%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET926^11 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n009.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 08:49:00 AM UTC 2026 % Result : Theorem 0.44s 0.64s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET926^11 : TPTP v9.2.1. Released v8.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n009.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 16:17:44 EDT 2026 % 0.17/0.35 % CPUTime : % 0.31/0.51 %----Proving TH0 % 0.44/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.44/0.64 % SZS status Theorem % 0.44/0.64 % SZS output start Proof % 0.44/0.64 ( % 0.44/0.64 (declare-sort $$unsorted 0) % 0.44/0.64 (declare-sort tptp.mworld 0) % 0.44/0.64 (declare-const tptp.mactual tptp.mworld) % 0.44/0.64 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.44/0.64 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 0.44/0.64 (declare-const tptp.qmltpeq (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.44/0.64 (declare-const tptp.empty (-> $$unsorted tptp.mworld Bool)) % 0.44/0.64 (declare-const tptp.in (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.44/0.64 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.empty_set $$unsorted) % 0.44/0.64 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.44/0.64 (define tptp.mnot () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.44/0.64 (define tptp.mand () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.64 (define tptp.mor () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.64 (define tptp.mimplies () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.64 (define tptp.mequiv () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.64 (define tptp.mbox () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.44/0.64 (define tptp.mdia () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (exists (@list _let_1) (and (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.44/0.64 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.44/0.64 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.44/0.64 (define @t1 () (@var "W" tptp.mworld)) % 0.44/0.64 (define @t2 () (_ tptp.mrel @t1)) % 0.44/0.64 (define @t3 () (@list @t1)) % 0.44/0.64 (define @t4 () (@var "V" tptp.mworld)) % 0.44/0.64 (define @t5 () (@var "U" tptp.mworld)) % 0.44/0.64 (define @t6 () (_ @t2 @t4)) % 0.44/0.64 (define @t7 () (@var "X" $$unsorted)) % 0.44/0.64 (define @t8 () (_ (_ tptp.eiw_di @t7) @t1)) % 0.44/0.64 (define @t9 () (@list @t7)) % 0.44/0.64 (define @t10 () (@var "__flatten_var_0" tptp.mworld)) % 0.44/0.64 (define @t11 () (_ tptp.qmltpeq @t7)) % 0.44/0.64 (define @t12 () (@list @t7 @t10)) % 0.44/0.64 (define @t13 () (@var "Y" $$unsorted)) % 0.44/0.64 (define @t14 () (_ tptp.qmltpeq @t13)) % 0.44/0.64 (define @t15 () (_ @t11 @t13)) % 0.44/0.64 (define @t16 () (@list @t13 @t10)) % 0.44/0.64 (define @t17 () (@var "Z" $$unsorted)) % 0.44/0.64 (define @t18 () (@var "C" $$unsorted)) % 0.44/0.64 (define @t19 () (@var "B" $$unsorted)) % 0.44/0.64 (define @t20 () (@var "A" $$unsorted)) % 0.44/0.64 (define @t21 () (_ (_ tptp.qmltpeq @t20) @t19)) % 0.44/0.64 (define @t22 () (_ tptp.mimplies @t21)) % 0.44/0.64 (define @t23 () (@list @t18 @t10)) % 0.44/0.64 (define @t24 () (@list @t19 @t10)) % 0.44/0.64 (define @t25 () (@list @t20 @t10)) % 0.44/0.64 (define @t26 () (_ tptp.set_difference @t18)) % 0.44/0.64 (define @t27 () (_ tptp.singleton @t20)) % 0.44/0.64 (define @t28 () (_ tptp.empty @t20)) % 0.44/0.64 (define @t29 () (_ tptp.mand @t21)) % 0.44/0.64 (define @t30 () (_ tptp.in @t19)) % 0.44/0.64 (define @t31 () (_ tptp.in @t20)) % 0.44/0.64 (define @t32 () (_ tptp.in @t18)) % 0.44/0.64 (define @t33 () (_ @t31 @t19)) % 0.44/0.64 (define @t34 () (_ tptp.set_difference @t27)) % 0.44/0.64 (define @t35 () (_ tptp.qmltpeq (_ @t34 @t19))) % 0.44/0.64 (define @t36 () (_ @t35 @t27)) % 0.44/0.64 (define @t37 () (lambda @t24 (_ (_ (_ tptp.mequiv @t36) (_ tptp.mnot @t33)) @t10))) % 0.44/0.64 (define @t38 () (lambda @t25 (_ (_ tptp.mforall_di @t37) @t10))) % 0.44/0.64 (define @t39 () (_ @t35 tptp.empty_set)) % 0.44/0.64 (define @t40 () (lambda @t24 (_ (_ (_ tptp.mequiv @t39) @t33) @t10))) % 0.44/0.64 (define @t41 () (lambda @t25 (_ (_ tptp.mforall_di @t40) @t10))) % 0.44/0.64 (define @t42 () (lambda @t24 (_ (_ (_ tptp.mor @t39) @t36) @t10))) % 0.44/0.64 (define @t43 () (lambda @t25 (_ (_ tptp.mforall_di @t42) @t10))) % 0.44/0.64 (define @t44 () (not (_ tptp.mlocal (_ tptp.mforall_di @t43)))) % 0.44/0.64 (define @t45 () (@var "Phi" (-> tptp.mworld Bool))) % 0.44/0.64 (define @t46 () (lambda (@list @t45) (_ @t45 tptp.mactual))) % 0.44/0.64 (define @t47 () (@var "A" (-> tptp.mworld Bool))) % 0.44/0.64 (define @t48 () (_ @t47 @t1)) % 0.44/0.64 (define @t49 () (lambda (@list @t47 @t1) (not @t48))) % 0.44/0.64 (define @t50 () (@var "B" (-> tptp.mworld Bool))) % 0.44/0.64 (define @t51 () (_ @t50 @t1)) % 0.44/0.64 (define @t52 () (@list @t47 @t50 @t1)) % 0.44/0.64 (define @t53 () (lambda @t52 (and @t48 @t51))) % 0.44/0.64 (define @t54 () (lambda @t52 (or @t48 @t51))) % 0.44/0.64 (define @t55 () (lambda @t52 (=> @t48 @t51))) % 0.44/0.64 (define @t56 () (lambda @t52 (= @t48 @t51))) % 0.44/0.64 (define @t57 () (_ @t45 @t4)) % 0.44/0.64 (define @t58 () (@list @t4)) % 0.44/0.64 (define @t59 () (@list @t45 @t1)) % 0.44/0.64 (define @t60 () (lambda @t59 (forall @t58 (=> @t6 @t57)))) % 0.44/0.64 (define @t61 () (lambda @t59 (exists @t58 (and @t6 @t57)))) % 0.44/0.64 (define @t62 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.44/0.64 (define @t63 () (_ (_ @t62 @t7) @t1)) % 0.44/0.64 (define @t64 () (forall @t9 (=> @t8 @t63))) % 0.44/0.64 (define @t65 () (@list @t62 @t1)) % 0.44/0.64 (define @t66 () (lambda @t65 @t64)) % 0.44/0.64 (define @t67 () (lambda @t65 (exists @t9 (and @t8 @t63)))) % 0.44/0.64 (define @t68 () (tptp.singleton @t7)) % 0.44/0.64 (define @t69 () (@var "BOUND_VARIABLE_9527" $$unsorted)) % 0.44/0.64 (define @t70 () (tptp.set_difference @t68 @t69)) % 0.44/0.64 (define @t71 () (not (tptp.eiw_di @t7 tptp.mactual))) % 0.44/0.64 (define @t72 () (@list @t7 @t69)) % 0.44/0.64 (define @t73 () (forall @t72 (or @t71 (not (tptp.eiw_di @t69 tptp.mactual)) (tptp.qmltpeq @t70 tptp.empty_set tptp.mactual) (tptp.qmltpeq @t70 @t68 tptp.mactual)))) % 0.44/0.64 (define @t74 () (tptp.qmltpeq @t70 @t68 @t1)) % 0.44/0.64 (define @t75 () (tptp.qmltpeq @t70 tptp.empty_set @t1)) % 0.44/0.64 (define @t76 () (not (tptp.eiw_di @t69 @t1))) % 0.44/0.64 (define @t77 () (tptp.eiw_di @t7 @t1)) % 0.44/0.64 (define @t78 () (not @t77)) % 0.44/0.64 (define @t79 () (or @t78 @t76 @t75 @t74)) % 0.44/0.64 (define @t80 () (lambda @t3 (forall @t72 @t79))) % 0.44/0.64 (define @t81 () (_ @t80 tptp.mactual)) % 0.44/0.64 (define @t82 () (or @t76 @t75 @t74)) % 0.44/0.64 (define @t83 () (or @t78 @t82)) % 0.44/0.64 (define @t84 () (forall @t72 @t83)) % 0.44/0.64 (define @t85 () (@list @t69)) % 0.44/0.64 (define @t86 () (forall @t85 @t83)) % 0.44/0.64 (define @t87 () (forall @t85 @t82)) % 0.44/0.64 (define @t88 () (@var "BOUND_VARIABLE_9506" $$unsorted)) % 0.44/0.64 (define @t89 () (@list @t88)) % 0.44/0.64 (define @t90 () (or @t78 @t87)) % 0.44/0.64 (define @t91 () (tptp.set_difference @t68 @t88)) % 0.44/0.64 (define @t92 () (@list @t88)) % 0.44/0.64 (define @t93 () (forall @t92 (or (not (tptp.eiw_di @t88 @t1)) (tptp.qmltpeq @t91 tptp.empty_set @t1) (tptp.qmltpeq @t91 @t68 @t1)))) % 0.44/0.64 (define @t94 () (tptp.singleton @t20)) % 0.44/0.64 (define @t95 () (tptp.set_difference @t94 @t88)) % 0.44/0.64 (define @t96 () (tptp.set_difference @t94 @t7)) % 0.44/0.64 (define @t97 () (tptp.qmltpeq @t96 @t94 @t10)) % 0.44/0.64 (define @t98 () (tptp.qmltpeq @t96 tptp.empty_set @t10)) % 0.44/0.64 (define @t99 () (not (tptp.eiw_di @t7 @t10))) % 0.44/0.64 (define @t100 () (forall @t9 (or @t99 @t98 @t97))) % 0.44/0.64 (define @t101 () (@list @t7)) % 0.44/0.64 (define @t102 () (lambda @t25 @t100)) % 0.44/0.64 (define @t103 () (or @t78 (_ @t102 @t7 @t1))) % 0.44/0.64 (define @t104 () (forall @t9 @t103)) % 0.44/0.64 (define @t105 () (lambda @t3 @t104)) % 0.44/0.64 (define @t106 () (_ @t62 @t7 @t1)) % 0.44/0.64 (define @t107 () (lambda @t65 (forall @t9 (or @t78 @t106)))) % 0.44/0.64 (define @t108 () (tptp.qmltpeq @t96 @t94 @t1)) % 0.44/0.64 (define @t109 () (tptp.qmltpeq @t96 tptp.empty_set @t1)) % 0.44/0.64 (define @t110 () (_ @t34 @t7)) % 0.44/0.64 (define @t111 () (_ tptp.qmltpeq @t96)) % 0.44/0.64 (define @t112 () (_ tptp.qmltpeq @t110)) % 0.44/0.64 (define @t113 () (_ (_ @t112 @t27) @t1)) % 0.44/0.64 (define @t114 () (_ (_ @t112 tptp.empty_set) @t1)) % 0.44/0.64 (define @t115 () (or @t78 @t114 @t113)) % 0.44/0.64 (define @t116 () (or @t114 @t113)) % 0.44/0.64 (define @t117 () (_ @t36 @t10)) % 0.44/0.64 (define @t118 () (_ @t39 @t10)) % 0.44/0.64 (define @t119 () (or @t118 @t117)) % 0.44/0.64 (define @t120 () (lambda @t24 @t119)) % 0.44/0.64 (define @t121 () (_ @t120 @t7 @t1)) % 0.44/0.64 (define @t122 () (or @t78 @t121)) % 0.44/0.64 (define @t123 () (forall @t9 @t122)) % 0.44/0.64 (define @t124 () (lambda @t3 @t123)) % 0.44/0.64 (define @t125 () (_ @t36 @t1)) % 0.44/0.64 (define @t126 () (_ @t39 @t1)) % 0.44/0.64 (define @t127 () (lambda @t3 (or @t126 @t125))) % 0.44/0.64 (define @t128 () (@list @t50 @t1)) % 0.44/0.64 (define @t129 () (lambda @t128 (or @t126 @t51))) % 0.44/0.64 (define @t130 () (_ @t54 @t39)) % 0.44/0.64 (define @t131 () (lambda @t24 (_ (_ @t130 @t36) @t10))) % 0.44/0.64 (define @t132 () (lambda @t25 (_ (_ @t107 @t131) @t10))) % 0.44/0.64 (define @t133 () (not @t8)) % 0.44/0.64 (define @t134 () (or @t133 @t63)) % 0.44/0.64 (define @t135 () (@quantifiers_skolemize @t73 0)) % 0.44/0.64 (define @t136 () (tptp.singleton @t135)) % 0.44/0.64 (define @t137 () (@quantifiers_skolemize @t73 1)) % 0.44/0.64 (define @t138 () (tptp.set_difference @t136 @t137)) % 0.44/0.65 (define @t139 () (tptp.qmltpeq @t138 @t136 tptp.mactual)) % 0.44/0.65 (define @t140 () (tptp.qmltpeq @t138 tptp.empty_set tptp.mactual)) % 0.44/0.65 (define @t141 () (tptp.eiw_di @t137 tptp.mactual)) % 0.44/0.65 (define @t142 () (not @t141)) % 0.44/0.65 (define @t143 () (tptp.eiw_di @t135 tptp.mactual)) % 0.44/0.65 (define @t144 () (not @t143)) % 0.44/0.65 (define @t145 () (or @t144 @t142 @t140 @t139)) % 0.44/0.65 (define @t146 () (@list true)) % 0.44/0.65 (define @t147 () (@list @t145)) % 0.44/0.65 (define @t148 () (@var "BOUND_VARIABLE_9389" $$unsorted)) % 0.44/0.65 (define @t149 () (tptp.set_difference @t68 @t148)) % 0.44/0.65 (define @t150 () (@list @t7 @t148)) % 0.44/0.65 (define @t151 () (forall @t150 (or @t71 (not (tptp.eiw_di @t148 tptp.mactual)) (= (tptp.in @t7 @t148 tptp.mactual) (tptp.qmltpeq @t149 tptp.empty_set tptp.mactual))))) % 0.44/0.65 (define @t152 () (= (tptp.in @t7 @t148 @t1) (tptp.qmltpeq @t149 tptp.empty_set @t1))) % 0.44/0.65 (define @t153 () (not (tptp.eiw_di @t148 @t1))) % 0.44/0.65 (define @t154 () (or @t78 @t153 @t152)) % 0.44/0.65 (define @t155 () (lambda @t3 (forall @t150 @t154))) % 0.44/0.65 (define @t156 () (_ @t155 tptp.mactual)) % 0.44/0.65 (define @t157 () (or @t153 @t152)) % 0.44/0.65 (define @t158 () (or @t78 @t157)) % 0.44/0.65 (define @t159 () (forall @t150 @t158)) % 0.44/0.65 (define @t160 () (@list @t148)) % 0.44/0.65 (define @t161 () (forall @t160 @t158)) % 0.44/0.65 (define @t162 () (forall @t160 @t157)) % 0.44/0.65 (define @t163 () (@var "BOUND_VARIABLE_9366" $$unsorted)) % 0.44/0.65 (define @t164 () (@list @t163)) % 0.44/0.65 (define @t165 () (or @t78 @t162)) % 0.44/0.65 (define @t166 () (@list @t163)) % 0.44/0.65 (define @t167 () (forall @t166 (or (not (tptp.eiw_di @t163 @t1)) (= (tptp.in @t7 @t163 @t1) (tptp.qmltpeq (tptp.set_difference @t68 @t163) tptp.empty_set @t1))))) % 0.44/0.65 (define @t168 () (tptp.in @t20 @t7 @t10)) % 0.44/0.65 (define @t169 () (forall @t9 (or @t99 (= @t168 @t98)))) % 0.44/0.65 (define @t170 () (lambda @t25 @t169)) % 0.44/0.65 (define @t171 () (or @t78 (_ @t170 @t7 @t1))) % 0.44/0.65 (define @t172 () (forall @t9 @t171)) % 0.44/0.65 (define @t173 () (lambda @t3 @t172)) % 0.44/0.65 (define @t174 () (tptp.in @t20 @t7 @t1)) % 0.44/0.65 (define @t175 () (_ (_ @t31 @t7) @t1)) % 0.44/0.65 (define @t176 () (= @t175 @t114)) % 0.44/0.65 (define @t177 () (or @t78 @t176)) % 0.44/0.65 (define @t178 () (_ @t33 @t10)) % 0.44/0.65 (define @t179 () (= @t178 @t118)) % 0.44/0.65 (define @t180 () (lambda @t24 @t179)) % 0.44/0.65 (define @t181 () (_ @t180 @t7 @t1)) % 0.44/0.65 (define @t182 () (or @t78 @t181)) % 0.44/0.65 (define @t183 () (forall @t9 @t182)) % 0.44/0.65 (define @t184 () (lambda @t3 @t183)) % 0.44/0.65 (define @t185 () (_ @t33 @t1)) % 0.44/0.65 (define @t186 () (lambda @t3 (= @t185 @t126))) % 0.44/0.65 (define @t187 () (lambda @t128 (= @t126 @t51))) % 0.44/0.65 (define @t188 () (_ @t56 @t39)) % 0.44/0.65 (define @t189 () (lambda @t24 (_ (_ @t188 @t33) @t10))) % 0.44/0.65 (define @t190 () (tptp.in @t135 @t137 tptp.mactual)) % 0.44/0.65 (define @t191 () (or @t144 @t142 (= @t190 @t140))) % 0.44/0.65 (define @t192 () (@list @t135 @t137)) % 0.44/0.65 (define @t193 () (= @t140 @t190)) % 0.44/0.65 (define @t194 () (or @t144 @t142 @t193)) % 0.44/0.65 (define @t195 () (@list false)) % 0.44/0.65 (define @t196 () (@list false false false)) % 0.44/0.65 (define @t197 () (@var "BOUND_VARIABLE_9287" $$unsorted)) % 0.44/0.65 (define @t198 () (tptp.set_difference @t68 @t197)) % 0.44/0.65 (define @t199 () (@list @t7 @t197)) % 0.44/0.65 (define @t200 () (forall @t199 (or @t71 (not (tptp.eiw_di @t197 tptp.mactual)) (= (not (tptp.in @t7 @t197 tptp.mactual)) (tptp.qmltpeq @t198 @t68 tptp.mactual))))) % 0.44/0.65 (define @t201 () (= (not (tptp.in @t7 @t197 @t1)) (tptp.qmltpeq @t198 @t68 @t1))) % 0.44/0.65 (define @t202 () (not (tptp.eiw_di @t197 @t1))) % 0.44/0.65 (define @t203 () (or @t78 @t202 @t201)) % 0.44/0.65 (define @t204 () (lambda @t3 (forall @t199 @t203))) % 0.44/0.65 (define @t205 () (_ @t204 tptp.mactual)) % 0.44/0.65 (define @t206 () (or @t202 @t201)) % 0.44/0.65 (define @t207 () (or @t78 @t206)) % 0.44/0.65 (define @t208 () (forall @t199 @t207)) % 0.44/0.65 (define @t209 () (@list @t197)) % 0.44/0.65 (define @t210 () (forall @t209 @t207)) % 0.44/0.65 (define @t211 () (forall @t209 @t206)) % 0.44/0.65 (define @t212 () (@var "BOUND_VARIABLE_9262" $$unsorted)) % 0.44/0.65 (define @t213 () (@list @t212)) % 0.44/0.65 (define @t214 () (or @t78 @t211)) % 0.44/0.65 (define @t215 () (@list @t212)) % 0.44/0.65 (define @t216 () (forall @t215 (or (not (tptp.eiw_di @t212 @t1)) (= (not (tptp.in @t7 @t212 @t1)) (tptp.qmltpeq (tptp.set_difference @t68 @t212) @t68 @t1))))) % 0.44/0.65 (define @t217 () (forall @t9 (or @t99 (= (not @t168) @t97)))) % 0.44/0.65 (define @t218 () (lambda @t25 @t217)) % 0.44/0.65 (define @t219 () (or @t78 (_ @t218 @t7 @t1))) % 0.44/0.65 (define @t220 () (forall @t9 @t219)) % 0.44/0.65 (define @t221 () (lambda @t3 @t220)) % 0.44/0.65 (define @t222 () (not @t175)) % 0.44/0.65 (define @t223 () (= @t222 @t113)) % 0.44/0.65 (define @t224 () (or @t78 @t223)) % 0.44/0.65 (define @t225 () (= @t117 (not @t178))) % 0.44/0.65 (define @t226 () (lambda @t24 @t225)) % 0.44/0.65 (define @t227 () (_ @t226 @t7 @t1)) % 0.44/0.65 (define @t228 () (or @t78 @t227)) % 0.44/0.65 (define @t229 () (forall @t9 @t228)) % 0.44/0.65 (define @t230 () (lambda @t3 @t229)) % 0.44/0.65 (define @t231 () (not @t185)) % 0.44/0.65 (define @t232 () (lambda @t3 @t231)) % 0.44/0.65 (define @t233 () (_ @t232 @t1)) % 0.44/0.65 (define @t234 () (lambda @t3 (= @t233 @t125))) % 0.44/0.65 (define @t235 () (_ @t49 @t33)) % 0.44/0.65 (define @t236 () (lambda @t128 (= @t125 @t51))) % 0.44/0.65 (define @t237 () (_ @t56 @t36)) % 0.44/0.65 (define @t238 () (lambda @t24 (_ (_ @t237 @t235) @t10))) % 0.44/0.65 (define @t239 () (not @t190)) % 0.44/0.65 (define @t240 () (or @t144 @t142 (= @t239 @t139))) % 0.44/0.65 (define @t241 () (= @t139 @t239)) % 0.44/0.65 (define @t242 () (or @t144 @t142 @t241)) % 0.44/0.65 (define @t243 () (not @t241)) % 0.44/0.65 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.44/0.65 (assume @p2 (forall (@list @t1 @t4 @t5) (=> (and (_ @t2 @t5) @t6) (_ (_ tptp.mrel @t5) @t4)))) % 0.44/0.65 (assume @p3 (forall @t3 (exists @t9 @t8))) % 0.44/0.65 (assume @p4 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t12 (_ (_ @t11 @t7) @t10))))) % 0.44/0.65 (assume @p5 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t12 (_ (_ tptp.mforall_di (lambda @t16 (_ (_ (_ tptp.mimplies @t15) (_ @t14 @t7)) @t10))) @t10))))) % 0.44/0.65 (assume @p6 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t12 (_ (_ tptp.mforall_di (lambda @t16 (_ (_ tptp.mforall_di (lambda (@list @t17 @t10) (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t15) (_ @t14 @t17))) (_ @t11 @t17)) @t10))) @t10))) @t10))))) % 0.44/0.65 (assume @p7 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ @t22 (_ (_ tptp.qmltpeq (_ (_ tptp.set_difference @t20) @t18)) (_ (_ tptp.set_difference @t19) @t18))) @t10))) @t10))) @t10))))) % 0.44/0.65 (assume @p8 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ @t22 (_ (_ tptp.qmltpeq (_ @t26 @t20)) (_ @t26 @t19))) @t10))) @t10))) @t10))))) % 0.44/0.65 (assume @p9 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mforall_di (lambda @t24 (_ (_ @t22 (_ (_ tptp.qmltpeq @t27) (_ tptp.singleton @t19))) @t10))) @t10))))) % 0.44/0.65 (assume @p10 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mforall_di (lambda @t24 (_ (_ (_ tptp.mimplies (_ @t29 @t28)) (_ tptp.empty @t19)) @t10))) @t10))))) % 0.44/0.65 (assume @p11 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ (_ tptp.mimplies (_ @t29 (_ @t31 @t18))) (_ @t30 @t18)) @t10))) @t10))) @t10))))) % 0.44/0.65 (assume @p12 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ (_ tptp.mimplies (_ @t29 (_ @t32 @t20))) (_ @t32 @t19)) @t10))) @t10))) @t10))))) % 0.44/0.65 (assume @p13 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mforall_di (lambda @t24 (_ (_ (_ tptp.mimplies @t33) (_ tptp.mnot (_ @t30 @t20))) @t10))) @t10))))) % 0.44/0.65 (assume @p14 (_ tptp.mlocal (_ tptp.empty tptp.empty_set))) % 0.44/0.65 (assume @p15 (_ tptp.mlocal (_ tptp.mforall_di @t38))) % 0.44/0.65 (assume @p16 (_ tptp.mlocal (_ tptp.mforall_di @t41))) % 0.44/0.65 (assume @p17 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t25 (_ @t28 @t10))))) % 0.44/0.65 (assume @p18 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t25 (_ (_ tptp.mnot @t28) @t10))))) % 0.44/0.65 (assume @p19 @t44) % 0.44/0.65 (assume @p20 true) % 0.44/0.65 (step @p21 (= tptp.mlocal @t46) :rule refl :args (@t46)) % 0.44/0.65 (step @p22 (= tptp.mnot @t49) :rule refl :args (@t49)) % 0.44/0.65 (step @p23 (= tptp.mand @t53) :rule refl :args (@t53)) % 0.44/0.65 (step @p24 (= tptp.mor @t54) :rule refl :args (@t54)) % 0.44/0.65 (step @p25 (= tptp.mimplies @t55) :rule refl :args (@t55)) % 0.44/0.65 (step @p26 (= tptp.mequiv @t56) :rule refl :args (@t56)) % 0.44/0.65 (step @p27 (= tptp.mbox @t60) :rule refl :args (@t60)) % 0.44/0.65 (step @p28 (= tptp.mdia @t61) :rule refl :args (@t61)) % 0.44/0.65 (step @p29 (= tptp.mforall_di @t66) :rule refl :args (@t66)) % 0.44/0.65 (step @p30 (= tptp.mexists_di @t67) :rule refl :args (@t67)) % 0.44/0.65 (step @p31 :rule beta-reduce :args ((= @t81 @t73))) % 0.44/0.65 (step @p32 :rule beta-reduce :args ((= (_ @t46 @t80) @t81))) % 0.44/0.65 (step @p33 :rule trans :premises (@p32 @p31)) % 0.44/0.65 (step @p34 :rule aci_norm :args ((= @t83 @t79))) % 0.44/0.65 (step @p35 :rule cong :premises (@p34) :args (@t84)) % 0.44/0.65 (step @p36 :rule quant-merge-prenex :args ((= (forall @t9 @t86) @t84))) % 0.44/0.65 (step @p37 :rule alpha_equiv :args (@t87 (@list @t69) @t89)) % 0.44/0.65 (step @p38 :rule refl :args (@t78)) % 0.44/0.65 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t90)) % 0.44/0.65 (step @p40 :rule quant-miniscope-or :args ((= @t86 @t90))) % 0.44/0.65 (step @p41 :rule trans :premises (@p40 @p39)) % 0.44/0.65 (step @p42 :rule symm :premises (@p41)) % 0.44/0.65 (step @p43 :rule cong :premises (@p42) :args ((forall @t9 (or @t78 @t93)))) % 0.44/0.65 (step @p44 :rule trans :premises (@p43 @p36)) % 0.44/0.65 (step @p45 :rule trans :premises (@p44 @p35)) % 0.44/0.65 (step @p46 :rule beta-reduce :args ((= (_ (lambda @t25 (forall @t92 (or (not (tptp.eiw_di @t88 @t10)) (tptp.qmltpeq @t95 tptp.empty_set @t10) (tptp.qmltpeq @t95 @t94 @t10)))) @t7 @t1) @t93))) % 0.44/0.65 (step @p47 :rule refl :args (@t1)) % 0.44/0.65 (step @p48 :rule refl :args (@t7)) % 0.44/0.65 (step @p49 :rule alpha_equiv :args (@t100 @t101 @t89)) % 0.44/0.65 (step @p50 :rule cong :premises (@p49) :args (@t102)) % 0.44/0.65 (step @p51 :rule ho_cong :premises (@p50 @p48 @p47)) % 0.44/0.65 (step @p52 :rule trans :premises (@p51 @p46)) % 0.44/0.65 (step @p53 :rule refl :args (@t78)) % 0.44/0.65 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t103)) % 0.44/0.65 (step @p55 :rule cong :premises (@p54) :args (@t104)) % 0.44/0.65 (step @p56 :rule trans :premises (@p55 @p45)) % 0.44/0.65 (step @p57 :rule cong :premises (@p56) :args (@t105)) % 0.44/0.65 (step @p58 :rule beta-reduce :args ((= (_ @t107 @t102) @t105))) % 0.44/0.65 (step @p59 :rule trans :premises (@p58 @p57)) % 0.44/0.65 (step @p60 :rule beta-reduce :args ((= (_ (lambda @t3 (forall @t9 (or @t78 @t109 @t108))) @t10) @t100))) % 0.44/0.65 (step @p61 :rule refl :args (@t10)) % 0.44/0.65 (step @p62 :rule refl :args ((tptp.qmltpeq @t110 @t27 @t1))) % 0.44/0.65 (step @p63 :rule refl :args (@t94)) % 0.44/0.65 (step @p64 :rule refl :args ((tptp.set_difference @t27 @t7))) % 0.44/0.65 (step @p65 :rule cong :premises (@p63 @p48) :args (@t96)) % 0.44/0.65 (step @p66 :rule trans :premises (@p65 @p64)) % 0.44/0.65 (step @p67 :rule cong :premises (@p66 @p63 @p47) :args (@t108)) % 0.44/0.65 (step @p68 :rule trans :premises (@p67 @p62)) % 0.44/0.65 (step @p69 :rule refl :args (tptp.qmltpeq)) % 0.44/0.65 (step @p70 :rule ho_cong :premises (@p69 @p66)) % 0.44/0.65 (step @p71 :rule ho_cong :premises (@p70 @p63)) % 0.44/0.65 (step @p72 :rule ho_cong :premises (@p71 @p47)) % 0.44/0.65 (step @p73 :rule cong :premises (@p72 @p68) :args ((= (_ (_ @t111 @t94) @t1) @t108))) % 0.44/0.65 (step @p74 :rule symm :premises (@p73)) % 0.44/0.65 (step @p75 :rule refl :args (@t113)) % 0.44/0.65 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 0.44/0.65 (step @p77 :rule refl :args (@t27)) % 0.44/0.65 (step @p78 :rule cong :premises (@p77 @p63) :args ((= @t27 @t94))) % 0.44/0.65 (step @p79 :rule symm :premises (@p78)) % 0.44/0.65 (step @p80 :rule eq_resolve :premises (@p77 @p79)) % 0.44/0.65 (step @p81 :rule refl :args (tptp.set_difference)) % 0.44/0.65 (step @p82 :rule ho_cong :premises (@p81 @p63)) % 0.44/0.65 (step @p83 :rule ho_cong :premises (@p82 @p48)) % 0.44/0.65 (step @p84 :rule cong :premises (@p83 @p66) :args ((= (_ (_ tptp.set_difference @t94) @t7) @t96))) % 0.44/0.65 (step @p85 :rule symm :premises (@p84)) % 0.44/0.65 (step @p86 :rule refl :args (@t110)) % 0.44/0.65 (step @p87 :rule eq_resolve :premises (@p86 @p85)) % 0.44/0.65 (step @p88 :rule ho_cong :premises (@p81 @p80)) % 0.44/0.65 (step @p89 :rule ho_cong :premises (@p88 @p48)) % 0.44/0.65 (step @p90 :rule trans :premises (@p89 @p87)) % 0.44/0.65 (step @p91 :rule ho_cong :premises (@p69 @p90)) % 0.44/0.65 (step @p92 :rule ho_cong :premises (@p91 @p80)) % 0.44/0.65 (step @p93 :rule ho_cong :premises (@p92 @p47)) % 0.44/0.65 (step @p94 :rule trans :premises (@p93 @p76)) % 0.44/0.65 (step @p95 :rule refl :args ((tptp.qmltpeq @t110 tptp.empty_set @t1))) % 0.44/0.65 (step @p96 :rule refl :args (tptp.empty_set)) % 0.44/0.65 (step @p97 :rule cong :premises (@p66 @p96 @p47) :args (@t109)) % 0.44/0.65 (step @p98 :rule trans :premises (@p97 @p95)) % 0.44/0.65 (step @p99 :rule ho_cong :premises (@p70 @p96)) % 0.44/0.65 (step @p100 :rule ho_cong :premises (@p99 @p47)) % 0.44/0.65 (step @p101 :rule cong :premises (@p100 @p98) :args ((= (_ (_ @t111 tptp.empty_set) @t1) @t109))) % 0.44/0.65 (step @p102 :rule symm :premises (@p101)) % 0.44/0.65 (step @p103 :rule refl :args (@t114)) % 0.44/0.65 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 0.44/0.65 (step @p105 :rule ho_cong :premises (@p91 @p96)) % 0.44/0.65 (step @p106 :rule ho_cong :premises (@p105 @p47)) % 0.44/0.65 (step @p107 :rule trans :premises (@p106 @p104)) % 0.44/0.65 (step @p108 :rule nary_cong :premises (@p38 @p107 @p94) :args (@t115)) % 0.44/0.65 (step @p109 :rule cong :premises (@p108) :args ((forall @t9 @t115))) % 0.44/0.65 (step @p110 :rule aci_norm :args ((= (or @t78 @t116) @t115))) % 0.44/0.65 (step @p111 :rule beta-reduce :args ((= @t121 @t116))) % 0.44/0.65 (step @p112 :rule nary_cong :premises (@p53 @p111) :args (@t122)) % 0.44/0.65 (step @p113 :rule trans :premises (@p112 @p110)) % 0.44/0.65 (step @p114 :rule cong :premises (@p113) :args (@t123)) % 0.44/0.65 (step @p115 :rule trans :premises (@p114 @p109)) % 0.44/0.65 (step @p116 :rule cong :premises (@p115) :args (@t124)) % 0.44/0.65 (step @p117 :rule beta-reduce :args ((= (_ @t107 @t120) @t124))) % 0.44/0.65 (step @p118 :rule trans :premises (@p117 @p116)) % 0.44/0.65 (step @p119 :rule beta-reduce :args ((= (_ @t127 @t10) @t119))) % 0.44/0.65 (step @p120 :rule beta-reduce :args ((= (_ @t129 @t36) @t127))) % 0.44/0.65 (step @p121 :rule refl :args (@t36)) % 0.44/0.65 (step @p122 :rule beta-reduce :args ((= @t130 @t129))) % 0.44/0.65 (step @p123 :rule ho_cong :premises (@p122 @p121)) % 0.44/0.65 (step @p124 :rule trans :premises (@p123 @p120)) % 0.44/0.65 (step @p125 :rule ho_cong :premises (@p124 @p61)) % 0.44/0.65 (step @p126 :rule trans :premises (@p125 @p119)) % 0.44/0.65 (step @p127 :rule cong :premises (@p126) :args (@t131)) % 0.44/0.65 (step @p128 :rule refl :args (@t107)) % 0.44/0.65 (step @p129 :rule ho_cong :premises (@p128 @p127)) % 0.44/0.65 (step @p130 :rule trans :premises (@p129 @p118)) % 0.44/0.65 (step @p131 :rule ho_cong :premises (@p130 @p61)) % 0.44/0.65 (step @p132 :rule trans :premises (@p131 @p60)) % 0.44/0.65 (step @p133 :rule cong :premises (@p132) :args (@t132)) % 0.44/0.65 (step @p134 :rule ho_cong :premises (@p128 @p133)) % 0.44/0.65 (step @p135 :rule trans :premises (@p134 @p59)) % 0.44/0.65 (step @p136 :rule refl :args (@t46)) % 0.44/0.65 (step @p137 :rule ho_cong :premises (@p136 @p135)) % 0.44/0.65 (step @p138 :rule trans :premises (@p137 @p33)) % 0.44/0.65 (step @p139 :rule cong :premises (@p138) :args ((not (_ @t46 (_ @t107 @t132))))) % 0.44/0.65 (step @p140 :rule refl :args (@t39)) % 0.44/0.65 (step @p141 :rule ho_cong :premises (@p24 @p140)) % 0.44/0.65 (step @p142 :rule ho_cong :premises (@p141 @p121)) % 0.44/0.65 (step @p143 :rule ho_cong :premises (@p142 @p61)) % 0.44/0.65 (step @p144 :rule cong :premises (@p143) :args (@t42)) % 0.44/0.65 (step @p145 :rule refl :args (@t106)) % 0.44/0.65 (step @p146 :rule refl :args (@t63)) % 0.44/0.65 (step @p147 :rule cong :premises (@p146 @p145) :args ((= @t63 @t106))) % 0.44/0.65 (step @p148 :rule symm :premises (@p147)) % 0.44/0.65 (step @p149 :rule eq_resolve :premises (@p146 @p148)) % 0.44/0.65 (step @p150 :rule refl :args (@t77)) % 0.44/0.65 (step @p151 :rule refl :args (@t8)) % 0.44/0.65 (step @p152 :rule cong :premises (@p151 @p150) :args ((= @t8 @t77))) % 0.44/0.65 (step @p153 :rule symm :premises (@p152)) % 0.44/0.65 (step @p154 :rule eq_resolve :premises (@p151 @p153)) % 0.44/0.65 (step @p155 :rule cong :premises (@p154) :args (@t133)) % 0.44/0.65 (step @p156 :rule nary_cong :premises (@p155 @p149) :args (@t134)) % 0.44/0.65 (step @p157 :rule cong :premises (@p156) :args ((forall @t9 @t134))) % 0.44/0.65 (step @p158 :rule bool-impl-elim :args (@t8 @t63)) % 0.44/0.65 (step @p159 :rule cong :premises (@p158) :args (@t64)) % 0.44/0.65 (step @p160 :rule trans :premises (@p159 @p157)) % 0.44/0.65 (step @p161 :rule cong :premises (@p160) :args (@t66)) % 0.44/0.65 (step @p162 :rule trans :premises (@p29 @p161)) % 0.44/0.65 (step @p163 :rule ho_cong :premises (@p162 @p144)) % 0.44/0.65 (step @p164 :rule ho_cong :premises (@p163 @p61)) % 0.44/0.65 (step @p165 :rule cong :premises (@p164) :args (@t43)) % 0.44/0.65 (step @p166 :rule ho_cong :premises (@p162 @p165)) % 0.44/0.65 (step @p167 :rule ho_cong :premises (@p21 @p166)) % 0.44/0.65 (step @p168 :rule cong :premises (@p167) :args (@t44)) % 0.44/0.65 (step @p169 :rule trans :premises (@p168 @p139)) % 0.44/0.65 (step @p170 :rule eq_resolve :premises (@p19 @p169)) % 0.44/0.65 (step @p171 :rule skolemize :premises (@p170)) % 0.44/0.65 (step @p172 :rule cnf_or_neg :args (@t145 2)) % 0.44/0.65 (step @p173 :rule chain_m_resolution :premises (@p172 @p171) :args ((not @t140) @t146 @t147)) % 0.44/0.65 (step @p174 :rule beta-reduce :args ((= @t156 @t151))) % 0.44/0.65 (step @p175 :rule beta-reduce :args ((= (_ @t46 @t155) @t156))) % 0.44/0.65 (step @p176 :rule trans :premises (@p175 @p174)) % 0.44/0.65 (step @p177 :rule aci_norm :args ((= @t158 @t154))) % 0.44/0.65 (step @p178 :rule cong :premises (@p177) :args (@t159)) % 0.44/0.65 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