%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET027^3 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:47:02 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET027^3 : TPTP v9.2.1. Released v8.1.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n009.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 14:42:29 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 0.37/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (declare-sort tptp.mworld 0) % 0.37/0.58 (declare-const tptp.mactual tptp.mworld) % 0.37/0.58 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.37/0.58 (declare-const tptp.subset (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.37/0.58 (declare-const tptp.member (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.37/0.58 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.37/0.58 (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)))))) % 0.37/0.58 (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))))))) % 0.37/0.58 (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))))))) % 0.37/0.58 (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))))))) % 0.37/0.58 (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))))))) % 0.37/0.58 (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)))))))) % 0.37/0.58 (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)))))))) % 0.37/0.58 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.58 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.58 (define @t1 () (@var "V" tptp.mworld)) % 0.37/0.58 (define @t2 () (@var "W" tptp.mworld)) % 0.37/0.58 (define @t3 () (_ (_ tptp.mrel @t2) @t1)) % 0.37/0.58 (define @t4 () (@list @t1)) % 0.37/0.58 (define @t5 () (@list @t2)) % 0.37/0.58 (define @t6 () (@var "__flatten_var_0" tptp.mworld)) % 0.37/0.58 (define @t7 () (@var "C" $$unsorted)) % 0.37/0.58 (define @t8 () (@var "D" $$unsorted)) % 0.37/0.58 (define @t9 () (_ tptp.member @t8)) % 0.37/0.58 (define @t10 () (_ @t9 @t7)) % 0.37/0.58 (define @t11 () (@var "B" $$unsorted)) % 0.37/0.58 (define @t12 () (_ @t9 @t11)) % 0.37/0.58 (define @t13 () (@list @t8 @t6)) % 0.37/0.58 (define @t14 () (lambda @t13 (_ (_ (_ tptp.mimplies @t12) @t10) @t6))) % 0.37/0.58 (define @t15 () (_ tptp.subset @t11)) % 0.37/0.58 (define @t16 () (_ @t15 @t7)) % 0.37/0.58 (define @t17 () (@list @t7 @t6)) % 0.37/0.58 (define @t18 () (lambda @t17 (_ (_ (_ tptp.mequiv @t16) (_ tptp.mforall_di @t14)) @t6))) % 0.37/0.58 (define @t19 () (@list @t11 @t6)) % 0.37/0.58 (define @t20 () (lambda @t19 (_ (_ tptp.mforall_di @t18) @t6))) % 0.37/0.58 (define @t21 () (_ @t15 @t8)) % 0.37/0.58 (define @t22 () (_ tptp.subset @t7)) % 0.37/0.58 (define @t23 () (_ @t22 @t8)) % 0.37/0.58 (define @t24 () (lambda @t13 (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t16) @t23)) @t21) @t6))) % 0.37/0.58 (define @t25 () (lambda @t17 (_ (_ tptp.mforall_di @t24) @t6))) % 0.37/0.58 (define @t26 () (lambda @t19 (_ (_ tptp.mforall_di @t25) @t6))) % 0.37/0.58 (define @t27 () (not (_ tptp.mlocal (_ tptp.mforall_di @t26)))) % 0.37/0.58 (define @t28 () (@var "Phi" (-> tptp.mworld Bool))) % 0.37/0.58 (define @t29 () (lambda (@list @t28) (_ @t28 tptp.mactual))) % 0.37/0.58 (define @t30 () (@var "A" (-> tptp.mworld Bool))) % 0.37/0.58 (define @t31 () (_ @t30 @t2)) % 0.37/0.58 (define @t32 () (lambda (@list @t30 @t2) (not @t31))) % 0.37/0.58 (define @t33 () (@var "B" (-> tptp.mworld Bool))) % 0.37/0.58 (define @t34 () (_ @t33 @t2)) % 0.37/0.58 (define @t35 () (@list @t30 @t33 @t2)) % 0.37/0.58 (define @t36 () (lambda @t35 (and @t31 @t34))) % 0.37/0.58 (define @t37 () (lambda @t35 (or @t31 @t34))) % 0.37/0.58 (define @t38 () (lambda @t35 (=> @t31 @t34))) % 0.37/0.58 (define @t39 () (lambda @t35 (= @t31 @t34))) % 0.37/0.58 (define @t40 () (_ @t28 @t1)) % 0.37/0.58 (define @t41 () (@list @t28 @t2)) % 0.37/0.58 (define @t42 () (lambda @t41 (forall @t4 (=> @t3 @t40)))) % 0.37/0.58 (define @t43 () (lambda @t41 (exists @t4 (and @t3 @t40)))) % 0.37/0.58 (define @t44 () (@var "X" $$unsorted)) % 0.37/0.58 (define @t45 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.37/0.58 (define @t46 () (_ (_ @t45 @t44) @t2)) % 0.37/0.58 (define @t47 () (@list @t44)) % 0.37/0.58 (define @t48 () (forall @t47 @t46)) % 0.37/0.58 (define @t49 () (@list @t45 @t2)) % 0.37/0.58 (define @t50 () (lambda @t49 @t48)) % 0.37/0.58 (define @t51 () (lambda @t49 (exists @t47 @t46))) % 0.37/0.58 (define @t52 () (@var "BOUND_VARIABLE_7746" $$unsorted)) % 0.37/0.58 (define @t53 () (@var "BOUND_VARIABLE_7707" $$unsorted)) % 0.37/0.58 (define @t54 () (@list @t53)) % 0.37/0.58 (define @t55 () (@list @t44 @t52)) % 0.37/0.58 (define @t56 () (forall @t55 (= (forall @t54 (or (not (tptp.member @t53 @t44 tptp.mactual)) (tptp.member @t53 @t52 tptp.mactual))) (tptp.subset @t44 @t52 tptp.mactual)))) % 0.37/0.58 (define @t57 () (tptp.member @t53 @t44 @t2)) % 0.37/0.58 (define @t58 () (= (forall @t54 (or (not @t57) (tptp.member @t53 @t52 @t2))) (tptp.subset @t44 @t52 @t2))) % 0.37/0.58 (define @t59 () (forall @t55 @t58)) % 0.37/0.58 (define @t60 () (lambda @t5 @t59)) % 0.37/0.58 (define @t61 () (_ @t60 tptp.mactual)) % 0.37/0.58 (define @t62 () (@list @t52)) % 0.37/0.58 (define @t63 () (forall @t62 @t58)) % 0.37/0.58 (define @t64 () (not (tptp.member @t53 @t11 @t6))) % 0.37/0.58 (define @t65 () (tptp.subset @t11 @t44 @t6)) % 0.37/0.58 (define @t66 () (forall @t47 (= (forall @t54 (or @t64 (tptp.member @t53 @t44 @t6))) @t65))) % 0.37/0.58 (define @t67 () (@list @t44)) % 0.37/0.58 (define @t68 () (lambda @t19 @t66)) % 0.37/0.58 (define @t69 () (forall @t47 (_ @t68 @t44 @t2))) % 0.37/0.58 (define @t70 () (lambda @t5 @t69)) % 0.37/0.58 (define @t71 () (_ @t45 @t44 @t2)) % 0.37/0.58 (define @t72 () (lambda @t49 (forall @t47 @t71))) % 0.37/0.58 (define @t73 () (tptp.subset @t11 @t44 @t2)) % 0.37/0.58 (define @t74 () (forall @t54 (or (not (tptp.member @t53 @t11 @t2)) @t57))) % 0.37/0.58 (define @t75 () (_ (_ @t15 @t44) @t2)) % 0.37/0.58 (define @t76 () (= @t75 @t74)) % 0.37/0.58 (define @t77 () (_ @t16 @t6)) % 0.37/0.58 (define @t78 () (forall @t47 (or (not (tptp.member @t44 @t11 @t6)) (tptp.member @t44 @t7 @t6)))) % 0.37/0.58 (define @t79 () (= @t77 @t78)) % 0.37/0.58 (define @t80 () (lambda @t17 @t79)) % 0.37/0.58 (define @t81 () (forall @t47 (_ @t80 @t44 @t2))) % 0.37/0.58 (define @t82 () (lambda @t5 @t81)) % 0.37/0.58 (define @t83 () (tptp.member @t44 @t7 @t2)) % 0.37/0.58 (define @t84 () (tptp.member @t44 @t11 @t2)) % 0.37/0.58 (define @t85 () (forall @t47 (or (not @t84) @t83))) % 0.37/0.58 (define @t86 () (_ @t16 @t2)) % 0.37/0.58 (define @t87 () (lambda @t5 @t85)) % 0.37/0.58 (define @t88 () (_ @t87 @t2)) % 0.37/0.58 (define @t89 () (lambda @t5 (= @t88 @t86))) % 0.37/0.58 (define @t90 () (@list @t33 @t2)) % 0.37/0.58 (define @t91 () (_ tptp.member @t44)) % 0.37/0.58 (define @t92 () (_ (_ @t91 @t7) @t2)) % 0.37/0.58 (define @t93 () (_ (_ @t91 @t11) @t2)) % 0.37/0.58 (define @t94 () (not @t93)) % 0.37/0.58 (define @t95 () (or @t94 @t92)) % 0.37/0.58 (define @t96 () (=> @t93 @t92)) % 0.37/0.58 (define @t97 () (=> (_ @t12 @t6) (_ @t10 @t6))) % 0.37/0.58 (define @t98 () (lambda @t13 @t97)) % 0.37/0.58 (define @t99 () (_ @t98 @t44 @t2)) % 0.37/0.58 (define @t100 () (forall @t47 @t99)) % 0.37/0.58 (define @t101 () (lambda @t5 @t100)) % 0.37/0.58 (define @t102 () (_ @t12 @t2)) % 0.37/0.58 (define @t103 () (lambda @t5 (=> @t102 (_ @t10 @t2)))) % 0.37/0.58 (define @t104 () (lambda @t90 (=> @t102 @t34))) % 0.37/0.58 (define @t105 () (_ @t38 @t12)) % 0.37/0.58 (define @t106 () (lambda @t13 (_ (_ @t105 @t10) @t6))) % 0.37/0.58 (define @t107 () (lambda @t90 (= @t86 @t34))) % 0.37/0.58 (define @t108 () (_ @t39 @t16)) % 0.37/0.58 (define @t109 () (lambda @t17 (_ (_ @t108 (_ @t72 @t106)) @t6))) % 0.37/0.58 (define @t110 () (@var "BOUND_VARIABLE_7896" $$unsorted)) % 0.37/0.58 (define @t111 () (@var "BOUND_VARIABLE_7921" $$unsorted)) % 0.37/0.58 (define @t112 () (@list @t44 @t111 @t110)) % 0.37/0.58 (define @t113 () (forall @t112 (or (not (tptp.subset @t44 @t111 tptp.mactual)) (not (tptp.subset @t111 @t110 tptp.mactual)) (tptp.subset @t44 @t110 tptp.mactual)))) % 0.37/0.58 (define @t114 () (@quantifiers_skolemize @t113 2)) % 0.37/0.58 (define @t115 () (tptp.member @t53 @t114 tptp.mactual)) % 0.37/0.58 (define @t116 () (@quantifiers_skolemize @t113 0)) % 0.37/0.58 (define @t117 () (not (tptp.member @t53 @t116 tptp.mactual))) % 0.37/0.58 (define @t118 () (forall @t54 (or @t117 @t115))) % 0.37/0.58 (define @t119 () (tptp.subset @t116 @t114 tptp.mactual)) % 0.37/0.58 (define @t120 () (= @t118 @t119)) % 0.37/0.58 (define @t121 () (= @t119 @t118)) % 0.37/0.58 (define @t122 () (@list false)) % 0.37/0.58 (define @t123 () (@list @t56)) % 0.37/0.58 (define @t124 () (tptp.subset @t44 @t110 @t2)) % 0.37/0.58 (define @t125 () (or (not (tptp.subset @t44 @t111 @t2)) (not (tptp.subset @t111 @t110 @t2)) @t124)) % 0.37/0.58 (define @t126 () (forall @t112 @t125)) % 0.37/0.58 (define @t127 () (lambda @t5 @t126)) % 0.37/0.58 (define @t128 () (_ @t127 tptp.mactual)) % 0.37/0.58 (define @t129 () (@list @t111 @t110)) % 0.37/0.58 (define @t130 () (forall @t129 @t125)) % 0.37/0.58 (define @t131 () (tptp.subset @t11 @t110 @t6)) % 0.37/0.58 (define @t132 () (@list @t44 @t110)) % 0.37/0.58 (define @t133 () (forall @t132 (or (not @t65) (not (tptp.subset @t44 @t110 @t6)) @t131))) % 0.37/0.58 (define @t134 () (lambda @t19 @t133)) % 0.37/0.58 (define @t135 () (forall @t47 (_ @t134 @t44 @t2))) % 0.37/0.58 (define @t136 () (lambda @t5 @t135)) % 0.37/0.58 (define @t137 () (tptp.subset @t11 @t110 @t2)) % 0.37/0.58 (define @t138 () (not @t124)) % 0.37/0.58 (define @t139 () (not @t73)) % 0.37/0.58 (define @t140 () (or @t139 @t138 @t137)) % 0.37/0.58 (define @t141 () (or @t138 @t137)) % 0.37/0.58 (define @t142 () (or @t139 @t141)) % 0.37/0.58 (define @t143 () (forall @t132 @t142)) % 0.37/0.58 (define @t144 () (@list @t110)) % 0.37/0.58 (define @t145 () (forall @t144 @t142)) % 0.37/0.58 (define @t146 () (forall @t144 @t141)) % 0.37/0.58 (define @t147 () (@var "BOUND_VARIABLE_7874" $$unsorted)) % 0.37/0.58 (define @t148 () (@list @t147)) % 0.37/0.58 (define @t149 () (or @t139 @t146)) % 0.37/0.58 (define @t150 () (@list @t147)) % 0.37/0.58 (define @t151 () (forall @t150 (or (not (tptp.subset @t44 @t147 @t2)) (tptp.subset @t11 @t147 @t2)))) % 0.37/0.58 (define @t152 () (not @t75)) % 0.37/0.58 (define @t153 () (or @t152 @t151)) % 0.37/0.58 (define @t154 () (not @t77)) % 0.37/0.58 (define @t155 () (forall @t47 (or (not (tptp.subset @t7 @t44 @t6)) @t65))) % 0.37/0.58 (define @t156 () (or @t154 @t155)) % 0.37/0.58 (define @t157 () (lambda @t17 @t156)) % 0.37/0.58 (define @t158 () (forall @t47 (_ @t157 @t44 @t2))) % 0.37/0.58 (define @t159 () (lambda @t5 @t158)) % 0.37/0.58 (define @t160 () (tptp.subset @t7 @t44 @t2)) % 0.37/0.58 (define @t161 () (not @t86)) % 0.37/0.58 (define @t162 () (_ (_ @t22 @t44) @t2)) % 0.37/0.58 (define @t163 () (not @t162)) % 0.37/0.58 (define @t164 () (or @t163 @t75)) % 0.37/0.59 (define @t165 () (forall @t47 @t164)) % 0.37/0.59 (define @t166 () (or @t161 @t165)) % 0.37/0.59 (define @t167 () (or @t161 @t164)) % 0.37/0.59 (define @t168 () (or @t161 @t163 @t75)) % 0.37/0.59 (define @t169 () (and @t86 @t162)) % 0.37/0.59 (define @t170 () (=> @t169 @t75)) % 0.37/0.59 (define @t171 () (=> (and @t77 (_ @t23 @t6)) (_ @t21 @t6))) % 0.37/0.59 (define @t172 () (lambda @t13 @t171)) % 0.37/0.59 (define @t173 () (_ @t172 @t44 @t2)) % 0.37/0.59 (define @t174 () (forall @t47 @t173)) % 0.37/0.59 (define @t175 () (lambda @t5 @t174)) % 0.37/0.59 (define @t176 () (and @t86 (_ @t23 @t2))) % 0.37/0.59 (define @t177 () (lambda @t5 (=> @t176 (_ @t21 @t2)))) % 0.37/0.59 (define @t178 () (lambda @t5 @t176)) % 0.37/0.59 (define @t179 () (_ @t178 @t2)) % 0.37/0.59 (define @t180 () (=> @t179 @t34)) % 0.37/0.59 (define @t181 () (lambda @t90 @t180)) % 0.37/0.59 (define @t182 () (lambda @t90 (and @t86 @t34))) % 0.37/0.59 (define @t183 () (_ @t36 @t16)) % 0.37/0.59 (define @t184 () (lambda @t13 (_ (_ (_ @t38 (_ @t183 @t23)) @t21) @t6))) % 0.37/0.59 (define @t185 () (lambda @t17 (_ (_ @t72 @t184) @t6))) % 0.37/0.59 (define @t186 () (lambda @t19 (_ (_ @t72 @t185) @t6))) % 0.37/0.59 (define @t187 () (@quantifiers_skolemize @t113 1)) % 0.37/0.59 (define @t188 () (tptp.subset @t187 @t114 tptp.mactual)) % 0.37/0.59 (define @t189 () (not @t188)) % 0.37/0.59 (define @t190 () (tptp.subset @t116 @t187 tptp.mactual)) % 0.37/0.59 (define @t191 () (not @t190)) % 0.37/0.59 (define @t192 () (or @t191 @t189 @t119)) % 0.37/0.59 (define @t193 () (@list true)) % 0.37/0.59 (define @t194 () (@list @t192)) % 0.37/0.59 (define @t195 () (not @t118)) % 0.37/0.59 (define @t196 () (@quantifiers_skolemize @t118 0)) % 0.37/0.59 (define @t197 () (tptp.member @t196 @t114 tptp.mactual)) % 0.37/0.59 (define @t198 () (tptp.member @t196 @t116 tptp.mactual)) % 0.37/0.59 (define @t199 () (not @t198)) % 0.37/0.59 (define @t200 () (or @t199 @t197)) % 0.37/0.59 (define @t201 () (@list @t200)) % 0.37/0.59 (define @t202 () (tptp.member @t53 @t187 tptp.mactual)) % 0.37/0.59 (define @t203 () (forall @t54 (or (not @t202) @t115))) % 0.37/0.59 (define @t204 () (= @t203 @t188)) % 0.37/0.59 (define @t205 () (= @t188 @t203)) % 0.37/0.59 (define @t206 () (@list false false)) % 0.37/0.59 (define @t207 () (@list @t196)) % 0.37/0.59 (define @t208 () (forall @t54 (or @t117 @t202))) % 0.37/0.59 (define @t209 () (= @t208 @t190)) % 0.37/0.59 (define @t210 () (= @t190 @t208)) % 0.37/0.59 (define @t211 () (tptp.member @t196 @t187 tptp.mactual)) % 0.37/0.59 (define @t212 () (or @t199 @t211)) % 0.37/0.59 (define @t213 () (not @t211)) % 0.37/0.59 (define @t214 () (or @t213 @t197)) % 0.37/0.59 (assume @p1 (forall @t5 (exists @t4 @t3))) % 0.37/0.59 (assume @p2 (_ tptp.mlocal (_ tptp.mforall_di @t20))) % 0.37/0.59 (assume @p3 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t19 (_ (_ @t15 @t11) @t6))))) % 0.37/0.59 (assume @p4 @t27) % 0.37/0.59 (assume @p5 true) % 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:args (@t175)) % 0.37/0.59 (step @p227 :rule beta-reduce :args ((= (_ @t72 @t172) @t175))) % 0.37/0.59 (step @p228 :rule trans :premises (@p227 @p226)) % 0.37/0.59 (step @p229 :rule beta-reduce :args ((= (_ @t177 @t6) @t171))) % 0.37/0.59 (step @p230 :rule beta-reduce :args ((= (_ (lambda @t90 (=> @t176 @t34)) @t21) @t177))) % 0.37/0.59 (step @p231 :rule refl :args (@t21)) % 0.37/0.59 (step @p232 :rule refl :args (@t34)) % 0.37/0.59 (step @p233 :rule beta-reduce :args ((= @t179 @t176))) % 0.37/0.59 (step @p234 :rule cong :premises (@p233 @p232) :args (@t180)) % 0.37/0.59 (step @p235 :rule cong :premises (@p234) :args (@t181)) % 0.37/0.59 (step @p236 :rule beta-reduce :args ((= (_ @t38 @t178) @t181))) % 0.37/0.59 (step @p237 :rule trans :premises (@p236 @p235)) % 0.37/0.59 (step @p238 :rule beta-reduce :args ((= (_ @t182 @t23) @t178))) % 0.37/0.59 (step @p239 :rule refl :args (@t23)) % 0.37/0.59 (step @p240 :rule beta-reduce :args ((= @t183 @t182))) % 0.37/0.59 (step @p241 :rule ho_cong 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(@p256 @p198)) % 0.37/0.59 (step @p258 :rule ho_cong :premises (@p257 @p33)) % 0.37/0.59 (step @p259 :rule trans :premises (@p258 @p169)) % 0.37/0.59 (step @p260 :rule cong :premises (@p259) :args (@t186)) % 0.37/0.59 (step @p261 :rule ho_cong :premises (@p97 @p260)) % 0.37/0.59 (step @p262 :rule trans :premises (@p261 @p168)) % 0.37/0.59 (step @p263 :rule ho_cong :premises (@p116 @p262)) % 0.37/0.59 (step @p264 :rule trans :premises (@p263 @p157)) % 0.37/0.59 (step @p265 :rule cong :premises (@p264) :args ((not (_ @t29 (_ @t72 @t186))))) % 0.37/0.59 (step @p266 :rule ho_cong :premises (@p8 @p133)) % 0.37/0.59 (step @p267 :rule ho_cong :premises (@p266 @p239)) % 0.37/0.59 (step @p268 :rule ho_cong :premises (@p10 @p267)) % 0.37/0.59 (step @p269 :rule ho_cong :premises (@p268 @p231)) % 0.37/0.59 (step @p270 :rule ho_cong :premises (@p269 @p33)) % 0.37/0.59 (step @p271 :rule cong :premises (@p270) :args (@t24)) % 0.37/0.59 (step @p272 :rule ho_cong :premises (@p131 @p271)) % 0.37/0.59 (step @p273 :rule ho_cong :premises (@p272 @p33)) % 0.37/0.59 (step @p274 :rule cong :premises (@p273) :args (@t25)) % 0.37/0.59 (step @p275 :rule ho_cong :premises (@p131 @p274)) % 0.37/0.59 (step @p276 :rule ho_cong :premises (@p275 @p33)) % 0.37/0.59 (step @p277 :rule cong :premises (@p276) :args (@t26)) % 0.37/0.59 (step @p278 :rule ho_cong :premises (@p131 @p277)) % 0.37/0.59 (step @p279 :rule ho_cong :premises (@p6 @p278)) % 0.37/0.59 (step @p280 :rule cong :premises (@p279) :args (@t27)) % 0.37/0.59 (step @p281 :rule trans :premises (@p280 @p265)) % 0.37/0.59 (step @p282 :rule eq_resolve :premises (@p4 @p281)) % 0.37/0.59 (step @p283 :rule skolemize :premises (@p282)) % 0.37/0.59 (step @p284 :rule cnf_or_neg :args (@t192 2)) % 0.37/0.59 (step @p285 :rule chain_m_resolution :premises (@p284 @p283) :args ((not @t119) @t193 @t194)) % 0.37/0.59 (step @p286 :rule cnf_equiv_pos2 :args (@t121)) % 0.37/0.59 (step @p287 :rule reordering :premises (@p286) :args ((or @t119 @t195 (not @t121)))) % 0.37/0.59 (step @p288 :rule chain_m_resolution :premises (@p287 @p285 @p154) :args (@t195 (@list true false) (@list @t119 @t121))) % 0.37/0.59 (step @p289 :rule skolemize :premises (@p288)) % 0.37/0.59 (step @p290 :rule cnf_or_neg :args (@t200 1)) % 0.37/0.59 (step @p291 :rule chain_m_resolution :premises (@p290 @p289) :args ((not @t197) @t193 @t201)) % 0.37/0.59 (step @p292 :rule eq-symm :args (@t203 @t188)) % 0.37/0.59 (step @p293 :rule cong :premises (@p146 @p292) :args ((=> @t56 @t204))) % 0.37/0.59 (assume-push @p346 @t56) % 0.37/0.59 (step @p295 :rule instantiate :premises (@p144) :args ((@list @t187 @t114))) % 0.37/0.59 (step-pop @p347 :rule scope :premises (@p295)) % 0.37/0.59 (step @p296 :rule process_scope :premises (@p347) :args (@t204)) % 0.37/0.59 (step @p298 :rule eq_resolve :premises (@p296 @p293)) % 0.37/0.59 (step @p299 :rule implies_elim :premises (@p298)) % 0.37/0.59 (step @p300 :rule chain_m_resolution :premises (@p299 @p144) :args (@t205 @t122 @t123)) % 0.37/0.59 (step @p301 :rule bool-double-not-elim :args (@t188)) % 0.37/0.59 (step @p302 :rule refl :args (@t192)) % 0.37/0.59 (step @p303 :rule nary_cong :premises (@p302 @p301) :args ((or @t192 (not @t189)))) % 0.37/0.59 (step @p304 :rule cnf_or_neg :args (@t192 1)) % 0.37/0.59 (step @p305 :rule eq_resolve :premises (@p304 @p303)) % 0.37/0.59 (step @p306 :rule reordering :premises (@p305) :args ((or @t188 @t192))) % 0.37/0.59 (step @p307 :rule chain_m_resolution :premises (@p306 @p283) :args (@t188 @t193 @t194)) % 0.37/0.59 (step @p308 :rule cnf_equiv_pos1 :args (@t205)) % 0.37/0.59 (step @p309 :rule reordering :premises (@p308) :args ((or @t189 @t203 (not @t205)))) % 0.37/0.59 (step @p310 :rule chain_m_resolution :premises (@p309 @p307 @p300) :args (@t203 @t206 (@list @t188 @t205))) % 0.37/0.59 (step @p311 :rule instantiate :premises (@p310) :args (@t207)) % 0.37/0.59 (step @p312 :rule eq-symm :args (@t208 @t190)) % 0.37/0.59 (step @p313 :rule cong :premises (@p146 @p312) :args ((=> @t56 @t209))) % 0.37/0.59 (assume-push @p348 @t56) % 0.37/0.59 (step @p315 :rule instantiate :premises (@p144) :args ((@list @t116 @t187))) % 0.37/0.59 (step-pop @p349 :rule scope :premises (@p315)) % 0.37/0.59 (step @p316 :rule process_scope :premises (@p349) :args (@t209)) % 0.37/0.59 (step @p318 :rule eq_resolve :premises (@p316 @p313)) % 0.37/0.59 (step @p319 :rule implies_elim :premises (@p318)) % 0.37/0.59 (step @p320 :rule chain_m_resolution :premises (@p319 @p144) :args (@t210 @t122 @t123)) % 0.37/0.59 (step @p321 :rule bool-double-not-elim :args (@t190)) % 0.37/0.59 (step @p322 :rule nary_cong :premises (@p302 @p321) :args ((or @t192 (not @t191)))) % 0.37/0.59 (step @p323 :rule cnf_or_neg :args (@t192 0)) % 0.37/0.59 (step @p324 :rule eq_resolve :premises (@p323 @p322)) % 0.37/0.59 (step @p325 :rule reordering :premises (@p324) :args ((or @t190 @t192))) % 0.37/0.59 (step @p326 :rule chain_m_resolution :premises (@p325 @p283) :args (@t190 @t193 @t194)) % 0.37/0.59 (step @p327 :rule cnf_equiv_pos1 :args (@t210)) % 0.37/0.59 (step @p328 :rule reordering :premises (@p327) :args ((or @t191 @t208 (not @t210)))) % 0.37/0.59 (step @p329 :rule chain_m_resolution :premises (@p328 @p326 @p320) :args (@t208 @t206 (@list @t190 @t210))) % 0.37/0.59 (step @p330 :rule instantiate :premises (@p329) :args (@t207)) % 0.37/0.59 (step @p331 :rule bool-double-not-elim :args (@t198)) % 0.37/0.59 (step @p332 :rule refl :args (@t200)) % 0.37/0.59 (step @p333 :rule nary_cong :premises (@p332 @p331) :args ((or @t200 (not @t199)))) % 0.37/0.59 (step @p334 :rule cnf_or_neg :args (@t200 0)) % 0.37/0.59 (step @p335 :rule eq_resolve :premises (@p334 @p333)) % 0.37/0.59 (step @p336 :rule reordering :premises (@p335) :args ((or @t198 @t200))) % 0.37/0.59 (step @p337 :rule chain_m_resolution :premises (@p336 @p289) :args (@t198 @t193 @t201)) % 0.37/0.59 (step @p338 :rule cnf_or_pos :args (@t212)) % 0.37/0.59 (step @p339 :rule reordering :premises (@p338) :args ((or @t199 @t211 (not @t212)))) % 0.37/0.59 (step @p340 :rule chain_m_resolution :premises (@p339 @p337 @p330) :args (@t211 @t206 (@list @t198 @t212))) % 0.37/0.59 (step @p341 :rule cnf_or_pos :args (@t214)) % 0.37/0.59 (step @p342 :rule reordering :premises (@p341) :args ((or @t197 @t213 (not @t214)))) % 0.37/0.59 (step @p343 false :rule chain_m_resolution :premises (@p342 @p340 @p311 @p291) :args (false (@list false false true) (@list @t211 @t214 @t197))) % 0.37/0.59 ) % 0.37/0.59 % SZS output end Proof % 0.37/0.59 % cvc5 exiting %------------------------------------------------------------------------------