%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU675^2 : 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 08:52:41 AM UTC 2026 % Result : Theorem 0.37s 0.59s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU675^2 : 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 % 0.15/0.34 % Computer : n015.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 17:45:49 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 0.37/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.59 % SZS status Theorem % 0.37/0.59 % SZS output start Proof % 0.37/0.59 ( % 0.37/0.59 (declare-sort $$unsorted 0) % 0.37/0.59 (declare-const tptp.emptyset $$unsorted) % 0.37/0.59 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.37/0.59 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.dsetconstrER Bool) % 0.37/0.59 (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)))))))) % 0.37/0.59 (define tptp.ex1 () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xphi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ tptp.singleton (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_1) (_ _let_2 _let_1))))))))) % 0.37/0.59 (define tptp.breln () (let ((_let_1 (@var "B" $$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))))))) % 0.37/0.59 (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" $$unsorted))) (lambda (@list _let_5 _let_4 _let_1) (and (_ (_ (_ tptp.breln _let_5) _let_4) _let_1) (forall (@list _let_3) (=> (_ (_ tptp.in _let_3) _let_5) (_ (_ tptp.ex1 _let_4) (lambda (@list _let_2) (_ (_ tptp.in (_ (_ tptp.kpair _let_3) _let_2)) _let_1))))))))))))) % 0.37/0.59 (define tptp.funcSet () (let ((_let_1 (@var "Xf" $$unsorted))) (let ((_let_2 (@var "B" $$unsorted))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ (_ tptp.dsetconstr (_ tptp.powerset (_ (_ tptp.cartprod _let_3) _let_2))) (lambda (@list _let_1) (_ (_ (_ tptp.func _let_3) _let_2) _let_1)))))))) % 0.37/0.59 (define @t1 () (@var "Xx" $$unsorted)) % 0.37/0.59 (define @t2 () (@var "Xphi" (-> $$unsorted Bool))) % 0.37/0.59 (define @t3 () (_ @t2 @t1)) % 0.37/0.59 (define @t4 () (@var "Xy" $$unsorted)) % 0.37/0.59 (define @t5 () (_ @t2 @t4)) % 0.37/0.59 (define @t6 () (@list @t4)) % 0.37/0.59 (define @t7 () (lambda @t6 @t5)) % 0.37/0.59 (define @t8 () (@var "A" $$unsorted)) % 0.37/0.59 (define @t9 () (_ tptp.dsetconstr @t8)) % 0.37/0.59 (define @t10 () (_ @t9 @t7)) % 0.37/0.59 (define @t11 () (_ tptp.in @t1)) % 0.37/0.59 (define @t12 () (_ @t11 @t10)) % 0.37/0.59 (define @t13 () (@list @t8 @t2 @t1)) % 0.37/0.59 (define @t14 () (forall @t13 (=> @t12 @t3))) % 0.37/0.59 (define @t15 () (= tptp.dsetconstrER @t14)) % 0.37/0.59 (define @t16 () (@var "Xf" $$unsorted)) % 0.37/0.59 (define @t17 () (@var "B" $$unsorted)) % 0.37/0.59 (define @t18 () (_ (_ (_ tptp.func @t8) @t17) @t16)) % 0.37/0.59 (define @t19 () (_ tptp.in @t16)) % 0.37/0.59 (define @t20 () (=> (_ @t19 (_ (_ tptp.funcSet @t8) @t17)) @t18)) % 0.37/0.59 (define @t21 () (@list @t8 @t17 @t16)) % 0.37/0.59 (define @t22 () (forall @t21 @t20)) % 0.37/0.59 (define @t23 () (=> tptp.dsetconstrER @t22)) % 0.37/0.59 (define @t24 () (not @t23)) % 0.37/0.59 (define @t25 () (_ (_ tptp.setadjoin @t1) tptp.emptyset)) % 0.37/0.59 (define @t26 () (= @t8 @t25)) % 0.37/0.59 (define @t27 () (_ @t11 @t8)) % 0.37/0.59 (define @t28 () (and @t27 @t26)) % 0.37/0.59 (define @t29 () (@list @t1)) % 0.37/0.59 (define @t30 () (exists @t29 @t28)) % 0.37/0.59 (define @t31 () (@list @t8)) % 0.37/0.59 (define @t32 () (lambda @t31 @t30)) % 0.37/0.59 (define @t33 () (lambda @t29 @t3)) % 0.37/0.59 (define @t34 () (_ @t9 @t33)) % 0.37/0.59 (define @t35 () (@list @t8 @t2)) % 0.37/0.59 (define @t36 () (lambda @t35 (_ tptp.singleton @t34))) % 0.37/0.59 (define @t37 () (_ (_ tptp.cartprod @t8) @t17)) % 0.37/0.59 (define @t38 () (@var "C" $$unsorted)) % 0.37/0.59 (define @t39 () (_ (_ tptp.subset @t38) @t37)) % 0.37/0.59 (define @t40 () (lambda (@list @t8 @t17 @t38) @t39)) % 0.37/0.59 (define @t41 () (@var "R" $$unsorted)) % 0.37/0.59 (define @t42 () (_ (_ tptp.kpair @t1) @t4)) % 0.37/0.59 (define @t43 () (_ tptp.in @t42)) % 0.37/0.59 (define @t44 () (_ @t43 @t41)) % 0.37/0.59 (define @t45 () (lambda @t6 @t44)) % 0.37/0.59 (define @t46 () (=> @t27 (_ (_ tptp.ex1 @t17) @t45))) % 0.37/0.59 (define @t47 () (forall @t29 @t46)) % 0.37/0.60 (define @t48 () (and (_ (_ (_ tptp.breln @t8) @t17) @t41) @t47)) % 0.37/0.60 (define @t49 () (@list @t8 @t17 @t41)) % 0.37/0.60 (define @t50 () (lambda @t49 @t48)) % 0.37/0.60 (define @t51 () (@list @t16)) % 0.37/0.60 (define @t52 () (lambda @t51 @t18)) % 0.37/0.60 (define @t53 () (_ tptp.powerset @t37)) % 0.37/0.60 (define @t54 () (_ tptp.dsetconstr @t53)) % 0.37/0.60 (define @t55 () (@list @t8 @t17)) % 0.37/0.60 (define @t56 () (lambda @t55 (_ @t54 @t52))) % 0.37/0.60 (define @t57 () (@var "BOUND_VARIABLE_7752" $$unsorted)) % 0.37/0.60 (define @t58 () (tptp.kpair @t1 @t4)) % 0.37/0.60 (define @t59 () (tptp.in @t58 @t57)) % 0.37/0.60 (define @t60 () (lambda @t6 @t59)) % 0.37/0.60 (define @t61 () (@var "BOUND_VARIABLE_7796" $$unsorted)) % 0.37/0.60 (define @t62 () (tptp.dsetconstr @t17 (lambda @t6 (tptp.in (tptp.kpair @t61 @t4) @t16)))) % 0.37/0.60 (define @t63 () (@var "BOUND_VARIABLE_7587" $$unsorted)) % 0.37/0.60 (define @t64 () (tptp.setadjoin @t63 tptp.emptyset)) % 0.37/0.60 (define @t65 () (@list @t63)) % 0.37/0.60 (define @t66 () (or (not (tptp.in @t61 @t8)) (not (forall @t65 (or (not (tptp.in @t63 @t62)) (not (= @t64 @t62))))))) % 0.37/0.60 (define @t67 () (tptp.cartprod @t8 @t17)) % 0.37/0.60 (define @t68 () (tptp.subset @t16 @t67)) % 0.37/0.60 (define @t69 () (and @t68 @t66)) % 0.37/0.60 (define @t70 () (tptp.dsetconstr @t17 @t60)) % 0.37/0.60 (define @t71 () (= @t64 @t70)) % 0.37/0.60 (define @t72 () (not @t71)) % 0.37/0.60 (define @t73 () (tptp.in @t63 @t70)) % 0.37/0.60 (define @t74 () (not @t73)) % 0.37/0.60 (define @t75 () (or @t74 @t72)) % 0.37/0.60 (define @t76 () (forall @t65 @t75)) % 0.37/0.60 (define @t77 () (not @t76)) % 0.37/0.60 (define @t78 () (tptp.in @t1 @t8)) % 0.37/0.60 (define @t79 () (not @t78)) % 0.37/0.60 (define @t80 () (or @t79 @t77)) % 0.37/0.60 (define @t81 () (forall @t29 @t80)) % 0.37/0.60 (define @t82 () (tptp.subset @t57 @t67)) % 0.37/0.60 (define @t83 () (and @t82 @t81)) % 0.37/0.60 (define @t84 () (@list @t57)) % 0.37/0.60 (define @t85 () (lambda @t84 @t83)) % 0.37/0.60 (define @t86 () (tptp.powerset @t67)) % 0.37/0.60 (define @t87 () (tptp.dsetconstr @t86 @t85)) % 0.37/0.60 (define @t88 () (tptp.in @t16 @t87)) % 0.37/0.60 (define @t89 () (not @t88)) % 0.37/0.60 (define @t90 () (or @t89 @t69)) % 0.37/0.60 (define @t91 () (forall (@list @t8 @t17 @t16 @t61) @t90)) % 0.37/0.60 (define @t92 () (@quantifiers_skolemize @t91 1)) % 0.37/0.60 (define @t93 () (tptp.dsetconstr @t92 @t60)) % 0.37/0.60 (define @t94 () (@quantifiers_skolemize @t91 0)) % 0.37/0.60 (define @t95 () (not (tptp.in @t1 @t94))) % 0.37/0.60 (define @t96 () (tptp.cartprod @t94 @t92)) % 0.37/0.60 (define @t97 () (and (tptp.subset @t57 @t96) (forall @t29 (or @t95 (not (forall @t65 (or (not (tptp.in @t63 @t93)) (not (= @t64 @t93))))))))) % 0.37/0.60 (define @t98 () (lambda @t84 @t97)) % 0.37/0.60 (define @t99 () (@purify @t98)) % 0.37/0.60 (define @t100 () (_ @t99 @t57)) % 0.37/0.60 (define @t101 () (_ @t98 @t57)) % 0.37/0.60 (define @t102 () (= @t100 @t101)) % 0.37/0.60 (define @t103 () (forall @t84 @t102)) % 0.37/0.60 (define @t104 () (@quantifiers_skolemize @t91 2)) % 0.37/0.60 (define @t105 () (tptp.dsetconstr @t92 (lambda @t6 (tptp.in @t58 @t104)))) % 0.37/0.60 (define @t106 () (forall @t29 (or @t95 (not (forall @t65 (or (not (tptp.in @t63 @t105)) (not (= @t64 @t105)))))))) % 0.37/0.60 (define @t107 () (tptp.subset @t104 @t96)) % 0.37/0.60 (define @t108 () (and @t107 @t106)) % 0.37/0.60 (define @t109 () (_ @t99 @t104)) % 0.37/0.60 (define @t110 () (forall @t84 (= @t97 @t100))) % 0.37/0.60 (define @t111 () (= @t108 @t109)) % 0.37/0.60 (define @t112 () (= @t109 @t108)) % 0.37/0.60 (define @t113 () (@list false)) % 0.37/0.60 (define @t114 () (_ @t2 @t1)) % 0.37/0.60 (define @t115 () (_ @t2 @t4)) % 0.37/0.60 (define @t116 () (lambda @t6 @t115)) % 0.37/0.60 (define @t117 () (tptp.dsetconstr @t8 @t116)) % 0.37/0.60 (define @t118 () (tptp.in @t1 @t117)) % 0.37/0.60 (define @t119 () (not @t118)) % 0.37/0.60 (define @t120 () (or @t119 @t114)) % 0.37/0.60 (define @t121 () (not @t12)) % 0.37/0.60 (define @t122 () (or @t121 @t3)) % 0.37/0.60 (define @t123 () (=> tptp.dsetconstrER @t91)) % 0.37/0.60 (define @t124 () (@list @t61)) % 0.37/0.60 (define @t125 () (forall @t124 @t90)) % 0.37/0.60 (define @t126 () (forall @t124 @t66)) % 0.37/0.60 (define @t127 () (@list @t1)) % 0.37/0.60 (define @t128 () (forall @t124 @t68)) % 0.37/0.60 (define @t129 () (and @t128 @t126)) % 0.37/0.60 (define @t130 () (forall @t124 @t69)) % 0.37/0.60 (define @t131 () (or @t89 @t130)) % 0.37/0.60 (define @t132 () (tptp.dsetconstr @t17 (lambda @t6 (tptp.in @t58 @t16)))) % 0.37/0.60 (define @t133 () (forall @t29 (or @t79 (not (forall @t65 (or (not (tptp.in @t63 @t132)) (not (= @t64 @t132)))))))) % 0.37/0.60 (define @t134 () (_ tptp.subset @t16)) % 0.37/0.60 (define @t135 () (_ @t134 @t37)) % 0.37/0.60 (define @t136 () (and @t135 @t133)) % 0.37/0.60 (define @t137 () (lambda @t6 (_ @t43 @t57))) % 0.37/0.60 (define @t138 () (_ (_ tptp.dsetconstr @t17) @t137)) % 0.37/0.60 (define @t139 () (not @t27)) % 0.37/0.60 (define @t140 () (_ tptp.subset @t57)) % 0.37/0.60 (define @t141 () (_ @t140 @t37)) % 0.37/0.60 (define @t142 () (lambda @t84 (and @t141 (forall @t29 (or @t139 (not (forall @t65 (or (not (_ (_ tptp.in @t63) @t138)) (not (= (_ (_ tptp.setadjoin @t63) tptp.emptyset) @t138)))))))))) % 0.37/0.60 (define @t143 () (_ @t54 @t142)) % 0.37/0.60 (define @t144 () (and @t141 @t81)) % 0.37/0.60 (define @t145 () (lambda @t84 @t144)) % 0.37/0.60 (define @t146 () (_ @t19 (_ @t54 @t145))) % 0.37/0.60 (define @t147 () (not @t146)) % 0.37/0.60 (define @t148 () (or @t147 @t136)) % 0.37/0.60 (define @t149 () (lambda @t51 @t136)) % 0.37/0.60 (define @t150 () (_ @t54 @t149)) % 0.37/0.60 (define @t151 () (=> (_ @t19 @t150) @t136)) % 0.37/0.60 (define @t152 () (tptp.in @t58 @t41)) % 0.37/0.60 (define @t153 () (tptp.dsetconstr @t17 (lambda @t6 @t152))) % 0.37/0.60 (define @t154 () (not (forall @t65 (or (not (tptp.in @t63 @t153)) (not (= @t64 @t153)))))) % 0.37/0.60 (define @t155 () (_ (_ tptp.subset @t41) @t37)) % 0.37/0.60 (define @t156 () (and @t155 (forall @t29 (or @t79 @t154)))) % 0.37/0.60 (define @t157 () (lambda (@list @t41) @t156)) % 0.37/0.60 (define @t158 () (lambda (@list @t17 @t41) @t156)) % 0.37/0.60 (define @t159 () (_ (lambda @t49 @t156) @t8)) % 0.37/0.60 (define @t160 () (lambda (@list @t17) @t150)) % 0.37/0.60 (define @t161 () (_ (lambda @t55 @t150) @t8)) % 0.37/0.60 (define @t162 () (_ (_ @t159 @t17) @t16)) % 0.37/0.60 (define @t163 () (=> (_ @t19 (_ @t161 @t17)) @t162)) % 0.37/0.60 (define @t164 () (forall @t21 @t163)) % 0.37/0.60 (define @t165 () (=> tptp.dsetconstrER @t164)) % 0.37/0.60 (define @t166 () (or @t139 @t154)) % 0.37/0.60 (define @t167 () (tptp.dsetconstr @t17 @t45)) % 0.37/0.60 (define @t168 () (= @t64 @t167)) % 0.37/0.60 (define @t169 () (not @t168)) % 0.37/0.60 (define @t170 () (tptp.in @t63 @t167)) % 0.37/0.60 (define @t171 () (not @t170)) % 0.37/0.60 (define @t172 () (or @t171 @t169)) % 0.37/0.60 (define @t173 () (not (= @t167 @t64))) % 0.37/0.60 (define @t174 () (or @t171 @t173)) % 0.37/0.60 (define @t175 () (forall @t65 @t174)) % 0.37/0.60 (define @t176 () (not @t175)) % 0.37/0.60 (define @t177 () (tptp.dsetconstr @t17 @t2)) % 0.37/0.60 (define @t178 () (not (tptp.in @t63 @t177))) % 0.37/0.60 (define @t179 () (@list @t2)) % 0.37/0.60 (define @t180 () (not (= @t64 @t177))) % 0.37/0.60 (define @t181 () (or @t178 @t180)) % 0.37/0.60 (define @t182 () (forall @t65 @t181)) % 0.37/0.60 (define @t183 () (not @t182)) % 0.37/0.60 (define @t184 () (tptp.setadjoin @t1 tptp.emptyset)) % 0.37/0.60 (define @t185 () (forall @t29 (or (not (tptp.in @t1 @t177)) (not (= @t184 @t177))))) % 0.37/0.60 (define @t186 () (not @t185)) % 0.37/0.60 (define @t187 () (lambda @t179 @t186)) % 0.37/0.60 (define @t188 () (tptp.dsetconstr @t8 @t2)) % 0.37/0.60 (define @t189 () (_ (lambda @t35 (not (forall @t29 (or (not (tptp.in @t1 @t188)) (not (= @t184 @t188)))))) @t17)) % 0.37/0.60 (define @t190 () (=> @t27 (_ @t189 @t45))) % 0.37/0.60 (define @t191 () (forall @t29 @t190)) % 0.37/0.60 (define @t192 () (lambda (@list @t38) @t39)) % 0.37/0.60 (define @t193 () (lambda (@list @t17 @t38) @t39)) % 0.37/0.60 (define @t194 () (_ @t40 @t8)) % 0.37/0.60 (define @t195 () (@var "BOUND_VARIABLE_7490" $$unsorted)) % 0.37/0.60 (define @t196 () (_ @t2 @t195)) % 0.37/0.60 (define @t197 () (@list @t195)) % 0.37/0.60 (define @t198 () (lambda @t197 @t196)) % 0.37/0.60 (define @t199 () (tptp.dsetconstr @t8 @t198)) % 0.37/0.60 (define @t200 () (= @t184 @t199)) % 0.37/0.60 (define @t201 () (not @t200)) % 0.37/0.60 (define @t202 () (tptp.in @t1 @t199)) % 0.37/0.60 (define @t203 () (not @t202)) % 0.37/0.60 (define @t204 () (or @t203 @t201)) % 0.37/0.60 (define @t205 () (_ @t2 @t195)) % 0.37/0.60 (define @t206 () (lambda @t197 @t205)) % 0.37/0.60 (define @t207 () (_ @t9 @t206)) % 0.37/0.60 (define @t208 () (= @t184 @t207)) % 0.37/0.60 (define @t209 () (not @t208)) % 0.37/0.60 (define @t210 () (tptp.in @t1 @t207)) % 0.37/0.60 (define @t211 () (not @t210)) % 0.37/0.60 (define @t212 () (or @t211 @t209)) % 0.37/0.60 (define @t213 () (= @t184 @t34)) % 0.37/0.60 (define @t214 () (not @t213)) % 0.37/0.60 (define @t215 () (tptp.in @t1 @t34)) % 0.37/0.60 (define @t216 () (not @t215)) % 0.37/0.60 (define @t217 () (or @t216 @t214)) % 0.37/0.60 (define @t218 () (not (= @t34 @t184))) % 0.37/0.60 (define @t219 () (or @t216 @t218)) % 0.37/0.60 (define @t220 () (forall @t29 @t219)) % 0.37/0.60 (define @t221 () (not @t220)) % 0.37/0.60 (define @t222 () (not @t26)) % 0.37/0.60 (define @t223 () (or @t139 @t222)) % 0.37/0.60 (define @t224 () (forall @t29 (not @t28))) % 0.37/0.60 (define @t225 () (not @t224)) % 0.37/0.60 (define @t226 () (tptp.powerset @t96)) % 0.37/0.60 (define @t227 () (@quantifiers_skolemize @t91 3)) % 0.37/0.60 (define @t228 () (tptp.dsetconstr @t92 (lambda @t6 (tptp.in (tptp.kpair @t227 @t4) @t104)))) % 0.37/0.60 (define @t229 () (or (not (tptp.in @t227 @t94)) (not (forall @t65 (or (not (tptp.in @t63 @t228)) (not (= @t64 @t228))))))) % 0.37/0.60 (define @t230 () (and @t107 @t229)) % 0.37/0.60 (define @t231 () (tptp.in @t104 (tptp.dsetconstr @t226 @t99))) % 0.37/0.60 (define @t232 () (not @t231)) % 0.37/0.60 (define @t233 () (or @t232 @t230)) % 0.37/0.60 (define @t234 () (not @t233)) % 0.37/0.60 (define @t235 () (not @t91)) % 0.37/0.60 (define @t236 () (tptp.dsetconstr @t226 @t98)) % 0.37/0.60 (define @t237 () (tptp.in @t104 @t236)) % 0.37/0.60 (define @t238 () (not @t237)) % 0.37/0.60 (define @t239 () (or @t238 @t230)) % 0.37/0.60 (define @t240 () (not @t239)) % 0.37/0.60 (define @t241 () (@list true)) % 0.37/0.60 (define @t242 () (@list @t233)) % 0.37/0.60 (define @t243 () (or @t232 @t109)) % 0.37/0.60 (define @t244 () (@list false false)) % 0.37/0.60 (define @t245 () (not @t108)) % 0.37/0.60 (define @t246 () (@list @t108)) % 0.37/0.60 (define @t247 () (@list true false)) % 0.37/0.60 (assume @p1 @t15) % 0.37/0.60 (assume @p2 @t24) % 0.37/0.60 (assume @p3 true) % 0.37/0.60 (step @p4 (= tptp.singleton @t32) :rule refl :args (@t32)) % 0.37/0.60 (step @p5 (= tptp.ex1 @t36) :rule refl :args (@t36)) % 0.37/0.60 (step @p6 (= tptp.breln @t40) :rule refl :args (@t40)) % 0.37/0.60 (step @p7 (= tptp.func @t50) :rule refl :args (@t50)) % 0.37/0.60 (step @p8 (= tptp.funcSet @t56) :rule refl :args (@t56)) % 0.37/0.60 (step @p9 :rule eq-symm :args (@t100 @t97)) % 0.37/0.60 (step @p10 :rule beta-reduce :args ((= @t101 @t97))) % 0.37/0.60 (step @p11 :rule refl :args (@t100)) % 0.37/0.60 (step @p12 :rule cong :premises (@p11 @p10) :args (@t102)) % 0.37/0.60 (step @p13 :rule trans :premises (@p12 @p9)) % 0.37/0.60 (step @p14 :rule cong :premises (@p13) :args (@t103)) % 0.37/0.60 (step @p15 :rule quant-unused-vars :args ((= (forall @t84 true) true))) % 0.37/0.60 (step @p16 :rule eq-refl :args (@t101)) % 0.37/0.60 (step @p17 :rule cong :premises (@p16) :args ((forall @t84 (= @t101 @t101)))) % 0.37/0.60 (step @p18 :rule trans :premises (@p17 @p15)) % 0.37/0.60 (step @p19 :rule refl :args (@t101)) % 0.37/0.60 (step @p20 :rule refl :args (@t57)) % 0.37/0.60 (step @p21 :rule skolem_intro :args (@t99)) % 0.37/0.60 (step @p22 :rule ho_cong :premises (@p21 @p20)) % 0.37/0.60 (step @p23 :rule cong :premises (@p22 @p19) :args (@t102)) % 0.37/0.60 (step @p24 :rule cong :premises (@p23) :args (@t103)) % 0.37/0.60 (step @p25 :rule trans :premises (@p24 @p18)) % 0.37/0.60 (step @p26 :rule true_elim :premises (@p25)) % 0.37/0.60 (step @p27 :rule eq_resolve :premises (@p26 @p14)) % 0.37/0.60 (step @p28 :rule eq-symm :args (@t108 @t109)) % 0.37/0.60 (step @p29 :rule refl :args (@t110)) % 0.37/0.60 (step @p30 :rule cong :premises (@p29 @p28) :args ((=> @t110 @t111))) % 0.37/0.60 (assume-push @p483 @t110) % 0.37/0.60 (step @p32 :rule instantiate :premises (@p27) :args ((@list @t104))) % 0.37/0.60 (step-pop @p484 :rule scope :premises (@p32)) % 0.37/0.60 (step @p33 :rule process_scope :premises (@p484) :args (@t111)) % 0.37/0.60 (step @p35 :rule eq_resolve :premises (@p33 @p30)) % 0.37/0.60 (step @p36 :rule implies_elim :premises (@p35)) % 0.37/0.60 (step @p37 :rule chain_m_resolution :premises (@p36 @p27) :args (@t112 @t113 (@list @t110))) % 0.37/0.60 (step @p38 :rule refl :args (@t91)) % 0.37/0.60 (step @p39 :rule refl :args (@t114)) % 0.37/0.60 (step @p40 :rule lambda-elim :args ((= @t116 @t2))) % 0.37/0.60 (step @p41 :rule refl :args (@t8)) % 0.37/0.60 (step @p42 :rule cong :premises (@p41 @p40) :args (@t117)) % 0.37/0.60 (step @p43 :rule refl :args (@t1)) % 0.37/0.60 (step @p44 :rule cong :premises (@p43 @p42) :args (@t118)) % 0.37/0.60 (step @p45 :rule cong :premises (@p44) :args (@t119)) % 0.37/0.60 (step @p46 :rule nary_cong :premises (@p45 @p39) :args (@t120)) % 0.37/0.60 (step @p47 :rule cong :premises (@p46) :args ((forall @t13 @t120))) % 0.37/0.60 (step @p48 :rule refl :args (@t114)) % 0.37/0.60 (step @p49 :rule refl :args (@t3)) % 0.37/0.60 (step @p50 :rule cong :premises (@p49 @p48) :args ((= @t3 @t114))) % 0.37/0.60 (step @p51 :rule symm :premises (@p50)) % 0.37/0.60 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 0.37/0.60 (step @p53 :rule refl :args ((tptp.in @t1 @t10))) % 0.37/0.60 (step @p54 :rule refl :args ((tptp.dsetconstr @t8 @t7))) % 0.37/0.60 (step @p55 :rule refl :args (@t115)) % 0.37/0.60 (step @p56 :rule cong :premises (@p55) :args (@t116)) % 0.37/0.60 (step @p57 :rule refl :args (@t8)) % 0.37/0.60 (step @p58 :rule cong :premises (@p57 @p56) :args (@t117)) % 0.37/0.60 (step @p59 :rule trans :premises (@p58 @p54)) % 0.37/0.60 (step @p60 :rule refl :args (@t1)) % 0.37/0.60 (step @p61 :rule cong :premises (@p60 @p59) :args (@t118)) % 0.37/0.60 (step @p62 :rule trans :premises (@p61 @p53)) % 0.37/0.60 (step @p63 :rule refl :args (@t11)) % 0.37/0.60 (step @p64 :rule ho_cong :premises (@p63 @p59)) % 0.37/0.60 (step @p65 :rule cong :premises (@p64 @p62) :args ((= (_ @t11 @t117) @t118))) % 0.37/0.60 (step @p66 :rule symm :premises (@p65)) % 0.37/0.60 (step @p67 :rule refl :args (@t12)) % 0.37/0.60 (step @p68 :rule eq_resolve :premises (@p67 @p66)) % 0.37/0.60 (step @p69 :rule refl :args (@t9)) % 0.37/0.60 (step @p70 :rule ho_cong :premises (@p69 @p56)) % 0.37/0.60 (step @p71 :rule cong :premises (@p70 @p59) :args ((= (_ @t9 @t116) @t117))) % 0.37/0.60 (step @p72 :rule symm :premises (@p71)) % 0.37/0.60 (step @p73 :rule refl :args (@t10)) % 0.37/0.60 (step @p74 :rule eq_resolve :premises (@p73 @p72)) % 0.37/0.60 (step @p75 :rule refl :args (@t5)) % 0.37/0.60 (step @p76 :rule cong :premises (@p75 @p55) :args ((= @t5 @t115))) % 0.37/0.60 (step @p77 :rule symm :premises (@p76)) % 0.37/0.60 (step @p78 :rule eq_resolve :premises (@p75 @p77)) % 0.37/0.60 (step @p79 :rule cong :premises (@p78) :args (@t7)) % 0.37/0.60 (step @p80 :rule ho_cong :premises (@p69 @p79)) % 0.37/0.60 (step @p81 :rule trans :premises (@p80 @p74)) % 0.37/0.60 (step @p82 :rule ho_cong :premises (@p63 @p81)) % 0.37/0.60 (step @p83 :rule trans :premises (@p82 @p68)) % 0.37/0.60 (step @p84 :rule cong :premises (@p83) :args (@t121)) % 0.37/0.60 (step @p85 :rule nary_cong :premises (@p84 @p52) :args (@t122)) % 0.37/0.60 (step @p86 :rule cong :premises (@p85) :args ((forall @t13 @t122))) % 0.37/0.60 (step @p87 :rule trans :premises (@p86 @p47)) % 0.37/0.60 (step @p88 :rule bool-impl-elim :args (@t12 @t3)) % 0.37/0.60 (step @p89 :rule cong :premises (@p88) :args (@t14)) % 0.37/0.60 (step @p90 :rule trans :premises (@p89 @p87)) % 0.37/0.60 (step @p91 :rule refl :args (tptp.dsetconstrER)) % 0.37/0.60 (step @p92 :rule cong :premises (@p91 @p90) :args (@t15)) % 0.37/0.60 (step @p93 :rule eq_resolve :premises (@p1 @p92)) % 0.37/0.60 (step @p94 :rule cong :premises (@p93 @p38) :args (@t123)) % 0.37/0.60 (step @p95 :rule cong :premises (@p94) :args ((not @t123))) % 0.37/0.60 (step @p96 :rule quant-merge-prenex :args ((= (forall @t21 @t125) @t91))) % 0.37/0.60 (step @p97 :rule alpha_equiv :args (@t126 (@list @t61) @t127)) % 0.37/0.60 (step @p98 :rule quant-unused-vars :args ((= @t128 @t68))) % 0.37/0.60 (step @p99 :rule nary_cong :premises (@p98 @p97) :args (@t129)) % 0.37/0.60 (step @p100 :rule quant-miniscope-and :args ((= @t130 @t129))) % 0.37/0.60 (step @p101 :rule trans :premises (@p100 @p99)) % 0.37/0.60 (step @p102 :rule refl :args (@t89)) % 0.37/0.60 (step @p103 :rule nary_cong :premises (@p102 @p101) :args (@t131)) % 0.37/0.60 (step @p104 :rule quant-miniscope-or :args ((= @t125 @t131))) % 0.37/0.60 (step @p105 :rule trans :premises (@p104 @p103)) % 0.37/0.60 (step @p106 :rule symm :premises (@p105)) % 0.37/0.60 (step @p107 :rule cong :premises (@p106) :args ((forall @t21 (or @t89 (and @t68 @t133))))) % 0.37/0.60 (step @p108 :rule trans :premises (@p107 @p96)) % 0.37/0.60 (step @p109 :rule refl :args (@t133)) % 0.37/0.60 (step @p110 :rule refl :args ((tptp.subset @t16 @t37))) % 0.37/0.60 (step @p111 :rule refl :args (@t67)) % 0.37/0.60 (step @p112 :rule refl :args (@t16)) % 0.37/0.60 (step @p113 :rule cong :premises (@p112 @p111) :args (@t68)) % 0.37/0.60 (step @p114 :rule trans :premises (@p113 @p110)) % 0.37/0.60 (step @p115 :rule refl :args (@t134)) % 0.37/0.60 (step @p116 :rule ho_cong :premises (@p115 @p111)) % 0.37/0.60 (step @p117 :rule cong :premises (@p116 @p114) :args ((= (_ @t134 @t67) @t68))) % 0.37/0.60 (step @p118 :rule symm :premises (@p117)) % 0.37/0.60 (step @p119 :rule refl :args (@t135)) % 0.37/0.60 (step @p120 :rule eq_resolve :premises (@p119 @p118)) % 0.37/0.60 (step @p121 :rule refl :args (@t37)) % 0.37/0.60 (step @p122 :rule cong :premises (@p121 @p111) :args ((= @t37 @t67))) % 0.37/0.60 (step @p123 :rule symm :premises (@p122)) % 0.37/0.60 (step @p124 :rule eq_resolve :premises (@p121 @p123)) % 0.37/0.60 (step @p125 :rule ho_cong :premises (@p115 @p124)) % 0.37/0.60 (step @p126 :rule trans :premises (@p125 @p120)) % 0.37/0.60 (step @p127 :rule nary_cong :premises (@p126 @p109) :args (@t136)) % 0.37/0.60 (step @p128 :rule refl :args ((tptp.in @t16 @t143))) % 0.37/0.60 (step @p129 :rule refl :args ((tptp.dsetconstr @t53 @t142))) % 0.37/0.60 (step @p130 :rule refl :args ((tptp.dsetconstr @t17 @t137))) % 0.37/0.60 (step @p131 :rule refl :args ((tptp.in @t42 @t57))) % 0.37/0.60 (step @p132 :rule refl :args (@t57)) % 0.37/0.60 (step @p133 :rule refl :args (@t58)) % 0.37/0.60 (step @p134 :rule cong :premises (@p133 @p132) :args (@t59)) % 0.37/0.60 (step @p135 :rule trans :premises (@p134 @p131)) % 0.37/0.60 (step @p136 :rule cong :premises (@p135) :args (@t60)) % 0.37/0.60 (step @p137 :rule refl :args (@t17)) % 0.37/0.60 (step @p138 :rule cong :premises (@p137 @p136) :args (@t70)) % 0.37/0.60 (step @p139 :rule trans :premises (@p138 @p130)) % 0.37/0.60 (step @p140 :rule refl :args (@t64)) % 0.37/0.60 (step @p141 :rule cong :premises (@p140 @p139) :args (@t71)) % 0.37/0.60 (step @p142 :rule cong :premises (@p141) :args (@t72)) % 0.37/0.60 (step @p143 :rule refl :args ((tptp.in @t63 @t138))) % 0.37/0.60 (step @p144 :rule refl :args (@t63)) % 0.37/0.60 (step @p145 :rule cong :premises (@p144 @p139) :args (@t73)) % 0.37/0.60 (step @p146 :rule trans :premises (@p145 @p143)) % 0.37/0.60 (step @p147 :rule cong :premises (@p146) :args (@t74)) % 0.37/0.60 (step @p148 :rule nary_cong :premises (@p147 @p142) :args (@t75)) % 0.37/0.60 (step @p149 :rule cong :premises (@p148) :args (@t76)) % 0.37/0.60 (step @p150 :rule cong :premises (@p149) :args (@t77)) % 0.37/0.60 (step @p151 :rule refl :args (@t78)) % 0.37/0.60 (step @p152 :rule cong :premises (@p151) :args (@t79)) % 0.37/0.60 (step @p153 :rule nary_cong :premises (@p152 @p150) :args (@t80)) % 0.37/0.60 (step @p154 :rule cong :premises (@p153) :args (@t81)) % 0.37/0.60 (step @p155 :rule refl :args ((tptp.subset @t57 @t37))) % 0.37/0.60 (step @p156 :rule cong :premises (@p132 @p111) :args (@t82)) % 0.37/0.60 (step @p157 :rule trans :premises (@p156 @p155)) % 0.37/0.60 (step @p158 :rule nary_cong :premises (@p157 @p154) :args (@t83)) % 0.37/0.60 (step @p159 :rule cong :premises (@p158) :args (@t85)) % 0.37/0.60 (step @p160 :rule refl :args ((tptp.powerset @t37))) % 0.37/0.60 (step @p161 :rule cong :premises (@p111) :args (@t86)) % 0.37/0.60 (step @p162 :rule trans :premises (@p161 @p160)) % 0.37/0.60 (step @p163 :rule cong :premises (@p162 @p159) :args (@t87)) % 0.37/0.60 (step @p164 :rule trans :premises (@p163 @p129)) % 0.37/0.60 (step @p165 :rule cong :premises (@p112 @p164) :args (@t88)) % 0.37/0.60 (step @p166 :rule trans :premises (@p165 @p128)) % 0.37/0.60 (step @p167 :rule refl :args (@t19)) % 0.37/0.60 (step @p168 :rule ho_cong :premises (@p167 @p164)) % 0.37/0.60 (step @p169 :rule cong :premises (@p168 @p166) :args ((= (_ @t19 @t87) @t88))) % 0.37/0.60 (step @p170 :rule symm :premises (@p169)) % 0.37/0.60 (step @p171 :rule refl :args ((_ @t19 @t143))) % 0.37/0.60 (step @p172 :rule eq_resolve :premises (@p171 @p170)) % 0.37/0.60 (step @p173 :rule refl :args (tptp.dsetconstr)) % 0.37/0.60 (step @p174 :rule ho_cong :premises (@p173 @p162)) % 0.37/0.60 (step @p175 :rule ho_cong :premises (@p174 @p159)) % 0.37/0.60 (step @p176 :rule cong :premises (@p175 @p164) :args ((= (_ (_ tptp.dsetconstr @t86) @t85) @t87))) % 0.37/0.60 (step @p177 :rule symm :premises (@p176)) % 0.37/0.60 (step @p178 :rule refl :args (@t143)) % 0.37/0.60 (step @p179 :rule eq_resolve :premises (@p178 @p177)) % 0.37/0.60 (step @p180 :rule refl :args (@t81)) % 0.37/0.60 (step @p181 :rule refl :args (@t140)) % 0.37/0.60 (step @p182 :rule ho_cong :premises (@p181 @p111)) % 0.37/0.60 (step @p183 :rule cong :premises (@p182 @p157) :args ((= (_ @t140 @t67) @t82))) % 0.37/0.60 (step @p184 :rule symm :premises (@p183)) % 0.37/0.60 (step @p185 :rule refl :args (@t141)) % 0.37/0.60 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.37/0.60 (step @p187 :rule ho_cong :premises (@p181 @p124)) % 0.37/0.60 (step @p188 :rule trans :premises (@p187 @p186)) % 0.37/0.60 (step @p189 :rule nary_cong :premises (@p188 @p180) :args (@t144)) % 0.37/0.60 (step @p190 :rule cong :premises (@p189) :args (@t145)) % 0.37/0.60 (step @p191 :rule refl :args (tptp.powerset)) % 0.37/0.60 (step @p192 :rule ho_cong :premises (@p191 @p111)) % 0.37/0.60 (step @p193 :rule cong :premises (@p192 @p162) :args ((= (_ tptp.powerset @t67) @t86))) % 0.37/0.60 (step @p194 :rule symm :premises (@p193)) % 0.37/0.60 (step @p195 :rule refl :args (@t53)) % 0.37/0.60 (step @p196 :rule eq_resolve :premises (@p195 @p194)) % 0.37/0.60 (step @p197 :rule ho_cong :premises (@p191 @p124)) % 0.37/0.60 (step @p198 :rule trans :premises (@p197 @p196)) % 0.37/0.60 (step @p199 :rule ho_cong :premises (@p173 @p198)) % 0.37/0.60 (step @p200 :rule ho_cong :premises (@p199 @p190)) % 0.37/0.60 (step @p201 :rule trans :premises (@p200 @p179)) % 0.37/0.60 (step @p202 :rule ho_cong :premises (@p167 @p201)) % 0.37/0.60 (step @p203 :rule trans :premises (@p202 @p172)) % 0.37/0.60 (step @p204 :rule cong :premises (@p203) :args (@t147)) % 0.37/0.60 (step @p205 :rule nary_cong :premises (@p204 @p127) :args (@t148)) % 0.37/0.60 (step @p206 :rule cong :premises (@p205) :args ((forall @t21 @t148))) % 0.37/0.60 (step @p207 :rule trans :premises (@p206 @p108)) % 0.37/0.60 (step @p208 :rule bool-impl-elim :args (@t146 @t136)) % 0.37/0.60 (step @p209 :rule cong :premises (@p208) :args ((forall @t21 (=> @t146 @t136)))) % 0.37/0.60 (step @p210 :rule trans :premises (@p209 @p207)) % 0.37/0.60 (step @p211 :rule refl :args (@t136)) % 0.37/0.60 (step @p212 :rule alpha_equiv :args (@t149 (@list @t16) (@list @t57))) % 0.37/0.60 (step @p213 :rule refl :args (@t54)) % 0.37/0.60 (step @p214 :rule ho_cong :premises (@p213 @p212)) % 0.37/0.60 (step @p215 :rule ho_cong :premises (@p167 @p214)) % 0.37/0.60 (step @p216 :rule cong :premises (@p215 @p211) :args (@t151)) % 0.37/0.60 (step @p217 :rule cong :premises (@p216) :args ((forall @t21 @t151))) % 0.37/0.60 (step @p218 :rule trans :premises (@p217 @p210)) % 0.37/0.60 (step @p219 :rule beta-reduce :args ((= (_ @t157 @t16) @t136))) % 0.37/0.60 (step @p220 :rule refl :args (@t16)) % 0.37/0.60 (step @p221 :rule beta-reduce :args ((= (_ @t158 @t17) @t157))) % 0.37/0.60 (step @p222 :rule refl :args (@t17)) % 0.37/0.60 (step @p223 :rule beta-reduce :args ((= @t159 @t158))) % 0.37/0.60 (step @p224 :rule ho_cong :premises (@p223 @p222)) % 0.37/0.60 (step @p225 :rule trans :premises (@p224 @p221)) % 0.37/0.60 (step @p226 :rule ho_cong :premises (@p225 @p220)) % 0.37/0.60 (step @p227 :rule trans :premises (@p226 @p219)) % 0.37/0.60 (step @p228 :rule beta-reduce :args ((= (_ @t160 @t17) @t150))) % 0.37/0.60 (step @p229 :rule beta-reduce :args ((= @t161 @t160))) % 0.37/0.60 (step @p230 :rule ho_cong :premises (@p229 @p222)) % 0.37/0.60 (step @p231 :rule trans :premises (@p230 @p228)) % 0.37/0.60 (step @p232 :rule refl :args (@t19)) % 0.37/0.60 (step @p233 :rule ho_cong :premises (@p232 @p231)) % 0.37/0.60 (step @p234 :rule cong :premises (@p233 @p227) :args (@t163)) % 0.37/0.60 (step @p235 :rule cong :premises (@p234) :args (@t164)) % 0.37/0.60 (step @p236 :rule trans :premises (@p235 @p218)) % 0.37/0.60 (step @p237 :rule cong :premises (@p91 @p236) :args (@t165)) % 0.37/0.60 (step @p238 :rule cong :premises (@p237) :args ((not @t165))) % 0.37/0.60 (step @p239 :rule refl :args (@t154)) % 0.37/0.60 (step @p240 :rule refl :args (@t27)) % 0.37/0.60 (step @p241 :rule cong :premises (@p240 @p151) :args ((= @t27 @t78))) % 0.37/0.60 (step @p242 :rule symm :premises (@p241)) % 0.37/0.60 (step @p243 :rule eq_resolve :premises (@p240 @p242)) % 0.37/0.60 (step @p244 :rule cong :premises (@p243) :args (@t139)) % 0.37/0.60 (step @p245 :rule nary_cong :premises (@p244 @p239) :args (@t166)) % 0.37/0.60 (step @p246 :rule cong :premises (@p245) :args ((forall @t29 @t166))) % 0.37/0.60 (step @p247 :rule bool-impl-elim :args (@t27 @t154)) % 0.37/0.60 (step @p248 :rule cong :premises (@p247) :args ((forall @t29 (=> @t27 @t154)))) % 0.37/0.60 (step @p249 :rule trans :premises (@p248 @p246)) % 0.37/0.60 (step @p250 :rule refl :args ((tptp.in @t42 @t41))) % 0.37/0.60 (step @p251 :rule refl :args (@t41)) % 0.37/0.60 (step @p252 :rule cong :premises (@p133 @p251) :args (@t152)) % 0.37/0.60 (step @p253 :rule trans :premises (@p252 @p250)) % 0.37/0.60 (step @p254 :rule refl :args (tptp.in)) % 0.37/0.60 (step @p255 :rule ho_cong :premises (@p254 @p133)) % 0.37/0.60 (step @p256 :rule ho_cong :premises (@p255 @p251)) % 0.37/0.60 (step @p257 :rule cong :premises (@p256 @p253) :args ((= (_ (_ tptp.in @t58) @t41) @t152))) % 0.37/0.60 (step @p258 :rule symm :premises (@p257)) % 0.37/0.60 (step @p259 :rule refl :args (@t44)) % 0.37/0.60 (step @p260 :rule eq_resolve :premises (@p259 @p258)) % 0.37/0.60 (step @p261 :rule refl :args (@t42)) % 0.37/0.60 (step @p262 :rule cong :premises (@p261 @p133) :args ((= @t42 @t58))) % 0.37/0.60 (step @p263 :rule symm :premises (@p262)) % 0.37/0.60 (step @p264 :rule eq_resolve :premises (@p261 @p263)) % 0.37/0.60 (step @p265 :rule ho_cong :premises (@p254 @p264)) % 0.37/0.60 (step @p266 :rule ho_cong :premises (@p265 @p251)) % 0.37/0.60 (step @p267 :rule trans :premises (@p266 @p260)) % 0.37/0.60 (step @p268 :rule cong :premises (@p267) :args (@t45)) % 0.37/0.60 (step @p269 :rule cong :premises (@p137 @p268) :args (@t167)) % 0.37/0.60 (step @p270 :rule refl :args (@t64)) % 0.37/0.60 (step @p271 :rule cong :premises (@p270 @p269) :args (@t168)) % 0.37/0.60 (step @p272 :rule cong :premises (@p271) :args (@t169)) % 0.37/0.60 (step @p273 :rule cong :premises (@p144 @p269) :args (@t170)) % 0.37/0.60 (step @p274 :rule cong :premises (@p273) :args (@t171)) % 0.37/0.60 (step @p275 :rule nary_cong :premises (@p274 @p272) :args (@t172)) % 0.37/0.60 (step @p276 :rule cong :premises (@p275) :args ((forall @t65 @t172))) % 0.37/0.60 (step @p277 :rule eq-symm :args (@t167 @t64)) % 0.37/0.60 (step @p278 :rule cong :premises (@p277) :args (@t173)) % 0.37/0.60 (step @p279 :rule refl :args (@t171)) % 0.37/0.60 (step @p280 :rule nary_cong :premises (@p279 @p278) :args (@t174)) % 0.37/0.60 (step @p281 :rule cong :premises (@p280) :args (@t175)) % 0.37/0.60 (step @p282 :rule trans :premises (@p281 @p276)) % 0.37/0.60 (step @p283 :rule cong :premises (@p282) :args (@t176)) % 0.37/0.60 (step @p284 :rule beta-reduce :args ((= (_ (lambda @t179 (not (forall @t65 (or @t178 (not (= @t177 @t64)))))) @t45) @t176))) % 0.37/0.60 (step @p285 :rule trans :premises (@p284 @p283)) % 0.37/0.60 (step @p286 :rule refl :args (@t45)) % 0.37/0.60 (step @p287 :rule eq-symm :args (@t64 @t177)) % 0.37/0.60 (step @p288 :rule cong :premises (@p287) :args (@t180)) % 0.37/0.60 (step @p289 :rule refl :args (@t178)) % 0.37/0.60 (step @p290 :rule nary_cong :premises (@p289 @p288) :args (@t181)) % 0.37/0.60 (step @p291 :rule cong :premises (@p290) :args (@t182)) % 0.37/0.60 (step @p292 :rule cong :premises (@p291) :args (@t183)) % 0.37/0.60 (step @p293 :rule cong :premises (@p292) :args ((lambda @t179 @t183))) % 0.37/0.60 (step @p294 :rule ho_cong :premises (@p293 @p286)) % 0.37/0.60 (step @p295 :rule trans :premises (@p294 @p285)) % 0.37/0.60 (step @p296 :rule refl :args (@t45)) % 0.37/0.60 (step @p297 :rule alpha_equiv :args (@t185 @t127 (@list @t63))) % 0.37/0.60 (step @p298 :rule cong :premises (@p297) :args (@t186)) % 0.37/0.60 (step @p299 :rule cong :premises (@p298) :args (@t187)) % 0.37/0.60 (step @p300 :rule ho_cong :premises (@p299 @p296)) % 0.37/0.60 (step @p301 :rule trans :premises (@p300 @p295)) % 0.37/0.60 (step @p302 :rule beta-reduce :args ((= @t189 @t187))) % 0.37/0.60 (step @p303 :rule ho_cong :premises (@p302 @p286)) % 0.37/0.60 (step @p304 :rule trans :premises (@p303 @p301)) % 0.37/0.60 (step @p305 :rule refl :args (@t27)) % 0.37/0.60 (step @p306 :rule cong :premises (@p305 @p304) :args (@t190)) % 0.37/0.60 (step @p307 :rule cong :premises (@p306) :args (@t191)) % 0.37/0.60 (step @p308 :rule trans :premises (@p307 @p249)) % 0.37/0.60 (step @p309 :rule beta-reduce :args ((= (_ @t192 @t41) @t155))) % 0.37/0.60 (step @p310 :rule refl :args (@t41)) % 0.37/0.60 (step @p311 :rule beta-reduce :args ((= (_ @t193 @t17) @t192))) % 0.37/0.60 (step @p312 :rule beta-reduce :args ((= @t194 @t193))) % 0.37/0.60 (step @p313 :rule ho_cong :premises (@p312 @p222)) % 0.37/0.60 (step @p314 :rule trans :premises (@p313 @p311)) % 0.37/0.60 (step @p315 :rule ho_cong :premises (@p314 @p310)) % 0.37/0.60 (step @p316 :rule trans :premises (@p315 @p309)) % 0.37/0.60 (step @p317 :rule nary_cong :premises (@p316 @p308) :args ((and (_ (_ @t194 @t17) @t41) @t191))) % 0.37/0.60 (step @p318 :rule lambda-elim :args ((= @t198 @t2))) % 0.37/0.60 (step @p319 :rule cong :premises (@p41 @p318) :args (@t199)) % 0.37/0.60 (step @p320 :rule refl :args (@t184)) % 0.37/0.60 (step @p321 :rule cong :premises (@p320 @p319) :args (@t200)) % 0.37/0.60 (step @p322 :rule cong :premises (@p321) :args (@t201)) % 0.37/0.60 (step @p323 :rule cong :premises (@p43 @p319) :args (@t202)) % 0.37/0.60 (step @p324 :rule cong :premises (@p323) :args (@t203)) % 0.37/0.60 (step @p325 :rule nary_cong :premises (@p324 @p322) :args (@t204)) % 0.37/0.60 (step @p326 :rule cong :premises (@p325) :args ((forall @t29 @t204))) % 0.37/0.60 (step @p327 :rule refl :args ((tptp.dsetconstr @t8 @t206))) % 0.37/0.60 (step @p328 :rule refl :args (@t196)) % 0.37/0.60 (step @p329 :rule cong :premises (@p328) :args (@t198)) % 0.37/0.60 (step @p330 :rule cong :premises (@p57 @p329) :args (@t199)) % 0.37/0.60 (step @p331 :rule trans :premises (@p330 @p327)) % 0.37/0.60 (step @p332 :rule ho_cong :premises (@p69 @p329)) % 0.37/0.60 (step @p333 :rule cong :premises (@p332 @p331) :args ((= (_ @t9 @t198) @t199))) % 0.37/0.60 (step @p334 :rule symm :premises (@p333)) % 0.37/0.60 (step @p335 :rule refl :args (@t207)) % 0.37/0.60 (step @p336 :rule eq_resolve :premises (@p335 @p334)) % 0.37/0.60 (step @p337 :rule refl :args (@t205)) % 0.37/0.60 (step @p338 :rule cong :premises (@p337 @p328) :args ((= @t205 @t196))) % 0.37/0.60 (step @p339 :rule symm :premises (@p338)) % 0.37/0.60 (step @p340 :rule eq_resolve :premises (@p337 @p339)) % 0.37/0.60 (step @p341 :rule cong :premises (@p340) :args (@t206)) % 0.37/0.60 (step @p342 :rule ho_cong :premises (@p69 @p341)) % 0.37/0.60 (step @p343 :rule trans :premises (@p342 @p336)) % 0.37/0.60 (step @p344 :rule refl :args (@t184)) % 0.37/0.60 (step @p345 :rule cong :premises (@p344 @p343) :args (@t208)) % 0.37/0.60 (step @p346 :rule cong :premises (@p345) :args (@t209)) % 0.37/0.60 (step @p347 :rule cong :premises (@p60 @p343) :args (@t210)) % 0.37/0.60 (step @p348 :rule cong :premises (@p347) :args (@t211)) % 0.37/0.60 (step @p349 :rule nary_cong :premises (@p348 @p346) :args (@t212)) % 0.37/0.60 (step @p350 :rule cong :premises (@p349) :args ((forall @t29 @t212))) % 0.37/0.60 (step @p351 :rule trans :premises (@p350 @p326)) % 0.37/0.60 (step @p352 :rule alpha_equiv :args (@t33 @t127 (@list @t195))) % 0.37/0.60 (step @p353 :rule ho_cong :premises (@p69 @p352)) % 0.37/0.60 (step @p354 :rule cong :premises (@p344 @p353) :args (@t213)) % 0.37/0.60 (step @p355 :rule cong :premises (@p354) :args (@t214)) % 0.37/0.60 (step @p356 :rule cong :premises (@p60 @p353) :args (@t215)) % 0.37/0.60 (step @p357 :rule cong :premises (@p356) :args (@t216)) % 0.37/0.60 (step @p358 :rule nary_cong :premises (@p357 @p355) :args (@t217)) % 0.37/0.60 (step @p359 :rule cong :premises (@p358) :args ((forall @t29 @t217))) % 0.37/0.60 (step @p360 :rule trans :premises (@p359 @p351)) % 0.37/0.60 (step @p361 :rule eq-symm :args (@t34 @t184)) % 0.37/0.60 (step @p362 :rule cong :premises (@p361) :args (@t218)) % 0.37/0.60 (step @p363 :rule refl :args (@t216)) % 0.37/0.60 (step @p364 :rule nary_cong :premises (@p363 @p362) :args (@t219)) % 0.37/0.60 (step @p365 :rule cong :premises (@p364) :args (@t220)) % 0.37/0.60 (step @p366 :rule trans :premises (@p365 @p360)) % 0.37/0.60 (step @p367 :rule cong :premises (@p366) :args (@t221)) % 0.37/0.60 (step @p368 :rule beta-reduce :args ((= (_ (lambda @t31 (not (forall @t29 (or @t79 (not (= @t8 @t184)))))) @t34) @t221))) % 0.37/0.60 (step @p369 :rule trans :premises (@p368 @p367)) % 0.37/0.60 (step @p370 :rule refl :args (@t34)) % 0.37/0.60 (step @p371 :rule refl :args (@t184)) % 0.37/0.60 (step @p372 :rule refl :args (@t25)) % 0.37/0.60 (step @p373 :rule cong :premises (@p372 @p371) :args ((= @t25 @t184))) % 0.37/0.60 (step @p374 :rule symm :premises (@p373)) % 0.37/0.60 (step @p375 :rule eq_resolve :premises (@p372 @p374)) % 0.37/0.60 (step @p376 :rule cong :premises (@p57 @p375) :args (@t26)) % 0.37/0.60 (step @p377 :rule cong :premises (@p376) :args (@t222)) % 0.37/0.60 (step @p378 :rule nary_cong :premises (@p244 @p377) :args (@t223)) % 0.37/0.60 (step @p379 :rule cong :premises (@p378) :args ((forall @t29 @t223))) % 0.37/0.60 (step @p380 :rule bool-and-de-morgan :args (@t27 @t26 true)) % 0.37/0.60 (step @p381 :rule cong :premises (@p380) :args (@t224)) % 0.37/0.60 (step @p382 :rule trans :premises (@p381 @p379)) % 0.37/0.60 (step @p383 :rule cong :premises (@p382) :args (@t225)) % 0.37/0.60 (step @p384 :rule exists-elim :args ((= @t30 @t225))) % 0.37/0.60 (step @p385 :rule trans :premises (@p384 @p383)) % 0.37/0.60 (step @p386 :rule cong :premises (@p385) :args (@t32)) % 0.37/0.60 (step @p387 :rule trans :premises (@p4 @p386)) % 0.37/0.60 (step @p388 :rule ho_cong :premises (@p387 @p370)) % 0.37/0.60 (step @p389 :rule trans :premises (@p388 @p369)) % 0.37/0.60 (step @p390 :rule cong :premises (@p389) :args (@t36)) % 0.37/0.60 (step @p391 :rule trans :premises (@p5 @p390)) % 0.37/0.60 (step @p392 :rule ho_cong :premises (@p391 @p222)) % 0.37/0.60 (step @p393 :rule ho_cong :premises (@p392 @p286)) % 0.37/0.60 (step @p394 :rule cong :premises (@p305 @p393) :args (@t46)) % 0.37/0.60 (step @p395 :rule cong :premises (@p394) :args (@t47)) % 0.37/0.60 (step @p396 :rule ho_cong :premises (@p6 @p41)) % 0.37/0.60 (step @p397 :rule ho_cong :premises (@p396 @p222)) % 0.37/0.60 (step @p398 :rule ho_cong :premises (@p397 @p310)) % 0.37/0.60 (step @p399 :rule nary_cong :premises (@p398 @p395) :args (@t48)) % 0.37/0.60 (step @p400 :rule trans :premises (@p399 @p317)) % 0.37/0.60 (step @p401 :rule cong :premises (@p400) :args (@t50)) % 0.37/0.60 (step @p402 :rule trans :premises (@p7 @p401)) % 0.37/0.60 (step @p403 :rule ho_cong :premises (@p402 @p41)) % 0.37/0.60 (step @p404 :rule ho_cong :premises (@p403 @p222)) % 0.37/0.60 (step @p405 :rule ho_cong :premises (@p404 @p220)) % 0.37/0.60 (step @p406 :rule cong :premises (@p227) :args ((lambda @t51 @t162))) % 0.37/0.60 (step @p407 :rule refl :args (@t54)) % 0.37/0.60 (step @p408 :rule ho_cong :premises (@p407 @p406)) % 0.37/0.60 (step @p409 :rule cong :premises (@p405) :args (@t52)) % 0.37/0.60 (step @p410 :rule ho_cong :premises (@p407 @p409)) % 0.37/0.60 (step @p411 :rule trans :premises (@p410 @p408)) % 0.37/0.60 (step @p412 :rule cong :premises (@p411) :args (@t56)) % 0.37/0.60 (step @p413 :rule trans :premises (@p8 @p412)) % 0.37/0.60 (step @p414 :rule ho_cong :premises (@p413 @p41)) % 0.37/0.60 (step @p415 :rule ho_cong :premises (@p414 @p222)) % 0.37/0.60 (step @p416 :rule ho_cong :premises (@p232 @p415)) % 0.37/0.60 (step @p417 :rule cong :premises (@p416 @p405) :args (@t20)) % 0.37/0.60 (step @p418 :rule cong :premises (@p417) :args (@t22)) % 0.37/0.60 (step @p419 :rule cong :premises (@p91 @p418) :args (@t23)) % 0.37/0.60 (step @p420 :rule cong :premises (@p419) :args (@t24)) % 0.37/0.60 (step @p421 :rule trans :premises (@p420 @p238)) % 0.37/0.60 (step @p422 :rule trans :premises (@p421 @p95)) % 0.37/0.60 (step @p423 :rule eq_resolve :premises (@p2 @p422)) % 0.37/0.60 (step @p424 :rule not_implies_elim1 :premises (@p423)) % 0.37/0.60 (step @p425 :rule instantiate :premises (@p424) :args ((@list @t226 @t99 @t104))) % 0.37/0.60 (step @p426 :rule not_implies_elim2 :premises (@p423)) % 0.37/0.60 (step @p427 :rule refl :args (@t234)) % 0.37/0.60 (step @p428 :rule bool-double-not-elim :args (@t91)) % 0.37/0.60 (step @p429 :rule nary_cong :premises (@p428 @p427) :args ((or (not @t235) @t234))) % 0.37/0.60 (step @p430 :rule refl :args (@t230)) % 0.37/0.60 (step @p431 :rule eq-refl :args (@t98)) % 0.37/0.60 (step @p432 :rule refl :args (@t98)) % 0.37/0.60 (step @p433 :rule cong :premises (@p432 @p21) :args ((= @t98 @t99))) % 0.37/0.60 (step @p434 :rule trans :premises (@p433 @p431)) % 0.37/0.60 (step @p435 :rule true_elim :premises (@p434)) % 0.37/0.60 (step @p436 :rule refl :args (@t226)) % 0.37/0.60 (step @p437 :rule cong :premises (@p436 @p435) :args (@t236)) % 0.37/0.60 (step @p438 :rule refl :args (@t104)) % 0.37/0.60 (step @p439 :rule cong :premises (@p438 @p437) :args (@t237)) % 0.37/0.60 (step @p440 :rule cong :premises (@p439) :args (@t238)) % 0.37/0.60 (step @p441 :rule nary_cong :premises (@p440 @p430) :args (@t239)) % 0.37/0.60 (step @p442 :rule cong :premises (@p441) :args (@t240)) % 0.37/0.60 (step @p443 :rule refl :args (@t235)) % 0.37/0.60 (step @p444 :rule cong :premises (@p443 @p442) :args ((=> @t235 @t240))) % 0.37/0.60 (assume-push @p485 @t235) % 0.37/0.60 (step @p446 :rule skolemize :premises (@p426)) % 0.37/0.60 (step-pop @p486 :rule scope :premises (@p446)) % 0.37/0.60 (step @p447 :rule process_scope :premises (@p486) :args (@t240)) % 0.37/0.60 (step @p449 :rule eq_resolve :premises (@p447 @p444)) % 0.37/0.60 (step @p450 :rule implies_elim :premises (@p449)) % 0.37/0.60 (step @p451 :rule eq_resolve :premises (@p450 @p429)) % 0.37/0.60 (step @p452 :rule chain_m_resolution :premises (@p451 @p426) :args (@t234 @t241 (@list @t91))) % 0.37/0.60 (step @p453 :rule bool-double-not-elim :args (@t231)) % 0.37/0.60 (step @p454 :rule refl :args (@t233)) % 0.37/0.60 (step @p455 :rule nary_cong :premises (@p454 @p453) :args ((or @t233 (not @t232)))) % 0.37/0.60 (step @p456 :rule cnf_or_neg :args (@t233 0)) % 0.37/0.60 (step @p457 :rule eq_resolve :premises (@p456 @p455)) % 0.37/0.60 (step @p458 :rule reordering :premises (@p457) :args ((or @t231 @t233))) % 0.37/0.60 (step @p459 :rule chain_m_resolution :premises (@p458 @p452) :args (@t231 @t241 @t242)) % 0.37/0.60 (step @p460 :rule cnf_or_pos :args (@t243)) % 0.37/0.60 (step @p461 :rule reordering :premises (@p460) :args ((or @t232 @t109 (not @t243)))) % 0.37/0.60 (step @p462 :rule chain_m_resolution :premises (@p461 @p459 @p425) :args (@t109 @t244 (@list @t231 @t243))) % 0.37/0.60 (step @p463 :rule cnf_equiv_pos1 :args (@t112)) % 0.37/0.60 (step @p464 :rule reordering :premises (@p463) :args ((or @t108 (not @t109) (not @t112)))) % 0.37/0.60 (step @p465 :rule chain_m_resolution :premises (@p464 @p462 @p37) :args (@t108 @t244 (@list @t109 @t112))) % 0.37/0.60 (step @p466 :rule cnf_and_pos :args (@t108 1)) % 0.37/0.60 (step @p467 :rule reordering :premises (@p466) :args ((or @t106 @t245))) % 0.37/0.60 (step @p468 :rule chain_m_resolution :premises (@p467 @p465) :args (@t106 @t113 @t246)) % 0.37/0.60 (step @p469 :rule cnf_and_pos :args (@t108 0)) % 0.37/0.60 (step @p470 :rule reordering :premises (@p469) :args ((or @t107 @t245))) % 0.37/0.60 (step @p471 :rule chain_m_resolution :premises (@p470 @p465) :args (@t107 @t113 @t246)) % 0.37/0.60 (step @p472 :rule cnf_or_neg :args (@t233 1)) % 0.37/0.60 (step @p473 :rule chain_m_resolution :premises (@p472 @p452) :args ((not @t230) @t241 @t242)) % 0.37/0.60 (step @p474 :rule cnf_and_neg :args (@t230)) % 0.37/0.60 (step @p475 :rule chain_m_resolution :premises (@p474 @p473 @p471) :args ((not @t229) @t247 (@list @t230 @t107))) % 0.37/0.60 (assume-push @p487 @t106) % 0.37/0.60 (step @p477 :rule instantiate :premises (@p468) :args ((@list @t227))) % 0.37/0.60 (step-pop @p488 :rule scope :premises (@p477)) % 0.37/0.60 (step @p478 :rule process_scope :premises (@p488) :args (@t229)) % 0.37/0.60 (step @p480 :rule implies_elim :premises (@p478)) % 0.37/0.60 (step @p481 :rule reordering :premises (@p480) :args ((or @t229 (not @t106)))) % 0.37/0.60 (step @p482 false :rule chain_m_resolution :premises (@p481 @p475 @p468) :args (false @t247 (@list @t229 @t106))) % 0.37/0.60 ) % 0.37/0.60 % SZS output end Proof % 0.37/0.60 % cvc5 exiting %------------------------------------------------------------------------------