0.66 (define @t281 () (not (tptp.in @t279 @t33))) % 0.46/0.66 (define @t282 () (not (tptp.in @t277 @t3))) % 0.46/0.66 (define @t283 () (or @t85 @t282 @t281 @t280)) % 0.46/0.66 (define @t284 () (@list @t2 @t277)) % 0.46/0.66 (define @t285 () (forall @t284 @t283)) % 0.46/0.66 (define @t286 () (_ tptp.subset @t33)) % 0.46/0.66 (define @t287 () (_ @t286 @t63)) % 0.46/0.66 (define @t288 () (not @t287)) % 0.46/0.66 (define @t289 () (or @t288 @t264 @t260 @t285)) % 0.46/0.66 (define @t290 () (=> @t259 @t285)) % 0.46/0.66 (define @t291 () (and @t287 @t263)) % 0.46/0.66 (define @t292 () (or @t282 @t281 @t280)) % 0.46/0.66 (define @t293 () (or @t85 @t292)) % 0.46/0.66 (define @t294 () (forall @t284 @t293)) % 0.46/0.66 (define @t295 () (@list @t277)) % 0.46/0.66 (define @t296 () (forall @t295 @t293)) % 0.46/0.66 (define @t297 () (forall @t295 @t292)) % 0.46/0.66 (define @t298 () (or @t85 @t297)) % 0.46/0.66 (define @t299 () (forall @t26 (or @t142 (not @t261) @t95))) % 0.46/0.66 (define @t300 () (or @t144 @t299)) % 0.46/0.66 (define @t301 () (not @t34)) % 0.46/0.66 (define @t302 () (or @t149 @t301 @t22)) % 0.46/0.66 (define @t303 () (or @t144 @t40)) % 0.46/0.66 (define @t304 () (=> (_ @t160 @t33) @t42)) % 0.46/0.66 (define @t305 () (forall @t44 @t304)) % 0.46/0.66 (define @t306 () (=> @t161 @t305)) % 0.46/0.66 (define @t307 () (forall @t16 @t306)) % 0.46/0.66 (define @t308 () (=> tptp.funcGraphProp2 @t307)) % 0.46/0.66 (define @t309 () (=> tptp.funcGraphProp1 @t308)) % 0.46/0.66 (define @t310 () (@quantifiers_skolemize @t103 4)) % 0.46/0.66 (define @t311 () (@quantifiers_skolemize @t103 2)) % 0.46/0.66 (define @t312 () (@quantifiers_skolemize @t103 1)) % 0.46/0.66 (define @t313 () (@quantifiers_skolemize @t103 0)) % 0.46/0.66 (define @t314 () (tptp.in @t310 @t313)) % 0.46/0.66 (define @t315 () (@quantifiers_skolemize @t103 5)) % 0.46/0.66 (define @t316 () (tptp.kpair @t310 @t315)) % 0.46/0.66 (define @t317 () (tptp.in @t316 @t311)) % 0.46/0.66 (define @t318 () (@quantifiers_skolemize @t103 3)) % 0.46/0.66 (define @t319 () (tptp.in @t316 @t318)) % 0.46/0.66 (define @t320 () (not @t319)) % 0.46/0.66 (define @t321 () (tptp.in @t315 @t312)) % 0.46/0.66 (define @t322 () (not @t321)) % 0.46/0.66 (define @t323 () (not @t314)) % 0.46/0.66 (define @t324 () (not (tptp.in @t2 @t313))) % 0.46/0.66 (define @t325 () (forall @t11 (or @t324 (= (tptp.ap @t313 @t312 @t311 @t2) (tptp.ap @t313 @t312 @t318 @t2))))) % 0.46/0.66 (define @t326 () (not @t325)) % 0.46/0.66 (define @t327 () (tptp.dsetconstr @t312 (lambda @t26 (tptp.in @t87 @t318)))) % 0.46/0.66 (define @t328 () (forall @t11 (or @t324 (not (forall @t91 (or (not (tptp.in @t89 @t327)) (not (= @t90 @t327)))))))) % 0.46/0.66 (define @t329 () (not @t328)) % 0.46/0.66 (define @t330 () (tptp.cartprod @t313 @t312)) % 0.46/0.66 (define @t331 () (tptp.subset @t318 @t330)) % 0.46/0.66 (define @t332 () (not @t331)) % 0.46/0.66 (define @t333 () (tptp.dsetconstr @t312 (lambda @t26 (tptp.in @t87 @t311)))) % 0.46/0.66 (define @t334 () (forall @t11 (or @t324 (not (forall @t91 (or (not (tptp.in @t89 @t333)) (not (= @t90 @t333)))))))) % 0.46/0.66 (define @t335 () (not @t334)) % 0.46/0.66 (define @t336 () (tptp.subset @t311 @t330)) % 0.46/0.66 (define @t337 () (not @t336)) % 0.46/0.66 (define @t338 () (or @t337 @t335 @t332 @t329 @t326 @t323 @t322 @t320 @t317)) % 0.46/0.66 (define @t339 () (@list true)) % 0.46/0.66 (define @t340 () (@list @t338)) % 0.46/0.66 (define @t341 () (tptp.ap @t313 @t312 @t311 @t310)) % 0.46/0.66 (define @t342 () (tptp.in (tptp.kpair @t310 @t341) @t311)) % 0.46/0.66 (define @t343 () (or @t337 @t335 @t323 @t342)) % 0.46/0.66 (define @t344 () (tptp.ap @t313 @t312 @t318 @t310)) % 0.46/0.66 (define @t345 () (or @t323 (= @t341 @t344))) % 0.46/0.66 (define @t346 () (= @t344 @t341)) % 0.46/0.66 (define @t347 () (or @t323 @t346)) % 0.46/0.66 (define @t348 () (= @t315 @t344)) % 0.46/0.66 (define @t349 () (or @t332 @t329 @t323 @t322 @t320 @t348)) % 0.46/0.66 (assume @p1 @t18) % 0.46/0.66 (assume @p2 @t32) % 0.46/0.66 (assume @p3 @t50) % 0.46/0.66 (assume @p4 true) % 0.46/0.66 (step @p5 (= tptp.singleton @t56) :rule refl :args (@t56)) % 0.46/0.66 (step @p6 (= tptp.ex1 @t62) :rule refl :args (@t62)) % 0.46/0.66 (step @p7 (= tptp.breln @t66) :rule refl :args (@t66)) % 0.46/0.66 (step @p8 (= tptp.func @t74) :rule refl :args (@t74)) % 0.46/0.66 (step @p9 :rule evaluate :args ((= false true))) % 0.46/0.66 (step @p10 :rule refl :args (@t103)) % 0.46/0.66 (step @p11 :rule eq-symm :args (@t105 @t106)) % 0.46/0.66 (step @p12 :rule refl :args (@t107)) % 0.46/0.66 (step @p13 :rule refl :args (@t108)) % 0.46/0.66 (step @p14 :rule refl :args (@t109)) % 0.46/0.66 (step @p15 :rule refl :args (@t98)) % 0.46/0.66 (step @p16 :rule refl :args (@t100)) % 0.46/0.66 (step @p17 :rule nary_cong :premises (@p16 @p15 @p14 @p13 @p12 @p11) :args (@t111)) % 0.46/0.66 (step @p18 :rule aci_norm :args ((= @t113 @t111))) % 0.46/0.66 (step @p19 :rule trans :premises (@p18 @p17)) % 0.46/0.66 (step @p20 :rule cong :premises (@p19) :args (@t114)) % 0.46/0.66 (step @p21 :rule quant-merge-prenex :args ((= (forall @t16 @t116) @t114))) % 0.46/0.66 (step @p22 :rule alpha_equiv :args (@t117 (@list @t104 @t106) (@list @t2 @t118))) % 0.46/0.66 (step @p23 :rule refl :args (@t98)) % 0.46/0.66 (step @p24 :rule refl :args (@t100)) % 0.46/0.66 (step @p25 :rule nary_cong :premises (@p24 @p23 @p22) :args (@t119)) % 0.46/0.66 (step @p26 :rule quant-miniscope-or :args ((= @t116 @t119))) % 0.46/0.66 (step @p27 :rule trans :premises (@p26 @p25)) % 0.46/0.66 (step @p28 :rule symm :premises (@p27)) % 0.46/0.66 (step @p29 :rule cong :premises (@p28) :args ((forall @t16 (or @t100 @t98 @t123)))) % 0.46/0.66 (step @p30 :rule trans :premises (@p29 @p21)) % 0.46/0.66 (step @p31 :rule trans :premises (@p30 @p20)) % 0.46/0.66 (step @p32 :rule refl :args (@t123)) % 0.46/0.66 (step @p33 :rule refl :args ((tptp.subset @t1 @t63))) % 0.46/0.66 (step @p34 :rule refl :args (@t93)) % 0.46/0.66 (step @p35 :rule refl :args (@t1)) % 0.46/0.66 (step @p36 :rule cong 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((= @t134 @t132))) % 0.46/0.66 (step @p68 :rule trans :premises (@p67 @p66)) % 0.46/0.66 (step @p69 :rule cong :premises (@p68) :args (@t135)) % 0.46/0.66 (step @p70 :rule quant-merge-prenex :args ((= (forall @t11 @t137) @t135))) % 0.46/0.66 (step @p71 :rule alpha_equiv :args (@t138 (@list @t118) @t139)) % 0.46/0.66 (step @p72 :rule refl :args (@t85)) % 0.46/0.66 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t140)) % 0.46/0.66 (step @p74 :rule quant-miniscope-or :args ((= @t137 @t140))) % 0.46/0.66 (step @p75 :rule trans :premises (@p74 @p73)) % 0.46/0.66 (step @p76 :rule symm :premises (@p75)) % 0.46/0.66 (step @p77 :rule cong :premises (@p76) :args ((forall @t11 (or @t85 @t143)))) % 0.46/0.66 (step @p78 :rule trans :premises (@p77 @p70)) % 0.46/0.66 (step @p79 :rule trans :premises (@p78 @p69)) % 0.46/0.66 (step @p80 :rule refl :args (@t143)) % 0.46/0.66 (step @p81 :rule refl :args (@t84)) % 0.46/0.66 (step @p82 :rule refl :args (@t10)) % 0.46/0.66 (step @p83 :rule cong :premises (@p82 @p81) :args ((= @t10 @t84))) % 0.46/0.66 (step @p84 :rule symm :premises (@p83)) % 0.46/0.66 (step @p85 :rule eq_resolve :premises (@p82 @p84)) % 0.46/0.66 (step @p86 :rule cong :premises (@p85) :args (@t144)) % 0.46/0.66 (step @p87 :rule nary_cong :premises (@p86 @p80) :args (@t145)) % 0.46/0.66 (step @p88 :rule cong :premises (@p87) :args ((forall @t11 @t145))) % 0.46/0.66 (step @p89 :rule trans :premises (@p88 @p79)) % 0.46/0.66 (step @p90 :rule bool-impl-elim :args (@t10 @t143)) % 0.46/0.66 (step @p91 :rule cong :premises (@p90) :args ((forall @t11 (=> @t10 @t143)))) % 0.46/0.66 (step @p92 :rule trans :premises (@p91 @p89)) % 0.46/0.66 (step @p93 :rule refl :args (@t83)) % 0.46/0.66 (step @p94 :rule refl :args (@t6)) % 0.46/0.66 (step @p95 :rule cong :premises (@p94 @p93) :args ((= @t6 @t83))) % 0.46/0.66 (step @p96 :rule symm :premises (@p95)) % 0.46/0.66 (step @p97 :rule eq_resolve :premises (@p94 @p96)) % 0.46/0.66 (step @p98 :rule refl :args (@t19)) % 0.46/0.66 (step @p99 :rule cong :premises (@p98 @p97) :args (@t146)) % 0.46/0.66 (step @p100 :rule refl :args ((tptp.in @t20 @t1))) % 0.46/0.66 (step @p101 :rule refl :args (@t87)) % 0.46/0.66 (step @p102 :rule cong :premises (@p101 @p35) :args (@t95)) % 0.46/0.66 (step @p103 :rule trans :premises (@p102 @p100)) % 0.46/0.66 (step @p104 :rule refl :args (tptp.in)) % 0.46/0.66 (step @p105 :rule ho_cong :premises (@p104 @p101)) % 0.46/0.66 (step @p106 :rule ho_cong :premises (@p105 @p35)) % 0.46/0.66 (step @p107 :rule cong :premises (@p106 @p103) :args ((= (_ @t147 @t1) @t95))) % 0.46/0.66 (step @p108 :rule symm :premises (@p107)) % 0.46/0.66 (step @p109 :rule refl :args (@t22)) % 0.46/0.66 (step @p110 :rule eq_resolve :premises (@p109 @p108)) % 0.46/0.66 (step @p111 :rule refl :args (@t20)) % 0.46/0.66 (step @p112 :rule cong :premises (@p111 @p101) :args ((= @t20 @t87))) % 0.46/0.66 (step @p113 :rule symm :premises (@p112)) % 0.46/0.66 (step @p114 :rule eq_resolve :premises (@p111 @p113)) % 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eq_resolve :premises (@p605 @p604)) % 0.46/0.66 (step @p607 :rule reordering :premises (@p606) :args ((or @t331 @t338))) % 0.46/0.66 (step @p608 :rule chain_m_resolution :premises (@p607 @p537) :args (@t331 @t339 @t340)) % 0.46/0.66 (step @p609 :rule cnf_or_pos :args (@t349)) % 0.46/0.66 (step @p610 :rule reordering :premises (@p609) :args ((or @t332 @t329 @t323 @t322 @t320 @t348 (not @t349)))) % 0.46/0.66 (step @p611 :rule chain_m_resolution :premises (@p610 @p608 @p602 @p544 @p596 @p590 @p584) :args (@t348 (@list false false false false false false) (@list @t331 @t328 @t314 @t321 @t319 @t349))) % 0.46/0.66 (step @p612 :rule trans :premises (@p611 @p582)) % 0.46/0.66 (step @p613 :rule refl :args (@t310)) % 0.46/0.66 (step @p614 :rule cong :premises (@p613 @p612) :args (@t316)) % 0.46/0.66 (step @p615 :rule cong :premises (@p614 @p561) :args (@t317)) % 0.46/0.66 (step @p616 :rule cnf_or_neg :args (@t338 8)) % 0.46/0.66 (step @p617 :rule chain_m_resolution :premises (@p616 @p537) :args ((not @t317) @t339 @t340)) % 0.46/0.66 (step @p618 :rule false_intro :premises (@p617)) % 0.46/0.66 (step @p619 :rule symm :premises (@p618)) % 0.46/0.66 (step @p620 :rule trans :premises (@p619 @p615 @p560)) % 0.46/0.66 (step @p621 false :rule eq_resolve :premises (@p620 @p9)) % 0.46/0.66 ) % 0.46/0.66 % SZS output end Proof % 0.46/0.66 % cvc5 exiting %------------------------------------------------------------------------------