%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET926^12 : 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 : n023.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 0.45s 0.66s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET926^12 : TPTP v9.2.1. Released v8.1.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n023.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 16:18:43 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.45/0.66 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.66 % SZS status Theorem % 0.45/0.66 % SZS output start Proof % 0.45/0.66 ( % 0.45/0.66 (declare-sort $$unsorted 0) % 0.45/0.66 (declare-sort tptp.mworld 0) % 0.45/0.66 (declare-const tptp.mactual tptp.mworld) % 0.45/0.66 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.45/0.66 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 0.45/0.66 (declare-const tptp.empty (-> $$unsorted tptp.mworld Bool)) % 0.45/0.66 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.66 (declare-const tptp.in (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.45/0.66 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.45/0.66 (declare-const tptp.qmltpeq (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.45/0.66 (declare-const tptp.empty_set $$unsorted) % 0.45/0.66 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.45/0.66 (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)))))) % 0.45/0.66 (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))))))) % 0.45/0.66 (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))))))) % 0.45/0.66 (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))))))) % 0.45/0.66 (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))))))) % 0.45/0.66 (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)))))))) % 0.45/0.66 (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)))))))) % 0.45/0.66 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.45/0.66 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.45/0.66 (define @t1 () (@var "V" tptp.mworld)) % 0.45/0.66 (define @t2 () (@var "W" tptp.mworld)) % 0.45/0.66 (define @t3 () (_ (_ tptp.mrel @t2) @t1)) % 0.45/0.66 (define @t4 () (@var "X" $$unsorted)) % 0.45/0.66 (define @t5 () (_ (_ tptp.eiw_di @t4) @t2)) % 0.45/0.66 (define @t6 () (@list @t4)) % 0.45/0.66 (define @t7 () (@list @t2)) % 0.45/0.66 (define @t8 () (@var "__flatten_var_0" tptp.mworld)) % 0.45/0.66 (define @t9 () (_ tptp.qmltpeq @t4)) % 0.45/0.66 (define @t10 () (@list @t4 @t8)) % 0.45/0.66 (define @t11 () (@var "Y" $$unsorted)) % 0.45/0.66 (define @t12 () (_ tptp.qmltpeq @t11)) % 0.45/0.66 (define @t13 () (_ @t9 @t11)) % 0.45/0.66 (define @t14 () (@list @t11 @t8)) % 0.45/0.66 (define @t15 () (@var "Z" $$unsorted)) % 0.45/0.66 (define @t16 () (@var "C" $$unsorted)) % 0.45/0.66 (define @t17 () (@var "B" $$unsorted)) % 0.45/0.66 (define @t18 () (@var "A" $$unsorted)) % 0.45/0.66 (define @t19 () (_ (_ tptp.qmltpeq @t18) @t17)) % 0.45/0.66 (define @t20 () (_ tptp.mimplies @t19)) % 0.45/0.66 (define @t21 () (@list @t16 @t8)) % 0.45/0.66 (define @t22 () (@list @t17 @t8)) % 0.45/0.66 (define @t23 () (@list @t18 @t8)) % 0.45/0.66 (define @t24 () (_ tptp.set_difference @t16)) % 0.45/0.66 (define @t25 () (_ tptp.singleton @t18)) % 0.45/0.66 (define @t26 () (_ tptp.empty @t18)) % 0.45/0.66 (define @t27 () (_ tptp.mand @t19)) % 0.45/0.66 (define @t28 () (_ tptp.in @t17)) % 0.45/0.66 (define @t29 () (_ tptp.in @t18)) % 0.45/0.66 (define @t30 () (_ tptp.in @t16)) % 0.45/0.66 (define @t31 () (_ @t29 @t17)) % 0.45/0.66 (define @t32 () (_ tptp.set_difference @t25)) % 0.45/0.66 (define @t33 () (_ tptp.qmltpeq (_ @t32 @t17))) % 0.45/0.66 (define @t34 () (_ @t33 @t25)) % 0.45/0.66 (define @t35 () (lambda @t22 (_ (_ (_ tptp.mequiv @t34) (_ tptp.mnot @t31)) @t8))) % 0.45/0.66 (define @t36 () (lambda @t23 (_ (_ tptp.mforall_di @t35) @t8))) % 0.45/0.66 (define @t37 () (_ @t33 tptp.empty_set)) % 0.45/0.66 (define @t38 () (lambda @t22 (_ (_ (_ tptp.mequiv @t37) @t31) @t8))) % 0.45/0.66 (define @t39 () (lambda @t23 (_ (_ tptp.mforall_di @t38) @t8))) % 0.45/0.66 (define @t40 () (lambda @t22 (_ (_ (_ tptp.mor @t37) @t34) @t8))) % 0.45/0.66 (define @t41 () (lambda @t23 (_ (_ tptp.mforall_di @t40) @t8))) % 0.45/0.66 (define @t42 () (not (_ tptp.mlocal (_ tptp.mforall_di @t41)))) % 0.45/0.66 (define @t43 () (@var "Phi" (-> tptp.mworld Bool))) % 0.45/0.66 (define @t44 () (lambda (@list @t43) (_ @t43 tptp.mactual))) % 0.45/0.66 (define @t45 () (@var "A" (-> tptp.mworld Bool))) % 0.45/0.66 (define @t46 () (_ @t45 @t2)) % 0.45/0.66 (define @t47 () (lambda (@list @t45 @t2) (not @t46))) % 0.45/0.66 (define @t48 () (@var "B" (-> tptp.mworld Bool))) % 0.45/0.66 (define @t49 () (_ @t48 @t2)) % 0.45/0.66 (define @t50 () (@list @t45 @t48 @t2)) % 0.45/0.66 (define @t51 () (lambda @t50 (and @t46 @t49))) % 0.45/0.66 (define @t52 () (lambda @t50 (or @t46 @t49))) % 0.45/0.66 (define @t53 () (lambda @t50 (=> @t46 @t49))) % 0.45/0.66 (define @t54 () (lambda @t50 (= @t46 @t49))) % 0.45/0.66 (define @t55 () (_ @t43 @t1)) % 0.45/0.66 (define @t56 () (@list @t1)) % 0.45/0.66 (define @t57 () (@list @t43 @t2)) % 0.45/0.66 (define @t58 () (lambda @t57 (forall @t56 (=> @t3 @t55)))) % 0.45/0.66 (define @t59 () (lambda @t57 (exists @t56 (and @t3 @t55)))) % 0.45/0.66 (define @t60 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.45/0.66 (define @t61 () (_ (_ @t60 @t4) @t2)) % 0.45/0.66 (define @t62 () (forall @t6 (=> @t5 @t61))) % 0.45/0.66 (define @t63 () (@list @t60 @t2)) % 0.45/0.66 (define @t64 () (lambda @t63 @t62)) % 0.45/0.66 (define @t65 () (lambda @t63 (exists @t6 (and @t5 @t61)))) % 0.45/0.66 (define @t66 () (tptp.singleton @t4)) % 0.45/0.66 (define @t67 () (@var "BOUND_VARIABLE_9507" $$unsorted)) % 0.45/0.66 (define @t68 () (tptp.set_difference @t66 @t67)) % 0.45/0.66 (define @t69 () (not (tptp.eiw_di @t4 tptp.mactual))) % 0.45/0.66 (define @t70 () (@list @t4 @t67)) % 0.45/0.66 (define @t71 () (forall @t70 (or @t69 (not (tptp.eiw_di @t67 tptp.mactual)) (tptp.qmltpeq @t68 tptp.empty_set tptp.mactual) (tptp.qmltpeq @t68 @t66 tptp.mactual)))) % 0.45/0.66 (define @t72 () (tptp.qmltpeq @t68 @t66 @t2)) % 0.45/0.66 (define @t73 () (tptp.qmltpeq @t68 tptp.empty_set @t2)) % 0.45/0.66 (define @t74 () (not (tptp.eiw_di @t67 @t2))) % 0.45/0.66 (define @t75 () (tptp.eiw_di @t4 @t2)) % 0.45/0.66 (define @t76 () (not @t75)) % 0.45/0.66 (define @t77 () (or @t76 @t74 @t73 @t72)) % 0.45/0.66 (define @t78 () (lambda @t7 (forall @t70 @t77))) % 0.45/0.66 (define @t79 () (_ @t78 tptp.mactual)) % 0.45/0.66 (define @t80 () (or @t74 @t73 @t72)) % 0.45/0.66 (define @t81 () (or @t76 @t80)) % 0.45/0.66 (define @t82 () (forall @t70 @t81)) % 0.45/0.66 (define @t83 () (@list @t67)) % 0.45/0.66 (define @t84 () (forall @t83 @t81)) % 0.45/0.66 (define @t85 () (forall @t83 @t80)) % 0.45/0.66 (define @t86 () (@var "BOUND_VARIABLE_9486" $$unsorted)) % 0.45/0.66 (define @t87 () (@list @t86)) % 0.45/0.66 (define @t88 () (or @t76 @t85)) % 0.45/0.66 (define @t89 () (tptp.set_difference @t66 @t86)) % 0.45/0.66 (define @t90 () (@list @t86)) % 0.45/0.66 (define @t91 () (forall @t90 (or (not (tptp.eiw_di @t86 @t2)) (tptp.qmltpeq @t89 tptp.empty_set @t2) (tptp.qmltpeq @t89 @t66 @t2)))) % 0.45/0.66 (define @t92 () (tptp.singleton @t18)) % 0.45/0.66 (define @t93 () (tptp.set_difference @t92 @t86)) % 0.45/0.66 (define @t94 () (tptp.set_difference @t92 @t4)) % 0.45/0.66 (define @t95 () (tptp.qmltpeq @t94 @t92 @t8)) % 0.45/0.66 (define @t96 () (tptp.qmltpeq @t94 tptp.empty_set @t8)) % 0.45/0.66 (define @t97 () (not (tptp.eiw_di @t4 @t8))) % 0.45/0.66 (define @t98 () (forall @t6 (or @t97 @t96 @t95))) % 0.45/0.66 (define @t99 () (@list @t4)) % 0.45/0.66 (define @t100 () (lambda @t23 @t98)) % 0.45/0.66 (define @t101 () (or @t76 (_ @t100 @t4 @t2))) % 0.45/0.66 (define @t102 () (forall @t6 @t101)) % 0.45/0.66 (define @t103 () (lambda @t7 @t102)) % 0.45/0.66 (define @t104 () (_ @t60 @t4 @t2)) % 0.45/0.66 (define @t105 () (lambda @t63 (forall @t6 (or @t76 @t104)))) % 0.45/0.66 (define @t106 () (tptp.qmltpeq @t94 @t92 @t2)) % 0.45/0.66 (define @t107 () (tptp.qmltpeq @t94 tptp.empty_set @t2)) % 0.45/0.66 (define @t108 () (_ @t32 @t4)) % 0.45/0.66 (define @t109 () (_ tptp.qmltpeq @t94)) % 0.45/0.66 (define @t110 () (_ tptp.qmltpeq @t108)) % 0.45/0.66 (define @t111 () (_ (_ @t110 @t25) @t2)) % 0.45/0.66 (define @t112 () (_ (_ @t110 tptp.empty_set) @t2)) % 0.45/0.66 (define @t113 () (or @t76 @t112 @t111)) % 0.45/0.66 (define @t114 () (or @t112 @t111)) % 0.45/0.66 (define @t115 () (_ @t34 @t8)) % 0.45/0.66 (define @t116 () (_ @t37 @t8)) % 0.45/0.66 (define @t117 () (or @t116 @t115)) % 0.45/0.66 (define @t118 () (lambda @t22 @t117)) % 0.45/0.66 (define @t119 () (_ @t118 @t4 @t2)) % 0.45/0.66 (define @t120 () (or @t76 @t119)) % 0.45/0.66 (define @t121 () (forall @t6 @t120)) % 0.45/0.66 (define @t122 () (lambda @t7 @t121)) % 0.45/0.66 (define @t123 () (_ @t34 @t2)) % 0.45/0.66 (define @t124 () (_ @t37 @t2)) % 0.45/0.66 (define @t125 () (lambda @t7 (or @t124 @t123))) % 0.45/0.66 (define @t126 () (@list @t48 @t2)) % 0.45/0.66 (define @t127 () (lambda @t126 (or @t124 @t49))) % 0.45/0.66 (define @t128 () (_ @t52 @t37)) % 0.45/0.66 (define @t129 () (lambda @t22 (_ (_ @t128 @t34) @t8))) % 0.45/0.66 (define @t130 () (lambda @t23 (_ (_ @t105 @t129) @t8))) % 0.45/0.66 (define @t131 () (not @t5)) % 0.45/0.66 (define @t132 () (or @t131 @t61)) % 0.45/0.66 (define @t133 () (@quantifiers_skolemize @t71 0)) % 0.45/0.66 (define @t134 () (tptp.singleton @t133)) % 0.45/0.66 (define @t135 () (@quantifiers_skolemize @t71 1)) % 0.45/0.66 (define @t136 () (tptp.set_difference @t134 @t135)) % 0.45/0.66 (define @t137 () (tptp.qmltpeq @t136 @t134 tptp.mactual)) % 0.45/0.66 (define @t138 () (tptp.qmltpeq @t136 tptp.empty_set tptp.mactual)) % 0.45/0.66 (define @t139 () (tptp.eiw_di @t135 tptp.mactual)) % 0.45/0.66 (define @t140 () (not @t139)) % 0.45/0.66 (define @t141 () (tptp.eiw_di @t133 tptp.mactual)) % 0.45/0.66 (define @t142 () (not @t141)) % 0.45/0.66 (define @t143 () (or @t142 @t140 @t138 @t137)) % 0.45/0.66 (define @t144 () (@list true)) % 0.45/0.66 (define @t145 () (@list @t143)) % 0.45/0.66 (define @t146 () (@var "BOUND_VARIABLE_9369" $$unsorted)) % 0.45/0.66 (define @t147 () (tptp.set_difference @t66 @t146)) % 0.45/0.66 (define @t148 () (@list @t4 @t146)) % 0.45/0.66 (define @t149 () (forall @t148 (or @t69 (not (tptp.eiw_di @t146 tptp.mactual)) (= (tptp.in @t4 @t146 tptp.mactual) (tptp.qmltpeq @t147 tptp.empty_set tptp.mactual))))) % 0.45/0.66 (define @t150 () (= (tptp.in @t4 @t146 @t2) (tptp.qmltpeq @t147 tptp.empty_set @t2))) % 0.45/0.66 (define @t151 () (not (tptp.eiw_di @t146 @t2))) % 0.45/0.66 (define @t152 () (or @t76 @t151 @t150)) % 0.45/0.66 (define @t153 () (lambda @t7 (forall @t148 @t152))) % 0.45/0.66 (define @t154 () (_ @t153 tptp.mactual)) % 0.45/0.66 (define @t155 () (or @t151 @t150)) % 0.45/0.66 (define @t156 () (or @t76 @t155)) % 0.45/0.66 (define @t157 () (forall @t148 @t156)) % 0.45/0.66 (define @t158 () (@list @t146)) % 0.45/0.66 (define @t159 () (forall @t158 @t156)) % 0.45/0.66 (define @t160 () (forall @t158 @t155)) % 0.45/0.66 (define @t161 () (@var "BOUND_VARIABLE_9346" $$unsorted)) % 0.45/0.66 (define @t162 () (@list @t161)) % 0.45/0.66 (define @t163 () (or @t76 @t160)) % 0.45/0.66 (define @t164 () (@list @t161)) % 0.45/0.66 (define @t165 () (forall @t164 (or (not (tptp.eiw_di @t161 @t2)) (= (tptp.in @t4 @t161 @t2) (tptp.qmltpeq (tptp.set_difference @t66 @t161) tptp.empty_set @t2))))) % 0.45/0.66 (define @t166 () (tptp.in @t18 @t4 @t8)) % 0.45/0.66 (define @t167 () (forall @t6 (or @t97 (= @t166 @t96)))) % 0.45/0.66 (define @t168 () (lambda @t23 @t167)) % 0.45/0.66 (define @t169 () (or @t76 (_ @t168 @t4 @t2))) % 0.45/0.66 (define @t170 () (forall @t6 @t169)) % 0.45/0.66 (define @t171 () (lambda @t7 @t170)) % 0.45/0.66 (define @t172 () (tptp.in @t18 @t4 @t2)) % 0.45/0.66 (define @t173 () (_ (_ @t29 @t4) @t2)) % 0.45/0.66 (define @t174 () (= @t173 @t112)) % 0.45/0.66 (define @t175 () (or @t76 @t174)) % 0.45/0.66 (define @t176 () (_ @t31 @t8)) % 0.45/0.66 (define @t177 () (= @t176 @t116)) % 0.45/0.66 (define @t178 () (lambda @t22 @t177)) % 0.45/0.66 (define @t179 () (_ @t178 @t4 @t2)) % 0.45/0.66 (define @t180 () (or @t76 @t179)) % 0.45/0.66 (define @t181 () (forall @t6 @t180)) % 0.45/0.66 (define @t182 () (lambda @t7 @t181)) % 0.45/0.66 (define @t183 () (_ @t31 @t2)) % 0.45/0.66 (define @t184 () (lambda @t7 (= @t183 @t124))) % 0.45/0.66 (define @t185 () (lambda @t126 (= @t124 @t49))) % 0.45/0.66 (define @t186 () (_ @t54 @t37)) % 0.45/0.66 (define @t187 () (lambda @t22 (_ (_ @t186 @t31) @t8))) % 0.45/0.66 (define @t188 () (tptp.in @t133 @t135 tptp.mactual)) % 0.45/0.66 (define @t189 () (or @t142 @t140 (= @t188 @t138))) % 0.45/0.66 (define @t190 () (@list @t133 @t135)) % 0.45/0.66 (define @t191 () (= @t138 @t188)) % 0.45/0.66 (define @t192 () (or @t142 @t140 @t191)) % 0.45/0.66 (define @t193 () (@list false)) % 0.45/0.66 (define @t194 () (@list false false false)) % 0.45/0.66 (define @t195 () (@var "BOUND_VARIABLE_9267" $$unsorted)) % 0.45/0.66 (define @t196 () (tptp.set_difference @t66 @t195)) % 0.45/0.66 (define @t197 () (@list @t4 @t195)) % 0.45/0.66 (define @t198 () (forall @t197 (or @t69 (not (tptp.eiw_di @t195 tptp.mactual)) (= (not (tptp.in @t4 @t195 tptp.mactual)) (tptp.qmltpeq @t196 @t66 tptp.mactual))))) % 0.45/0.66 (define @t199 () (= (not (tptp.in @t4 @t195 @t2)) (tptp.qmltpeq @t196 @t66 @t2))) % 0.45/0.66 (define @t200 () (not (tptp.eiw_di @t195 @t2))) % 0.45/0.66 (define @t201 () (or @t76 @t200 @t199)) % 0.45/0.66 (define @t202 () (lambda @t7 (forall @t197 @t201))) % 0.45/0.66 (define @t203 () (_ @t202 tptp.mactual)) % 0.45/0.66 (define @t204 () (or @t200 @t199)) % 0.45/0.66 (define @t205 () (or @t76 @t204)) % 0.45/0.66 (define @t206 () (forall @t197 @t205)) % 0.45/0.66 (define @t207 () (@list @t195)) % 0.45/0.66 (define @t208 () (forall @t207 @t205)) % 0.45/0.66 (define @t209 () (forall @t207 @t204)) % 0.45/0.66 (define @t210 () (@var "BOUND_VARIABLE_9242" $$unsorted)) % 0.45/0.66 (define @t211 () (@list @t210)) % 0.45/0.66 (define @t212 () (or @t76 @t209)) % 0.45/0.66 (define @t213 () (@list @t210)) % 0.45/0.66 (define @t214 () (forall @t213 (or (not (tptp.eiw_di @t210 @t2)) (= (not (tptp.in @t4 @t210 @t2)) (tptp.qmltpeq (tptp.set_difference @t66 @t210) @t66 @t2))))) % 0.45/0.66 (define @t215 () (forall @t6 (or @t97 (= (not @t166) @t95)))) % 0.45/0.66 (define @t216 () (lambda @t23 @t215)) % 0.45/0.66 (define @t217 () (or @t76 (_ @t216 @t4 @t2))) % 0.45/0.66 (define @t218 () (forall @t6 @t217)) % 0.45/0.66 (define @t219 () (lambda @t7 @t218)) % 0.45/0.66 (define @t220 () (not @t173)) % 0.45/0.66 (define @t221 () (= @t220 @t111)) % 0.45/0.66 (define @t222 () (or @t76 @t221)) % 0.45/0.66 (define @t223 () (= @t115 (not @t176))) % 0.45/0.66 (define @t224 () (lambda @t22 @t223)) % 0.45/0.66 (define @t225 () (_ @t224 @t4 @t2)) % 0.45/0.66 (define @t226 () (or @t76 @t225)) % 0.45/0.66 (define @t227 () (forall @t6 @t226)) % 0.45/0.66 (define @t228 () (lambda @t7 @t227)) % 0.45/0.66 (define @t229 () (not @t183)) % 0.45/0.66 (define @t230 () (lambda @t7 @t229)) % 0.45/0.66 (define @t231 () (_ @t230 @t2)) % 0.45/0.66 (define @t232 () (lambda @t7 (= @t231 @t123))) % 0.45/0.66 (define @t233 () (_ @t47 @t31)) % 0.45/0.66 (define @t234 () (lambda @t126 (= @t123 @t49))) % 0.45/0.66 (define @t235 () (_ @t54 @t34)) % 0.45/0.66 (define @t236 () (lambda @t22 (_ (_ @t235 @t233) @t8))) % 0.45/0.66 (define @t237 () (not @t188)) % 0.45/0.66 (define @t238 () (or @t142 @t140 (= @t237 @t137))) % 0.45/0.66 (define @t239 () (= @t137 @t237)) % 0.45/0.66 (define @t240 () (or @t142 @t140 @t239)) % 0.45/0.66 (define @t241 () (not @t239)) % 0.45/0.66 (assume @p1 (forall (@list @t2 @t1) @t3)) % 0.45/0.66 (assume @p2 (forall @t7 (exists @t6 @t5))) % 0.45/0.66 (assume @p3 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ @t9 @t4) @t8))))) % 0.45/0.66 (assume @p4 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mforall_di (lambda @t14 (_ (_ (_ tptp.mimplies @t13) (_ @t12 @t4)) @t8))) @t8))))) % 0.45/0.66 (assume @p5 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mforall_di (lambda @t14 (_ (_ tptp.mforall_di (lambda (@list @t15 @t8) (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t13) (_ @t12 @t15))) (_ @t9 @t15)) @t8))) @t8))) @t8))))) % 0.45/0.66 (assume @p6 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ @t20 (_ (_ tptp.qmltpeq (_ (_ tptp.set_difference @t18) @t16)) (_ (_ tptp.set_difference @t17) @t16))) @t8))) @t8))) @t8))))) % 0.45/0.66 (assume @p7 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ @t20 (_ (_ tptp.qmltpeq (_ @t24 @t18)) (_ @t24 @t17))) @t8))) @t8))) @t8))))) % 0.45/0.66 (assume @p8 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ @t20 (_ (_ tptp.qmltpeq @t25) (_ tptp.singleton @t17))) @t8))) @t8))))) % 0.45/0.66 (assume @p9 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ (_ tptp.mimplies (_ @t27 @t26)) (_ tptp.empty @t17)) @t8))) @t8))))) % 0.45/0.66 (assume @p10 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t27 (_ @t29 @t16))) (_ @t28 @t16)) @t8))) @t8))) @t8))))) % 0.45/0.66 (assume @p11 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t27 (_ @t30 @t18))) (_ @t30 @t17)) @t8))) @t8))) @t8))))) % 0.45/0.66 (assume @p12 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ (_ tptp.mimplies @t31) (_ tptp.mnot (_ @t28 @t18))) @t8))) @t8))))) % 0.45/0.66 (assume @p13 (_ tptp.mlocal (_ tptp.empty tptp.empty_set))) % 0.45/0.66 (assume @p14 (_ tptp.mlocal (_ tptp.mforall_di @t36))) % 0.45/0.66 (assume @p15 (_ tptp.mlocal (_ tptp.mforall_di @t39))) % 0.45/0.66 (assume @p16 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t23 (_ @t26 @t8))))) % 0.45/0.66 (assume @p17 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t23 (_ (_ tptp.mnot @t26) @t8))))) % 0.45/0.66 (assume @p18 @t42) % 0.45/0.66 (assume @p19 true) % 0.45/0.66 (step @p20 (= tptp.mlocal @t44) :rule refl :args (@t44)) % 0.45/0.66 (step @p21 (= tptp.mnot @t47) :rule refl :args (@t47)) % 0.45/0.66 (step @p22 (= tptp.mand @t51) :rule refl :args (@t51)) % 0.45/0.66 (step @p23 (= tptp.mor @t52) :rule refl :args (@t52)) % 0.45/0.66 (step @p24 (= tptp.mimplies @t53) :rule refl :args (@t53)) % 0.45/0.66 (step @p25 (= tptp.mequiv @t54) :rule refl :args (@t54)) % 0.45/0.66 (step @p26 (= tptp.mbox @t58) :rule refl :args (@t58)) % 0.45/0.66 (step @p27 (= tptp.mdia @t59) :rule refl :args (@t59)) % 0.45/0.66 (step @p28 (= tptp.mforall_di @t64) :rule refl :args (@t64)) % 0.45/0.66 (step @p29 (= tptp.mexists_di @t65) :rule refl :args (@t65)) % 0.45/0.66 (step @p30 :rule beta-reduce :args ((= @t79 @t71))) % 0.45/0.66 (step @p31 :rule beta-reduce :args ((= (_ @t44 @t78) @t79))) % 0.45/0.66 (step @p32 :rule trans :premises (@p31 @p30)) % 0.45/0.66 (step @p33 :rule aci_norm :args ((= @t81 @t77))) % 0.45/0.66 (step @p34 :rule cong :premises (@p33) :args (@t82)) % 0.45/0.66 (step @p35 :rule quant-merge-prenex :args ((= (forall @t6 @t84) @t82))) % 0.45/0.66 (step @p36 :rule alpha_equiv :args (@t85 (@list @t67) @t87)) % 0.45/0.66 (step @p37 :rule refl :args (@t76)) % 0.45/0.66 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t88)) % 0.45/0.66 (step @p39 :rule quant-miniscope-or :args ((= @t84 @t88))) % 0.45/0.66 (step @p40 :rule trans :premises (@p39 @p38)) % 0.45/0.66 (step @p41 :rule symm :premises (@p40)) % 0.45/0.66 (step @p42 :rule cong :premises (@p41) :args ((forall @t6 (or @t76 @t91)))) % 0.45/0.66 (step @p43 :rule trans :premises (@p42 @p35)) % 0.45/0.66 (step @p44 :rule trans :premises (@p43 @p34)) % 0.45/0.66 (step @p45 :rule beta-reduce :args ((= (_ (lambda @t23 (forall @t90 (or (not (tptp.eiw_di @t86 @t8)) (tptp.qmltpeq @t93 tptp.empty_set @t8) (tptp.qmltpeq @t93 @t92 @t8)))) @t4 @t2) @t91))) % 0.45/0.66 (step @p46 :rule refl :args (@t2)) % 0.45/0.66 (step @p47 :rule refl :args (@t4)) % 0.45/0.66 (step @p48 :rule alpha_equiv :args (@t98 @t99 @t87)) % 0.45/0.66 (step @p49 :rule cong :premises (@p48) :args (@t100)) % 0.45/0.66 (step @p50 :rule ho_cong :premises (@p49 @p47 @p46)) % 0.45/0.66 (step @p51 :rule trans :premises (@p50 @p45)) % 0.45/0.66 (step @p52 :rule refl :args (@t76)) % 0.45/0.66 (step @p53 :rule nary_cong :premises (@p52 @p51) :args (@t101)) % 0.45/0.66 (step @p54 :rule cong :premises (@p53) :args (@t102)) % 0.45/0.66 (step @p55 :rule trans :premises (@p54 @p44)) % 0.45/0.66 (step @p56 :rule cong :premises (@p55) :args (@t103)) % 0.45/0.66 (step @p57 :rule beta-reduce :args ((= (_ @t105 @t100) @t103))) % 0.45/0.66 (step @p58 :rule trans :premises (@p57 @p56)) % 0.45/0.66 (step @p59 :rule beta-reduce :args ((= (_ (lambda @t7 (forall @t6 (or @t76 @t107 @t106))) @t8) @t98))) % 0.45/0.66 (step @p60 :rule refl :args (@t8)) % 0.45/0.66 (step @p61 :rule refl :args ((tptp.qmltpeq @t108 @t25 @t2))) % 0.45/0.66 (step @p62 :rule refl :args (@t92)) % 0.45/0.66 (step @p63 :rule refl :args ((tptp.set_difference @t25 @t4))) % 0.45/0.66 (step @p64 :rule cong :premises (@p62 @p47) :args (@t94)) % 0.45/0.66 (step @p65 :rule trans :premises (@p64 @p63)) % 0.45/0.66 (step @p66 :rule cong :premises (@p65 @p62 @p46) :args (@t106)) % 0.45/0.66 (step @p67 :rule trans :premises (@p66 @p61)) % 0.45/0.66 (step @p68 :rule refl :args (tptp.qmltpeq)) % 0.45/0.66 (step @p69 :rule ho_cong :premises (@p68 @p65)) % 0.45/0.66 (step @p70 :rule ho_cong :premises (@p69 @p62)) % 0.45/0.66 (step @p71 :rule ho_cong :premises (@p70 @p46)) % 0.45/0.66 (step @p72 :rule cong :premises (@p71 @p67) :args ((= (_ (_ @t109 @t92) @t2) @t106))) % 0.45/0.66 (step @p73 :rule symm :premises (@p72)) % 0.45/0.66 (step @p74 :rule refl :args (@t111)) % 0.45/0.66 (step @p75 :rule eq_resolve :premises (@p74 @p73)) % 0.45/0.66 (step @p76 :rule refl :args (@t25)) % 0.45/0.66 (step @p77 :rule cong :premises (@p76 @p62) :args ((= @t25 @t92))) % 0.45/0.66 (step @p78 :rule symm :premises (@p77)) % 0.45/0.66 (step @p79 :rule eq_resolve :premises (@p76 @p78)) % 0.45/0.66 (step @p80 :rule refl :args (tptp.set_difference)) % 0.45/0.66 (step @p81 :rule ho_cong :premises (@p80 @p62)) % 0.45/0.66 (step @p82 :rule ho_cong :premises (@p81 @p47)) % 0.45/0.66 (step @p83 :rule cong :premises (@p82 @p65) :args ((= (_ (_ tptp.set_difference @t92) @t4) @t94))) % 0.45/0.66 (step @p84 :rule symm :premises (@p83)) % 0.45/0.66 (step @p85 :rule refl :args (@t108)) % 0.45/0.66 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 0.45/0.66 (step @p87 :rule ho_cong :premises (@p80 @p79)) % 0.45/0.66 (step @p88 :rule ho_cong :premises (@p87 @p47)) % 0.45/0.66 (step @p89 :rule trans :premises (@p88 @p86)) % 0.45/0.66 (step @p90 :rule ho_cong :premises (@p68 @p89)) % 0.45/0.66 (step @p91 :rule ho_cong :premises (@p90 @p79)) % 0.45/0.66 (step @p92 :rule ho_cong :premises (@p91 @p46)) % 0.45/0.66 (step @p93 :rule trans :premises (@p92 @p75)) % 0.45/0.66 (step @p94 :rule refl :args ((tptp.qmltpeq @t108 tptp.empty_set @t2))) % 0.45/0.66 (step @p95 :rule refl :args (tptp.empty_set)) % 0.45/0.66 (step @p96 :rule cong :premises (@p65 @p95 @p46) :args (@t107)) % 0.45/0.66 (step @p97 :rule trans :premises (@p96 @p94)) % 0.45/0.66 (step @p98 :rule ho_cong :premises (@p69 @p95)) % 0.45/0.66 (step @p99 :rule ho_cong :premises (@p98 @p46)) % 0.45/0.66 (step @p100 :rule cong :premises (@p99 @p97) :args ((= (_ (_ @t109 tptp.empty_set) @t2) @t107))) % 0.45/0.66 (step @p101 :rule symm :premises (@p100)) % 0.45/0.66 (step @p102 :rule refl :args (@t112)) % 0.45/0.66 (step @p103 :rule eq_resolve :premises (@p102 @p101)) % 0.45/0.66 (step @p104 :rule ho_cong :premises (@p90 @p95)) % 0.45/0.66 (step @p105 :rule ho_cong :premises (@p104 @p46)) % 0.45/0.66 (step @p106 :rule trans :premises (@p105 @p103)) % 0.45/0.66 (step @p107 :rule nary_cong :premises (@p37 @p106 @p93) :args (@t113)) % 0.45/0.66 (step @p108 :rule cong :premises (@p107) :args ((forall @t6 @t113))) % 0.45/0.66 (step @p109 :rule aci_norm :args ((= (or @t76 @t114) @t113))) % 0.45/0.66 (step @p110 :rule beta-reduce :args ((= @t119 @t114))) % 0.45/0.66 (step @p111 :rule nary_cong :premises (@p52 @p110) :args (@t120)) % 0.45/0.66 (step @p112 :rule trans :premises (@p111 @p109)) % 0.45/0.66 (step @p113 :rule cong :premises (@p112) :args (@t121)) % 0.45/0.66 (step @p114 :rule trans :premises (@p113 @p108)) % 0.45/0.66 (step @p115 :rule cong :premises (@p114) :args (@t122)) % 0.45/0.66 (step @p116 :rule beta-reduce :args ((= (_ @t105 @t118) @t122))) % 0.45/0.66 (step @p117 :rule trans :premises (@p116 @p115)) % 0.45/0.66 (step @p118 :rule beta-reduce :args ((= (_ @t125 @t8) @t117))) % 0.45/0.66 (step @p119 :rule beta-reduce :args ((= (_ @t127 @t34) @t125))) % 0.45/0.66 (step @p120 :rule refl :args (@t34)) % 0.45/0.66 (step @p121 :rule beta-reduce :args ((= @t128 @t127))) % 0.45/0.66 (step @p122 :rule ho_cong :premises (@p121 @p120)) % 0.45/0.66 (step @p123 :rule trans :premises (@p122 @p119)) % 0.45/0.66 (step @p124 :rule ho_cong :premises (@p123 @p60)) % 0.45/0.66 (step @p125 :rule trans :premises (@p124 @p118)) % 0.45/0.66 (step @p126 :rule cong :premises (@p125) :args (@t129)) % 0.45/0.66 (step @p127 :rule refl :args (@t105)) % 0.45/0.66 (step @p128 :rule ho_cong :premises (@p127 @p126)) % 0.45/0.66 (step @p129 :rule trans :premises (@p128 @p117)) % 0.45/0.66 (step @p130 :rule ho_cong :premises (@p129 @p60)) % 0.45/0.66 (step @p131 :rule trans :premises (@p130 @p59)) % 0.45/0.66 (step @p132 :rule cong :premises (@p131) :args (@t130)) % 0.45/0.66 (step @p133 :rule ho_cong :premises (@p127 @p132)) % 0.45/0.66 (step @p134 :rule trans :premises (@p133 @p58)) % 0.45/0.66 (step @p135 :rule refl :args (@t44)) % 0.45/0.66 (step @p136 :rule ho_cong :premises (@p135 @p134)) % 0.45/0.66 (step @p137 :rule trans :premises (@p136 @p32)) % 0.45/0.66 (step @p138 :rule cong :premises (@p137) :args ((not (_ @t44 (_ @t105 @t130))))) % 0.45/0.66 (step @p139 :rule refl :args (@t37)) % 0.45/0.66 (step @p140 :rule ho_cong :premises (@p23 @p139)) % 0.45/0.66 (step @p141 :rule ho_cong :premises (@p140 @p120)) % 0.45/0.66 (step @p142 :rule ho_cong :premises (@p141 @p60)) % 0.45/0.66 (step @p143 :rule cong :premises (@p142) :args (@t40)) % 0.45/0.66 (step @p144 :rule refl :args (@t104)) % 0.45/0.66 (step @p145 :rule refl :args (@t61)) % 0.45/0.66 (step @p146 :rule cong :premises (@p145 @p144) :args ((= @t61 @t104))) % 0.45/0.66 (step @p147 :rule symm :premises (@p146)) % 0.45/0.66 (step @p148 :rule eq_resolve :premises (@p145 @p147)) % 0.45/0.66 (step @p149 :rule refl :args (@t75)) % 0.45/0.66 (step @p150 :rule refl :args (@t5)) % 0.45/0.66 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t5 @t75))) % 0.45/0.66 (step @p152 :rule symm :premises (@p151)) % 0.45/0.66 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.45/0.66 (step @p154 :rule cong :premises (@p153) :args (@t131)) % 0.45/0.66 (step @p155 :rule nary_cong :premises (@p154 @p148) :args (@t132)) % 0.45/0.66 (step @p156 :rule cong :premises (@p155) :args ((forall @t6 @t132))) % 0.45/0.66 (step @p157 :rule bool-impl-elim :args (@t5 @t61)) % 0.45/0.66 (step @p158 :rule cong :premises (@p157) :args (@t62)) % 0.45/0.66 (step @p159 :rule trans :premises (@p158 @p156)) % 0.45/0.66 (step @p160 :rule cong :premises (@p159) :args (@t64)) % 0.45/0.66 (step @p161 :rule trans :premises (@p28 @p160)) % 0.45/0.66 (step @p162 :rule ho_cong :premises (@p161 @p143)) % 0.45/0.66 (step @p163 :rule ho_cong :premises (@p162 @p60)) % 0.45/0.66 (step @p164 :rule cong :premises (@p163) :args (@t41)) % 0.45/0.66 (step @p165 :rule ho_cong :premises (@p161 @p164)) % 0.45/0.66 (step @p166 :rule ho_cong :premises (@p20 @p165)) % 0.45/0.66 (step @p167 :rule cong :premises (@p166) :args (@t42)) % 0.45/0.66 (step @p168 :rule trans :premises (@p167 @p138)) % 0.45/0.66 (step @p169 :rule eq_resolve :premises (@p18 @p168)) % 0.45/0.66 (step @p170 :rule skolemize :premises (@p169)) % 0.45/0.66 (step @p171 :rule cnf_or_neg :args (@t143 2)) % 0.45/0.66 (step @p172 :rule chain_m_resolution :premises (@p171 @p170) :args ((not @t138) @t144 @t145)) % 0.45/0.66 (step @p173 :rule beta-reduce :args ((= @t154 @t149))) % 0.45/0.66 (step @p174 :rule beta-reduce :args ((= (_ @t44 @t153) @t154))) % 0.45/0.66 (step @p175 :rule trans :premises (@p174 @p173)) % 0.45/0.66 (step @p176 :rule aci_norm :args ((= @t156 @t152))) % 0.45/0.66 (step @p177 :rule cong :premises (@p176) :args (@t157)) % 0.45/0.66 (step @p178 :rule quant-merge-prenex :args ((= (forall @t6 @t159) @t157))) % 0.45/0.66 (step @p179 :rule alpha_equiv :args (@t160 (@list @t146) @t162)) % 0.45/0.66 (step @p180 :rule nary_cong :premises (@p37 @p179) :args (@t163)) % 0.45/0.66 (step @p181 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@t193 (@list @t198))) % 0.45/0.66 (step @p365 :rule cnf_or_pos :args (@t240)) % 0.45/0.66 (step @p366 :rule reordering :premises (@p365) :args ((or @t142 @t140 @t239 (not @t240)))) % 0.45/0.66 (step @p367 :rule chain_m_resolution :premises (@p366 @p271 @p265 @p364) :args (@t239 @t194 (@list @t141 @t139 @t240))) % 0.45/0.66 (step @p368 :rule cnf_or_neg :args (@t143 3)) % 0.45/0.66 (step @p369 :rule chain_m_resolution :premises (@p368 @p170) :args ((not @t137) @t144 @t145)) % 0.45/0.66 (step @p370 :rule bool-double-not-elim :args (@t188)) % 0.45/0.66 (step @p371 :rule refl :args (@t137)) % 0.45/0.66 (step @p372 :rule refl :args (@t241)) % 0.45/0.66 (step @p373 :rule nary_cong :premises (@p372 @p371 @p370) :args ((or @t241 @t137 (not @t237)))) % 0.45/0.66 (step @p374 :rule cnf_equiv_pos2 :args (@t239)) % 0.45/0.66 (step @p375 :rule eq_resolve :premises (@p374 @p373)) % 0.45/0.66 (step @p376 :rule reordering :premises (@p375) :args ((or @t137 @t188 @t241))) % 0.45/0.66 (step @p377 :rule chain_m_resolution :premises (@p376 @p369 @p367) :args (@t188 (@list true false) (@list @t137 @t239))) % 0.45/0.66 (step @p378 :rule cnf_equiv_pos2 :args (@t191)) % 0.45/0.66 (step @p379 :rule reordering :premises (@p378) :args ((or @t138 @t237 (not @t191)))) % 0.45/0.66 (step @p380 false :rule chain_m_resolution :premises (@p379 @p377 @p274 @p172) :args (false (@list false false true) (@list @t188 @t191 @t138))) % 0.45/0.66 ) % 0.45/0.66 % SZS output end Proof % 0.45/0.66 % cvc5 exiting %------------------------------------------------------------------------------