%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU686^2 : 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 : n017.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 0.44s 0.63s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU686^2 : TPTP v9.2.1. Released v3.7.0. % 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 : n017.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 17:45:16 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.44/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.44/0.63 % SZS status Theorem % 0.44/0.63 % SZS output start Proof % 0.44/0.63 ( % 0.44/0.63 (declare-sort $$unsorted 0) % 0.44/0.63 (declare-const tptp.emptyset $$unsorted) % 0.44/0.63 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.44/0.63 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.funcGraphProp1 Bool) % 0.44/0.63 (declare-const tptp.ex1E2 Bool) % 0.44/0.63 (declare-const tptp.app Bool) % 0.44/0.63 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.63 (define tptp.singleton () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_2) (= _let_2 (_ (_ tptp.setadjoin _let_1) tptp.emptyset)))))))) % 0.44/0.63 (define tptp.ex1 () (let ((_let_1 (@var "Xx" $$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))))))))) % 0.44/0.63 (define tptp.breln () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (let ((_let_3 (@var "C" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (_ (_ tptp.subset _let_3) (_ (_ tptp.cartprod _let_2) _let_1))))))) % 0.44/0.63 (define tptp.func () (let ((_let_1 (@var "R" $$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))))))))))))) % 0.44/0.63 (define @t1 () (@var "B" $$unsorted)) % 0.44/0.63 (define @t2 () (@var "Xx" $$unsorted)) % 0.44/0.63 (define @t3 () (@var "Xf" $$unsorted)) % 0.44/0.63 (define @t4 () (@var "A" $$unsorted)) % 0.44/0.63 (define @t5 () (_ (_ (_ (_ tptp.ap @t4) @t1) @t3) @t2)) % 0.44/0.63 (define @t6 () (_ (_ tptp.in @t5) @t1)) % 0.44/0.63 (define @t7 () (_ (_ tptp.in @t2) @t4)) % 0.44/0.63 (define @t8 () (@list @t2)) % 0.44/0.63 (define @t9 () (forall @t8 (=> @t7 @t6))) % 0.44/0.63 (define @t10 () (_ (_ (_ tptp.func @t4) @t1) @t3)) % 0.44/0.63 (define @t11 () (=> @t10 @t9)) % 0.44/0.63 (define @t12 () (@list @t4 @t1 @t3)) % 0.44/0.63 (define @t13 () (forall @t12 @t11)) % 0.44/0.63 (define @t14 () (= tptp.app @t13)) % 0.44/0.63 (define @t15 () (@var "Xy" $$unsorted)) % 0.44/0.63 (define @t16 () (= @t2 @t15)) % 0.44/0.63 (define @t17 () (@var "Xphi" (-> $$unsorted Bool))) % 0.44/0.63 (define @t18 () (_ @t17 @t15)) % 0.44/0.63 (define @t19 () (=> @t18 @t16)) % 0.44/0.63 (define @t20 () (_ @t17 @t2)) % 0.44/0.63 (define @t21 () (=> @t20 @t19)) % 0.44/0.63 (define @t22 () (_ tptp.in @t15)) % 0.44/0.63 (define @t23 () (_ @t22 @t4)) % 0.44/0.63 (define @t24 () (@list @t15)) % 0.44/0.63 (define @t25 () (forall @t24 (=> @t23 @t21))) % 0.44/0.63 (define @t26 () (=> @t7 @t25)) % 0.44/0.63 (define @t27 () (forall @t8 @t26)) % 0.44/0.63 (define @t28 () (lambda @t8 @t20)) % 0.44/0.63 (define @t29 () (=> (_ (_ tptp.ex1 @t4) @t28) @t27)) % 0.44/0.63 (define @t30 () (@list @t4 @t17)) % 0.44/0.63 (define @t31 () (forall @t30 @t29)) % 0.44/0.63 (define @t32 () (= tptp.ex1E2 @t31)) % 0.44/0.63 (define @t33 () (_ tptp.kpair @t2)) % 0.44/0.63 (define @t34 () (_ @t33 @t5)) % 0.44/0.63 (define @t35 () (_ (_ tptp.in @t34) @t3)) % 0.44/0.63 (define @t36 () (forall @t8 (=> @t7 @t35))) % 0.44/0.63 (define @t37 () (=> @t10 @t36)) % 0.44/0.63 (define @t38 () (forall @t12 @t37)) % 0.44/0.63 (define @t39 () (= tptp.funcGraphProp1 @t38)) % 0.44/0.63 (define @t40 () (_ @t33 @t15)) % 0.44/0.63 (define @t41 () (_ tptp.in @t40)) % 0.44/0.63 (define @t42 () (_ @t41 @t3)) % 0.44/0.63 (define @t43 () (=> @t42 (= @t5 @t15))) % 0.44/0.63 (define @t44 () (_ @t22 @t1)) % 0.44/0.63 (define @t45 () (=> @t44 @t43)) % 0.44/0.63 (define @t46 () (forall @t24 @t45)) % 0.44/0.63 (define @t47 () (=> @t7 @t46)) % 0.44/0.63 (define @t48 () (forall @t8 @t47)) % 0.44/0.63 (define @t49 () (=> @t10 @t48)) % 0.44/0.63 (define @t50 () (forall @t12 @t49)) % 0.44/0.63 (define @t51 () (=> tptp.funcGraphProp1 @t50)) % 0.44/0.63 (define @t52 () (=> tptp.ex1E2 @t51)) % 0.44/0.63 (define @t53 () (=> tptp.app @t52)) % 0.44/0.63 (define @t54 () (not @t53)) % 0.44/0.63 (define @t55 () (_ (_ tptp.setadjoin @t2) tptp.emptyset)) % 0.44/0.63 (define @t56 () (= @t4 @t55)) % 0.44/0.63 (define @t57 () (and @t7 @t56)) % 0.44/0.63 (define @t58 () (exists @t8 @t57)) % 0.44/0.63 (define @t59 () (@list @t4)) % 0.44/0.63 (define @t60 () (lambda @t59 @t58)) % 0.44/0.63 (define @t61 () (_ tptp.dsetconstr @t4)) % 0.44/0.63 (define @t62 () (_ @t61 @t28)) % 0.44/0.63 (define @t63 () (lambda @t30 (_ tptp.singleton @t62))) % 0.44/0.63 (define @t64 () (_ (_ tptp.cartprod @t4) @t1)) % 0.44/0.63 (define @t65 () (@var "C" $$unsorted)) % 0.44/0.63 (define @t66 () (_ (_ tptp.subset @t65) @t64)) % 0.44/0.63 (define @t67 () (lambda (@list @t4 @t1 @t65) @t66)) % 0.44/0.63 (define @t68 () (@var "R" $$unsorted)) % 0.44/0.63 (define @t69 () (_ @t41 @t68)) % 0.44/0.63 (define @t70 () (lambda @t24 @t69)) % 0.44/0.63 (define @t71 () (=> @t7 (_ (_ tptp.ex1 @t1) @t70))) % 0.44/0.63 (define @t72 () (forall @t8 @t71)) % 0.44/0.63 (define @t73 () (and (_ (_ (_ tptp.breln @t4) @t1) @t68) @t72)) % 0.44/0.63 (define @t74 () (@list @t4 @t1 @t68)) % 0.44/0.63 (define @t75 () (lambda @t74 @t73)) % 0.44/0.63 (define @t76 () (@var "BOUND_VARIABLE_7964" $$unsorted)) % 0.44/0.63 (define @t77 () (tptp.ap @t4 @t1 @t3 @t76)) % 0.44/0.63 (define @t78 () (@var "BOUND_VARIABLE_7966" $$unsorted)) % 0.44/0.63 (define @t79 () (not (tptp.in (tptp.kpair @t76 @t78) @t3))) % 0.44/0.63 (define @t80 () (not (tptp.in @t78 @t1))) % 0.44/0.63 (define @t81 () (not (tptp.in @t76 @t4))) % 0.44/0.63 (define @t82 () (tptp.kpair @t2 @t15)) % 0.44/0.63 (define @t83 () (tptp.in @t82 @t3)) % 0.44/0.63 (define @t84 () (tptp.dsetconstr @t1 (lambda @t24 @t83))) % 0.44/0.63 (define @t85 () (@var "BOUND_VARIABLE_7577" $$unsorted)) % 0.44/0.63 (define @t86 () (tptp.setadjoin @t85 tptp.emptyset)) % 0.44/0.63 (define @t87 () (@list @t85)) % 0.44/0.63 (define @t88 () (tptp.in @t2 @t4)) % 0.44/0.63 (define @t89 () (not @t88)) % 0.44/0.63 (define @t90 () (forall @t8 (or @t89 (not (forall @t87 (or (not (tptp.in @t85 @t84)) (not (= @t86 @t84)))))))) % 0.44/0.63 (define @t91 () (not @t90)) % 0.44/0.63 (define @t92 () (tptp.cartprod @t4 @t1)) % 0.44/0.63 (define @t93 () (tptp.subset @t3 @t92)) % 0.44/0.63 (define @t94 () (not @t93)) % 0.44/0.63 (define @t95 () (@list @t4 @t1 @t3 @t76 @t78)) % 0.44/0.63 (define @t96 () (forall @t95 (or @t94 @t91 @t81 @t80 @t79 (= @t78 @t77)))) % 0.44/0.63 (define @t97 () (@var "BOUND_VARIABLE_7899" $$unsorted)) % 0.44/0.63 (define @t98 () (tptp.in (tptp.kpair @t97 (tptp.ap @t4 @t1 @t3 @t97)) @t3)) % 0.44/0.63 (define @t99 () (not (tptp.in @t97 @t4))) % 0.44/0.63 (define @t100 () (or @t99 @t98)) % 0.44/0.63 (define @t101 () (or @t94 @t91 @t100)) % 0.44/0.63 (define @t102 () (forall (@list @t4 @t1 @t3 @t97) @t101)) % 0.44/0.63 (define @t103 () (@list @t97)) % 0.44/0.63 (define @t104 () (forall @t103 @t101)) % 0.44/0.63 (define @t105 () (forall @t103 @t100)) % 0.44/0.63 (define @t106 () (@list @t2)) % 0.44/0.63 (define @t107 () (or @t94 @t91 @t105)) % 0.44/0.63 (define @t108 () (tptp.ap @t4 @t1 @t3 @t2)) % 0.44/0.63 (define @t109 () (tptp.kpair @t2 @t108)) % 0.44/0.63 (define @t110 () (tptp.in @t109 @t3)) % 0.44/0.63 (define @t111 () (forall @t8 (or @t89 @t110))) % 0.44/0.63 (define @t112 () (_ tptp.subset @t3)) % 0.44/0.63 (define @t113 () (_ @t112 @t64)) % 0.44/0.63 (define @t114 () (not @t113)) % 0.44/0.63 (define @t115 () (or @t114 @t91 @t111)) % 0.44/0.63 (define @t116 () (or @t114 @t91)) % 0.44/0.63 (define @t117 () (and @t113 @t90)) % 0.44/0.63 (define @t118 () (not @t117)) % 0.44/0.63 (define @t119 () (not @t7)) % 0.44/0.63 (define @t120 () (or @t119 @t35)) % 0.44/0.63 (define @t121 () (tptp.in @t82 @t68)) % 0.44/0.63 (define @t122 () (tptp.dsetconstr @t1 (lambda @t24 @t121))) % 0.44/0.63 (define @t123 () (not (forall @t87 (or (not (tptp.in @t85 @t122)) (not (= @t86 @t122)))))) % 0.44/0.63 (define @t124 () (_ (_ tptp.subset @t68) @t64)) % 0.44/0.63 (define @t125 () (and @t124 (forall @t8 (or @t89 @t123)))) % 0.44/0.63 (define @t126 () (lambda (@list @t68) @t125)) % 0.44/0.63 (define @t127 () (lambda (@list @t1 @t68) @t125)) % 0.44/0.63 (define @t128 () (_ (lambda @t74 @t125) @t4)) % 0.44/0.63 (define @t129 () (_ (_ @t128 @t1) @t3)) % 0.44/0.63 (define @t130 () (=> @t129 @t36)) % 0.44/0.63 (define @t131 () (forall @t12 @t130)) % 0.44/0.63 (define @t132 () (or @t119 @t123)) % 0.44/0.63 (define @t133 () (_ tptp.in @t82)) % 0.44/0.63 (define @t134 () (tptp.dsetconstr @t1 @t70)) % 0.44/0.63 (define @t135 () (= @t86 @t134)) % 0.44/0.63 (define @t136 () (not @t135)) % 0.44/0.63 (define @t137 () (tptp.in @t85 @t134)) % 0.44/0.63 (define @t138 () (not @t137)) % 0.44/0.63 (define @t139 () (or @t138 @t136)) % 0.44/0.63 (define @t140 () (not (= @t134 @t86))) % 0.44/0.63 (define @t141 () (or @t138 @t140)) % 0.44/0.63 (define @t142 () (forall @t87 @t141)) % 0.44/0.63 (define @t143 () (not @t142)) % 0.44/0.63 (define @t144 () (tptp.dsetconstr @t1 @t17)) % 0.44/0.63 (define @t145 () (not (tptp.in @t85 @t144))) % 0.44/0.63 (define @t146 () (@list @t17)) % 0.44/0.63 (define @t147 () (not (= @t86 @t144))) % 0.44/0.63 (define @t148 () (or @t145 @t147)) % 0.44/0.63 (define @t149 () (forall @t87 @t148)) % 0.44/0.63 (define @t150 () (not @t149)) % 0.44/0.63 (define @t151 () (tptp.setadjoin @t2 tptp.emptyset)) % 0.44/0.63 (define @t152 () (forall @t8 (or (not (tptp.in @t2 @t144)) (not (= @t151 @t144))))) % 0.44/0.63 (define @t153 () (not @t152)) % 0.44/0.63 (define @t154 () (lambda @t146 @t153)) % 0.44/0.63 (define @t155 () (tptp.dsetconstr @t4 @t17)) % 0.44/0.63 (define @t156 () (forall @t8 (or (not (tptp.in @t2 @t155)) (not (= @t151 @t155))))) % 0.44/0.63 (define @t157 () (not @t156)) % 0.44/0.63 (define @t158 () (lambda @t30 @t157)) % 0.44/0.63 (define @t159 () (_ @t158 @t1)) % 0.44/0.63 (define @t160 () (=> @t7 (_ @t159 @t70))) % 0.44/0.63 (define @t161 () (forall @t8 @t160)) % 0.44/0.63 (define @t162 () (lambda (@list @t65) @t66)) % 0.44/0.63 (define @t163 () (lambda (@list @t1 @t65) @t66)) % 0.44/0.63 (define @t164 () (_ @t67 @t4)) % 0.44/0.63 (define @t165 () (@var "BOUND_VARIABLE_7478" $$unsorted)) % 0.44/0.63 (define @t166 () (_ @t17 @t165)) % 0.44/0.63 (define @t167 () (@list @t165)) % 0.44/0.63 (define @t168 () (lambda @t167 @t166)) % 0.44/0.63 (define @t169 () (tptp.dsetconstr @t4 @t168)) % 0.44/0.63 (define @t170 () (= @t151 @t169)) % 0.44/0.63 (define @t171 () (not @t170)) % 0.44/0.63 (define @t172 () (tptp.in @t2 @t169)) % 0.44/0.63 (define @t173 () (not @t172)) % 0.44/0.63 (define @t174 () (or @t173 @t171)) % 0.44/0.63 (define @t175 () (_ @t17 @t165)) % 0.44/0.63 (define @t176 () (lambda @t167 @t175)) % 0.44/0.63 (define @t177 () (_ @t61 @t176)) % 0.44/0.63 (define @t178 () (= @t151 @t177)) % 0.44/0.63 (define @t179 () (not @t178)) % 0.44/0.63 (define @t180 () (tptp.in @t2 @t177)) % 0.44/0.63 (define @t181 () (not @t180)) % 0.44/0.63 (define @t182 () (or @t181 @t179)) % 0.44/0.63 (define @t183 () (= @t151 @t62)) % 0.44/0.63 (define @t184 () (not @t183)) % 0.44/0.63 (define @t185 () (tptp.in @t2 @t62)) % 0.44/0.63 (define @t186 () (not @t185)) % 0.44/0.63 (define @t187 () (or @t186 @t184)) % 0.44/0.63 (define @t188 () (not (= @t62 @t151))) % 0.44/0.63 (define @t189 () (or @t186 @t188)) % 0.44/0.63 (define @t190 () (forall @t8 @t189)) % 0.44/0.63 (define @t191 () (not @t190)) % 0.44/0.63 (define @t192 () (not @t56)) % 0.44/0.63 (define @t193 () (or @t119 @t192)) % 0.44/0.63 (define @t194 () (forall @t8 (not @t57))) % 0.44/0.63 (define @t195 () (not @t194)) % 0.44/0.63 (define @t196 () (=> tptp.funcGraphProp1 @t96)) % 0.44/0.63 (define @t197 () (@var "BOUND_VARIABLE_7859" $$unsorted)) % 0.44/0.63 (define @t198 () (@var "BOUND_VARIABLE_7857" $$unsorted)) % 0.44/0.63 (define @t199 () (= @t198 @t197)) % 0.44/0.63 (define @t200 () (not (_ @t17 @t197))) % 0.44/0.63 (define @t201 () (not (tptp.in @t197 @t4))) % 0.44/0.63 (define @t202 () (not (_ @t17 @t198))) % 0.44/0.63 (define @t203 () (not (tptp.in @t198 @t4))) % 0.44/0.63 (define @t204 () (@var "BOUND_VARIABLE_7849" $$unsorted)) % 0.44/0.63 (define @t205 () (tptp.setadjoin @t204 tptp.emptyset)) % 0.44/0.63 (define @t206 () (not (= @t205 @t155))) % 0.44/0.63 (define @t207 () (not (tptp.in @t204 @t155))) % 0.44/0.63 (define @t208 () (or @t207 @t206 @t203 @t202 @t201 @t200 @t199)) % 0.44/0.63 (define @t209 () (or @t203 @t202 @t201 @t200 @t199)) % 0.44/0.63 (define @t210 () (or @t207 @t206)) % 0.44/0.63 (define @t211 () (or @t210 @t209)) % 0.44/0.63 (define @t212 () (@list @t4 @t17 @t204 @t198 @t197)) % 0.44/0.63 (define @t213 () (forall @t212 @t211)) % 0.44/0.63 (define @t214 () (forall (@list @t204 @t198 @t197) @t211)) % 0.44/0.63 (define @t215 () (forall (@list @t198 @t197) @t209)) % 0.44/0.63 (define @t216 () (@var "BOUND_VARIABLE_7832" $$unsorted)) % 0.44/0.63 (define @t217 () (forall (@list @t204) @t210)) % 0.44/0.63 (define @t218 () (or @t217 @t215)) % 0.44/0.63 (define @t219 () (= @t2 @t216)) % 0.44/0.63 (define @t220 () (not (_ @t17 @t216))) % 0.44/0.63 (define @t221 () (not (tptp.in @t216 @t4))) % 0.44/0.63 (define @t222 () (_ @t17 @t2)) % 0.44/0.63 (define @t223 () (not @t222)) % 0.44/0.63 (define @t224 () (or @t89 @t223 @t221 @t220 @t219)) % 0.44/0.63 (define @t225 () (@list @t2 @t216)) % 0.44/0.63 (define @t226 () (forall @t225 @t224)) % 0.44/0.63 (define @t227 () (or @t221 @t220 @t219)) % 0.44/0.63 (define @t228 () (or @t89 @t223 @t227)) % 0.44/0.63 (define @t229 () (forall @t225 @t228)) % 0.44/0.63 (define @t230 () (@list @t216)) % 0.44/0.63 (define @t231 () (forall @t230 @t228)) % 0.44/0.63 (define @t232 () (forall @t230 @t227)) % 0.44/0.63 (define @t233 () (@list @t15)) % 0.44/0.63 (define @t234 () (or @t89 @t223 @t232)) % 0.44/0.63 (define @t235 () (_ @t17 @t15)) % 0.44/0.63 (define @t236 () (tptp.in @t15 @t4)) % 0.44/0.63 (define @t237 () (forall @t24 (or (not @t236) (not @t235) @t16))) % 0.44/0.63 (define @t238 () (not @t20)) % 0.44/0.63 (define @t239 () (or @t119 @t238 @t237)) % 0.44/0.63 (define @t240 () (or @t238 @t237)) % 0.44/0.63 (define @t241 () (not @t18)) % 0.44/0.63 (define @t242 () (not @t23)) % 0.44/0.63 (define @t243 () (or @t242 @t241 @t16)) % 0.44/0.63 (define @t244 () (forall @t24 @t243)) % 0.44/0.63 (define @t245 () (or @t238 @t244)) % 0.44/0.63 (define @t246 () (or @t238 @t243)) % 0.44/0.63 (define @t247 () (or @t242 @t238 @t241 @t16)) % 0.44/0.63 (define @t248 () (or @t238 @t241 @t16)) % 0.44/0.63 (define @t249 () (@var "BOUND_VARIABLE_7786" $$unsorted)) % 0.44/0.63 (define @t250 () (_ @t17 @t249)) % 0.44/0.63 (define @t251 () (@list @t249)) % 0.44/0.63 (define @t252 () (lambda @t251 @t250)) % 0.44/0.63 (define @t253 () (tptp.dsetconstr @t4 @t252)) % 0.44/0.63 (define @t254 () (= @t151 @t253)) % 0.44/0.63 (define @t255 () (not @t254)) % 0.44/0.63 (define @t256 () (tptp.in @t2 @t253)) % 0.44/0.63 (define @t257 () (not @t256)) % 0.44/0.63 (define @t258 () (or @t257 @t255)) % 0.44/0.63 (define @t259 () (_ @t17 @t249)) % 0.44/0.63 (define @t260 () (lambda @t251 @t259)) % 0.44/0.63 (define @t261 () (tptp.dsetconstr @t4 @t260)) % 0.44/0.63 (define @t262 () (= @t151 @t261)) % 0.44/0.63 (define @t263 () (not @t262)) % 0.44/0.63 (define @t264 () (tptp.in @t2 @t261)) % 0.44/0.63 (define @t265 () (not @t264)) % 0.44/0.63 (define @t266 () (or @t265 @t263)) % 0.44/0.63 (define @t267 () (tptp.dsetconstr @t4 @t28)) % 0.44/0.63 (define @t268 () (= @t151 @t267)) % 0.44/0.63 (define @t269 () (not @t268)) % 0.44/0.63 (define @t270 () (tptp.in @t2 @t267)) % 0.44/0.63 (define @t271 () (not @t270)) % 0.44/0.63 (define @t272 () (or @t271 @t269)) % 0.44/0.63 (define @t273 () (forall @t8 @t272)) % 0.44/0.63 (define @t274 () (not @t273)) % 0.44/0.63 (define @t275 () (lambda @t146 @t157)) % 0.44/0.63 (define @t276 () (_ @t158 @t4)) % 0.44/0.63 (define @t277 () (=> (_ @t276 @t28) @t27)) % 0.44/0.63 (define @t278 () (forall @t30 @t277)) % 0.44/0.63 (define @t279 () (=> tptp.ex1E2 @t196)) % 0.44/0.63 (define @t280 () (@var "BOUND_VARIABLE_7758" $$unsorted)) % 0.44/0.63 (define @t281 () (tptp.in (tptp.ap @t4 @t1 @t3 @t280) @t1)) % 0.44/0.63 (define @t282 () (not (tptp.in @t280 @t4))) % 0.44/0.63 (define @t283 () (or @t282 @t281)) % 0.44/0.63 (define @t284 () (or @t94 @t91 @t283)) % 0.44/0.63 (define @t285 () (forall (@list @t4 @t1 @t3 @t280) @t284)) % 0.44/0.63 (define @t286 () (@list @t280)) % 0.44/0.63 (define @t287 () (forall @t286 @t284)) % 0.44/0.63 (define @t288 () (forall @t286 @t283)) % 0.44/0.63 (define @t289 () (or @t94 @t91 @t288)) % 0.44/0.63 (define @t290 () (tptp.in @t108 @t1)) % 0.44/0.63 (define @t291 () (forall @t8 (or @t89 @t290))) % 0.44/0.63 (define @t292 () (or @t114 @t91 @t291)) % 0.44/0.63 (define @t293 () (or @t119 @t6)) % 0.44/0.63 (define @t294 () (=> @t129 @t9)) % 0.44/0.63 (define @t295 () (forall @t12 @t294)) % 0.44/0.63 (define @t296 () (=> tptp.app @t279)) % 0.44/0.63 (define @t297 () (= @t77 @t78)) % 0.44/0.63 (define @t298 () (or @t94 @t91 @t81 @t80 @t79 @t297)) % 0.44/0.63 (define @t299 () (or @t81 @t80 @t79 @t297)) % 0.44/0.63 (define @t300 () (or @t94 @t91 @t299)) % 0.44/0.63 (define @t301 () (forall @t95 @t300)) % 0.44/0.63 (define @t302 () (@list @t76 @t78)) % 0.44/0.63 (define @t303 () (forall @t302 @t300)) % 0.44/0.63 (define @t304 () (forall @t302 @t299)) % 0.44/0.63 (define @t305 () (@var "BOUND_VARIABLE_7942" $$unsorted)) % 0.44/0.63 (define @t306 () (or @t94 @t91 @t304)) % 0.44/0.63 (define @t307 () (not (tptp.in (tptp.kpair @t2 @t305) @t3))) % 0.44/0.63 (define @t308 () (not (tptp.in @t305 @t1))) % 0.44/0.63 (define @t309 () (@list @t2 @t305)) % 0.44/0.63 (define @t310 () (forall @t309 (or @t89 @t308 @t307 (= @t108 @t305)))) % 0.44/0.63 (define @t311 () (or @t114 @t91 @t310)) % 0.44/0.63 (define @t312 () (= @t305 @t108)) % 0.44/0.63 (define @t313 () (or @t89 @t308 @t307 @t312)) % 0.44/0.63 (define @t314 () (or @t308 @t307 @t312)) % 0.44/0.63 (define @t315 () (or @t89 @t314)) % 0.44/0.63 (define @t316 () (forall @t309 @t315)) % 0.44/0.63 (define @t317 () (@list @t305)) % 0.44/0.63 (define @t318 () (forall @t317 @t315)) % 0.44/0.63 (define @t319 () (forall @t317 @t314)) % 0.44/0.63 (define @t320 () (or @t89 @t319)) % 0.44/0.63 (define @t321 () (tptp.in @t15 @t1)) % 0.44/0.63 (define @t322 () (forall @t24 (or (not @t321) (not @t83) (= @t15 @t108)))) % 0.44/0.63 (define @t323 () (or @t119 @t322)) % 0.44/0.63 (define @t324 () (= @t15 @t5)) % 0.44/0.63 (define @t325 () (not @t42)) % 0.44/0.63 (define @t326 () (not @t44)) % 0.44/0.63 (define @t327 () (or @t326 @t325 @t324)) % 0.44/0.63 (define @t328 () (=> @t42 @t324)) % 0.44/0.63 (define @t329 () (=> @t129 @t48)) % 0.44/0.63 (define @t330 () (forall @t12 @t329)) % 0.44/0.63 (define @t331 () (=> tptp.funcGraphProp1 @t330)) % 0.44/0.63 (define @t332 () (=> tptp.ex1E2 @t331)) % 0.44/0.63 (define @t333 () (=> tptp.app @t332)) % 0.44/0.63 (define @t334 () (@quantifiers_skolemize @t96 1)) % 0.44/0.63 (define @t335 () (@quantifiers_skolemize @t96 4)) % 0.44/0.63 (define @t336 () (tptp.in @t335 @t334)) % 0.44/0.63 (define @t337 () (@quantifiers_skolemize @t96 3)) % 0.44/0.63 (define @t338 () (@quantifiers_skolemize @t96 2)) % 0.44/0.63 (define @t339 () (@quantifiers_skolemize @t96 0)) % 0.44/0.63 (define @t340 () (tptp.ap @t339 @t334 @t338 @t337)) % 0.44/0.63 (define @t341 () (= @t335 @t340)) % 0.44/0.63 (define @t342 () (tptp.in (tptp.kpair @t337 @t335) @t338)) % 0.44/0.63 (define @t343 () (not @t342)) % 0.44/0.63 (define @t344 () (not @t336)) % 0.44/0.63 (define @t345 () (tptp.in @t337 @t339)) % 0.44/0.63 (define @t346 () (not @t345)) % 0.44/0.63 (define @t347 () (tptp.dsetconstr @t334 (lambda @t24 (tptp.in @t82 @t338)))) % 0.44/0.63 (define @t348 () (forall @t8 (or (not (tptp.in @t2 @t339)) (not (forall @t87 (or (not (tptp.in @t85 @t347)) (not (= @t86 @t347)))))))) % 0.44/0.63 (define @t349 () (not @t348)) % 0.44/0.63 (define @t350 () (tptp.subset @t338 (tptp.cartprod @t339 @t334))) % 0.44/0.63 (define @t351 () (not @t350)) % 0.44/0.63 (define @t352 () (or @t351 @t349 @t346 @t344 @t343 @t341)) % 0.44/0.63 (define @t353 () (@list true)) % 0.44/0.63 (define @t354 () (@list @t352)) % 0.44/0.63 (define @t355 () (@list @t339 @t334 @t338 @t337)) % 0.44/0.63 (define @t356 () (tptp.in @t340 @t334)) % 0.44/0.63 (define @t357 () (or @t351 @t349 @t346 @t356)) % 0.44/0.63 (define @t358 () (@list false false false false)) % 0.44/0.63 (define @t359 () (tptp.in (tptp.kpair @t337 @t15) @t338)) % 0.44/0.63 (define @t360 () (lambda @t24 @t359)) % 0.44/0.63 (define @t361 () (tptp.dsetconstr @t334 @t360)) % 0.44/0.63 (define @t362 () (forall @t87 (or (not (tptp.in @t85 @t361)) (not (= @t86 @t361))))) % 0.44/0.63 (define @t363 () (not @t362)) % 0.44/0.63 (define @t364 () (or @t346 @t363)) % 0.44/0.63 (define @t365 () (@list false false)) % 0.44/0.63 (define @t366 () (@purify @t360)) % 0.44/0.63 (define @t367 () (tptp.dsetconstr @t334 @t366)) % 0.44/0.63 (define @t368 () (@quantifiers_skolemize @t362 0)) % 0.44/0.63 (define @t369 () (tptp.setadjoin @t368 tptp.emptyset)) % 0.44/0.63 (define @t370 () (= @t369 @t367)) % 0.44/0.63 (define @t371 () (not @t370)) % 0.44/0.63 (define @t372 () (tptp.in @t368 @t367)) % 0.44/0.63 (define @t373 () (not @t372)) % 0.44/0.63 (define @t374 () (or @t373 @t371)) % 0.44/0.63 (define @t375 () (not @t374)) % 0.44/0.63 (define @t376 () (= @t361 @t369)) % 0.44/0.63 (define @t377 () (not @t376)) % 0.44/0.63 (define @t378 () (tptp.in @t368 @t361)) % 0.44/0.63 (define @t379 () (not @t378)) % 0.44/0.63 (define @t380 () (or @t379 @t377)) % 0.44/0.63 (define @t381 () (not @t380)) % 0.44/0.63 (define @t382 () (not (= @t369 @t361))) % 0.44/0.63 (define @t383 () (or @t379 @t382)) % 0.44/0.63 (define @t384 () (not @t383)) % 0.44/0.63 (define @t385 () (@list @t374)) % 0.44/0.63 (define @t386 () (_ @t366 @t340)) % 0.44/0.63 (define @t387 () (not @t386)) % 0.44/0.63 (define @t388 () (not @t356)) % 0.44/0.63 (define @t389 () (_ @t366 @t335)) % 0.44/0.63 (define @t390 () (not @t389)) % 0.44/0.63 (define @t391 () (not (= @t367 @t369))) % 0.44/0.63 (define @t392 () (or @t373 @t391 @t344 @t390 @t388 @t387 @t341)) % 0.44/0.63 (define @t393 () (forall @t212 (or @t207 (not (= @t155 @t205)) @t203 @t202 @t201 @t200 @t199))) % 0.44/0.63 (define @t394 () (or @t373 @t371 @t344 @t390 @t388 @t387 @t341)) % 0.44/0.63 (define @t395 () (_ @t366 @t15)) % 0.44/0.63 (define @t396 () (_ @t360 @t15)) % 0.44/0.63 (define @t397 () (= @t395 @t396)) % 0.44/0.63 (define @t398 () (forall @t24 @t397)) % 0.44/0.63 (define @t399 () (= @t342 @t389)) % 0.44/0.63 (define @t400 () (tptp.in (tptp.kpair @t337 @t340) @t338)) % 0.44/0.63 (define @t401 () (or @t351 @t349 @t346 @t400)) % 0.44/0.63 (define @t402 () (= @t400 @t386)) % 0.44/0.63 (assume @p1 @t14) % 0.44/0.63 (assume @p2 @t32) % 0.44/0.63 (assume @p3 @t39) % 0.44/0.63 (assume @p4 @t54) % 0.44/0.63 (assume @p5 true) % 0.44/0.63 (step @p6 (= tptp.singleton @t60) :rule refl :args (@t60)) % 0.44/0.63 (step @p7 (= tptp.ex1 @t63) :rule refl :args (@t63)) % 0.44/0.63 (step @p8 (= tptp.breln @t67) :rule refl :args (@t67)) % 0.44/0.63 (step @p9 (= tptp.func @t75) :rule refl :args (@t75)) % 0.44/0.63 (step @p10 :rule refl :args (@t96)) % 0.44/0.63 (step @p11 :rule aci_norm :args ((= @t101 (or @t94 @t91 @t99 @t98)))) % 0.44/0.63 (step @p12 :rule cong :premises (@p11) :args (@t102)) % 0.44/0.63 (step @p13 :rule quant-merge-prenex :args ((= (forall @t12 @t104) @t102))) % 0.44/0.63 (step @p14 :rule alpha_equiv :args (@t105 (@list @t97) @t106)) % 0.44/0.63 (step @p15 :rule refl :args (@t91)) % 0.44/0.63 (step @p16 :rule refl :args (@t94)) % 0.44/0.63 (step @p17 :rule nary_cong :premises (@p16 @p15 @p14) :args (@t107)) % 0.44/0.63 (step @p18 :rule quant-miniscope-or :args ((= @t104 @t107))) % 0.44/0.63 (step @p19 :rule trans :premises (@p18 @p17)) % 0.44/0.63 (step @p20 :rule symm :premises (@p19)) % 0.44/0.63 (step @p21 :rule cong :premises (@p20) :args ((forall @t12 (or @t94 @t91 @t111)))) % 0.44/0.63 (step @p22 :rule trans :premises (@p21 @p13)) % 0.44/0.63 (step @p23 :rule trans :premises (@p22 @p12)) % 0.44/0.63 (step @p24 :rule refl :args (@t111)) % 0.44/0.63 (step @p25 :rule refl :args ((tptp.subset @t3 @t64))) % 0.44/0.63 (step @p26 :rule refl :args (@t92)) % 0.44/0.63 (step @p27 :rule refl :args (@t3)) % 0.44/0.63 (step @p28 :rule cong :premises (@p27 @p26) :args (@t93)) % 0.44/0.63 (step @p29 :rule trans :premises (@p28 @p25)) % 0.44/0.63 (step @p30 :rule refl :args (@t112)) % 0.44/0.63 (step @p31 :rule ho_cong :premises (@p30 @p26)) % 0.44/0.63 (step @p32 :rule cong :premises (@p31 @p29) :args ((= (_ @t112 @t92) @t93))) % 0.44/0.63 (step @p33 :rule symm :premises (@p32)) % 0.44/0.63 (step @p34 :rule refl :args (@t113)) % 0.44/0.63 (step @p35 :rule eq_resolve :premises (@p34 @p33)) % 0.44/0.63 (step @p36 :rule refl :args (@t64)) % 0.44/0.63 (step @p37 :rule cong :premises (@p36 @p26) :args ((= @t64 @t92))) % 0.44/0.63 (step @p38 :rule symm :premises (@p37)) % 0.44/0.63 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 0.44/0.63 (step @p40 :rule ho_cong :premises (@p30 @p39)) % 0.44/0.63 (step @p41 :rule trans :premises (@p40 @p35)) % 0.44/0.63 (step @p42 :rule cong :premises (@p41) :args (@t114)) % 0.44/0.63 (step @p43 :rule nary_cong :premises (@p42 @p15 @p24) :args (@t115)) % 0.44/0.63 (step @p44 :rule cong :premises (@p43) :args ((forall @t12 @t115))) % 0.44/0.63 (step @p45 :rule trans :premises (@p44 @p23)) % 0.44/0.63 (step @p46 :rule aci_norm :args ((= (or @t116 @t111) @t115))) % 0.44/0.63 (step @p47 :rule bool-and-de-morgan :args (@t113 @t90 true)) % 0.44/0.63 (step @p48 :rule nary_cong :premises (@p47 @p24) :args ((or @t118 @t111))) % 0.44/0.63 (step @p49 :rule trans :premises (@p48 @p46)) % 0.44/0.63 (step @p50 :rule bool-impl-elim :args (@t117 @t111)) % 0.44/0.63 (step @p51 :rule trans :premises (@p50 @p49)) % 0.44/0.63 (step @p52 :rule cong :premises (@p51) :args ((forall @t12 (=> @t117 @t111)))) % 0.44/0.63 (step @p53 :rule trans :premises (@p52 @p45)) % 0.44/0.63 (step @p54 :rule refl :args ((tptp.in @t34 @t3))) % 0.44/0.63 (step @p55 :rule refl :args ((tptp.kpair @t2 @t5))) % 0.44/0.63 (step @p56 :rule refl :args (@t108)) % 0.44/0.63 (step @p57 :rule refl :args (@t2)) % 0.44/0.63 (step @p58 :rule cong :premises (@p57 @p56) :args (@t109)) % 0.44/0.63 (step @p59 :rule trans :premises (@p58 @p55)) % 0.44/0.63 (step @p60 :rule cong :premises (@p59 @p27) :args (@t110)) % 0.44/0.63 (step @p61 :rule trans :premises (@p60 @p54)) % 0.44/0.63 (step @p62 :rule refl :args (tptp.in)) % 0.44/0.63 (step @p63 :rule ho_cong :premises (@p62 @p59)) % 0.44/0.63 (step @p64 :rule ho_cong :premises (@p63 @p27)) % 0.44/0.63 (step @p65 :rule cong :premises (@p64 @p61) :args ((= (_ (_ tptp.in @t109) @t3) @t110))) % 0.44/0.63 (step @p66 :rule symm :premises (@p65)) % 0.44/0.63 (step @p67 :rule refl :args (@t35)) % 0.44/0.63 (step @p68 :rule eq_resolve :premises (@p67 @p66)) % 0.44/0.63 (step @p69 :rule refl :args (@t33)) % 0.44/0.63 (step @p70 :rule ho_cong :premises (@p69 @p56)) % 0.44/0.63 (step @p71 :rule cong :premises (@p70 @p59) :args ((= (_ @t33 @t108) @t109))) % 0.44/0.63 (step @p72 :rule symm :premises (@p71)) % 0.44/0.63 (step @p73 :rule refl :args (@t34)) % 0.44/0.63 (step @p74 :rule eq_resolve :premises (@p73 @p72)) % 0.44/0.63 (step @p75 :rule refl :args (@t5)) % 0.44/0.63 (step @p76 :rule cong :premises (@p75 @p56) :args ((= @t5 @t108))) % 0.44/0.63 (step @p77 :rule symm :premises (@p76)) % 0.44/0.63 (step @p78 :rule eq_resolve :premises (@p75 @p77)) % 0.44/0.63 (step @p79 :rule ho_cong :premises (@p69 @p78)) % 0.44/0.63 (step @p80 :rule trans :premises (@p79 @p74)) % 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