%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU685^2 : 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 : n015.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 08:52:43 AM UTC 2026 % Result : Theorem 0.37s 0.61s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU685^2 : TPTP v9.2.1. Released v3.7.0. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n015.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 17:47:04 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.37/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.61 % SZS status Theorem % 0.37/0.61 % SZS output start Proof % 0.37/0.61 ( % 0.37/0.61 (declare-sort $$unsorted 0) % 0.37/0.61 (declare-const tptp.emptyset $$unsorted) % 0.37/0.61 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.37/0.61 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.funcGraphProp1 Bool) % 0.37/0.61 (declare-const tptp.infuncsetfunc Bool) % 0.37/0.61 (declare-const tptp.funcSet (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.61 (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)))))))) % 0.37/0.61 (define tptp.ex1 () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xphi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ tptp.singleton (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_1) (_ _let_2 _let_1))))))))) % 0.37/0.61 (define tptp.breln () (let ((_let_1 (@var "B" $$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))))))) % 0.37/0.61 (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" $$unsorted))) (lambda (@list _let_5 _let_4 _let_1) (and (_ (_ (_ tptp.breln _let_5) _let_4) _let_1) (forall (@list _let_3) (=> (_ (_ tptp.in _let_3) _let_5) (_ (_ tptp.ex1 _let_4) (lambda (@list _let_2) (_ (_ tptp.in (_ (_ tptp.kpair _let_3) _let_2)) _let_1))))))))))))) % 0.37/0.61 (define @t1 () (@var "Xf" $$unsorted)) % 0.37/0.61 (define @t2 () (@var "B" $$unsorted)) % 0.37/0.61 (define @t3 () (@var "A" $$unsorted)) % 0.37/0.61 (define @t4 () (_ (_ (_ tptp.func @t3) @t2) @t1)) % 0.37/0.61 (define @t5 () (_ (_ tptp.funcSet @t3) @t2)) % 0.37/0.61 (define @t6 () (_ tptp.in @t1)) % 0.37/0.61 (define @t7 () (_ @t6 @t5)) % 0.37/0.61 (define @t8 () (=> @t7 @t4)) % 0.37/0.61 (define @t9 () (@list @t3 @t2 @t1)) % 0.37/0.61 (define @t10 () (forall @t9 @t8)) % 0.37/0.61 (define @t11 () (= tptp.infuncsetfunc @t10)) % 0.37/0.61 (define @t12 () (@var "Xx" $$unsorted)) % 0.37/0.61 (define @t13 () (_ (_ (_ (_ tptp.ap @t3) @t2) @t1) @t12)) % 0.37/0.61 (define @t14 () (_ tptp.kpair @t12)) % 0.37/0.61 (define @t15 () (_ @t14 @t13)) % 0.37/0.61 (define @t16 () (_ (_ tptp.in @t15) @t1)) % 0.37/0.61 (define @t17 () (_ (_ tptp.in @t12) @t3)) % 0.37/0.61 (define @t18 () (@list @t12)) % 0.37/0.61 (define @t19 () (forall @t18 (=> @t17 @t16))) % 0.37/0.61 (define @t20 () (=> @t4 @t19)) % 0.37/0.61 (define @t21 () (forall @t9 @t20)) % 0.37/0.61 (define @t22 () (= tptp.funcGraphProp1 @t21)) % 0.37/0.61 (define @t23 () (=> @t7 @t19)) % 0.37/0.61 (define @t24 () (forall @t9 @t23)) % 0.37/0.61 (define @t25 () (=> tptp.funcGraphProp1 @t24)) % 0.37/0.61 (define @t26 () (=> tptp.infuncsetfunc @t25)) % 0.37/0.61 (define @t27 () (not @t26)) % 0.37/0.61 (define @t28 () (_ (_ tptp.setadjoin @t12) tptp.emptyset)) % 0.37/0.61 (define @t29 () (= @t3 @t28)) % 0.37/0.61 (define @t30 () (and @t17 @t29)) % 0.37/0.61 (define @t31 () (exists @t18 @t30)) % 0.37/0.61 (define @t32 () (@list @t3)) % 0.37/0.61 (define @t33 () (lambda @t32 @t31)) % 0.37/0.61 (define @t34 () (@var "Xphi" (-> $$unsorted Bool))) % 0.37/0.61 (define @t35 () (lambda @t18 (_ @t34 @t12))) % 0.37/0.61 (define @t36 () (_ tptp.dsetconstr @t3)) % 0.37/0.61 (define @t37 () (_ @t36 @t35)) % 0.37/0.61 (define @t38 () (@list @t3 @t34)) % 0.37/0.61 (define @t39 () (lambda @t38 (_ tptp.singleton @t37))) % 0.37/0.61 (define @t40 () (_ (_ tptp.cartprod @t3) @t2)) % 0.37/0.61 (define @t41 () (@var "C" $$unsorted)) % 0.37/0.61 (define @t42 () (_ (_ tptp.subset @t41) @t40)) % 0.37/0.61 (define @t43 () (lambda (@list @t3 @t2 @t41) @t42)) % 0.37/0.61 (define @t44 () (@var "R" $$unsorted)) % 0.37/0.61 (define @t45 () (@var "Xy" $$unsorted)) % 0.37/0.61 (define @t46 () (_ @t14 @t45)) % 0.37/0.61 (define @t47 () (_ (_ tptp.in @t46) @t44)) % 0.37/0.61 (define @t48 () (@list @t45)) % 0.37/0.61 (define @t49 () (lambda @t48 @t47)) % 0.37/0.61 (define @t50 () (=> @t17 (_ (_ tptp.ex1 @t2) @t49))) % 0.37/0.61 (define @t51 () (forall @t18 @t50)) % 0.37/0.61 (define @t52 () (and (_ (_ (_ tptp.breln @t3) @t2) @t44) @t51)) % 0.37/0.61 (define @t53 () (@list @t3 @t2 @t44)) % 0.37/0.61 (define @t54 () (lambda @t53 @t52)) % 0.37/0.61 (define @t55 () (@var "BOUND_VARIABLE_7794" $$unsorted)) % 0.37/0.61 (define @t56 () (tptp.in (tptp.kpair @t55 (tptp.ap @t3 @t2 @t1 @t55)) @t1)) % 0.37/0.61 (define @t57 () (not (tptp.in @t55 @t3))) % 0.37/0.61 (define @t58 () (tptp.funcSet @t3 @t2)) % 0.37/0.61 (define @t59 () (tptp.in @t1 @t58)) % 0.37/0.61 (define @t60 () (not @t59)) % 0.37/0.61 (define @t61 () (or @t60 @t57 @t56)) % 0.37/0.61 (define @t62 () (@list @t3 @t2 @t1 @t55)) % 0.37/0.61 (define @t63 () (forall @t62 @t61)) % 0.37/0.61 (define @t64 () (@var "BOUND_VARIABLE_7773" $$unsorted)) % 0.37/0.61 (define @t65 () (tptp.in (tptp.kpair @t64 (tptp.ap @t3 @t2 @t1 @t64)) @t1)) % 0.37/0.61 (define @t66 () (not (tptp.in @t64 @t3))) % 0.37/0.61 (define @t67 () (tptp.kpair @t12 @t45)) % 0.37/0.61 (define @t68 () (tptp.dsetconstr @t2 (lambda @t48 (tptp.in @t67 @t1)))) % 0.37/0.61 (define @t69 () (@var "BOUND_VARIABLE_7577" $$unsorted)) % 0.37/0.61 (define @t70 () (tptp.setadjoin @t69 tptp.emptyset)) % 0.37/0.61 (define @t71 () (@list @t69)) % 0.37/0.61 (define @t72 () (tptp.in @t12 @t3)) % 0.37/0.61 (define @t73 () (not @t72)) % 0.37/0.61 (define @t74 () (forall @t18 (or @t73 (not (forall @t71 (or (not (tptp.in @t69 @t68)) (not (= @t70 @t68)))))))) % 0.37/0.61 (define @t75 () (not @t74)) % 0.37/0.61 (define @t76 () (tptp.cartprod @t3 @t2)) % 0.37/0.61 (define @t77 () (tptp.subset @t1 @t76)) % 0.37/0.61 (define @t78 () (not @t77)) % 0.37/0.61 (define @t79 () (or @t66 @t65)) % 0.37/0.61 (define @t80 () (or @t78 @t75 @t79)) % 0.37/0.61 (define @t81 () (forall (@list @t3 @t2 @t1 @t64) @t80)) % 0.37/0.61 (define @t82 () (@list @t64)) % 0.37/0.61 (define @t83 () (forall @t82 @t80)) % 0.37/0.61 (define @t84 () (forall @t82 @t79)) % 0.37/0.61 (define @t85 () (@list @t12)) % 0.37/0.61 (define @t86 () (or @t78 @t75 @t84)) % 0.37/0.61 (define @t87 () (tptp.ap @t3 @t2 @t1 @t12)) % 0.37/0.61 (define @t88 () (tptp.kpair @t12 @t87)) % 0.37/0.61 (define @t89 () (tptp.in @t88 @t1)) % 0.37/0.61 (define @t90 () (forall @t18 (or @t73 @t89))) % 0.37/0.61 (define @t91 () (_ tptp.subset @t1)) % 0.37/0.61 (define @t92 () (_ @t91 @t40)) % 0.37/0.61 (define @t93 () (not @t92)) % 0.37/0.61 (define @t94 () (or @t93 @t75 @t90)) % 0.37/0.61 (define @t95 () (and @t92 @t74)) % 0.37/0.61 (define @t96 () (not @t17)) % 0.37/0.61 (define @t97 () (or @t96 @t16)) % 0.37/0.61 (define @t98 () (tptp.in @t67 @t44)) % 0.37/0.61 (define @t99 () (tptp.dsetconstr @t2 (lambda @t48 @t98))) % 0.37/0.61 (define @t100 () (not (forall @t71 (or (not (tptp.in @t69 @t99)) (not (= @t70 @t99)))))) % 0.37/0.61 (define @t101 () (_ (_ tptp.subset @t44) @t40)) % 0.37/0.61 (define @t102 () (and @t101 (forall @t18 (or @t73 @t100)))) % 0.37/0.61 (define @t103 () (lambda (@list @t44) @t102)) % 0.37/0.61 (define @t104 () (lambda (@list @t2 @t44) @t102)) % 0.37/0.61 (define @t105 () (_ (lambda @t53 @t102) @t3)) % 0.37/0.61 (define @t106 () (_ (_ @t105 @t2) @t1)) % 0.37/0.61 (define @t107 () (=> @t106 @t19)) % 0.37/0.61 (define @t108 () (forall @t9 @t107)) % 0.37/0.61 (define @t109 () (or @t96 @t100)) % 0.37/0.61 (define @t110 () (tptp.dsetconstr @t2 @t49)) % 0.37/0.61 (define @t111 () (= @t70 @t110)) % 0.37/0.61 (define @t112 () (not @t111)) % 0.37/0.61 (define @t113 () (tptp.in @t69 @t110)) % 0.37/0.61 (define @t114 () (not @t113)) % 0.37/0.61 (define @t115 () (or @t114 @t112)) % 0.37/0.61 (define @t116 () (not (= @t110 @t70))) % 0.37/0.61 (define @t117 () (or @t114 @t116)) % 0.37/0.61 (define @t118 () (forall @t71 @t117)) % 0.37/0.61 (define @t119 () (not @t118)) % 0.37/0.61 (define @t120 () (tptp.dsetconstr @t2 @t34)) % 0.37/0.61 (define @t121 () (not (tptp.in @t69 @t120))) % 0.37/0.61 (define @t122 () (@list @t34)) % 0.37/0.61 (define @t123 () (not (= @t70 @t120))) % 0.37/0.61 (define @t124 () (or @t121 @t123)) % 0.37/0.61 (define @t125 () (forall @t71 @t124)) % 0.37/0.61 (define @t126 () (not @t125)) % 0.37/0.61 (define @t127 () (tptp.setadjoin @t12 tptp.emptyset)) % 0.37/0.61 (define @t128 () (forall @t18 (or (not (tptp.in @t12 @t120)) (not (= @t127 @t120))))) % 0.37/0.61 (define @t129 () (not @t128)) % 0.37/0.61 (define @t130 () (lambda @t122 @t129)) % 0.37/0.61 (define @t131 () (tptp.dsetconstr @t3 @t34)) % 0.37/0.61 (define @t132 () (_ (lambda @t38 (not (forall @t18 (or (not (tptp.in @t12 @t131)) (not (= @t127 @t131)))))) @t2)) % 0.37/0.61 (define @t133 () (=> @t17 (_ @t132 @t49))) % 0.37/0.61 (define @t134 () (forall @t18 @t133)) % 0.37/0.61 (define @t135 () (lambda (@list @t41) @t42)) % 0.37/0.61 (define @t136 () (lambda (@list @t2 @t41) @t42)) % 0.37/0.61 (define @t137 () (_ @t43 @t3)) % 0.37/0.61 (define @t138 () (@var "BOUND_VARIABLE_7478" $$unsorted)) % 0.37/0.61 (define @t139 () (_ @t34 @t138)) % 0.37/0.61 (define @t140 () (@list @t138)) % 0.37/0.61 (define @t141 () (lambda @t140 @t139)) % 0.37/0.61 (define @t142 () (tptp.dsetconstr @t3 @t141)) % 0.37/0.61 (define @t143 () (= @t127 @t142)) % 0.37/0.61 (define @t144 () (not @t143)) % 0.37/0.61 (define @t145 () (tptp.in @t12 @t142)) % 0.37/0.61 (define @t146 () (not @t145)) % 0.37/0.61 (define @t147 () (or @t146 @t144)) % 0.37/0.61 (define @t148 () (_ @t34 @t138)) % 0.37/0.61 (define @t149 () (lambda @t140 @t148)) % 0.37/0.61 (define @t150 () (_ @t36 @t149)) % 0.37/0.61 (define @t151 () (= @t127 @t150)) % 0.37/0.61 (define @t152 () (not @t151)) % 0.37/0.61 (define @t153 () (tptp.in @t12 @t150)) % 0.37/0.61 (define @t154 () (not @t153)) % 0.37/0.61 (define @t155 () (or @t154 @t152)) % 0.37/0.61 (define @t156 () (= @t127 @t37)) % 0.37/0.61 (define @t157 () (not @t156)) % 0.37/0.61 (define @t158 () (tptp.in @t12 @t37)) % 0.37/0.61 (define @t159 () (not @t158)) % 0.37/0.61 (define @t160 () (or @t159 @t157)) % 0.37/0.61 (define @t161 () (not (= @t37 @t127))) % 0.37/0.61 (define @t162 () (or @t159 @t161)) % 0.37/0.61 (define @t163 () (forall @t18 @t162)) % 0.37/0.61 (define @t164 () (not @t163)) % 0.37/0.61 (define @t165 () (not @t29)) % 0.37/0.61 (define @t166 () (or @t96 @t165)) % 0.37/0.61 (define @t167 () (forall @t18 (not @t30))) % 0.37/0.61 (define @t168 () (not @t167)) % 0.37/0.61 (define @t169 () (=> tptp.funcGraphProp1 @t63)) % 0.37/0.61 (define @t170 () (@var "BOUND_VARIABLE_7727" $$unsorted)) % 0.37/0.61 (define @t171 () (tptp.dsetconstr @t2 (lambda @t48 (tptp.in (tptp.kpair @t170 @t45) @t1)))) % 0.37/0.61 (define @t172 () (or (not (tptp.in @t170 @t3)) (not (forall @t71 (or (not (tptp.in @t69 @t171)) (not (= @t70 @t171))))))) % 0.37/0.61 (define @t173 () (and @t77 @t172)) % 0.37/0.61 (define @t174 () (or @t60 @t173)) % 0.37/0.61 (define @t175 () (@list @t170)) % 0.37/0.61 (define @t176 () (forall @t175 @t174)) % 0.37/0.61 (define @t177 () (forall @t175 @t172)) % 0.37/0.61 (define @t178 () (forall @t175 @t77)) % 0.37/0.61 (define @t179 () (and @t178 @t177)) % 0.37/0.61 (define @t180 () (forall @t175 @t173)) % 0.37/0.61 (define @t181 () (or @t60 @t180)) % 0.37/0.61 (define @t182 () (not @t7)) % 0.37/0.61 (define @t183 () (or @t182 @t95)) % 0.37/0.61 (define @t184 () (=> @t7 @t106)) % 0.37/0.61 (define @t185 () (forall @t9 @t184)) % 0.37/0.61 (define @t186 () (=> tptp.infuncsetfunc @t169)) % 0.37/0.61 (define @t187 () (or @t57 @t56)) % 0.37/0.61 (define @t188 () (or @t60 @t187)) % 0.37/0.61 (define @t189 () (forall @t62 @t188)) % 0.37/0.61 (define @t190 () (@list @t55)) % 0.37/0.61 (define @t191 () (forall @t190 @t188)) % 0.37/0.61 (define @t192 () (forall @t190 @t187)) % 0.37/0.61 (define @t193 () (or @t60 @t192)) % 0.37/0.61 (define @t194 () (or @t182 @t90)) % 0.37/0.61 (define @t195 () (@quantifiers_skolemize @t63 1)) % 0.37/0.61 (define @t196 () (@quantifiers_skolemize @t63 0)) % 0.37/0.61 (define @t197 () (@quantifiers_skolemize @t63 2)) % 0.37/0.61 (define @t198 () (tptp.in @t197 (tptp.funcSet @t196 @t195))) % 0.37/0.61 (define @t199 () (@quantifiers_skolemize @t63 3)) % 0.37/0.61 (define @t200 () (tptp.in (tptp.kpair @t199 (tptp.ap @t196 @t195 @t197 @t199)) @t197)) % 0.37/0.61 (define @t201 () (tptp.in @t199 @t196)) % 0.37/0.61 (define @t202 () (not @t201)) % 0.37/0.61 (define @t203 () (not @t198)) % 0.37/0.61 (define @t204 () (or @t203 @t202 @t200)) % 0.37/0.61 (define @t205 () (@list true)) % 0.37/0.61 (define @t206 () (@list @t204)) % 0.37/0.61 (define @t207 () (@list @t196 @t195 @t197 @t199)) % 0.37/0.61 (define @t208 () (tptp.dsetconstr @t195 (lambda @t48 (tptp.in (tptp.kpair @t199 @t45) @t197)))) % 0.37/0.61 (define @t209 () (tptp.subset @t197 (tptp.cartprod @t196 @t195))) % 0.37/0.61 (define @t210 () (and @t209 (or @t202 (not (forall @t71 (or (not (tptp.in @t69 @t208)) (not (= @t70 @t208)))))))) % 0.37/0.61 (define @t211 () (or @t203 @t210)) % 0.37/0.61 (define @t212 () (tptp.dsetconstr @t195 (lambda @t48 (tptp.in @t67 @t197)))) % 0.37/0.61 (define @t213 () (forall @t18 (or (not (tptp.in @t12 @t196)) (not (forall @t71 (or (not (tptp.in @t69 @t212)) (not (= @t70 @t212)))))))) % 0.37/0.61 (define @t214 () (not @t213)) % 0.37/0.61 (define @t215 () (not @t209)) % 0.37/0.61 (define @t216 () (or @t215 @t214 @t202 @t200)) % 0.37/0.61 (define @t217 () (@quantifiers_skolemize @t213 0)) % 0.37/0.61 (define @t218 () (tptp.dsetconstr @t195 (lambda @t48 (tptp.in (tptp.kpair @t217 @t45) @t197)))) % 0.37/0.61 (define @t219 () (or (not (tptp.in @t217 @t196)) (not (forall @t71 (or (not (tptp.in @t69 @t218)) (not (= @t70 @t218))))))) % 0.37/0.61 (define @t220 () (and @t209 @t219)) % 0.37/0.61 (define @t221 () (not @t220)) % 0.37/0.61 (define @t222 () (or @t203 @t220)) % 0.37/0.61 (assume @p1 @t11) % 0.37/0.61 (assume @p2 @t22) % 0.37/0.61 (assume @p3 @t27) % 0.37/0.61 (assume @p4 true) % 0.37/0.61 (step @p5 (= tptp.singleton @t33) :rule refl :args (@t33)) % 0.37/0.61 (step @p6 (= tptp.ex1 @t39) :rule refl :args (@t39)) % 0.37/0.61 (step @p7 (= tptp.breln @t43) :rule refl :args (@t43)) % 0.37/0.61 (step @p8 (= tptp.func @t54) :rule refl :args (@t54)) % 0.37/0.61 (step @p9 :rule refl :args (@t63)) % 0.37/0.61 (step @p10 :rule aci_norm :args ((= @t80 (or @t78 @t75 @t66 @t65)))) % 0.37/0.61 (step @p11 :rule cong :premises (@p10) :args (@t81)) % 0.37/0.61 (step @p12 :rule quant-merge-prenex :args ((= (forall @t9 @t83) @t81))) % 0.37/0.61 (step @p13 :rule alpha_equiv :args (@t84 (@list @t64) @t85)) % 0.37/0.61 (step @p14 :rule refl :args (@t75)) % 0.37/0.61 (step @p15 :rule refl :args (@t78)) % 0.37/0.61 (step @p16 :rule nary_cong :premises (@p15 @p14 @p13) :args (@t86)) % 0.37/0.61 (step @p17 :rule quant-miniscope-or :args ((= @t83 @t86))) % 0.37/0.61 (step @p18 :rule trans :premises (@p17 @p16)) % 0.37/0.61 (step @p19 :rule symm :premises (@p18)) % 0.37/0.61 (step @p20 :rule cong :premises (@p19) :args ((forall @t9 (or @t78 @t75 @t90)))) % 0.37/0.61 (step @p21 :rule trans :premises (@p20 @p12)) % 0.37/0.61 (step @p22 :rule trans :premises (@p21 @p11)) % 0.37/0.61 (step @p23 :rule refl :args (@t90)) % 0.37/0.61 (step @p24 :rule refl :args ((tptp.subset @t1 @t40))) % 0.37/0.61 (step @p25 :rule refl :args (@t76)) % 0.37/0.61 (step @p26 :rule refl :args (@t1)) % 0.37/0.61 (step @p27 :rule cong :premises (@p26 @p25) :args (@t77)) % 0.37/0.61 (step @p28 :rule trans :premises (@p27 @p24)) % 0.37/0.61 (step @p29 :rule refl :args (@t91)) % 0.37/0.61 (step @p30 :rule ho_cong :premises (@p29 @p25)) % 0.37/0.61 (step @p31 :rule cong :premises (@p30 @p28) :args ((= (_ @t91 @t76) @t77))) % 0.37/0.61 (step @p32 :rule symm :premises (@p31)) % 0.37/0.61 (step @p33 :rule refl :args (@t92)) % 0.37/0.61 (step @p34 :rule eq_resolve :premises (@p33 @p32)) % 0.37/0.61 (step @p35 :rule refl :args (@t40)) % 0.37/0.61 (step @p36 :rule cong :premises (@p35 @p25) :args ((= @t40 @t76))) % 0.37/0.61 (step @p37 :rule symm :premises (@p36)) % 0.37/0.61 (step @p38 :rule eq_resolve :premises (@p35 @p37)) % 0.37/0.61 (step @p39 :rule ho_cong :premises (@p29 @p38)) % 0.37/0.61 (step @p40 :rule trans :premises (@p39 @p34)) % 0.37/0.61 (step @p41 :rule cong :premises (@p40) :args (@t93)) % 0.37/0.61 (step @p42 :rule nary_cong :premises (@p41 @p14 @p23) :args (@t94)) % 0.37/0.61 (step @p43 :rule cong :premises (@p42) :args ((forall @t9 @t94))) % 0.37/0.61 (step @p44 :rule trans :premises (@p43 @p22)) % 0.37/0.61 (step @p45 :rule aci_norm :args ((= (or (or @t93 @t75) @t90) @t94))) % 0.37/0.61 (step @p46 :rule bool-and-de-morgan :args (@t92 @t74 true)) % 0.37/0.61 (step @p47 :rule nary_cong :premises (@p46 @p23) :args ((or (not @t95) @t90))) % 0.37/0.61 (step @p48 :rule trans :premises (@p47 @p45)) % 0.37/0.61 (step @p49 :rule bool-impl-elim :args (@t95 @t90)) % 0.37/0.61 (step @p50 :rule trans :premises (@p49 @p48)) % 0.37/0.61 (step @p51 :rule cong :premises (@p50) :args ((forall @t9 (=> @t95 @t90)))) % 0.37/0.61 (step @p52 :rule trans :premises (@p51 @p44)) % 0.37/0.61 (step @p53 :rule refl :args ((tptp.in @t15 @t1))) % 0.37/0.61 (step @p54 :rule refl :args ((tptp.kpair @t12 @t13))) % 0.37/0.61 (step @p55 :rule refl :args (@t87)) % 0.37/0.61 (step @p56 :rule refl :args (@t12)) % 0.37/0.61 (step @p57 :rule cong :premises (@p56 @p55) :args (@t88)) % 0.37/0.61 (step @p58 :rule trans :premises (@p57 @p54)) % 0.37/0.61 (step @p59 :rule cong :premises (@p58 @p26) :args (@t89)) % 0.37/0.61 (step @p60 :rule trans :premises (@p59 @p53)) % 0.37/0.61 (step @p61 :rule refl :args (tptp.in)) % 0.37/0.61 (step @p62 :rule ho_cong :premises (@p61 @p58)) % 0.37/0.61 (step @p63 :rule ho_cong :premises (@p62 @p26)) % 0.37/0.61 (step @p64 :rule cong :premises (@p63 @p60) :args ((= (_ (_ tptp.in @t88) @t1) @t89))) % 0.37/0.61 (step @p65 :rule symm :premises (@p64)) % 0.37/0.61 (step @p66 :rule refl :args (@t16)) % 0.37/0.61 (step @p67 :rule eq_resolve :premises (@p66 @p65)) % 0.37/0.61 (step @p68 :rule refl :args (@t14)) % 0.37/0.61 (step @p69 :rule ho_cong :premises (@p68 @p55)) % 0.37/0.61 (step @p70 :rule cong :premises (@p69 @p58) :args ((= (_ @t14 @t87) @t88))) % 0.37/0.61 (step @p71 :rule symm :premises (@p70)) % 0.37/0.61 (step @p72 :rule refl :args (@t15)) % 0.37/0.61 (step @p73 :rule eq_resolve :premises (@p72 @p71)) % 0.37/0.61 (step @p74 :rule refl :args (@t13)) % 0.37/0.61 (step @p75 :rule cong :premises (@p74 @p55) :args ((= @t13 @t87))) % 0.37/0.61 (step @p76 :rule symm :premises (@p75)) % 0.37/0.61 (step @p77 :rule eq_resolve :premises (@p74 @p76)) % 0.37/0.61 (step @p78 :rule ho_cong :premises (@p68 @p77)) % 0.37/0.61 (step @p79 :rule trans :premises (@p78 @p73)) % 0.37/0.61 (step @p80 :rule ho_cong :premises (@p61 @p79)) % 0.37/0.61 (step @p81 :rule ho_cong :premises (@p80 @p26)) % 0.37/0.61 (step @p82 :rule trans :premises (@p81 @p67)) % 0.37/0.61 (step @p83 :rule refl :args (@t72)) % 0.37/0.61 (step @p84 :rule refl :args (@t17)) % 0.37/0.61 (step @p85 :rule cong :premises (@p84 @p83) :args ((= @t17 @t72))) % 0.37/0.61 (step @p86 :rule symm :premises (@p85)) % 0.37/0.61 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 0.37/0.61 (step @p88 :rule cong :premises (@p87) :args (@t96)) % 0.37/0.61 (step @p89 :rule nary_cong :premises (@p88 @p82) :args (@t97)) % 0.37/0.61 (step @p90 :rule cong :premises (@p89) :args ((forall @t18 @t97))) % 0.37/0.61 (step @p91 :rule bool-impl-elim :args (@t17 @t16)) % 0.37/0.61 (step @p92 :rule cong :premises (@p91) :args (@t19)) % 0.37/0.61 (step @p93 :rule trans :premises (@p92 @p90)) % 0.37/0.61 (step @p94 :rule beta-reduce :args ((= (_ @t103 @t1) @t95))) % 0.37/0.61 (step @p95 :rule refl :args (@t1)) % 0.37/0.61 (step @p96 :rule beta-reduce :args ((= (_ @t104 @t2) @t103))) % 0.37/0.61 (step @p97 :rule refl :args (@t2)) % 0.37/0.61 (step @p98 :rule beta-reduce :args ((= @t105 @t104))) % 0.37/0.61 (step @p99 :rule ho_cong :premises (@p98 @p97)) % 0.37/0.61 (step @p100 :rule trans :premises (@p99 @p96)) % 0.37/0.61 (step @p101 :rule ho_cong :premises (@p100 @p95)) % 0.37/0.61 (step @p102 :rule trans :premises (@p101 @p94)) % 0.37/0.61 (step @p103 :rule cong :premises (@p102 @p93) :args (@t107)) % 0.37/0.61 (step @p104 :rule cong :premises (@p103) :args (@t108)) % 0.37/0.61 (step @p105 :rule trans :premises (@p104 @p52)) % 0.37/0.61 (step @p106 :rule refl :args (tptp.funcGraphProp1)) % 0.37/0.61 (step @p107 :rule cong :premises (@p106 @p105) :args ((= tptp.funcGraphProp1 @t108))) % 0.37/0.61 (step @p108 :rule refl :args (@t19)) % 0.37/0.61 (step @p109 :rule refl :args (@t3)) % 0.37/0.61 (step @p110 :rule refl :args (@t100)) % 0.37/0.61 (step @p111 :rule nary_cong :premises (@p88 @p110) :args (@t109)) % 0.37/0.61 (step @p112 :rule cong :premises (@p111) :args ((forall @t18 @t109))) % 0.37/0.61 (step @p113 :rule bool-impl-elim :args (@t17 @t100)) % 0.37/0.61 (step @p114 :rule cong :premises (@p113) :args ((forall @t18 (=> @t17 @t100)))) % 0.37/0.61 (step @p115 :rule trans :premises (@p114 @p112)) % 0.37/0.61 (step @p116 :rule refl :args ((tptp.in @t46 @t44))) % 0.37/0.61 (step @p117 :rule refl :args (@t44)) % 0.37/0.61 (step @p118 :rule refl :args (@t67)) % 0.37/0.61 (step @p119 :rule cong :premises (@p118 @p117) :args (@t98)) % 0.37/0.61 (step @p120 :rule trans :premises (@p119 @p116)) % 0.37/0.61 (step @p121 :rule ho_cong :premises (@p61 @p118)) % 0.37/0.61 (step @p122 :rule ho_cong :premises (@p121 @p117)) % 0.37/0.61 (step @p123 :rule cong :premises (@p122 @p120) :args ((= (_ (_ tptp.in @t67) @t44) @t98))) % 0.37/0.61 (step @p124 :rule symm :premises (@p123)) % 0.37/0.61 (step @p125 :rule refl :args (@t47)) % 0.37/0.61 (step @p126 :rule eq_resolve :premises (@p125 @p124)) % 0.37/0.61 (step @p127 :rule refl :args (@t46)) % 0.37/0.61 (step @p128 :rule cong :premises (@p127 @p118) :args ((= @t46 @t67))) % 0.37/0.61 (step @p129 :rule symm :premises (@p128)) % 0.37/0.61 (step @p130 :rule eq_resolve :premises (@p127 @p129)) % 0.37/0.61 (step @p131 :rule ho_cong :premises (@p61 @p130)) % 0.37/0.61 (step @p132 :rule ho_cong :premises (@p131 @p117)) % 0.37/0.61 (step @p133 :rule trans :premises (@p132 @p126)) % 0.37/0.61 (step @p134 :rule cong :premises (@p133) :args (@t49)) % 0.37/0.61 (step @p135 :rule refl :args (@t2)) % 0.37/0.61 (step @p136 :rule cong :premises (@p135 @p134) :args (@t110)) % 0.37/0.61 (step @p137 :rule refl :args (@t70)) % 0.37/0.61 (step @p138 :rule cong :premises (@p137 @p136) :args (@t111)) % 0.37/0.61 (step @p139 :rule cong :premises (@p138) :args (@t112)) % 0.37/0.61 (step @p140 :rule refl :args (@t69)) % 0.37/0.61 (step @p141 :rule cong :premises (@p140 @p136) :args (@t113)) % 0.37/0.61 (step @p142 :rule cong :premises (@p141) :args (@t114)) % 0.37/0.61 (step @p143 :rule nary_cong :premises (@p142 @p139) :args (@t115)) % 0.37/0.61 (step @p144 :rule cong :premises (@p143) :args ((forall @t71 @t115))) % 0.37/0.61 (step @p145 :rule eq-symm :args (@t110 @t70)) % 0.37/0.61 (step @p146 :rule cong :premises (@p145) :args (@t116)) % 0.37/0.61 (step @p147 :rule refl :args (@t114)) % 0.37/0.61 (step @p148 :rule nary_cong :premises (@p147 @p146) :args (@t117)) % 0.37/0.61 (step @p149 :rule cong :premises (@p148) :args (@t118)) % 0.37/0.61 (step @p150 :rule trans :premises (@p149 @p144)) % 0.37/0.61 (step @p151 :rule cong :premises (@p150) :args (@t119)) % 0.37/0.61 (step @p152 :rule beta-reduce :args ((= (_ (lambda @t122 (not (forall @t71 (or @t121 (not (= @t120 @t70)))))) @t49) @t119))) % 0.37/0.61 (step @p153 :rule trans :premises (@p152 @p151)) % 0.37/0.61 (step @p154 :rule refl :args (@t49)) % 0.37/0.61 (step @p155 :rule eq-symm :args (@t70 @t120)) % 0.37/0.61 (step @p156 :rule cong :premises (@p155) :args (@t123)) % 0.37/0.61 (step @p157 :rule refl :args (@t121)) % 0.37/0.61 (step @p158 :rule nary_cong :premises (@p157 @p156) :args (@t124)) % 0.37/0.61 (step @p159 :rule cong :premises (@p158) :args (@t125)) % 0.37/0.61 (step @p160 :rule cong :premises (@p159) :args (@t126)) % 0.37/0.61 (step @p161 :rule cong :premises (@p160) :args ((lambda @t122 @t126))) % 0.37/0.61 (step @p162 :rule ho_cong :premises (@p161 @p154)) % 0.37/0.61 (step @p163 :rule trans :premises (@p162 @p153)) % 0.37/0.61 (step @p164 :rule refl :args (@t49)) % 0.37/0.61 (step @p165 :rule alpha_equiv :args (@t128 @t85 (@list @t69))) % 0.37/0.61 (step @p166 :rule cong :premises (@p165) :args (@t129)) % 0.37/0.61 (step @p167 :rule cong :premises (@p166) :args (@t130)) % 0.37/0.61 (step @p168 :rule ho_cong :premises (@p167 @p164)) % 0.37/0.61 (step @p169 :rule trans :premises (@p168 @p163)) % 0.37/0.61 (step @p170 :rule beta-reduce :args ((= @t132 @t130))) % 0.37/0.61 (step @p171 :rule ho_cong :premises (@p170 @p154)) % 0.37/0.61 (step @p172 :rule trans :premises (@p171 @p169)) % 0.37/0.61 (step @p173 :rule refl :args (@t17)) % 0.37/0.61 (step @p174 :rule cong :premises (@p173 @p172) :args (@t133)) % 0.37/0.61 (step @p175 :rule cong :premises (@p174) :args (@t134)) % 0.37/0.61 (step @p176 :rule trans :premises (@p175 @p115)) % 0.37/0.61 (step @p177 :rule beta-reduce :args ((= (_ @t135 @t44) @t101))) % 0.37/0.61 (step @p178 :rule refl :args (@t44)) % 0.37/0.61 (step @p179 :rule beta-reduce :args ((= (_ @t136 @t2) @t135))) % 0.37/0.61 (step @p180 :rule beta-reduce :args ((= @t137 @t136))) % 0.37/0.61 (step @p181 :rule ho_cong :premises (@p180 @p97)) % 0.37/0.61 (step @p182 :rule trans :premises (@p181 @p179)) % 0.37/0.61 (step @p183 :rule ho_cong :premises (@p182 @p178)) % 0.37/0.61 (step @p184 :rule trans :premises (@p183 @p177)) % 0.37/0.61 (step @p185 :rule nary_cong :premises (@p184 @p176) :args ((and (_ (_ @t137 @t2) @t44) @t134))) % 0.37/0.61 (step @p186 :rule lambda-elim :args ((= @t141 @t34))) % 0.37/0.61 (step @p187 :rule cong :premises (@p109 @p186) :args (@t142)) % 0.37/0.61 (step @p188 :rule refl :args (@t127)) % 0.37/0.61 (step @p189 :rule cong :premises (@p188 @p187) :args (@t143)) % 0.37/0.61 (step @p190 :rule cong :premises (@p189) :args (@t144)) % 0.37/0.61 (step @p191 :rule refl :args (@t12)) % 0.37/0.61 (step @p192 :rule cong :premises (@p191 @p187) :args (@t145)) % 0.37/0.61 (step @p193 :rule cong :premises (@p192) :args (@t146)) % 0.37/0.61 (step @p194 :rule nary_cong :premises (@p193 @p190) :args (@t147)) % 0.37/0.61 (step @p195 :rule cong :premises (@p194) :args ((forall @t18 @t147))) % 0.37/0.61 (step @p196 :rule refl :args ((tptp.dsetconstr @t3 @t149))) % 0.37/0.61 (step @p197 :rule refl :args (@t139)) % 0.37/0.61 (step @p198 :rule cong :premises (@p197) :args (@t141)) % 0.37/0.61 (step @p199 :rule refl :args (@t3)) % 0.37/0.61 (step @p200 :rule cong :premises (@p199 @p198) :args (@t142)) % 0.37/0.61 (step @p201 :rule trans :premises (@p200 @p196)) % 0.37/0.61 (step @p202 :rule refl :args (@t36)) % 0.37/0.61 (step @p203 :rule ho_cong :premises (@p202 @p198)) % 0.37/0.61 (step @p204 :rule cong :premises (@p203 @p201) :args ((= (_ @t36 @t141) @t142))) % 0.37/0.61 (step @p205 :rule symm :premises (@p204)) % 0.37/0.61 (step @p206 :rule refl :args (@t150)) % 0.37/0.61 (step @p207 :rule eq_resolve :premises (@p206 @p205)) % 0.37/0.61 (step @p208 :rule refl :args (@t148)) % 0.37/0.61 (step @p209 :rule cong :premises (@p208 @p197) :args ((= @t148 @t139))) % 0.37/0.61 (step @p210 :rule symm :premises (@p209)) % 0.37/0.61 (step @p211 :rule eq_resolve :premises (@p208 @p210)) % 0.37/0.61 (step @p212 :rule cong :premises (@p211) :args (@t149)) % 0.37/0.61 (step @p213 :rule ho_cong :premises (@p202 @p212)) % 0.37/0.61 (step @p214 :rule trans :premises (@p213 @p207)) % 0.37/0.61 (step @p215 :rule refl :args (@t127)) % 0.37/0.61 (step @p216 :rule cong :premises (@p215 @p214) :args (@t151)) % 0.37/0.61 (step @p217 :rule cong :premises (@p216) :args (@t152)) % 0.37/0.61 (step @p218 :rule cong :premises (@p56 @p214) :args (@t153)) % 0.37/0.61 (step @p219 :rule cong :premises (@p218) :args (@t154)) % 0.37/0.61 (step @p220 :rule nary_cong :premises (@p219 @p217) :args (@t155)) % 0.37/0.61 (step @p221 :rule cong :premises (@p220) :args ((forall @t18 @t155))) % 0.37/0.61 (step @p222 :rule trans :premises (@p221 @p195)) % 0.37/0.61 (step @p223 :rule alpha_equiv :args (@t35 @t85 (@list @t138))) % 0.37/0.61 (step @p224 :rule ho_cong :premises (@p202 @p223)) % 0.37/0.61 (step @p225 :rule cong :premises (@p215 @p224) :args (@t156)) % 0.37/0.61 (step @p226 :rule cong :premises (@p225) :args (@t157)) % 0.37/0.61 (step @p227 :rule cong :premises (@p56 @p224) :args (@t158)) % 0.37/0.61 (step @p228 :rule cong :premises (@p227) :args (@t159)) % 0.37/0.61 (step @p229 :rule nary_cong :premises (@p228 @p226) :args (@t160)) % 0.37/0.61 (step @p230 :rule cong :premises (@p229) :args ((forall @t18 @t160))) % 0.37/0.61 (step @p231 :rule trans :premises (@p230 @p222)) % 0.37/0.61 (step @p232 :rule eq-symm :args (@t37 @t127)) % 0.37/0.61 (step @p233 :rule cong :premises (@p232) :args (@t161)) % 0.37/0.61 (step @p234 :rule refl :args (@t159)) % 0.37/0.61 (step @p235 :rule nary_cong :premises (@p234 @p233) :args (@t162)) % 0.37/0.61 (step @p236 :rule cong :premises (@p235) :args (@t163)) % 0.37/0.61 (step @p237 :rule trans :premises (@p236 @p231)) % 0.37/0.61 (step @p238 :rule cong :premises (@p237) :args (@t164)) % 0.37/0.61 (step @p239 :rule beta-reduce :args ((= (_ (lambda @t32 (not (forall @t18 (or @t73 (not (= @t3 @t127)))))) @t37) @t164))) % 0.37/0.61 (step @p240 :rule trans :premises (@p239 @p238)) % 0.37/0.61 (step @p241 :rule refl :args (@t37)) % 0.37/0.61 (step @p242 :rule refl :args (@t127)) % 0.37/0.61 (step @p243 :rule refl :args (@t28)) % 0.37/0.61 (step @p244 :rule cong :premises (@p243 @p242) :args ((= @t28 @t127))) % 0.37/0.61 (step @p245 :rule symm :premises (@p244)) % 0.37/0.61 (step @p246 :rule eq_resolve :premises (@p243 @p245)) % 0.37/0.61 (step @p247 :rule cong :premises (@p199 @p246) :args (@t29)) % 0.37/0.61 (step @p248 :rule cong :premises (@p247) :args (@t165)) % 0.37/0.61 (step @p249 :rule nary_cong :premises (@p88 @p248) :args (@t166)) % 0.37/0.61 (step @p250 :rule cong :premises (@p249) :args ((forall @t18 @t166))) % 0.37/0.61 (step @p251 :rule bool-and-de-morgan :args (@t17 @t29 true)) % 0.37/0.61 (step @p252 :rule cong :premises (@p251) :args (@t167)) % 0.37/0.61 (step @p253 :rule trans :premises (@p252 @p250)) % 0.37/0.61 (step @p254 :rule cong :premises (@p253) :args (@t168)) % 0.37/0.61 (step @p255 :rule exists-elim :args ((= @t31 @t168))) % 0.37/0.61 (step @p256 :rule trans :premises (@p255 @p254)) % 0.37/0.61 (step @p257 :rule cong :premises (@p256) :args (@t33)) % 0.37/0.61 (step @p258 :rule trans :premises (@p5 @p257)) % 0.37/0.61 (step @p259 :rule ho_cong :premises (@p258 @p241)) % 0.37/0.61 (step @p260 :rule trans :premises (@p259 @p240)) % 0.37/0.61 (step @p261 :rule cong :premises (@p260) :args (@t39)) % 0.37/0.61 (step @p262 :rule trans :premises (@p6 @p261)) % 0.37/0.61 (step @p263 :rule ho_cong :premises (@p262 @p97)) % 0.37/0.61 (step @p264 :rule ho_cong :premises (@p263 @p154)) % 0.37/0.61 (step @p265 :rule cong :premises (@p173 @p264) :args (@t50)) % 0.37/0.61 (step @p266 :rule cong :premises (@p265) :args (@t51)) % 0.37/0.61 (step @p267 :rule ho_cong :premises (@p7 @p109)) % 0.37/0.61 (step @p268 :rule ho_cong :premises (@p267 @p97)) % 0.37/0.61 (step @p269 :rule ho_cong :premises (@p268 @p178)) % 0.37/0.61 (step @p270 :rule nary_cong :premises (@p269 @p266) :args (@t52)) % 0.37/0.61 (step @p271 :rule trans :premises (@p270 @p185)) % 0.37/0.61 (step @p272 :rule cong :premises (@p271) :args (@t54)) % 0.37/0.61 (step @p273 :rule trans :premises (@p8 @p272)) % 0.37/0.61 (step @p274 :rule ho_cong :premises (@p273 @p109)) % 0.37/0.61 (step @p275 :rule ho_cong :premises (@p274 @p97)) % 0.37/0.61 (step @p276 :rule ho_cong :premises (@p275 @p95)) % 0.37/0.61 (step @p277 :rule cong :premises (@p276 @p108) :args (@t20)) % 0.37/0.61 (step @p278 :rule cong :premises (@p277) :args (@t21)) % 0.37/0.61 (step @p279 :rule cong :premises (@p106 @p278) :args (@t22)) % 0.37/0.61 (step @p280 :rule trans :premises (@p279 @p107)) % 0.37/0.61 (step @p281 :rule eq_resolve :premises (@p2 @p280)) % 0.37/0.61 (step @p282 :rule cong :premises (@p281 @p9) :args (@t169)) % 0.37/0.61 (step @p283 :rule quant-merge-prenex :args ((= (forall @t9 @t176) (forall (@list @t3 @t2 @t1 @t170) @t174)))) % 0.37/0.61 (step @p284 :rule alpha_equiv :args (@t177 (@list @t170) @t85)) % 0.37/0.61 (step @p285 :rule quant-unused-vars :args ((= @t178 @t77))) % 0.37/0.61 (step @p286 :rule nary_cong :premises (@p285 @p284) :args (@t179)) % 0.37/0.61 (step @p287 :rule quant-miniscope-and :args ((= @t180 @t179))) % 0.37/0.61 (step @p288 :rule trans :premises (@p287 @p286)) % 0.37/0.61 (step @p289 :rule refl :args (@t60)) % 0.37/0.61 (step @p290 :rule nary_cong :premises (@p289 @p288) :args (@t181)) % 0.37/0.61 (step @p291 :rule quant-miniscope-or :args ((= @t176 @t181))) % 0.37/0.61 (step @p292 :rule trans :premises (@p291 @p290)) % 0.37/0.61 (step @p293 :rule symm :premises (@p292)) % 0.37/0.61 (step @p294 :rule cong :premises (@p293) :args ((forall @t9 (or @t60 (and @t77 @t74))))) % 0.37/0.61 (step @p295 :rule trans :premises (@p294 @p283)) % 0.37/0.61 (step @p296 :rule refl :args (@t74)) % 0.37/0.61 (step @p297 :rule nary_cong :premises (@p40 @p296) :args (@t95)) % 0.37/0.61 (step @p298 :rule refl :args ((tptp.in @t1 @t5))) % 0.37/0.61 (step @p299 :rule refl :args (@t58)) % 0.37/0.61 (step @p300 :rule cong :premises (@p26 @p299) :args (@t59)) % 0.37/0.61 (step @p301 :rule trans :premises (@p300 @p298)) % 0.37/0.61 (step @p302 :rule refl :args (@t6)) % 0.37/0.61 (step @p303 :rule ho_cong :premises (@p302 @p299)) % 0.37/0.61 (step @p304 :rule cong :premises (@p303 @p301) :args ((= (_ @t6 @t58) @t59))) % 0.37/0.61 (step @p305 :rule symm :premises (@p304)) % 0.37/0.61 (step @p306 :rule refl :args (@t7)) % 0.37/0.61 (step @p307 :rule eq_resolve :premises (@p306 @p305)) % 0.37/0.61 (step @p308 :rule refl :args (@t5)) % 0.37/0.61 (step @p309 :rule cong :premises (@p308 @p299) :args ((= @t5 @t58))) % 0.37/0.61 (step @p310 :rule symm :premises (@p309)) % 0.37/0.61 (step @p311 :rule eq_resolve :premises (@p308 @p310)) % 0.37/0.61 (step @p312 :rule ho_cong :premises (@p302 @p311)) % 0.37/0.61 (step @p313 :rule trans :premises (@p312 @p307)) % 0.37/0.61 (step @p314 :rule cong :premises (@p313) :args (@t182)) % 0.37/0.61 (step @p315 :rule nary_cong :premises (@p314 @p297) :args (@t183)) % 0.37/0.61 (step @p316 :rule cong :premises (@p315) :args ((forall @t9 @t183))) % 0.37/0.61 (step @p317 :rule trans :premises (@p316 @p295)) % 0.37/0.61 (step @p318 :rule bool-impl-elim :args (@t7 @t95)) % 0.37/0.61 (step @p319 :rule cong :premises (@p318) :args ((forall @t9 (=> @t7 @t95)))) % 0.37/0.61 (step @p320 :rule trans :premises (@p319 @p317)) % 0.37/0.61 (step @p321 :rule refl :args (@t7)) % 0.37/0.61 (step @p322 :rule cong :premises (@p321 @p102) :args (@t184)) % 0.37/0.61 (step @p323 :rule cong :premises (@p322) :args (@t185)) % 0.37/0.61 (step @p324 :rule trans :premises (@p323 @p320)) % 0.37/0.61 (step @p325 :rule refl :args (tptp.infuncsetfunc)) % 0.37/0.61 (step @p326 :rule cong :premises (@p325 @p324) :args ((= tptp.infuncsetfunc @t185))) % 0.37/0.61 (step @p327 :rule cong :premises (@p321 @p276) :args (@t8)) % 0.37/0.61 (step @p328 :rule cong :premises (@p327) :args (@t10)) % 0.37/0.61 (step @p329 :rule cong :premises (@p325 @p328) :args (@t11)) % 0.37/0.61 (step @p330 :rule trans :premises (@p329 @p326)) % 0.37/0.61 (step @p331 :rule eq_resolve :premises (@p1 @p330)) % 0.37/0.61 (step @p332 :rule cong :premises (@p331 @p282) :args (@t186)) % 0.37/0.61 (step @p333 :rule cong :premises (@p332) :args ((not @t186))) % 0.37/0.61 (step @p334 :rule aci_norm :args ((= @t188 @t61))) % 0.37/0.61 (step @p335 :rule cong :premises (@p334) :args (@t189)) % 0.37/0.61 (step @p336 :rule quant-merge-prenex :args ((= (forall @t9 @t191) @t189))) % 0.37/0.61 (step @p337 :rule alpha_equiv :args (@t192 (@list @t55) @t85)) % 0.37/0.61 (step @p338 :rule nary_cong :premises (@p289 @p337) :args (@t193)) % 0.37/0.61 (step @p339 :rule quant-miniscope-or :args ((= @t191 @t193))) % 0.37/0.61 (step @p340 :rule trans :premises (@p339 @p338)) % 0.37/0.61 (step @p341 :rule symm :premises (@p340)) % 0.37/0.61 (step @p342 :rule cong :premises (@p341) :args ((forall @t9 (or @t60 @t90)))) % 0.37/0.61 (step @p343 :rule trans :premises (@p342 @p336)) % 0.37/0.61 (step @p344 :rule trans :premises (@p343 @p335)) % 0.37/0.61 (step @p345 :rule nary_cong :premises (@p314 @p23) :args (@t194)) % 0.37/0.61 (step @p346 :rule cong :premises (@p345) :args ((forall @t9 @t194))) % 0.37/0.61 (step @p347 :rule trans :premises (@p346 @p344)) % 0.37/0.61 (step @p348 :rule bool-impl-elim :args (@t7 @t90)) % 0.37/0.61 (step @p349 :rule cong :premises (@p348) :args ((forall @t9 (=> @t7 @t90)))) % 0.37/0.61 (step @p350 :rule trans :premises (@p349 @p347)) % 0.37/0.61 (step @p351 :rule cong :premises (@p321 @p93) :args (@t23)) % 0.37/0.61 (step @p352 :rule cong :premises (@p351) :args (@t24)) % 0.37/0.61 (step @p353 :rule trans :premises (@p352 @p350)) % 0.37/0.61 (step @p354 :rule cong :premises (@p106 @p353) :args (@t25)) % 0.37/0.61 (step @p355 :rule cong :premises (@p325 @p354) :args (@t26)) % 0.37/0.61 (step @p356 :rule cong :premises (@p355) :args (@t27)) % 0.37/0.61 (step @p357 :rule trans :premises (@p356 @p333)) % 0.37/0.61 (step @p358 :rule eq_resolve :premises (@p3 @p357)) % 0.37/0.61 (step @p359 :rule not_implies_elim2 :premises (@p358)) % 0.37/0.61 (step @p360 :rule not_implies_elim2 :premises (@p359)) % 0.37/0.61 (step @p361 :rule skolemize :premises (@p360)) % 0.37/0.61 (step @p362 :rule bool-double-not-elim :args (@t198)) % 0.37/0.61 (step @p363 :rule refl :args (@t204)) % 0.37/0.61 (step @p364 :rule nary_cong :premises (@p363 @p362) :args ((or @t204 (not @t203)))) % 0.37/0.61 (step @p365 :rule cnf_or_neg :args (@t204 0)) % 0.37/0.61 (step @p366 :rule eq_resolve :premises (@p365 @p364)) % 0.37/0.61 (step @p367 :rule reordering :premises (@p366) :args ((or @t198 @t204))) % 0.37/0.61 (step @p368 :rule chain_m_resolution :premises (@p367 @p361) :args (@t198 @t205 @t206)) % 0.37/0.61 (step @p369 :rule not_implies_elim1 :premises (@p359)) % 0.37/0.61 (step @p370 :rule instantiate :premises (@p369) :args (@t207)) % 0.37/0.61 (step @p371 :rule not_implies_elim1 :premises (@p358)) % 0.37/0.61 (step @p372 :rule instantiate :premises (@p371) :args (@t207)) % 0.37/0.61 (step @p373 :rule cnf_or_pos :args (@t211)) % 0.37/0.61 (step @p374 :rule reordering :premises (@p373) :args ((or @t203 @t210 (not @t211)))) % 0.37/0.61 (step @p375 :rule chain_m_resolution :premises (@p374 @p368 @p372) :args (@t210 (@list false false) (@list @t198 @t211))) % 0.37/0.61 (step @p376 :rule cnf_and_pos :args (@t210 0)) % 0.37/0.61 (step @p377 :rule reordering :premises (@p376) :args ((or @t209 (not @t210)))) % 0.37/0.61 (step @p378 :rule chain_m_resolution :premises (@p377 @p375) :args (@t209 (@list false) (@list @t210))) % 0.37/0.61 (step @p379 :rule cnf_or_neg :args (@t204 2)) % 0.37/0.61 (step @p380 :rule chain_m_resolution :premises (@p379 @p361) :args ((not @t200) @t205 @t206)) % 0.37/0.61 (step @p381 :rule bool-double-not-elim :args (@t201)) % 0.37/0.61 (step @p382 :rule nary_cong :premises (@p363 @p381) :args ((or @t204 (not @t202)))) % 0.37/0.61 (step @p383 :rule cnf_or_neg :args (@t204 1)) % 0.37/0.61 (step @p384 :rule eq_resolve :premises (@p383 @p382)) % 0.37/0.61 (step @p385 :rule reordering :premises (@p384) :args ((or @t201 @t204))) % 0.37/0.61 (step @p386 :rule chain_m_resolution :premises (@p385 @p361) :args (@t201 @t205 @t206)) % 0.37/0.61 (step @p387 :rule cnf_or_pos :args (@t216)) % 0.37/0.61 (step @p388 :rule reordering :premises (@p387) :args ((or @t202 @t200 @t215 @t214 (not @t216)))) % 0.37/0.61 (step @p389 :rule chain_m_resolution :premises (@p388 @p386 @p380 @p378 @p370) :args (@t214 (@list false true false false) (@list @t201 @t200 @t209 @t216))) % 0.37/0.61 (step @p390 :rule skolemize :premises (@p389)) % 0.37/0.61 (step @p391 :rule cnf_and_pos :args (@t220 1)) % 0.37/0.61 (step @p392 :rule reordering :premises (@p391) :args ((or @t219 @t221))) % 0.37/0.61 (step @p393 :rule chain_m_resolution :premises (@p392 @p390) :args (@t221 @t205 (@list @t219))) % 0.37/0.61 (step @p394 :rule instantiate :premises (@p371) :args ((@list @t196 @t195 @t197 @t217))) % 0.37/0.61 (step @p395 :rule cnf_or_pos :args (@t222)) % 0.37/0.61 (step @p396 :rule reordering :premises (@p395) :args ((or @t203 @t220 (not @t222)))) % 0.37/0.61 (step @p397 false :rule chain_m_resolution :premises (@p396 @p394 @p393 @p368) :args (false (@list false true false) (@list @t222 @t220 @t198))) % 0.37/0.61 ) % 0.37/0.61 % SZS output end Proof % 0.37/0.61 % cvc5 exiting %------------------------------------------------------------------------------