%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET574^20 : 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 : n019.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 08:48:04 AM UTC 2026 % Result : Theorem 0.36s 0.60s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET574^20 : 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 : n019.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 16:02:34 EDT 2026 % 0.15/0.34 % CPUTime : % 0.26/0.49 %----Proving TH0 % 0.36/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.60 % SZS status Theorem % 0.36/0.60 % SZS output start Proof % 0.36/0.60 ( % 0.36/0.60 (declare-sort $$unsorted 0) % 0.36/0.60 (declare-sort tptp.mworld 0) % 0.36/0.60 (declare-const tptp.mactual tptp.mworld) % 0.36/0.60 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.36/0.60 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 0.36/0.60 (declare-const tptp.intersect (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.36/0.60 (declare-const tptp.member (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.36/0.60 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.36/0.60 (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)))))) % 0.36/0.60 (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))))))) % 0.36/0.60 (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))))))) % 0.36/0.60 (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))))))) % 0.36/0.60 (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))))))) % 0.36/0.60 (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)))))))) % 0.36/0.60 (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)))))))) % 0.36/0.60 (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)))))))) % 0.36/0.60 (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)))))))) % 0.36/0.60 (define @t1 () (@var "W" tptp.mworld)) % 0.36/0.60 (define @t2 () (_ tptp.mrel @t1)) % 0.36/0.60 (define @t3 () (@list @t1)) % 0.36/0.60 (define @t4 () (@var "X" $$unsorted)) % 0.36/0.60 (define @t5 () (_ tptp.eiw_di @t4)) % 0.36/0.60 (define @t6 () (_ @t5 @t1)) % 0.36/0.60 (define @t7 () (@list @t4)) % 0.36/0.60 (define @t8 () (@var "V" tptp.mworld)) % 0.36/0.60 (define @t9 () (@var "__flatten_var_0" tptp.mworld)) % 0.36/0.60 (define @t10 () (@var "C" $$unsorted)) % 0.36/0.60 (define @t11 () (@var "D" $$unsorted)) % 0.36/0.60 (define @t12 () (_ tptp.member @t11)) % 0.36/0.60 (define @t13 () (_ @t12 @t10)) % 0.36/0.60 (define @t14 () (@var "B" $$unsorted)) % 0.36/0.60 (define @t15 () (_ @t12 @t14)) % 0.36/0.60 (define @t16 () (@list @t11 @t9)) % 0.36/0.60 (define @t17 () (lambda @t16 (_ (_ (_ tptp.mand @t15) @t13) @t9))) % 0.36/0.60 (define @t18 () (_ tptp.intersect @t14)) % 0.36/0.60 (define @t19 () (_ @t18 @t10)) % 0.36/0.60 (define @t20 () (@list @t10 @t9)) % 0.36/0.60 (define @t21 () (lambda @t20 (_ (_ (_ tptp.mequiv @t19) (_ tptp.mexists_di @t17)) @t9))) % 0.36/0.60 (define @t22 () (@list @t14 @t9)) % 0.36/0.60 (define @t23 () (lambda @t22 (_ (_ tptp.mforall_di @t21) @t9))) % 0.36/0.60 (define @t24 () (_ tptp.intersect @t10)) % 0.36/0.60 (define @t25 () (_ @t24 @t11)) % 0.36/0.60 (define @t26 () (_ tptp.member @t14)) % 0.36/0.60 (define @t27 () (_ @t26 @t11)) % 0.36/0.60 (define @t28 () (_ @t26 @t10)) % 0.36/0.60 (define @t29 () (lambda @t16 (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t28) @t27)) @t25) @t9))) % 0.36/0.60 (define @t30 () (lambda @t20 (_ (_ tptp.mforall_di @t29) @t9))) % 0.36/0.60 (define @t31 () (lambda @t22 (_ (_ tptp.mforall_di @t30) @t9))) % 0.36/0.60 (define @t32 () (not (_ tptp.mlocal (_ tptp.mforall_di @t31)))) % 0.36/0.60 (define @t33 () (@var "Phi" (-> tptp.mworld Bool))) % 0.36/0.60 (define @t34 () (lambda (@list @t33) (_ @t33 tptp.mactual))) % 0.36/0.60 (define @t35 () (@var "A" (-> tptp.mworld Bool))) % 0.36/0.60 (define @t36 () (_ @t35 @t1)) % 0.36/0.60 (define @t37 () (lambda (@list @t35 @t1) (not @t36))) % 0.36/0.60 (define @t38 () (@var "B" (-> tptp.mworld Bool))) % 0.36/0.60 (define @t39 () (_ @t38 @t1)) % 0.36/0.60 (define @t40 () (@list @t35 @t38 @t1)) % 0.36/0.60 (define @t41 () (lambda @t40 (and @t36 @t39))) % 0.36/0.60 (define @t42 () (lambda @t40 (or @t36 @t39))) % 0.36/0.60 (define @t43 () (lambda @t40 (=> @t36 @t39))) % 0.36/0.60 (define @t44 () (lambda @t40 (= @t36 @t39))) % 0.36/0.60 (define @t45 () (_ @t33 @t8)) % 0.36/0.60 (define @t46 () (_ @t2 @t8)) % 0.36/0.60 (define @t47 () (@list @t8)) % 0.36/0.60 (define @t48 () (@list @t33 @t1)) % 0.36/0.60 (define @t49 () (lambda @t48 (forall @t47 (=> @t46 @t45)))) % 0.36/0.60 (define @t50 () (lambda @t48 (exists @t47 (and @t46 @t45)))) % 0.36/0.60 (define @t51 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.36/0.60 (define @t52 () (_ (_ @t51 @t4) @t1)) % 0.36/0.60 (define @t53 () (forall @t7 (=> @t6 @t52))) % 0.36/0.60 (define @t54 () (@list @t51 @t1)) % 0.36/0.60 (define @t55 () (lambda @t54 @t53)) % 0.36/0.60 (define @t56 () (and @t6 @t52)) % 0.36/0.60 (define @t57 () (exists @t7 @t56)) % 0.36/0.60 (define @t58 () (lambda @t54 @t57)) % 0.36/0.60 (define @t59 () (@var "BOUND_VARIABLE_7848" $$unsorted)) % 0.36/0.60 (define @t60 () (@var "BOUND_VARIABLE_7765" $$unsorted)) % 0.36/0.60 (define @t61 () (not (tptp.eiw_di @t60 tptp.mactual))) % 0.36/0.60 (define @t62 () (@list @t60)) % 0.36/0.60 (define @t63 () (not (tptp.eiw_di @t4 tptp.mactual))) % 0.36/0.60 (define @t64 () (@list @t4 @t59)) % 0.36/0.60 (define @t65 () (forall @t64 (or @t63 (not (tptp.eiw_di @t59 tptp.mactual)) (= (not (forall @t62 (or @t61 (not (tptp.member @t60 @t4 tptp.mactual)) (not (tptp.member @t60 @t59 tptp.mactual))))) (tptp.intersect @t4 @t59 tptp.mactual))))) % 0.36/0.60 (define @t66 () (not (tptp.member @t60 @t4 @t1))) % 0.36/0.60 (define @t67 () (not (tptp.eiw_di @t60 @t1))) % 0.36/0.60 (define @t68 () (= (not (forall @t62 (or @t67 @t66 (not (tptp.member @t60 @t59 @t1))))) (tptp.intersect @t4 @t59 @t1))) % 0.36/0.60 (define @t69 () (not (tptp.eiw_di @t59 @t1))) % 0.36/0.60 (define @t70 () (tptp.eiw_di @t4 @t1)) % 0.36/0.60 (define @t71 () (not @t70)) % 0.36/0.60 (define @t72 () (or @t71 @t69 @t68)) % 0.36/0.60 (define @t73 () (lambda @t3 (forall @t64 @t72))) % 0.36/0.60 (define @t74 () (_ @t73 tptp.mactual)) % 0.36/0.60 (define @t75 () (or @t69 @t68)) % 0.36/0.60 (define @t76 () (or @t71 @t75)) % 0.36/0.60 (define @t77 () (forall @t64 @t76)) % 0.36/0.60 (define @t78 () (@list @t59)) % 0.36/0.60 (define @t79 () (forall @t78 @t76)) % 0.36/0.60 (define @t80 () (forall @t78 @t75)) % 0.36/0.60 (define @t81 () (@var "BOUND_VARIABLE_7819" $$unsorted)) % 0.36/0.60 (define @t82 () (@list @t81)) % 0.36/0.60 (define @t83 () (or @t71 @t80)) % 0.36/0.60 (define @t84 () (@list @t81)) % 0.36/0.60 (define @t85 () (forall @t84 (or (not (tptp.eiw_di @t81 @t1)) (= (not (forall @t62 (or @t67 @t66 (not (tptp.member @t60 @t81 @t1))))) (tptp.intersect @t4 @t81 @t1))))) % 0.36/0.60 (define @t86 () (not (tptp.member @t60 @t14 @t9))) % 0.36/0.60 (define @t87 () (not (tptp.eiw_di @t60 @t9))) % 0.36/0.60 (define @t88 () (not (tptp.eiw_di @t4 @t9))) % 0.36/0.60 (define @t89 () (forall @t7 (or @t88 (= (not (forall @t62 (or @t87 @t86 (not (tptp.member @t60 @t4 @t9))))) (tptp.intersect @t14 @t4 @t9))))) % 0.36/0.60 (define @t90 () (@list @t4)) % 0.36/0.60 (define @t91 () (lambda @t22 @t89)) % 0.36/0.60 (define @t92 () (or @t71 (_ @t91 @t4 @t1))) % 0.36/0.60 (define @t93 () (forall @t7 @t92)) % 0.36/0.60 (define @t94 () (lambda @t3 @t93)) % 0.36/0.60 (define @t95 () (_ @t51 @t4 @t1)) % 0.36/0.60 (define @t96 () (lambda @t54 (forall @t7 (or @t71 @t95)))) % 0.36/0.60 (define @t97 () (tptp.intersect @t14 @t4 @t1)) % 0.36/0.60 (define @t98 () (not (forall @t62 (or @t67 (not (tptp.member @t60 @t14 @t1)) @t66)))) % 0.36/0.60 (define @t99 () (or @t71 (= @t97 @t98))) % 0.36/0.60 (define @t100 () (_ (_ @t18 @t4) @t1)) % 0.36/0.60 (define @t101 () (= @t100 @t98)) % 0.36/0.60 (define @t102 () (or @t71 @t101)) % 0.36/0.60 (define @t103 () (_ @t19 @t9)) % 0.36/0.60 (define @t104 () (forall @t7 (or @t88 (not (tptp.member @t4 @t14 @t9)) (not (tptp.member @t4 @t10 @t9))))) % 0.36/0.60 (define @t105 () (not @t104)) % 0.36/0.60 (define @t106 () (= @t103 @t105)) % 0.36/0.60 (define @t107 () (lambda @t20 @t106)) % 0.36/0.60 (define @t108 () (or @t71 (_ @t107 @t4 @t1))) % 0.36/0.60 (define @t109 () (forall @t7 @t108)) % 0.36/0.60 (define @t110 () (lambda @t3 @t109)) % 0.36/0.60 (define @t111 () (tptp.member @t4 @t10 @t1)) % 0.36/0.60 (define @t112 () (tptp.member @t4 @t14 @t1)) % 0.36/0.60 (define @t113 () (not (forall @t7 (or @t71 (not @t112) (not @t111))))) % 0.36/0.60 (define @t114 () (_ @t19 @t1)) % 0.36/0.60 (define @t115 () (lambda @t3 @t113)) % 0.36/0.60 (define @t116 () (_ @t115 @t1)) % 0.36/0.60 (define @t117 () (lambda @t3 (= @t116 @t114))) % 0.36/0.60 (define @t118 () (@list @t38 @t1)) % 0.36/0.60 (define @t119 () (_ tptp.member @t4)) % 0.36/0.60 (define @t120 () (_ (_ @t119 @t10) @t1)) % 0.36/0.60 (define @t121 () (not @t120)) % 0.36/0.60 (define @t122 () (_ (_ @t119 @t14) @t1)) % 0.36/0.60 (define @t123 () (not @t122)) % 0.36/0.60 (define @t124 () (or @t71 @t123 @t121)) % 0.36/0.60 (define @t125 () (and @t122 @t120)) % 0.36/0.60 (define @t126 () (or @t71 (not @t125))) % 0.36/0.60 (define @t127 () (and (_ @t15 @t9) (_ @t13 @t9))) % 0.36/0.60 (define @t128 () (lambda @t16 @t127)) % 0.36/0.60 (define @t129 () (_ @t128 @t4 @t1)) % 0.36/0.60 (define @t130 () (not @t129)) % 0.36/0.60 (define @t131 () (or @t71 @t130)) % 0.36/0.60 (define @t132 () (forall @t7 @t131)) % 0.36/0.60 (define @t133 () (not @t132)) % 0.36/0.60 (define @t134 () (lambda @t3 @t133)) % 0.36/0.60 (define @t135 () (lambda @t54 (not (forall @t7 (or @t71 (not @t95)))))) % 0.36/0.60 (define @t136 () (_ @t15 @t1)) % 0.36/0.60 (define @t137 () (lambda @t3 (and @t136 (_ @t13 @t1)))) % 0.36/0.60 (define @t138 () (lambda @t118 (and @t136 @t39))) % 0.36/0.60 (define @t139 () (_ @t41 @t15)) % 0.36/0.60 (define @t140 () (lambda @t16 (_ (_ @t139 @t13) @t9))) % 0.36/0.60 (define @t141 () (lambda @t118 (= @t114 @t39))) % 0.36/0.60 (define @t142 () (_ @t44 @t19)) % 0.36/0.60 (define @t143 () (lambda @t20 (_ (_ @t142 (_ @t135 @t140)) @t9))) % 0.36/0.60 (define @t144 () (not @t52)) % 0.36/0.60 (define @t145 () (not @t6)) % 0.36/0.60 (define @t146 () (or @t145 @t144)) % 0.36/0.60 (define @t147 () (forall @t7 (not @t56))) % 0.36/0.60 (define @t148 () (not @t147)) % 0.36/0.60 (define @t149 () (or @t145 @t52)) % 0.36/0.60 (define @t150 () (@var "BOUND_VARIABLE_8152" $$unsorted)) % 0.36/0.60 (define @t151 () (@var "BOUND_VARIABLE_8150" $$unsorted)) % 0.36/0.60 (define @t152 () (@list @t4 @t151 @t150)) % 0.36/0.60 (define @t153 () (forall @t152 (or @t63 (not (tptp.eiw_di @t151 tptp.mactual)) (not (tptp.member @t4 @t151 tptp.mactual)) (not (tptp.eiw_di @t150 tptp.mactual)) (not (tptp.member @t4 @t150 tptp.mactual)) (tptp.intersect @t151 @t150 tptp.mactual)))) % 0.36/0.60 (define @t154 () (@quantifiers_skolemize @t153 2)) % 0.36/0.60 (define @t155 () (@quantifiers_skolemize @t153 1)) % 0.36/0.60 (define @t156 () (forall @t62 (or @t61 (not (tptp.member @t60 @t155 tptp.mactual)) (not (tptp.member @t60 @t154 tptp.mactual))))) % 0.36/0.60 (define @t157 () (not @t156)) % 0.36/0.60 (define @t158 () (tptp.intersect @t155 @t154 tptp.mactual)) % 0.36/0.60 (define @t159 () (tptp.eiw_di @t154 tptp.mactual)) % 0.36/0.60 (define @t160 () (not @t159)) % 0.36/0.60 (define @t161 () (tptp.eiw_di @t155 tptp.mactual)) % 0.36/0.60 (define @t162 () (not @t161)) % 0.36/0.60 (define @t163 () (or @t162 @t160 (= @t157 @t158))) % 0.36/0.60 (define @t164 () (= @t158 @t157)) % 0.36/0.60 (define @t165 () (or @t162 @t160 @t164)) % 0.36/0.60 (define @t166 () (tptp.intersect @t151 @t150 @t1)) % 0.36/0.60 (define @t167 () (not (tptp.member @t4 @t150 @t1))) % 0.36/0.60 (define @t168 () (not (tptp.eiw_di @t150 @t1))) % 0.36/0.60 (define @t169 () (not (tptp.member @t4 @t151 @t1))) % 0.36/0.60 (define @t170 () (not (tptp.eiw_di @t151 @t1))) % 0.36/0.60 (define @t171 () (or @t71 @t170 @t169 @t168 @t167 @t166)) % 0.36/0.60 (define @t172 () (lambda @t3 (forall @t152 @t171))) % 0.36/0.60 (define @t173 () (_ @t172 tptp.mactual)) % 0.36/0.60 (define @t174 () (or @t170 @t169 @t168 @t167 @t166)) % 0.36/0.60 (define @t175 () (or @t71 @t174)) % 0.36/0.60 (define @t176 () (forall @t152 @t175)) % 0.36/0.60 (define @t177 () (@list @t151 @t150)) % 0.36/0.60 (define @t178 () (forall @t177 @t175)) % 0.36/0.60 (define @t179 () (forall @t177 @t174)) % 0.36/0.60 (define @t180 () (@var "BOUND_VARIABLE_8098" $$unsorted)) % 0.36/0.60 (define @t181 () (@var "BOUND_VARIABLE_8127" $$unsorted)) % 0.36/0.60 (define @t182 () (or @t71 @t179)) % 0.36/0.60 (define @t183 () (not (tptp.eiw_di @t180 @t1))) % 0.36/0.60 (define @t184 () (@list @t181 @t180)) % 0.36/0.60 (define @t185 () (forall @t184 (or (not (tptp.eiw_di @t181 @t1)) (not (tptp.member @t4 @t181 @t1)) @t183 (not (tptp.member @t4 @t180 @t1)) (tptp.intersect @t181 @t180 @t1)))) % 0.36/0.60 (define @t186 () (not (tptp.member @t14 @t180 @t9))) % 0.36/0.60 (define @t187 () (not (tptp.eiw_di @t180 @t9))) % 0.36/0.60 (define @t188 () (not (tptp.member @t14 @t4 @t9))) % 0.36/0.60 (define @t189 () (@list @t4 @t180)) % 0.36/0.60 (define @t190 () (forall @t189 (or @t88 @t188 @t187 @t186 (tptp.intersect @t4 @t180 @t9)))) % 0.36/0.60 (define @t191 () (lambda @t22 @t190)) % 0.36/0.60 (define @t192 () (or @t71 (_ @t191 @t4 @t1))) % 0.36/0.60 (define @t193 () (forall @t7 @t192)) % 0.36/0.60 (define @t194 () (lambda @t3 @t193)) % 0.36/0.60 (define @t195 () (tptp.intersect @t4 @t180 @t1)) % 0.36/0.60 (define @t196 () (not (tptp.member @t14 @t180 @t1))) % 0.36/0.60 (define @t197 () (tptp.member @t14 @t4 @t1)) % 0.36/0.60 (define @t198 () (not @t197)) % 0.36/0.60 (define @t199 () (or @t71 @t198 @t183 @t196 @t195)) % 0.36/0.60 (define @t200 () (or @t183 @t196 @t195)) % 0.36/0.60 (define @t201 () (or @t71 @t198 @t200)) % 0.36/0.60 (define @t202 () (forall @t189 @t201)) % 0.36/0.60 (define @t203 () (@list @t180)) % 0.36/0.60 (define @t204 () (forall @t203 @t201)) % 0.36/0.60 (define @t205 () (forall @t203 @t200)) % 0.36/0.60 (define @t206 () (@var "BOUND_VARIABLE_8072" $$unsorted)) % 0.36/0.60 (define @t207 () (@list @t206)) % 0.36/0.60 (define @t208 () (or @t71 @t198 @t205)) % 0.36/0.60 (define @t209 () (@list @t206)) % 0.36/0.60 (define @t210 () (forall @t209 (or (not (tptp.eiw_di @t206 @t1)) (not (tptp.member @t14 @t206 @t1)) (tptp.intersect @t4 @t206 @t1)))) % 0.36/0.60 (define @t211 () (_ (_ @t26 @t4) @t1)) % 0.36/0.60 (define @t212 () (not @t211)) % 0.36/0.60 (define @t213 () (or @t71 @t212 @t210)) % 0.36/0.60 (define @t214 () (or @t212 @t210)) % 0.36/0.60 (define @t215 () (_ @t28 @t9)) % 0.36/0.60 (define @t216 () (not @t215)) % 0.36/0.60 (define @t217 () (forall @t7 (or @t88 @t188 (tptp.intersect @t10 @t4 @t9)))) % 0.36/0.60 (define @t218 () (or @t216 @t217)) % 0.36/0.60 (define @t219 () (lambda @t20 @t218)) % 0.36/0.60 (define @t220 () (or @t71 (_ @t219 @t4 @t1))) % 0.36/0.60 (define @t221 () (forall @t7 @t220)) % 0.36/0.60 (define @t222 () (lambda @t3 @t221)) % 0.36/0.60 (define @t223 () (tptp.intersect @t10 @t4 @t1)) % 0.36/0.60 (define @t224 () (_ @t28 @t1)) % 0.36/0.60 (define @t225 () (not @t224)) % 0.36/0.60 (define @t226 () (_ (_ @t24 @t4) @t1)) % 0.36/0.60 (define @t227 () (or @t71 @t212 @t226)) % 0.36/0.60 (define @t228 () (forall @t7 @t227)) % 0.36/0.60 (define @t229 () (or @t225 @t228)) % 0.36/0.60 (define @t230 () (or @t225 @t227)) % 0.36/0.60 (define @t231 () (or @t71 @t225 @t212 @t226)) % 0.36/0.60 (define @t232 () (or @t225 @t212 @t226)) % 0.36/0.60 (define @t233 () (and @t224 @t211)) % 0.36/0.60 (define @t234 () (=> @t233 @t226)) % 0.36/0.60 (define @t235 () (or @t71 @t234)) % 0.36/0.60 (define @t236 () (=> (and @t215 (_ @t27 @t9)) (_ @t25 @t9))) % 0.36/0.60 (define @t237 () (lambda @t16 @t236)) % 0.36/0.60 (define @t238 () (_ @t237 @t4 @t1)) % 0.36/0.60 (define @t239 () (or @t71 @t238)) % 0.36/0.60 (define @t240 () (forall @t7 @t239)) % 0.36/0.60 (define @t241 () (lambda @t3 @t240)) % 0.36/0.60 (define @t242 () (and @t224 (_ @t27 @t1))) % 0.36/0.60 (define @t243 () (lambda @t3 (=> @t242 (_ @t25 @t1)))) % 0.36/0.60 (define @t244 () (lambda @t3 @t242)) % 0.36/0.60 (define @t245 () (_ @t244 @t1)) % 0.36/0.60 (define @t246 () (=> @t245 @t39)) % 0.36/0.60 (define @t247 () (lambda @t118 @t246)) % 0.36/0.60 (define @t248 () (lambda @t118 (and @t224 @t39))) % 0.36/0.60 (define @t249 () (_ @t41 @t28)) % 0.36/0.60 (define @t250 () (lambda @t16 (_ (_ (_ @t43 (_ @t249 @t27)) @t25) @t9))) % 0.36/0.60 (define @t251 () (lambda @t20 (_ (_ @t96 @t250) @t9))) % 0.36/0.60 (define @t252 () (lambda @t22 (_ (_ @t96 @t251) @t9))) % 0.36/0.60 (define @t253 () (@quantifiers_skolemize @t153 0)) % 0.36/0.60 (define @t254 () (tptp.member @t253 @t154 tptp.mactual)) % 0.36/0.60 (define @t255 () (not @t254)) % 0.36/0.60 (define @t256 () (tptp.member @t253 @t155 tptp.mactual)) % 0.36/0.60 (define @t257 () (not @t256)) % 0.36/0.60 (define @t258 () (tptp.eiw_di @t253 tptp.mactual)) % 0.36/0.60 (define @t259 () (not @t258)) % 0.36/0.60 (define @t260 () (or @t259 @t162 @t257 @t160 @t255 @t158)) % 0.36/0.60 (define @t261 () (@list true)) % 0.36/0.60 (define @t262 () (@list @t260)) % 0.36/0.60 (define @t263 () (@list false false false)) % 0.36/0.60 (define @t264 () (not @t164)) % 0.36/0.60 (define @t265 () (@list true false)) % 0.36/0.60 (define @t266 () (or @t259 @t257 @t255)) % 0.36/0.60 (define @t267 () (not @t266)) % 0.36/0.60 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.36/0.60 (assume @p2 (forall @t3 (exists @t7 @t6))) % 0.36/0.60 (assume @p3 (forall (@list @t1 @t8 @t4) (=> (and @t6 (_ (_ tptp.mrel @t8) @t1)) (_ @t5 @t8)))) % 0.36/0.60 (assume @p4 (_ tptp.mlocal (_ tptp.mforall_di @t23))) % 0.36/0.60 (assume @p5 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t20 (_ (_ (_ tptp.mimplies @t19) (_ @t24 @t14)) @t9))) @t9))))) % 0.36/0.60 (assume @p6 @t32) % 0.36/0.60 (assume @p7 true) % 0.36/0.60 (step @p8 (= tptp.mlocal @t34) :rule refl :args (@t34)) % 0.36/0.60 (step @p9 (= tptp.mnot @t37) :rule refl :args (@t37)) % 0.36/0.60 (step @p10 (= tptp.mand @t41) :rule refl :args (@t41)) % 0.36/0.60 (step @p11 (= tptp.mor @t42) :rule refl :args (@t42)) % 0.36/0.60 (step @p12 (= tptp.mimplies @t43) :rule refl :args (@t43)) % 0.36/0.60 (step @p13 (= tptp.mequiv @t44) :rule refl :args (@t44)) % 0.36/0.60 (step @p14 (= tptp.mbox @t49) :rule refl :args (@t49)) % 0.36/0.60 (step @p15 (= tptp.mdia @t50) :rule refl :args (@t50)) % 0.36/0.60 (step @p16 (= tptp.mforall_di @t55) :rule refl :args (@t55)) % 0.36/0.60 (step @p17 (= tptp.mexists_di @t58) :rule refl :args (@t58)) % 0.36/0.60 (step @p18 :rule beta-reduce :args ((= @t74 @t65))) % 0.36/0.60 (step @p19 :rule beta-reduce :args ((= (_ @t34 @t73) @t74))) % 0.36/0.60 (step @p20 :rule trans :premises (@p19 @p18)) % 0.36/0.60 (step @p21 :rule aci_norm :args ((= @t76 @t72))) % 0.36/0.60 (step @p22 :rule cong :premises (@p21) :args (@t77)) % 0.36/0.60 (step @p23 :rule quant-merge-prenex :args ((= (forall @t7 @t79) @t77))) % 0.36/0.60 (step @p24 :rule alpha_equiv :args (@t80 (@list @t59) @t82)) % 0.36/0.60 (step @p25 :rule refl :args (@t71)) % 0.36/0.60 (step @p26 :rule nary_cong :premises (@p25 @p24) :args (@t83)) % 0.36/0.60 (step @p27 :rule quant-miniscope-or :args ((= @t79 @t83))) % 0.36/0.60 (step @p28 :rule trans :premises (@p27 @p26)) % 0.36/0.60 (step @p29 :rule symm :premises (@p28)) % 0.36/0.60 (step @p30 :rule cong :premises (@p29) :args ((forall @t7 (or @t71 @t85)))) % 0.36/0.60 (step @p31 :rule trans :premises (@p30 @p23)) % 0.36/0.60 (step @p32 :rule trans :premises (@p31 @p22)) % 0.36/0.60 (step @p33 :rule beta-reduce :args ((= (_ (lambda @t22 (forall @t84 (or (not (tptp.eiw_di @t81 @t9)) (= (not (forall @t62 (or @t87 @t86 (not (tptp.member @t60 @t81 @t9))))) (tptp.intersect @t14 @t81 @t9))))) @t4 @t1) @t85))) % 0.36/0.60 (step @p34 :rule refl :args (@t1)) % 0.36/0.60 (step @p35 :rule refl :args (@t4)) % 0.36/0.60 (step @p36 :rule alpha_equiv :args (@t89 @t90 @t82)) % 0.36/0.60 (step @p37 :rule cong :premises (@p36) :args (@t91)) % 0.36/0.60 (step @p38 :rule ho_cong :premises (@p37 @p35 @p34)) % 0.36/0.60 (step @p39 :rule trans :premises (@p38 @p33)) % 0.36/0.60 (step @p40 :rule refl :args (@t71)) % 0.36/0.60 (step @p41 :rule nary_cong :premises (@p40 @p39) :args (@t92)) % 0.36/0.60 (step @p42 :rule cong :premises (@p41) :args (@t93)) % 0.36/0.60 (step @p43 :rule trans :premises (@p42 @p32)) % 0.36/0.60 (step @p44 :rule cong :premises (@p43) :args (@t94)) % 0.36/0.60 (step @p45 :rule beta-reduce :args ((= (_ @t96 @t91) @t94))) % 0.36/0.60 (step @p46 :rule trans :premises (@p45 @p44)) % 0.36/0.60 (step @p47 :rule beta-reduce :args ((= (_ (lambda @t3 (forall @t7 (or @t71 (= @t98 @t97)))) @t9) @t89))) % 0.36/0.60 (step @p48 :rule refl :args (@t9)) % 0.36/0.60 (step @p49 :rule eq-symm :args (@t97 @t98)) % 0.36/0.60 (step @p50 :rule nary_cong :premises (@p40 @p49) :args (@t99)) % 0.36/0.60 (step @p51 :rule cong :premises (@p50) :args ((forall @t7 @t99))) % 0.36/0.60 (step @p52 :rule refl :args (@t98)) % 0.36/0.60 (step @p53 :rule refl :args (@t97)) % 0.36/0.60 (step @p54 :rule refl :args (@t100)) % 0.36/0.60 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t100 @t97))) % 0.36/0.60 (step @p56 :rule symm :premises (@p55)) % 0.36/0.60 (step @p57 :rule eq_resolve :premises (@p54 @p56)) % 0.36/0.60 (step @p58 :rule cong :premises (@p57 @p52) :args (@t101)) % 0.36/0.60 (step @p59 :rule nary_cong :premises (@p25 @p58) :args (@t102)) % 0.36/0.60 (step @p60 :rule cong :premises (@p59) :args ((forall @t7 @t102))) % 0.36/0.60 (step @p61 :rule trans :premises (@p60 @p51)) % 0.36/0.60 (step @p62 :rule beta-reduce :args ((= (_ (lambda @t20 (= @t103 (not (forall @t62 (or @t87 @t86 (not (tptp.member @t60 @t10 @t9))))))) @t4 @t1) @t101))) % 0.36/0.60 (step @p63 :rule alpha_equiv :args (@t104 @t90 (@list @t60))) % 0.36/0.60 (step @p64 :rule cong :premises (@p63) :args (@t105)) % 0.36/0.60 (step @p65 :rule refl :args (@t103)) % 0.36/0.60 (step @p66 :rule cong :premises (@p65 @p64) :args (@t106)) % 0.36/0.60 (step @p67 :rule cong :premises (@p66) :args (@t107)) % 0.36/0.60 (step @p68 :rule ho_cong :premises (@p67 @p35 @p34)) % 0.36/0.60 (step @p69 :rule trans :premises (@p68 @p62)) % 0.36/0.60 (step @p70 :rule nary_cong :premises (@p40 @p69) :args (@t108)) % 0.36/0.60 (step @p71 :rule cong :premises (@p70) :args (@t109)) % 0.36/0.60 (step @p72 :rule trans :premises (@p71 @p61)) % 0.36/0.60 (step @p73 :rule cong :premises (@p72) :args (@t110)) % 0.36/0.60 (step @p74 :rule beta-reduce :args ((= (_ @t96 @t107) @t110))) % 0.36/0.60 (step @p75 :rule trans :premises (@p74 @p73)) % 0.36/0.60 (step @p76 :rule beta-reduce :args ((= (_ (lambda @t3 (= @t114 @t113)) @t9) @t106))) % 0.36/0.60 (step @p77 :rule beta-reduce :args ((= @t116 @t113))) % 0.36/0.60 (step @p78 :rule refl :args (@t114)) % 0.36/0.60 (step @p79 :rule cong :premises (@p78 @p77) :args ((= @t114 @t116))) % 0.36/0.60 (step @p80 :rule eq-symm :args (@t116 @t114)) % 0.36/0.60 (step @p81 :rule trans :premises (@p80 @p79)) % 0.36/0.60 (step @p82 :rule cong :premises (@p81) :args (@t117)) % 0.36/0.60 (step @p83 :rule beta-reduce :args ((= (_ (lambda @t118 (= @t39 @t114)) @t115) @t117))) % 0.36/0.60 (step @p84 :rule trans :premises (@p83 @p82)) % 0.36/0.60 (step @p85 :rule refl :args (@t111)) % 0.36/0.60 (step @p86 :rule refl :args (@t120)) % 0.36/0.60 (step @p87 :rule cong :premises (@p86 @p85) :args ((= @t120 @t111))) % 0.36/0.60 (step @p88 :rule symm :premises (@p87)) % 0.36/0.60 (step @p89 :rule eq_resolve :premises (@p86 @p88)) % 0.36/0.60 (step @p90 :rule cong :premises (@p89) :args (@t121)) % 0.36/0.60 (step @p91 :rule refl :args (@t112)) % 0.36/0.60 (step @p92 :rule refl :args (@t122)) % 0.36/0.60 (step @p93 :rule cong :premises (@p92 @p91) :args ((= @t122 @t112))) % 0.36/0.60 (step @p94 :rule symm :premises (@p93)) % 0.36/0.60 (step @p95 :rule eq_resolve :premises (@p92 @p94)) % 0.36/0.60 (step @p96 :rule cong :premises (@p95) :args (@t123)) % 0.36/0.60 (step @p97 :rule nary_cong :premises (@p25 @p96 @p90) :args (@t124)) % 0.36/0.60 (step @p98 :rule cong :premises (@p97) :args ((forall @t7 @t124))) % 0.36/0.60 (step @p99 :rule aci_norm :args ((= (or @t71 (or @t123 @t121)) @t124))) % 0.36/0.60 (step @p100 :rule bool-and-de-morgan :args (@t122 @t120 true)) % 0.36/0.60 (step @p101 :rule nary_cong :premises (@p25 @p100) :args (@t126)) % 0.36/0.60 (step @p102 :rule trans :premises (@p101 @p99)) % 0.36/0.60 (step @p103 :rule cong :premises (@p102) :args ((forall @t7 @t126))) % 0.36/0.60 (step @p104 :rule trans :premises (@p103 @p98)) % 0.36/0.60 (step @p105 :rule beta-reduce :args ((= @t129 @t125))) % 0.36/0.60 (step @p106 :rule cong :premises (@p105) :args (@t130)) % 0.36/0.60 (step @p107 :rule nary_cong :premises (@p40 @p106) :args (@t131)) % 0.36/0.60 (step @p108 :rule cong :premises (@p107) :args (@t132)) % 0.36/0.60 (step @p109 :rule trans :premises (@p108 @p104)) % 0.36/0.60 (step @p110 :rule cong :premises (@p109) :args (@t133)) % 0.36/0.60 (step @p111 :rule cong :premises (@p110) :args (@t134)) % 0.36/0.60 (step @p112 :rule beta-reduce :args ((= (_ @t135 @t128) @t134))) % 0.36/0.60 (step @p113 :rule trans :premises (@p112 @p111)) % 0.36/0.60 (step @p114 :rule beta-reduce :args ((= (_ @t137 @t9) @t127))) % 0.36/0.60 (step @p115 :rule beta-reduce :args ((= (_ @t138 @t13) @t137))) % 0.36/0.60 (step @p116 :rule refl :args (@t13)) % 0.36/0.60 (step @p117 :rule beta-reduce :args ((= @t139 @t138))) % 0.36/0.60 (step @p118 :rule ho_cong :premises (@p117 @p116)) % 0.36/0.60 (step @p119 :rule trans :premises (@p118 @p115)) % 0.36/0.60 (step @p120 :rule ho_cong :premises (@p119 @p48)) % 0.36/0.60 (step @p121 :rule trans :premises (@p120 @p114)) % 0.36/0.60 (step @p122 :rule cong :premises (@p121) :args (@t140)) % 0.36/0.60 (step @p123 :rule refl :args (@t135)) % 0.36/0.60 (step @p124 :rule ho_cong :premises (@p123 @p122)) % 0.36/0.60 (step @p125 :rule trans :premises (@p124 @p113)) % 0.36/0.60 (step @p126 :rule eq-symm :args (@t114 @t39)) % 0.36/0.60 (step @p127 :rule cong :premises (@p126) :args (@t141)) % 0.36/0.60 (step @p128 :rule beta-reduce :args ((= @t142 @t141))) % 0.36/0.60 (step @p129 :rule trans :premises (@p128 @p127)) % 0.36/0.60 (step @p130 :rule ho_cong :premises (@p129 @p125)) % 0.36/0.60 (step @p131 :rule trans :premises (@p130 @p84)) % 0.36/0.60 (step @p132 :rule ho_cong :premises (@p131 @p48)) % 0.36/0.60 (step @p133 :rule trans :premises (@p132 @p76)) % 0.36/0.60 (step @p134 :rule cong :premises (@p133) :args (@t143)) % 0.36/0.60 (step @p135 :rule refl :args (@t96)) % 0.36/0.60 (step @p136 :rule ho_cong :premises (@p135 @p134)) % 0.36/0.60 (step @p137 :rule trans :premises (@p136 @p75)) % 0.36/0.60 (step @p138 :rule ho_cong :premises (@p137 @p48)) % 0.36/0.60 (step @p139 :rule trans :premises (@p138 @p47)) % 0.36/0.60 (step @p140 :rule cong :premises (@p139) :args ((lambda @t22 (_ (_ @t96 @t143) @t9)))) % 0.36/0.60 (step @p141 :rule ho_cong :premises (@p135 @p140)) % 0.36/0.60 (step @p142 :rule trans :premises (@p141 @p46)) % 0.36/0.60 (step 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5)) % 0.36/0.60 (step @p375 :rule chain_m_resolution :premises (@p374 @p357) :args ((not @t158) @t261 @t262)) % 0.36/0.60 (step @p376 :rule bool-double-not-elim :args (@t156)) % 0.36/0.60 (step @p377 :rule refl :args (@t158)) % 0.36/0.60 (step @p378 :rule refl :args (@t264)) % 0.36/0.60 (step @p379 :rule nary_cong :premises (@p378 @p377 @p376) :args ((or @t264 @t158 (not @t157)))) % 0.36/0.60 (step @p380 :rule cnf_equiv_pos2 :args (@t164)) % 0.36/0.60 (step @p381 :rule eq_resolve :premises (@p380 @p379)) % 0.36/0.60 (step @p382 :rule reordering :premises (@p381) :args ((or @t158 @t156 @t264))) % 0.36/0.60 (step @p383 :rule chain_m_resolution :premises (@p382 @p375 @p373) :args (@t156 @t265 (@list @t158 @t164))) % 0.36/0.60 (step @p384 :rule bool-double-not-elim :args (@t254)) % 0.36/0.60 (step @p385 :rule nary_cong :premises (@p359 @p384) :args ((or @t260 (not @t255)))) % 0.36/0.60 (step @p386 :rule cnf_or_neg :args (@t260 4)) % 0.36/0.60 (step @p387 :rule eq_resolve :premises (@p386 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(@p399) :args ((or @t258 @t260))) % 0.36/0.60 (step @p401 :rule chain_m_resolution :premises (@p400 @p357) :args (@t258 @t261 @t262)) % 0.36/0.60 (step @p402 :rule cnf_or_pos :args (@t266)) % 0.36/0.60 (step @p403 :rule reordering :premises (@p402) :args ((or @t259 @t257 @t255 @t267))) % 0.36/0.60 (step @p404 :rule chain_m_resolution :premises (@p403 @p401 @p395 @p389) :args (@t267 @t263 (@list @t258 @t256 @t254))) % 0.36/0.60 (assume-push @p413 @t156) % 0.36/0.60 (step @p406 :rule instantiate :premises (@p383) :args ((@list @t253))) % 0.36/0.60 (step-pop @p414 :rule scope :premises (@p406)) % 0.36/0.60 (step @p407 :rule process_scope :premises (@p414) :args (@t266)) % 0.36/0.60 (step @p409 :rule implies_elim :premises (@p407)) % 0.36/0.60 (step @p410 false :rule chain_m_resolution :premises (@p409 @p404 @p383) :args (false @t265 (@list @t266 @t156))) % 0.36/0.60 ) % 0.36/0.60 % SZS output end Proof % 0.36/0.60 % cvc5 exiting %------------------------------------------------------------------------------