%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET926^8 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n026.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 0.65s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET926^8 : TPTP v9.2.1. Released v8.1.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n026.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 16:18:25 EDT 2026 % 0.15/0.34 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.44/0.65 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.44/0.65 % SZS status Theorem % 0.44/0.65 % SZS output start Proof % 0.44/0.65 ( % 0.44/0.65 (declare-sort $$unsorted 0) % 0.44/0.65 (declare-sort tptp.mworld 0) % 0.44/0.65 (declare-const tptp.mactual tptp.mworld) % 0.44/0.65 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.44/0.65 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 0.44/0.65 (declare-const tptp.empty (-> $$unsorted tptp.mworld Bool)) % 0.44/0.65 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.in (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.44/0.65 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.qmltpeq (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.44/0.65 (declare-const tptp.empty_set $$unsorted) % 0.44/0.65 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.44/0.65 (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)))))) % 0.44/0.65 (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))))))) % 0.44/0.65 (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))))))) % 0.44/0.65 (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))))))) % 0.44/0.65 (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))))))) % 0.44/0.65 (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)))))))) % 0.44/0.65 (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)))))))) % 0.44/0.65 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.44/0.65 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.44/0.65 (define @t1 () (@var "W" tptp.mworld)) % 0.44/0.65 (define @t2 () (_ tptp.mrel @t1)) % 0.44/0.65 (define @t3 () (@list @t1)) % 0.44/0.65 (define @t4 () (@var "X" $$unsorted)) % 0.44/0.65 (define @t5 () (_ (_ tptp.eiw_di @t4) @t1)) % 0.44/0.65 (define @t6 () (@list @t4)) % 0.44/0.65 (define @t7 () (@var "__flatten_var_0" tptp.mworld)) % 0.44/0.65 (define @t8 () (_ tptp.qmltpeq @t4)) % 0.44/0.65 (define @t9 () (@list @t4 @t7)) % 0.44/0.65 (define @t10 () (@var "Y" $$unsorted)) % 0.44/0.65 (define @t11 () (_ tptp.qmltpeq @t10)) % 0.44/0.65 (define @t12 () (_ @t8 @t10)) % 0.44/0.65 (define @t13 () (@list @t10 @t7)) % 0.44/0.65 (define @t14 () (@var "Z" $$unsorted)) % 0.44/0.65 (define @t15 () (@var "C" $$unsorted)) % 0.44/0.65 (define @t16 () (@var "B" $$unsorted)) % 0.44/0.65 (define @t17 () (@var "A" $$unsorted)) % 0.44/0.65 (define @t18 () (_ (_ tptp.qmltpeq @t17) @t16)) % 0.44/0.65 (define @t19 () (_ tptp.mimplies @t18)) % 0.44/0.65 (define @t20 () (@list @t15 @t7)) % 0.44/0.65 (define @t21 () (@list @t16 @t7)) % 0.44/0.65 (define @t22 () (@list @t17 @t7)) % 0.44/0.65 (define @t23 () (_ tptp.set_difference @t15)) % 0.44/0.65 (define @t24 () (_ tptp.singleton @t17)) % 0.44/0.65 (define @t25 () (_ tptp.empty @t17)) % 0.44/0.65 (define @t26 () (_ tptp.mand @t18)) % 0.44/0.65 (define @t27 () (_ tptp.in @t16)) % 0.44/0.65 (define @t28 () (_ tptp.in @t17)) % 0.44/0.65 (define @t29 () (_ tptp.in @t15)) % 0.44/0.65 (define @t30 () (_ @t28 @t16)) % 0.44/0.65 (define @t31 () (_ tptp.set_difference @t24)) % 0.44/0.65 (define @t32 () (_ tptp.qmltpeq (_ @t31 @t16))) % 0.44/0.65 (define @t33 () (_ @t32 @t24)) % 0.44/0.65 (define @t34 () (lambda @t21 (_ (_ (_ tptp.mequiv @t33) (_ tptp.mnot @t30)) @t7))) % 0.44/0.65 (define @t35 () (lambda @t22 (_ (_ tptp.mforall_di @t34) @t7))) % 0.44/0.65 (define @t36 () (_ @t32 tptp.empty_set)) % 0.44/0.65 (define @t37 () (lambda @t21 (_ (_ (_ tptp.mequiv @t36) @t30) @t7))) % 0.44/0.65 (define @t38 () (lambda @t22 (_ (_ tptp.mforall_di @t37) @t7))) % 0.44/0.65 (define @t39 () (lambda @t21 (_ (_ (_ tptp.mor @t36) @t33) @t7))) % 0.44/0.65 (define @t40 () (lambda @t22 (_ (_ tptp.mforall_di @t39) @t7))) % 0.44/0.65 (define @t41 () (not (_ tptp.mlocal (_ tptp.mforall_di @t40)))) % 0.44/0.65 (define @t42 () (@var "Phi" (-> tptp.mworld Bool))) % 0.44/0.65 (define @t43 () (lambda (@list @t42) (_ @t42 tptp.mactual))) % 0.44/0.65 (define @t44 () (@var "A" (-> tptp.mworld Bool))) % 0.44/0.65 (define @t45 () (_ @t44 @t1)) % 0.44/0.65 (define @t46 () (lambda (@list @t44 @t1) (not @t45))) % 0.44/0.65 (define @t47 () (@var "B" (-> tptp.mworld Bool))) % 0.44/0.65 (define @t48 () (_ @t47 @t1)) % 0.44/0.65 (define @t49 () (@list @t44 @t47 @t1)) % 0.44/0.65 (define @t50 () (lambda @t49 (and @t45 @t48))) % 0.44/0.65 (define @t51 () (lambda @t49 (or @t45 @t48))) % 0.44/0.65 (define @t52 () (lambda @t49 (=> @t45 @t48))) % 0.44/0.65 (define @t53 () (lambda @t49 (= @t45 @t48))) % 0.44/0.65 (define @t54 () (@var "V" tptp.mworld)) % 0.44/0.65 (define @t55 () (_ @t42 @t54)) % 0.44/0.65 (define @t56 () (_ @t2 @t54)) % 0.44/0.65 (define @t57 () (@list @t54)) % 0.44/0.65 (define @t58 () (@list @t42 @t1)) % 0.44/0.65 (define @t59 () (lambda @t58 (forall @t57 (=> @t56 @t55)))) % 0.44/0.65 (define @t60 () (lambda @t58 (exists @t57 (and @t56 @t55)))) % 0.44/0.65 (define @t61 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.44/0.65 (define @t62 () (_ (_ @t61 @t4) @t1)) % 0.44/0.65 (define @t63 () (forall @t6 (=> @t5 @t62))) % 0.44/0.65 (define @t64 () (@list @t61 @t1)) % 0.44/0.65 (define @t65 () (lambda @t64 @t63)) % 0.44/0.65 (define @t66 () (lambda @t64 (exists @t6 (and @t5 @t62)))) % 0.44/0.65 (define @t67 () (tptp.singleton @t4)) % 0.44/0.65 (define @t68 () (@var "BOUND_VARIABLE_9508" $$unsorted)) % 0.44/0.65 (define @t69 () (tptp.set_difference @t67 @t68)) % 0.44/0.65 (define @t70 () (not (tptp.eiw_di @t4 tptp.mactual))) % 0.44/0.65 (define @t71 () (@list @t4 @t68)) % 0.44/0.65 (define @t72 () (forall @t71 (or @t70 (not (tptp.eiw_di @t68 tptp.mactual)) (tptp.qmltpeq @t69 tptp.empty_set tptp.mactual) (tptp.qmltpeq @t69 @t67 tptp.mactual)))) % 0.44/0.65 (define @t73 () (tptp.qmltpeq @t69 @t67 @t1)) % 0.44/0.65 (define @t74 () (tptp.qmltpeq @t69 tptp.empty_set @t1)) % 0.44/0.65 (define @t75 () (not (tptp.eiw_di @t68 @t1))) % 0.44/0.65 (define @t76 () (tptp.eiw_di @t4 @t1)) % 0.44/0.65 (define @t77 () (not @t76)) % 0.44/0.65 (define @t78 () (or @t77 @t75 @t74 @t73)) % 0.44/0.65 (define @t79 () (lambda @t3 (forall @t71 @t78))) % 0.44/0.65 (define @t80 () (_ @t79 tptp.mactual)) % 0.44/0.65 (define @t81 () (or @t75 @t74 @t73)) % 0.44/0.65 (define @t82 () (or @t77 @t81)) % 0.44/0.65 (define @t83 () (forall @t71 @t82)) % 0.44/0.65 (define @t84 () (@list @t68)) % 0.44/0.65 (define @t85 () (forall @t84 @t82)) % 0.44/0.65 (define @t86 () (forall @t84 @t81)) % 0.44/0.65 (define @t87 () (@var "BOUND_VARIABLE_9487" $$unsorted)) % 0.44/0.65 (define @t88 () (@list @t87)) % 0.44/0.65 (define @t89 () (or @t77 @t86)) % 0.44/0.65 (define @t90 () (tptp.set_difference @t67 @t87)) % 0.44/0.65 (define @t91 () (@list @t87)) % 0.44/0.65 (define @t92 () (forall @t91 (or (not (tptp.eiw_di @t87 @t1)) (tptp.qmltpeq @t90 tptp.empty_set @t1) (tptp.qmltpeq @t90 @t67 @t1)))) % 0.44/0.65 (define @t93 () (tptp.singleton @t17)) % 0.44/0.65 (define @t94 () (tptp.set_difference @t93 @t87)) % 0.44/0.65 (define @t95 () (tptp.set_difference @t93 @t4)) % 0.44/0.65 (define @t96 () (tptp.qmltpeq @t95 @t93 @t7)) % 0.44/0.65 (define @t97 () (tptp.qmltpeq @t95 tptp.empty_set @t7)) % 0.44/0.65 (define @t98 () (not (tptp.eiw_di @t4 @t7))) % 0.44/0.65 (define @t99 () (forall @t6 (or @t98 @t97 @t96))) % 0.44/0.65 (define @t100 () (@list @t4)) % 0.44/0.65 (define @t101 () (lambda @t22 @t99)) % 0.44/0.65 (define @t102 () (or @t77 (_ @t101 @t4 @t1))) % 0.44/0.65 (define @t103 () (forall @t6 @t102)) % 0.44/0.65 (define @t104 () (lambda @t3 @t103)) % 0.44/0.65 (define @t105 () (_ @t61 @t4 @t1)) % 0.44/0.65 (define @t106 () (lambda @t64 (forall @t6 (or @t77 @t105)))) % 0.44/0.65 (define @t107 () (tptp.qmltpeq @t95 @t93 @t1)) % 0.44/0.65 (define @t108 () (tptp.qmltpeq @t95 tptp.empty_set @t1)) % 0.44/0.65 (define @t109 () (_ @t31 @t4)) % 0.44/0.65 (define @t110 () (_ tptp.qmltpeq @t95)) % 0.44/0.65 (define @t111 () (_ tptp.qmltpeq @t109)) % 0.44/0.65 (define @t112 () (_ (_ @t111 @t24) @t1)) % 0.44/0.65 (define @t113 () (_ (_ @t111 tptp.empty_set) @t1)) % 0.44/0.65 (define @t114 () (or @t77 @t113 @t112)) % 0.44/0.65 (define @t115 () (or @t113 @t112)) % 0.44/0.65 (define @t116 () (_ @t33 @t7)) % 0.44/0.65 (define @t117 () (_ @t36 @t7)) % 0.44/0.65 (define @t118 () (or @t117 @t116)) % 0.44/0.65 (define @t119 () (lambda @t21 @t118)) % 0.44/0.65 (define @t120 () (_ @t119 @t4 @t1)) % 0.44/0.65 (define @t121 () (or @t77 @t120)) % 0.44/0.65 (define @t122 () (forall @t6 @t121)) % 0.44/0.65 (define @t123 () (lambda @t3 @t122)) % 0.44/0.65 (define @t124 () (_ @t33 @t1)) % 0.44/0.65 (define @t125 () (_ @t36 @t1)) % 0.44/0.65 (define @t126 () (lambda @t3 (or @t125 @t124))) % 0.44/0.65 (define @t127 () (@list @t47 @t1)) % 0.44/0.65 (define @t128 () (lambda @t127 (or @t125 @t48))) % 0.44/0.65 (define @t129 () (_ @t51 @t36)) % 0.44/0.65 (define @t130 () (lambda @t21 (_ (_ @t129 @t33) @t7))) % 0.44/0.65 (define @t131 () (lambda @t22 (_ (_ @t106 @t130) @t7))) % 0.44/0.65 (define @t132 () (not @t5)) % 0.44/0.65 (define @t133 () (or @t132 @t62)) % 0.44/0.65 (define @t134 () (@quantifiers_skolemize @t72 0)) % 0.44/0.65 (define @t135 () (tptp.singleton @t134)) % 0.44/0.65 (define @t136 () (@quantifiers_skolemize @t72 1)) % 0.44/0.65 (define @t137 () (tptp.set_difference @t135 @t136)) % 0.44/0.65 (define @t138 () (tptp.qmltpeq @t137 @t135 tptp.mactual)) % 0.44/0.65 (define @t139 () (tptp.qmltpeq @t137 tptp.empty_set tptp.mactual)) % 0.44/0.65 (define @t140 () (tptp.eiw_di @t136 tptp.mactual)) % 0.44/0.65 (define @t141 () (not @t140)) % 0.44/0.65 (define @t142 () (tptp.eiw_di @t134 tptp.mactual)) % 0.44/0.65 (define @t143 () (not @t142)) % 0.44/0.65 (define @t144 () (or @t143 @t141 @t139 @t138)) % 0.44/0.65 (define @t145 () (@list true)) % 0.44/0.65 (define @t146 () (@list @t144)) % 0.44/0.65 (define @t147 () (@var "BOUND_VARIABLE_9370" $$unsorted)) % 0.44/0.65 (define @t148 () (tptp.set_difference @t67 @t147)) % 0.44/0.65 (define @t149 () (@list @t4 @t147)) % 0.44/0.65 (define @t150 () (forall @t149 (or @t70 (not (tptp.eiw_di @t147 tptp.mactual)) (= (tptp.in @t4 @t147 tptp.mactual) (tptp.qmltpeq @t148 tptp.empty_set tptp.mactual))))) % 0.44/0.65 (define @t151 () (= (tptp.in @t4 @t147 @t1) (tptp.qmltpeq @t148 tptp.empty_set @t1))) % 0.44/0.65 (define @t152 () (not (tptp.eiw_di @t147 @t1))) % 0.44/0.65 (define @t153 () (or @t77 @t152 @t151)) % 0.44/0.65 (define @t154 () (lambda @t3 (forall @t149 @t153))) % 0.44/0.65 (define @t155 () (_ @t154 tptp.mactual)) % 0.44/0.65 (define @t156 () (or @t152 @t151)) % 0.44/0.65 (define @t157 () (or @t77 @t156)) % 0.44/0.65 (define @t158 () (forall @t149 @t157)) % 0.44/0.65 (define @t159 () (@list @t147)) % 0.44/0.65 (define @t160 () (forall @t159 @t157)) % 0.44/0.65 (define @t161 () (forall @t159 @t156)) % 0.44/0.65 (define @t162 () (@var "BOUND_VARIABLE_9347" $$unsorted)) % 0.44/0.65 (define @t163 () (@list @t162)) % 0.44/0.65 (define @t164 () (or @t77 @t161)) % 0.44/0.65 (define @t165 () (@list @t162)) % 0.44/0.65 (define @t166 () (forall @t165 (or (not (tptp.eiw_di @t162 @t1)) (= (tptp.in @t4 @t162 @t1) (tptp.qmltpeq (tptp.set_difference @t67 @t162) tptp.empty_set @t1))))) % 0.44/0.65 (define @t167 () (tptp.in @t17 @t4 @t7)) % 0.44/0.65 (define @t168 () (forall @t6 (or @t98 (= @t167 @t97)))) % 0.44/0.65 (define @t169 () (lambda @t22 @t168)) % 0.44/0.65 (define @t170 () (or @t77 (_ @t169 @t4 @t1))) % 0.44/0.65 (define @t171 () (forall @t6 @t170)) % 0.44/0.65 (define @t172 () (lambda @t3 @t171)) % 0.44/0.65 (define @t173 () (tptp.in @t17 @t4 @t1)) % 0.44/0.65 (define @t174 () (_ (_ @t28 @t4) @t1)) % 0.44/0.65 (define @t175 () (= @t174 @t113)) % 0.44/0.65 (define @t176 () (or @t77 @t175)) % 0.44/0.65 (define @t177 () (_ @t30 @t7)) % 0.44/0.65 (define @t178 () (= @t177 @t117)) % 0.44/0.65 (define @t179 () (lambda @t21 @t178)) % 0.44/0.65 (define @t180 () (_ @t179 @t4 @t1)) % 0.44/0.65 (define @t181 () (or @t77 @t180)) % 0.44/0.65 (define @t182 () (forall @t6 @t181)) % 0.44/0.65 (define @t183 () (lambda @t3 @t182)) % 0.44/0.65 (define @t184 () (_ @t30 @t1)) % 0.44/0.65 (define @t185 () (lambda @t3 (= @t184 @t125))) % 0.44/0.65 (define @t186 () (lambda @t127 (= @t125 @t48))) % 0.44/0.65 (define @t187 () (_ @t53 @t36)) % 0.44/0.65 (define @t188 () (lambda @t21 (_ (_ @t187 @t30) @t7))) % 0.44/0.65 (define @t189 () (tptp.in @t134 @t136 tptp.mactual)) % 0.44/0.65 (define @t190 () (or @t143 @t141 (= @t189 @t139))) % 0.44/0.65 (define @t191 () (@list @t134 @t136)) % 0.44/0.65 (define @t192 () (= @t139 @t189)) % 0.44/0.65 (define @t193 () (or @t143 @t141 @t192)) % 0.44/0.65 (define @t194 () (@list false)) % 0.44/0.65 (define @t195 () (@list false false false)) % 0.44/0.65 (define @t196 () (@var "BOUND_VARIABLE_9268" $$unsorted)) % 0.44/0.65 (define @t197 () (tptp.set_difference @t67 @t196)) % 0.44/0.65 (define @t198 () (@list @t4 @t196)) % 0.44/0.65 (define @t199 () (forall @t198 (or @t70 (not (tptp.eiw_di @t196 tptp.mactual)) (= (not (tptp.in @t4 @t196 tptp.mactual)) (tptp.qmltpeq @t197 @t67 tptp.mactual))))) % 0.44/0.65 (define @t200 () (= (not (tptp.in @t4 @t196 @t1)) (tptp.qmltpeq @t197 @t67 @t1))) % 0.44/0.65 (define @t201 () (not (tptp.eiw_di @t196 @t1))) % 0.44/0.65 (define @t202 () (or @t77 @t201 @t200)) % 0.44/0.65 (define @t203 () (lambda @t3 (forall @t198 @t202))) % 0.44/0.65 (define @t204 () (_ @t203 tptp.mactual)) % 0.44/0.65 (define @t205 () (or @t201 @t200)) % 0.44/0.65 (define @t206 () (or @t77 @t205)) % 0.44/0.65 (define @t207 () (forall @t198 @t206)) % 0.44/0.65 (define @t208 () (@list @t196)) % 0.44/0.65 (define @t209 () (forall @t208 @t206)) % 0.44/0.65 (define @t210 () (forall @t208 @t205)) % 0.44/0.65 (define @t211 () (@var "BOUND_VARIABLE_9243" $$unsorted)) % 0.44/0.65 (define @t212 () (@list @t211)) % 0.44/0.65 (define @t213 () (or @t77 @t210)) % 0.44/0.65 (define @t214 () (@list @t211)) % 0.44/0.65 (define @t215 () (forall @t214 (or (not (tptp.eiw_di @t211 @t1)) (= (not (tptp.in @t4 @t211 @t1)) (tptp.qmltpeq (tptp.set_difference @t67 @t211) @t67 @t1))))) % 0.44/0.65 (define @t216 () (forall @t6 (or @t98 (= (not @t167) @t96)))) % 0.44/0.65 (define @t217 () (lambda @t22 @t216)) % 0.44/0.65 (define @t218 () (or @t77 (_ @t217 @t4 @t1))) % 0.44/0.65 (define @t219 () (forall @t6 @t218)) % 0.44/0.65 (define @t220 () (lambda @t3 @t219)) % 0.44/0.65 (define @t221 () (not @t174)) % 0.44/0.65 (define @t222 () (= @t221 @t112)) % 0.44/0.65 (define @t223 () (or @t77 @t222)) % 0.44/0.65 (define @t224 () (= @t116 (not @t177))) % 0.44/0.65 (define @t225 () (lambda @t21 @t224)) % 0.44/0.65 (define @t226 () (_ @t225 @t4 @t1)) % 0.44/0.65 (define @t227 () (or @t77 @t226)) % 0.44/0.65 (define @t228 () (forall @t6 @t227)) % 0.44/0.65 (define @t229 () (lambda @t3 @t228)) % 0.44/0.65 (define @t230 () (not @t184)) % 0.44/0.65 (define @t231 () (lambda @t3 @t230)) % 0.44/0.65 (define @t232 () (_ @t231 @t1)) % 0.44/0.65 (define @t233 () (lambda @t3 (= @t232 @t124))) % 0.44/0.65 (define @t234 () (_ @t46 @t30)) % 0.44/0.65 (define @t235 () (lambda @t127 (= @t124 @t48))) % 0.44/0.65 (define @t236 () (_ @t53 @t33)) % 0.44/0.65 (define @t237 () (lambda @t21 (_ (_ @t236 @t234) @t7))) % 0.44/0.65 (define @t238 () (not @t189)) % 0.44/0.65 (define @t239 () (or @t143 @t141 (= @t238 @t138))) % 0.44/0.65 (define @t240 () (= @t138 @t238)) % 0.44/0.65 (define @t241 () (or @t143 @t141 @t240)) % 0.44/0.65 (define @t242 () (not @t240)) % 0.44/0.65 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.44/0.65 (assume @p2 (forall @t3 (exists @t6 @t5))) % 0.44/0.65 (assume @p3 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t9 (_ (_ @t8 @t4) @t7))))) % 0.44/0.65 (assume @p4 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t9 (_ (_ tptp.mforall_di (lambda @t13 (_ (_ (_ tptp.mimplies @t12) (_ @t11 @t4)) @t7))) @t7))))) % 0.44/0.65 (assume @p5 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t9 (_ (_ tptp.mforall_di (lambda @t13 (_ (_ tptp.mforall_di (lambda (@list @t14 @t7) (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t12) (_ @t11 @t14))) (_ @t8 @t14)) @t7))) @t7))) @t7))))) % 0.44/0.65 (assume @p6 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ tptp.mforall_di (lambda @t20 (_ (_ @t19 (_ (_ tptp.qmltpeq (_ (_ tptp.set_difference @t17) @t15)) (_ (_ tptp.set_difference @t16) @t15))) @t7))) @t7))) @t7))))) % 0.44/0.65 (assume @p7 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ tptp.mforall_di (lambda @t20 (_ (_ @t19 (_ (_ tptp.qmltpeq (_ @t23 @t17)) (_ @t23 @t16))) @t7))) @t7))) @t7))))) % 0.44/0.65 (assume @p8 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ @t19 (_ (_ tptp.qmltpeq @t24) (_ tptp.singleton @t16))) @t7))) @t7))))) % 0.44/0.65 (assume @p9 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t26 @t25)) (_ tptp.empty @t16)) @t7))) @t7))))) % 0.44/0.65 (assume @p10 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ tptp.mforall_di (lambda @t20 (_ (_ (_ tptp.mimplies (_ @t26 (_ @t28 @t15))) (_ @t27 @t15)) @t7))) @t7))) @t7))))) % 0.44/0.65 (assume @p11 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ tptp.mforall_di (lambda @t20 (_ (_ (_ tptp.mimplies (_ @t26 (_ @t29 @t17))) (_ @t29 @t16)) @t7))) @t7))) @t7))))) % 0.44/0.65 (assume @p12 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ (_ tptp.mimplies @t30) (_ tptp.mnot (_ @t27 @t17))) @t7))) @t7))))) % 0.44/0.65 (assume @p13 (_ tptp.mlocal (_ tptp.empty tptp.empty_set))) % 0.44/0.65 (assume @p14 (_ tptp.mlocal (_ tptp.mforall_di @t35))) % 0.44/0.65 (assume @p15 (_ tptp.mlocal (_ tptp.mforall_di @t38))) % 0.44/0.65 (assume @p16 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t22 (_ @t25 @t7))))) % 0.44/0.65 (assume @p17 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t22 (_ (_ tptp.mnot @t25) @t7))))) % 0.44/0.65 (assume @p18 @t41) % 0.44/0.65 (assume @p19 true) % 0.44/0.65 (step @p20 (= tptp.mlocal @t43) :rule refl :args (@t43)) % 0.44/0.65 (step @p21 (= tptp.mnot @t46) :rule refl :args (@t46)) % 0.44/0.65 (step @p22 (= tptp.mand @t50) :rule refl :args (@t50)) % 0.44/0.65 (step @p23 (= tptp.mor @t51) :rule refl :args (@t51)) % 0.44/0.65 (step @p24 (= tptp.mimplies @t52) :rule refl :args (@t52)) % 0.44/0.65 (step @p25 (= tptp.mequiv @t53) :rule refl :args (@t53)) % 0.44/0.65 (step @p26 (= tptp.mbox @t59) :rule refl :args (@t59)) % 0.44/0.65 (step @p27 (= tptp.mdia @t60) :rule refl :args (@t60)) % 0.44/0.65 (step @p28 (= tptp.mforall_di @t65) :rule refl :args (@t65)) % 0.44/0.65 (step @p29 (= tptp.mexists_di @t66) :rule refl :args (@t66)) % 0.44/0.65 (step @p30 :rule beta-reduce :args ((= @t80 @t72))) % 0.44/0.65 (step @p31 :rule beta-reduce :args ((= (_ @t43 @t79) @t80))) % 0.44/0.65 (step @p32 :rule trans :premises (@p31 @p30)) % 0.44/0.65 (step @p33 :rule aci_norm :args ((= @t82 @t78))) % 0.44/0.65 (step @p34 :rule cong :premises (@p33) :args (@t83)) % 0.44/0.65 (step @p35 :rule quant-merge-prenex :args ((= (forall @t6 @t85) @t83))) % 0.44/0.65 (step @p36 :rule alpha_equiv :args (@t86 (@list @t68) @t88)) % 0.44/0.65 (step @p37 :rule refl :args (@t77)) % 0.44/0.65 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t89)) % 0.44/0.65 (step @p39 :rule quant-miniscope-or :args ((= @t85 @t89))) % 0.44/0.66 (step @p40 :rule trans :premises (@p39 @p38)) % 0.44/0.66 (step @p41 :rule symm :premises (@p40)) % 0.44/0.66 (step @p42 :rule cong :premises (@p41) :args ((forall @t6 (or @t77 @t92)))) % 0.44/0.66 (step @p43 :rule trans :premises (@p42 @p35)) % 0.44/0.66 (step @p44 :rule trans :premises (@p43 @p34)) % 0.44/0.66 (step @p45 :rule beta-reduce :args ((= (_ (lambda @t22 (forall @t91 (or (not (tptp.eiw_di @t87 @t7)) (tptp.qmltpeq @t94 tptp.empty_set @t7) (tptp.qmltpeq @t94 @t93 @t7)))) @t4 @t1) @t92))) % 0.44/0.66 (step @p46 :rule refl :args (@t1)) % 0.44/0.66 (step @p47 :rule refl :args (@t4)) % 0.44/0.66 (step @p48 :rule alpha_equiv :args (@t99 @t100 @t88)) % 0.44/0.66 (step @p49 :rule cong :premises (@p48) :args (@t101)) % 0.44/0.66 (step @p50 :rule ho_cong :premises (@p49 @p47 @p46)) % 0.44/0.66 (step @p51 :rule trans :premises (@p50 @p45)) % 0.44/0.66 (step @p52 :rule refl :args (@t77)) % 0.44/0.66 (step @p53 :rule nary_cong :premises (@p52 @p51) :args (@t102)) % 0.44/0.66 (step @p54 :rule cong :premises (@p53) :args (@t103)) % 0.44/0.66 (step @p55 :rule trans :premises (@p54 @p44)) % 0.44/0.66 (step @p56 :rule cong :premises (@p55) :args (@t104)) % 0.44/0.66 (step @p57 :rule beta-reduce :args ((= (_ @t106 @t101) @t104))) % 0.44/0.66 (step @p58 :rule trans :premises (@p57 @p56)) % 0.44/0.66 (step @p59 :rule beta-reduce :args ((= (_ (lambda @t3 (forall @t6 (or @t77 @t108 @t107))) @t7) @t99))) % 0.44/0.66 (step @p60 :rule refl :args (@t7)) % 0.44/0.66 (step @p61 :rule refl :args ((tptp.qmltpeq @t109 @t24 @t1))) % 0.44/0.66 (step @p62 :rule refl :args (@t93)) % 0.44/0.66 (step @p63 :rule refl :args ((tptp.set_difference @t24 @t4))) % 0.44/0.66 (step @p64 :rule cong :premises (@p62 @p47) :args (@t95)) % 0.44/0.66 (step @p65 :rule trans :premises (@p64 @p63)) % 0.44/0.66 (step @p66 :rule cong :premises (@p65 @p62 @p46) :args (@t107)) % 0.44/0.66 (step @p67 :rule trans :premises (@p66 @p61)) % 0.44/0.66 (step @p68 :rule refl :args (tptp.qmltpeq)) % 0.44/0.66 (step @p69 :rule ho_cong :premises (@p68 @p65)) % 0.44/0.66 (step @p70 :rule ho_cong :premises (@p69 @p62)) % 0.44/0.66 (step @p71 :rule ho_cong :premises (@p70 @p46)) % 0.44/0.66 (step @p72 :rule cong :premises (@p71 @p67) :args ((= (_ (_ @t110 @t93) @t1) @t107))) % 0.44/0.66 (step @p73 :rule symm :premises (@p72)) % 0.44/0.66 (step @p74 :rule refl :args (@t112)) % 0.44/0.66 (step @p75 :rule eq_resolve :premises (@p74 @p73)) % 0.44/0.66 (step @p76 :rule refl :args (@t24)) % 0.44/0.66 (step @p77 :rule cong :premises (@p76 @p62) :args ((= @t24 @t93))) % 0.44/0.66 (step @p78 :rule symm :premises (@p77)) % 0.44/0.66 (step @p79 :rule eq_resolve :premises (@p76 @p78)) % 0.44/0.66 (step @p80 :rule refl :args (tptp.set_difference)) % 0.44/0.66 (step @p81 :rule ho_cong :premises (@p80 @p62)) % 0.44/0.66 (step @p82 :rule ho_cong :premises (@p81 @p47)) % 0.44/0.66 (step @p83 :rule cong :premises (@p82 @p65) :args ((= (_ (_ tptp.set_difference @t93) @t4) @t95))) % 0.44/0.66 (step @p84 :rule symm :premises (@p83)) % 0.44/0.66 (step @p85 :rule refl :args (@t109)) % 0.44/0.66 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 0.44/0.66 (step @p87 :rule ho_cong :premises (@p80 @p79)) % 0.44/0.66 (step @p88 :rule ho_cong :premises (@p87 @p47)) % 0.44/0.66 (step @p89 :rule trans :premises (@p88 @p86)) % 0.44/0.66 (step @p90 :rule ho_cong :premises (@p68 @p89)) % 0.44/0.66 (step @p91 :rule ho_cong :premises (@p90 @p79)) % 0.44/0.66 (step @p92 :rule ho_cong :premises (@p91 @p46)) % 0.44/0.66 (step @p93 :rule trans :premises (@p92 @p75)) % 0.44/0.66 (step @p94 :rule refl :args ((tptp.qmltpeq @t109 tptp.empty_set @t1))) % 0.44/0.66 (step @p95 :rule refl :args (tptp.empty_set)) % 0.44/0.66 (step @p96 :rule cong :premises (@p65 @p95 @p46) :args (@t108)) % 0.44/0.66 (step @p97 :rule trans :premises (@p96 @p94)) % 0.44/0.66 (step @p98 :rule ho_cong :premises (@p69 @p95)) % 0.44/0.66 (step @p99 :rule ho_cong :premises (@p98 @p46)) % 0.44/0.66 (step @p100 :rule cong :premises (@p99 @p97) :args ((= (_ (_ @t110 tptp.empty_set) @t1) @t108))) % 0.44/0.66 (step @p101 :rule symm :premises (@p100)) % 0.44/0.66 (step @p102 :rule refl :args (@t113)) % 0.44/0.66 (step @p103 :rule eq_resolve :premises (@p102 @p101)) % 0.44/0.66 (step @p104 :rule ho_cong :premises (@p90 @p95)) % 0.44/0.66 (step @p105 :rule ho_cong :premises (@p104 @p46)) % 0.44/0.66 (step @p106 :rule trans :premises (@p105 @p103)) % 0.44/0.66 (step @p107 :rule nary_cong :premises (@p37 @p106 @p93) :args (@t114)) % 0.44/0.66 (step @p108 :rule cong :premises (@p107) :args ((forall @t6 @t114))) % 0.44/0.66 (step @p109 :rule aci_norm :args ((= (or @t77 @t115) @t114))) % 0.44/0.66 (step @p110 :rule beta-reduce :args ((= @t120 @t115))) % 0.44/0.66 (step @p111 :rule nary_cong :premises (@p52 @p110) :args (@t121)) % 0.44/0.66 (step @p112 :rule trans :premises (@p111 @p109)) % 0.44/0.66 (step @p113 :rule cong :premises (@p112) :args (@t122)) % 0.44/0.66 (step @p114 :rule trans :premises (@p113 @p108)) % 0.44/0.66 (step @p115 :rule cong :premises (@p114) :args (@t123)) % 0.44/0.66 (step @p116 :rule beta-reduce :args ((= (_ @t106 @t119) @t123))) % 0.44/0.66 (step @p117 :rule trans :premises (@p116 @p115)) % 0.44/0.66 (step @p118 :rule beta-reduce :args ((= (_ @t126 @t7) @t118))) % 0.44/0.66 (step @p119 :rule beta-reduce :args ((= (_ @t128 @t33) @t126))) % 0.44/0.66 (step @p120 :rule refl :args (@t33)) % 0.44/0.66 (step @p121 :rule beta-reduce :args ((= @t129 @t128))) % 0.44/0.66 (step @p122 :rule ho_cong :premises (@p121 @p120)) % 0.44/0.66 (step @p123 :rule trans :premises (@p122 @p119)) % 0.44/0.66 (step @p124 :rule ho_cong :premises (@p123 @p60)) % 0.44/0.66 (step @p125 :rule trans :premises (@p124 @p118)) % 0.44/0.66 (step @p126 :rule cong :premises (@p125) :args (@t130)) % 0.44/0.66 (step @p127 :rule refl :args (@t106)) % 0.44/0.66 (step @p128 :rule ho_cong :premises (@p127 @p126)) % 0.44/0.66 (step @p129 :rule trans :premises (@p128 @p117)) % 0.44/0.66 (step @p130 :rule ho_cong :premises (@p129 @p60)) % 0.44/0.66 (step @p131 :rule trans :premises (@p130 @p59)) % 0.44/0.66 (step @p132 :rule cong :premises (@p131) :args (@t131)) % 0.44/0.66 (step @p133 :rule ho_cong :premises (@p127 @p132)) % 0.44/0.66 (step @p134 :rule trans :premises (@p133 @p58)) % 0.44/0.66 (step @p135 :rule refl :args (@t43)) % 0.44/0.66 (step @p136 :rule ho_cong :premises (@p135 @p134)) % 0.44/0.66 (step @p137 :rule trans :premises (@p136 @p32)) % 0.44/0.66 (step @p138 :rule cong :premises (@p137) :args ((not (_ @t43 (_ @t106 @t131))))) % 0.44/0.66 (step @p139 :rule refl :args (@t36)) % 0.44/0.66 (step @p140 :rule ho_cong :premises (@p23 @p139)) % 0.44/0.66 (step @p141 :rule ho_cong :premises (@p140 @p120)) % 0.44/0.66 (step @p142 :rule ho_cong :premises (@p141 @p60)) % 0.44/0.66 (step @p143 :rule cong :premises (@p142) :args (@t39)) % 0.44/0.66 (step @p144 :rule refl :args (@t105)) % 0.44/0.66 (step @p145 :rule refl :args (@t62)) % 0.44/0.66 (step @p146 :rule cong :premises (@p145 @p144) :args ((= @t62 @t105))) % 0.44/0.66 (step @p147 :rule symm :premises (@p146)) % 0.44/0.66 (step @p148 :rule eq_resolve :premises (@p145 @p147)) % 0.44/0.66 (step @p149 :rule refl :args (@t76)) % 0.44/0.66 (step @p150 :rule refl :args (@t5)) % 0.44/0.66 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t5 @t76))) % 0.44/0.66 (step @p152 :rule symm :premises (@p151)) % 0.44/0.66 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.44/0.66 (step @p154 :rule cong :premises (@p153) :args (@t132)) % 0.44/0.66 (step @p155 :rule nary_cong :premises (@p154 @p148) :args (@t133)) % 0.44/0.66 (step @p156 :rule cong :premises (@p155) :args ((forall @t6 @t133))) % 0.44/0.66 (step @p157 :rule bool-impl-elim :args (@t5 @t62)) % 0.44/0.66 (step @p158 :rule cong :premises (@p157) :args (@t63)) % 0.44/0.66 (step @p159 :rule trans :premises (@p158 @p156)) % 0.44/0.66 (step @p160 :rule cong :premises (@p159) :args (@t65)) % 0.44/0.66 (step @p161 :rule trans :premises (@p28 @p160)) % 0.44/0.66 (step @p162 :rule ho_cong :premises (@p161 @p143)) % 0.44/0.66 (step @p163 :rule ho_cong :premises (@p162 @p60)) % 0.44/0.66 (step @p164 :rule cong :premises (@p163) :args (@t40)) % 0.44/0.66 (step @p165 :rule ho_cong :premises (@p161 @p164)) % 0.44/0.66 (step @p166 :rule ho_cong :premises (@p20 @p165)) % 0.44/0.66 (step @p167 :rule cong :premises (@p166) :args (@t41)) % 0.44/0.66 (step @p168 :rule trans :premises (@p167 @p138)) % 0.44/0.66 (step @p169 :rule eq_resolve :premises (@p18 @p168)) % 0.44/0.66 (step @p170 :rule skolemize :premises (@p169)) % 0.44/0.66 (step @p171 :rule cnf_or_neg :args (@t144 2)) % 0.44/0.66 (step @p172 :rule chain_m_resolution :premises (@p171 @p170) :args ((not @t139) @t145 @t146)) % 0.44/0.66 (step @p173 :rule beta-reduce :args ((= @t155 @t150))) % 0.44/0.66 (step @p174 :rule beta-reduce :args ((= (_ @t43 @t154) @t155))) % 0.44/0.66 (step @p175 :rule trans :premises (@p174 @p173)) % 0.44/0.66 (step @p176 :rule aci_norm :args ((= @t157 @t153))) % 0.44/0.66 (step @p177 :rule cong :premises (@p176) :args (@t158)) % 0.44/0.66 (step @p178 :rule quant-merge-prenex :args ((= (forall @t6 @t160) @t158))) % 0.44/0.66 (step @p179 :rule alpha_equiv :args (@t161 (@list @t147) @t163)) % 0.44/0.66 (step @p180 :rule nary_cong :premises (@p37 @p179) :args 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0.44/0.66 (step @p377 :rule chain_m_resolution :premises (@p376 @p369 @p367) :args (@t189 (@list true false) (@list @t138 @t240))) % 0.44/0.66 (step @p378 :rule cnf_equiv_pos2 :args (@t192)) % 0.44/0.66 (step @p379 :rule reordering :premises (@p378) :args ((or @t139 @t238 (not @t192)))) % 0.44/0.66 (step @p380 false :rule chain_m_resolution :premises (@p379 @p377 @p274 @p172) :args (false (@list false false true) (@list @t189 @t192 @t139))) % 0.44/0.66 ) % 0.44/0.66 % SZS output end Proof % 0.44/0.66 % cvc5 exiting %------------------------------------------------------------------------------