%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL959^24 : TPTP v9.3.1. 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 : n028.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:24:16 AM UTC 2026 % Result : Theorem 3.33s 3.62s % Output : Proof 3.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL959^24 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.11/0.38 % Computer : n028.cluster.edu % 0.11/0.38 % Model : x86_64 x86_64 % 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.38 % Memory : 8046.5625MB % 0.11/0.38 % OS : Linux 6.8.0-71-generic % 0.11/0.38 % CPULimit : 300 % 0.11/0.38 % WCLimit : 300 % 0.11/0.38 % DateTime : Fri Sep 4 16:42:13 UTC 2026 % 0.11/0.39 % CPUTime : % 0.21/0.46 %----Proving TH0 % 3.33/3.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 3.33/3.62 % SZS status Theorem % 3.33/3.62 % SZS output start Proof % 3.33/3.62 ( % 3.33/3.62 (declare-sort $$unsorted 0) % 3.33/3.62 (declare-sort tptp.mworld 0) % 3.33/3.62 (declare-const tptp.mactual tptp.mworld) % 3.33/3.62 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 3.33/3.62 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 3.33/3.62 (declare-const tptp.f (-> $$unsorted tptp.mworld Bool)) % 3.33/3.62 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 3.33/3.62 (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)))))) % 3.33/3.62 (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))))))) % 3.33/3.62 (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))))))) % 3.33/3.62 (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))))))) % 3.33/3.62 (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))))))) % 3.33/3.62 (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)))))))) % 3.33/3.62 (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)))))))) % 3.33/3.62 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 3.33/3.62 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 3.33/3.62 (define @t1 () (@var "V" tptp.mworld)) % 3.33/3.62 (define @t2 () (@var "W" tptp.mworld)) % 3.33/3.62 (define @t3 () (_ (_ tptp.mrel @t2) @t1)) % 3.33/3.62 (define @t4 () (forall (@list @t2 @t1) @t3)) % 3.33/3.62 (define @t5 () (@var "X" $$unsorted)) % 3.33/3.62 (define @t6 () (_ tptp.eiw_di @t5)) % 3.33/3.62 (define @t7 () (_ @t6 @t2)) % 3.33/3.62 (define @t8 () (@list @t5)) % 3.33/3.62 (define @t9 () (@list @t2)) % 3.33/3.62 (define @t10 () (_ @t6 @t1)) % 3.33/3.62 (define @t11 () (_ (_ tptp.mrel @t1) @t2)) % 3.33/3.62 (define @t12 () (and @t7 @t11)) % 3.33/3.62 (define @t13 () (@list @t2 @t1 @t5)) % 3.33/3.62 (define @t14 () (forall @t13 (=> @t12 @t10))) % 3.33/3.62 (define @t15 () (@var "__flatten_var_0" tptp.mworld)) % 3.33/3.62 (define @t16 () (_ tptp.f @t5)) % 3.33/3.62 (define @t17 () (@list @t5 @t15)) % 3.33/3.62 (define @t18 () (lambda @t17 (_ (_ tptp.mbox @t16) @t15))) % 3.33/3.62 (define @t19 () (_ tptp.mbox (_ tptp.mnot (_ tptp.mbox (_ tptp.mforall_di @t18))))) % 3.33/3.62 (define @t20 () (@var "Y" $$unsorted)) % 3.33/3.62 (define @t21 () (_ tptp.f @t20)) % 3.33/3.62 (define @t22 () (@list @t20 @t15)) % 3.33/3.62 (define @t23 () (lambda @t22 (_ (_ tptp.mbox (_ tptp.mnot (_ tptp.mbox @t21))) @t15))) % 3.33/3.62 (define @t24 () (_ tptp.mexists_di @t23)) % 3.33/3.62 (define @t25 () (not (_ tptp.mlocal (_ (_ tptp.mand (_ tptp.mbox (_ (_ tptp.mimplies @t19) @t24))) (_ tptp.mbox (_ (_ tptp.mimplies @t24) @t19)))))) % 3.33/3.62 (define @t26 () (@var "Phi" (-> tptp.mworld Bool))) % 3.33/3.62 (define @t27 () (lambda (@list @t26) (_ @t26 tptp.mactual))) % 3.33/3.62 (define @t28 () (@var "A" (-> tptp.mworld Bool))) % 3.33/3.62 (define @t29 () (_ @t28 @t2)) % 3.33/3.62 (define @t30 () (lambda (@list @t28 @t2) (not @t29))) % 3.33/3.62 (define @t31 () (@var "B" (-> tptp.mworld Bool))) % 3.33/3.62 (define @t32 () (_ @t31 @t2)) % 3.33/3.62 (define @t33 () (@list @t28 @t31 @t2)) % 3.33/3.62 (define @t34 () (lambda @t33 (and @t29 @t32))) % 3.33/3.62 (define @t35 () (lambda @t33 (or @t29 @t32))) % 3.33/3.62 (define @t36 () (lambda @t33 (=> @t29 @t32))) % 3.33/3.62 (define @t37 () (lambda @t33 (= @t29 @t32))) % 3.33/3.62 (define @t38 () (_ @t26 @t1)) % 3.33/3.62 (define @t39 () (@list @t1)) % 3.33/3.62 (define @t40 () (forall @t39 (=> @t3 @t38))) % 3.33/3.62 (define @t41 () (@list @t26 @t2)) % 3.33/3.62 (define @t42 () (lambda @t41 @t40)) % 3.33/3.62 (define @t43 () (lambda @t41 (exists @t39 (and @t3 @t38)))) % 3.33/3.62 (define @t44 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 3.33/3.62 (define @t45 () (_ (_ @t44 @t5) @t2)) % 3.33/3.62 (define @t46 () (forall @t8 (=> @t7 @t45))) % 3.33/3.62 (define @t47 () (@list @t44 @t2)) % 3.33/3.62 (define @t48 () (lambda @t47 @t46)) % 3.33/3.62 (define @t49 () (and @t7 @t45)) % 3.33/3.62 (define @t50 () (exists @t8 @t49)) % 3.33/3.62 (define @t51 () (lambda @t47 @t50)) % 3.33/3.62 (define @t52 () (@var "BOUND_VARIABLE_7719" tptp.mworld)) % 3.33/3.62 (define @t53 () (@var "BOUND_VARIABLE_7717" $$unsorted)) % 3.33/3.62 (define @t54 () (tptp.f @t53 @t52)) % 3.33/3.62 (define @t55 () (@var "BOUND_VARIABLE_7745" tptp.mworld)) % 3.33/3.62 (define @t56 () (not (tptp.mrel @t55 @t52))) % 3.33/3.62 (define @t57 () (not (tptp.eiw_di @t53 @t55))) % 3.33/3.62 (define @t58 () (@var "BOUND_VARIABLE_7866" tptp.mworld)) % 3.33/3.62 (define @t59 () (@list @t55 @t53 @t52)) % 3.33/3.62 (define @t60 () (not (forall @t59 (or (not (tptp.mrel @t58 @t55)) @t57 @t56 @t54)))) % 3.33/3.62 (define @t61 () (@var "BOUND_VARIABLE_7796" tptp.mworld)) % 3.33/3.62 (define @t62 () (tptp.f @t5 @t61)) % 3.33/3.62 (define @t63 () (@var "BOUND_VARIABLE_7850" tptp.mworld)) % 3.33/3.62 (define @t64 () (not (tptp.mrel @t63 @t61))) % 3.33/3.62 (define @t65 () (@list @t61)) % 3.33/3.62 (define @t66 () (not (forall @t65 (or @t64 @t62)))) % 3.33/3.62 (define @t67 () (@list @t63)) % 3.33/3.62 (define @t68 () (tptp.eiw_di @t5 @t1)) % 3.33/3.62 (define @t69 () (not @t68)) % 3.33/3.62 (define @t70 () (not (forall @t8 (or @t69 (not (forall @t67 (or (not (tptp.mrel @t1 @t63)) @t66))))))) % 3.33/3.62 (define @t71 () (@list @t58)) % 3.33/3.62 (define @t72 () (forall @t71 (or (not (tptp.mrel @t1 @t58)) @t60))) % 3.33/3.62 (define @t73 () (not @t72)) % 3.33/3.62 (define @t74 () (not (tptp.mrel tptp.mactual @t1))) % 3.33/3.62 (define @t75 () (forall @t39 (or @t74 @t73 @t70))) % 3.33/3.62 (define @t76 () (@quantifiers_skolemize @t75 0)) % 3.33/3.62 (define @t77 () (forall @t71 (or (not (tptp.mrel @t76 @t58)) @t60))) % 3.33/3.62 (define @t78 () (not (tptp.mrel @t76 @t63))) % 3.33/3.62 (define @t79 () (forall @t8 (or (not (tptp.eiw_di @t5 @t76)) (not (forall @t67 (or @t78 @t66)))))) % 3.33/3.62 (define @t80 () (not @t79)) % 3.33/3.62 (define @t81 () (not @t77)) % 3.33/3.62 (define @t82 () (or (not (tptp.mrel tptp.mactual @t76)) @t81 @t80)) % 3.33/3.62 (define @t83 () (forall @t59 (or (not (tptp.mrel @t76 @t55)) @t57 @t56 @t54))) % 3.33/3.62 (define @t84 () (not @t83)) % 3.33/3.62 (define @t85 () (tptp.mrel @t76 @t76)) % 3.33/3.62 (define @t86 () (not @t85)) % 3.33/3.62 (define @t87 () (or @t86 @t84)) % 3.33/3.62 (define @t88 () (@quantifiers_skolemize @t83 1)) % 3.33/3.62 (define @t89 () (tptp.f @t88 @t61)) % 3.33/3.62 (define @t90 () (forall @t67 (or @t78 (not (forall @t65 (or @t64 @t89)))))) % 3.33/3.62 (define @t91 () (not @t90)) % 3.33/3.62 (define @t92 () (tptp.eiw_di @t88 @t76)) % 3.33/3.62 (define @t93 () (not @t92)) % 3.33/3.62 (define @t94 () (or @t93 @t91)) % 3.33/3.62 (define @t95 () (tptp.mrel @t2 @t1)) % 3.33/3.62 (define @t96 () (@quantifiers_skolemize @t83 2)) % 3.33/3.62 (define @t97 () (tptp.f @t88 @t96)) % 3.33/3.62 (define @t98 () (@quantifiers_skolemize @t83 0)) % 3.33/3.62 (define @t99 () (tptp.eiw_di @t88 @t98)) % 3.33/3.62 (define @t100 () (not @t99)) % 3.33/3.62 (define @t101 () (tptp.mrel @t76 @t98)) % 3.33/3.62 (define @t102 () (not @t101)) % 3.33/3.62 (define @t103 () (or @t102 @t100 (not (tptp.mrel @t98 @t96)) @t97)) % 3.33/3.62 (define @t104 () (not @t103)) % 3.33/3.62 (define @t105 () (tptp.mrel @t1 @t2)) % 3.33/3.62 (define @t106 () (not @t11)) % 3.33/3.62 (define @t107 () (tptp.eiw_di @t5 @t2)) % 3.33/3.62 (define @t108 () (not @t7)) % 3.33/3.62 (define @t109 () (or @t108 @t106 @t10)) % 3.33/3.62 (define @t110 () (or @t100 @t102 @t92)) % 3.33/3.62 (define @t111 () (@quantifiers_skolemize @t90 0)) % 3.33/3.62 (define @t112 () (tptp.mrel @t111 @t96)) % 3.33/3.62 (define @t113 () (not @t112)) % 3.33/3.62 (define @t114 () (or @t113 @t97)) % 3.33/3.62 (define @t115 () (forall @t65 (or (not (tptp.mrel @t111 @t61)) @t89))) % 3.33/3.62 (define @t116 () (not @t115)) % 3.33/3.62 (define @t117 () (or (not (tptp.mrel @t76 @t111)) @t116)) % 3.33/3.62 (define @t118 () (not @t117)) % 3.33/3.62 (define @t119 () (not @t82)) % 3.33/3.62 (define @t120 () (not @t75)) % 3.33/3.62 (define @t121 () (@list false)) % 3.33/3.62 (define @t122 () (@var "BOUND_VARIABLE_7985" tptp.mworld)) % 3.33/3.62 (define @t123 () (not (forall @t59 (or (not (tptp.mrel @t122 @t55)) @t57 @t56 @t54)))) % 3.33/3.62 (define @t124 () (not (tptp.mrel @t1 @t122))) % 3.33/3.62 (define @t125 () (@var "BOUND_VARIABLE_7973" $$unsorted)) % 3.33/3.62 (define @t126 () (@var "BOUND_VARIABLE_7936" tptp.mworld)) % 3.33/3.62 (define @t127 () (not (tptp.mrel @t126 @t61))) % 3.33/3.62 (define @t128 () (not (tptp.mrel @t1 @t126))) % 3.33/3.62 (define @t129 () (@list @t126)) % 3.33/3.62 (define @t130 () (not (forall @t129 (or @t128 (not (forall @t65 (or @t127 (tptp.f @t125 @t61)))))))) % 3.33/3.62 (define @t131 () (not (tptp.eiw_di @t125 @t1))) % 3.33/3.62 (define @t132 () (@list @t1 @t125 @t122)) % 3.33/3.62 (define @t133 () (forall @t132 (or @t74 @t131 @t130 @t124 @t123))) % 3.33/3.62 (define @t134 () (not @t95)) % 3.33/3.62 (define @t135 () (or @t134 @t131 @t130 @t124 @t123)) % 3.33/3.62 (define @t136 () (forall @t132 @t135)) % 3.33/3.62 (define @t137 () (or @t134 @t73 @t70)) % 3.33/3.62 (define @t138 () (forall @t39 @t137)) % 3.33/3.62 (define @t139 () (lambda @t9 (and @t138 @t136))) % 3.33/3.62 (define @t140 () (_ @t139 tptp.mactual)) % 3.33/3.62 (define @t141 () (lambda @t9 @t136)) % 3.33/3.62 (define @t142 () (_ @t141 @t2)) % 3.33/3.62 (define @t143 () (and @t138 @t142)) % 3.33/3.62 (define @t144 () (lambda @t9 @t143)) % 3.33/3.62 (define @t145 () (@list @t31 @t2)) % 3.33/3.62 (define @t146 () (or @t124 @t123)) % 3.33/3.62 (define @t147 () (or @t131 @t130)) % 3.33/3.62 (define @t148 () (or @t134 @t147 @t146)) % 3.33/3.62 (define @t149 () (forall @t132 @t148)) % 3.33/3.62 (define @t150 () (forall (@list @t125 @t122) @t148)) % 3.33/3.62 (define @t151 () (forall (@list @t122) @t146)) % 3.33/3.62 (define @t152 () (@var "BOUND_VARIABLE_7924" tptp.mworld)) % 3.33/3.62 (define @t153 () (@list @t152)) % 3.33/3.62 (define @t154 () (forall (@list @t125) @t147)) % 3.33/3.62 (define @t155 () (or @t134 @t154 @t151)) % 3.33/3.62 (define @t156 () (not (forall @t59 (or (not (tptp.mrel @t152 @t55)) @t57 @t56 @t54)))) % 3.33/3.62 (define @t157 () (@list @t152)) % 3.33/3.62 (define @t158 () (forall @t157 (or (not (tptp.mrel @t1 @t152)) @t156))) % 3.33/3.62 (define @t159 () (not (forall @t65 (or @t127 @t62)))) % 3.33/3.62 (define @t160 () (forall @t8 (or @t69 (not (forall @t129 (or @t128 @t159)))))) % 3.33/3.62 (define @t161 () (or @t134 @t160 @t158)) % 3.33/3.62 (define @t162 () (not @t160)) % 3.33/3.62 (define @t163 () (=> @t162 @t158)) % 3.33/3.62 (define @t164 () (or @t134 @t163)) % 3.33/3.62 (define @t165 () (not @t107)) % 3.33/3.62 (define @t166 () (not (forall @t59 (or (not (tptp.mrel @t1 @t55)) @t57 @t56 @t54)))) % 3.33/3.62 (define @t167 () (forall @t39 (or @t134 @t166))) % 3.33/3.62 (define @t168 () (@list @t1)) % 3.33/3.62 (define @t169 () (not (tptp.mrel @t1 @t61))) % 3.33/3.62 (define @t170 () (forall @t39 (or @t134 (not (forall @t65 (or @t169 @t62)))))) % 3.33/3.62 (define @t171 () (not @t170)) % 3.33/3.62 (define @t172 () (or @t165 @t171)) % 3.33/3.62 (define @t173 () (forall @t8 @t172)) % 3.33/3.62 (define @t174 () (not @t173)) % 3.33/3.62 (define @t175 () (=> @t174 @t167)) % 3.33/3.62 (define @t176 () (lambda @t9 @t175)) % 3.33/3.62 (define @t177 () (or @t134 (_ @t176 @t1))) % 3.33/3.62 (define @t178 () (forall @t39 @t177)) % 3.33/3.62 (define @t179 () (lambda @t9 @t178)) % 3.33/3.62 (define @t180 () (_ @t26 @t1)) % 3.33/3.62 (define @t181 () (lambda @t41 (forall @t39 (or @t134 @t180)))) % 3.33/3.62 (define @t182 () (lambda @t9 @t167)) % 3.33/3.62 (define @t183 () (_ @t182 @t2)) % 3.33/3.62 (define @t184 () (=> @t174 @t183)) % 3.33/3.62 (define @t185 () (lambda @t9 @t184)) % 3.33/3.62 (define @t186 () (not (tptp.mrel @t1 @t52))) % 3.33/3.62 (define @t187 () (not (tptp.eiw_di @t53 @t1))) % 3.33/3.62 (define @t188 () (or @t134 @t187 @t186 @t54)) % 3.33/3.62 (define @t189 () (@list @t1 @t53 @t52)) % 3.33/3.62 (define @t190 () (forall @t189 @t188)) % 3.33/3.62 (define @t191 () (not @t190)) % 3.33/3.62 (define @t192 () (lambda @t9 @t191)) % 3.33/3.62 (define @t193 () (or @t134 (_ @t192 @t1))) % 3.33/3.62 (define @t194 () (forall @t39 @t193)) % 3.33/3.62 (define @t195 () (lambda @t9 @t194)) % 3.33/3.62 (define @t196 () (lambda @t9 @t190)) % 3.33/3.62 (define @t197 () (_ @t196 @t2)) % 3.33/3.62 (define @t198 () (not @t197)) % 3.33/3.62 (define @t199 () (lambda @t9 @t198)) % 3.33/3.62 (define @t200 () (or @t187 @t186 @t54)) % 3.33/3.62 (define @t201 () (or @t134 @t200)) % 3.33/3.62 (define @t202 () (forall @t189 @t201)) % 3.33/3.62 (define @t203 () (@list @t53 @t52)) % 3.33/3.62 (define @t204 () (forall @t203 @t201)) % 3.33/3.62 (define @t205 () (forall @t203 @t200)) % 3.33/3.62 (define @t206 () (@var "BOUND_VARIABLE_7693" tptp.mworld)) % 3.33/3.62 (define @t207 () (or @t134 @t205)) % 3.33/3.62 (define @t208 () (tptp.f @t5 @t206)) % 3.33/3.62 (define @t209 () (@list @t5 @t206)) % 3.33/3.62 (define @t210 () (forall @t209 (or @t69 (not (tptp.mrel @t1 @t206)) @t208))) % 3.33/3.62 (define @t211 () (not (tptp.mrel @t2 @t206))) % 3.33/3.62 (define @t212 () (or @t165 @t211 @t208)) % 3.33/3.62 (define @t213 () (lambda @t9 (forall @t209 @t212))) % 3.33/3.62 (define @t214 () (_ @t213 @t1)) % 3.33/3.62 (define @t215 () (or @t134 @t214)) % 3.33/3.62 (define @t216 () (forall @t39 @t215)) % 3.33/3.62 (define @t217 () (lambda @t9 @t216)) % 3.33/3.62 (define @t218 () (or @t211 @t208)) % 3.33/3.62 (define @t219 () (or @t165 @t218)) % 3.33/3.62 (define @t220 () (forall @t209 @t219)) % 3.33/3.62 (define @t221 () (@list @t206)) % 3.33/3.62 (define @t222 () (forall @t221 @t219)) % 3.33/3.62 (define @t223 () (forall @t221 @t218)) % 3.33/3.62 (define @t224 () (or @t165 @t223)) % 3.33/3.62 (define @t225 () (tptp.f @t5 @t1)) % 3.33/3.62 (define @t226 () (forall @t39 (or @t134 @t225))) % 3.33/3.62 (define @t227 () (not (tptp.mrel @t15 @t1))) % 3.33/3.62 (define @t228 () (forall @t39 (or @t227 @t225))) % 3.33/3.62 (define @t229 () (lambda @t17 @t228)) % 3.33/3.62 (define @t230 () (_ @t229 @t5 @t2)) % 3.33/3.62 (define @t231 () (or @t165 @t230)) % 3.33/3.62 (define @t232 () (forall @t8 @t231)) % 3.33/3.62 (define @t233 () (lambda @t9 @t232)) % 3.33/3.62 (define @t234 () (_ @t44 @t5 @t2)) % 3.33/3.62 (define @t235 () (lambda @t47 (forall @t8 (or @t165 @t234)))) % 3.33/3.62 (define @t236 () (_ @t16 @t1)) % 3.33/3.62 (define @t237 () (or @t134 @t236)) % 3.33/3.62 (define @t238 () (_ @t16 @t1)) % 3.33/3.62 (define @t239 () (or @t134 @t238)) % 3.33/3.62 (define @t240 () (forall @t39 @t239)) % 3.33/3.62 (define @t241 () (lambda @t9 @t240)) % 3.33/3.62 (define @t242 () (_ @t181 @t16)) % 3.33/3.62 (define @t243 () (lambda @t17 (_ @t242 @t15))) % 3.33/3.62 (define @t244 () (lambda @t9 @t174)) % 3.33/3.62 (define @t245 () (_ @t244 @t2)) % 3.33/3.62 (define @t246 () (=> @t245 @t32)) % 3.33/3.62 (define @t247 () (lambda @t145 @t246)) % 3.33/3.62 (define @t248 () (tptp.f @t20 @t61)) % 3.33/3.62 (define @t249 () (not (forall @t65 (or @t169 @t248)))) % 3.33/3.62 (define @t250 () (forall @t39 (or @t227 @t249))) % 3.33/3.62 (define @t251 () (lambda @t22 @t250)) % 3.33/3.62 (define @t252 () (_ @t251 @t5 @t2)) % 3.33/3.62 (define @t253 () (not @t252)) % 3.33/3.62 (define @t254 () (or @t165 @t253)) % 3.33/3.62 (define @t255 () (forall @t8 @t254)) % 3.33/3.62 (define @t256 () (not @t255)) % 3.33/3.62 (define @t257 () (lambda @t9 @t256)) % 3.33/3.62 (define @t258 () (lambda @t47 (not (forall @t8 (or @t165 (not @t234)))))) % 3.33/3.62 (define @t259 () (tptp.f @t20 @t1)) % 3.33/3.62 (define @t260 () (forall @t39 (or @t134 @t259))) % 3.33/3.62 (define @t261 () (not @t260)) % 3.33/3.62 (define @t262 () (lambda @t9 @t261)) % 3.33/3.62 (define @t263 () (or @t134 (_ @t262 @t1))) % 3.33/3.62 (define @t264 () (forall @t39 @t263)) % 3.33/3.62 (define @t265 () (lambda @t9 @t264)) % 3.33/3.62 (define @t266 () (lambda @t9 @t260)) % 3.33/3.62 (define @t267 () (_ @t266 @t2)) % 3.33/3.62 (define @t268 () (not @t267)) % 3.33/3.62 (define @t269 () (lambda @t9 @t268)) % 3.33/3.62 (define @t270 () (_ @t21 @t1)) % 3.33/3.62 (define @t271 () (or @t134 @t270)) % 3.33/3.62 (define @t272 () (_ @t21 @t1)) % 3.33/3.62 (define @t273 () (or @t134 @t272)) % 3.33/3.62 (define @t274 () (forall @t39 @t273)) % 3.33/3.62 (define @t275 () (lambda @t9 @t274)) % 3.33/3.62 (define @t276 () (_ @t181 @t21)) % 3.33/3.62 (define @t277 () (lambda @t22 (_ (_ @t181 (_ @t30 @t276)) @t15))) % 3.33/3.62 (define @t278 () (lambda @t9 @t138)) % 3.33/3.62 (define @t279 () (_ @t278 @t2)) % 3.33/3.62 (define @t280 () (and @t279 @t32)) % 3.33/3.62 (define @t281 () (lambda @t145 @t280)) % 3.33/3.62 (define @t282 () (=> @t72 @t70)) % 3.33/3.62 (define @t283 () (or @t134 @t282)) % 3.33/3.62 (define @t284 () (=> @t167 @t174)) % 3.33/3.62 (define @t285 () (lambda @t9 @t284)) % 3.33/3.62 (define @t286 () (or @t134 (_ @t285 @t1))) % 3.33/3.62 (define @t287 () (forall @t39 @t286)) % 3.33/3.62 (define @t288 () (lambda @t9 @t287)) % 3.33/3.62 (define @t289 () (=> @t167 @t245)) % 3.33/3.62 (define @t290 () (lambda @t9 @t289)) % 3.33/3.62 (define @t291 () (=> @t183 @t32)) % 3.33/3.62 (define @t292 () (lambda @t145 @t291)) % 3.33/3.62 (define @t293 () (_ @t181 (_ @t30 (_ @t181 (_ @t235 @t243))))) % 3.33/3.62 (define @t294 () (_ @t258 @t277)) % 3.33/3.62 (define @t295 () (not @t3)) % 3.33/3.62 (define @t296 () (or @t295 @t38)) % 3.33/3.62 (define @t297 () (or @t108 @t45)) % 3.33/3.62 (define @t298 () (not @t45)) % 3.33/3.62 (define @t299 () (or @t108 @t298)) % 3.33/3.62 (define @t300 () (forall @t8 (not @t49))) % 3.33/3.62 (define @t301 () (not @t300)) % 3.33/3.62 (define @t302 () (not @t133)) % 3.33/3.62 (define @t303 () (@quantifiers_skolemize @t133 2)) % 3.33/3.62 (define @t304 () (forall @t59 (or (not (tptp.mrel @t303 @t55)) @t57 @t56 @t54))) % 3.33/3.62 (define @t305 () (not @t304)) % 3.33/3.62 (define @t306 () (@quantifiers_skolemize @t133 0)) % 3.33/3.62 (define @t307 () (tptp.mrel @t306 @t303)) % 3.33/3.62 (define @t308 () (not @t307)) % 3.33/3.62 (define @t309 () (@quantifiers_skolemize @t133 1)) % 3.33/3.62 (define @t310 () (tptp.f @t309 @t61)) % 3.33/3.62 (define @t311 () (forall @t129 (or (not (tptp.mrel @t306 @t126)) (not (forall @t65 (or @t127 @t310)))))) % 3.33/3.62 (define @t312 () (not @t311)) % 3.33/3.62 (define @t313 () (tptp.eiw_di @t309 @t306)) % 3.33/3.62 (define @t314 () (not @t313)) % 3.33/3.62 (define @t315 () (or (not (tptp.mrel tptp.mactual @t306)) @t314 @t312 @t308 @t305)) % 3.33/3.62 (define @t316 () (not @t315)) % 3.33/3.62 (define @t317 () (@list true)) % 3.33/3.62 (define @t318 () (@list @t315)) % 3.33/3.62 (define @t319 () (forall @t65 (or (not (tptp.mrel @t303 @t61)) @t310))) % 3.33/3.62 (define @t320 () (@quantifiers_skolemize @t319 0)) % 3.33/3.62 (define @t321 () (not @t319)) % 3.33/3.62 (define @t322 () (or @t308 @t321)) % 3.33/3.62 (define @t323 () (tptp.f @t309 @t320)) % 3.33/3.62 (define @t324 () (or (not (tptp.mrel @t303 @t320)) @t323)) % 3.33/3.62 (define @t325 () (not @t324)) % 3.33/3.62 (define @t326 () (tptp.mrel @t306 @t320)) % 3.33/3.62 (define @t327 () (not @t326)) % 3.33/3.62 (define @t328 () (tptp.mrel @t303 @t306)) % 3.33/3.62 (define @t329 () (not @t328)) % 3.33/3.62 (define @t330 () (or @t329 @t314 @t327 @t323)) % 3.33/3.62 (define @t331 () (not @t330)) % 3.33/3.62 (assume @p1 @t4) % 3.33/3.62 (assume @p2 (forall @t9 (exists @t8 @t7))) % 3.33/3.62 (assume @p3 @t14) % 3.33/3.62 (assume @p4 @t25) % 3.33/3.62 (assume @p5 true) % 3.33/3.62 (step @p6 (= tptp.mlocal @t27) :rule refl :args (@t27)) % 3.33/3.62 (step @p7 (= tptp.mnot @t30) :rule refl :args (@t30)) % 3.33/3.62 (step @p8 (= tptp.mand @t34) :rule refl :args (@t34)) % 3.33/3.62 (step @p9 (= tptp.mor @t35) :rule refl :args (@t35)) % 3.33/3.62 (step @p10 (= tptp.mimplies @t36) :rule refl :args (@t36)) % 3.33/3.62 (step @p11 (= tptp.mequiv @t37) :rule refl :args (@t37)) % 3.33/3.62 (step @p12 (= tptp.mbox @t42) :rule refl :args (@t42)) % 3.33/3.62 (step @p13 (= tptp.mdia @t43) :rule refl :args (@t43)) % 3.33/3.62 (step @p14 (= tptp.mforall_di @t48) :rule refl :args (@t48)) % 3.33/3.62 (step @p15 (= tptp.mexists_di @t51) :rule refl :args (@t51)) % 3.33/3.62 (step @p16 :rule bool-double-not-elim :args (@t77)) % 3.33/3.62 (step @p17 :rule refl :args (@t82)) % 3.33/3.62 (step @p18 :rule nary_cong :premises (@p17 @p16) :args ((or @t82 (not @t81)))) % 3.33/3.62 (step @p19 :rule cnf_or_neg :args (@t82 1)) % 3.33/3.62 (step @p20 :rule eq_resolve :premises (@p19 @p18)) % 3.33/3.62 (step @p21 :rule reordering :premises (@p20) :args ((or @t77 @t82))) % 3.33/3.62 (step @p22 :rule bool-double-not-elim :args (@t79)) % 3.33/3.62 (step @p23 :rule nary_cong :premises (@p17 @p22) :args ((or @t82 (not @t80)))) % 3.33/3.62 (step @p24 :rule cnf_or_neg :args (@t82 2)) % 3.33/3.62 (step @p25 :rule eq_resolve :premises (@p24 @p23)) % 3.33/3.62 (step @p26 :rule reordering :premises (@p25) :args ((or @t79 @t82))) % 3.33/3.62 (assume-push @p521 @t77) % 3.33/3.62 (step @p28 :rule instantiate :premises (@p521) :args ((@list @t76))) % 3.33/3.62 (step-pop @p522 :rule scope :premises (@p28)) % 3.33/3.62 (step @p29 :rule process_scope :premises (@p522) :args (@t87)) % 3.33/3.62 (step @p31 :rule implies_elim :premises (@p29)) % 3.33/3.62 (assume-push @p523 @t79) % 3.33/3.62 (step @p33 :rule instantiate :premises (@p523) :args ((@list @t88))) % 3.33/3.62 (step-pop @p524 :rule scope :premises (@p33)) % 3.33/3.62 (step @p34 :rule process_scope :premises (@p524) :args (@t94)) % 3.33/3.62 (step @p36 :rule implies_elim :premises (@p34)) % 3.33/3.62 (step @p37 :rule refl :args (@t95)) % 3.33/3.62 (step @p38 :rule refl :args (@t3)) % 3.33/3.62 (step @p39 :rule cong :premises (@p38 @p37) :args ((= @t3 @t95))) % 3.33/3.62 (step @p40 :rule symm :premises (@p39)) % 3.33/3.62 (step @p41 :rule eq_resolve :premises (@p38 @p40)) % 3.33/3.62 (step @p42 :rule cong :premises (@p41) :args (@t4)) % 3.33/3.62 (step @p43 :rule eq_resolve :premises (@p1 @p42)) % 3.33/3.62 (step @p44 :rule instantiate :premises (@p43) :args ((@list @t76 @t76))) % 3.33/3.62 (step @p45 :rule cnf_or_pos :args (@t87)) % 3.33/3.62 (step @p46 :rule reordering :premises (@p45) :args ((or @t86 @t84 (not @t87)))) % 3.33/3.62 (step @p47 :rule refl :args (@t104)) % 3.33/3.62 (step @p48 :rule bool-double-not-elim :args (@t83)) % 3.33/3.62 (step @p49 :rule nary_cong :premises (@p48 @p47) :args ((or (not @t84) @t104))) % 3.33/3.62 (assume-push @p525 @t84) % 3.33/3.62 (step @p51 :rule skolemize :premises (@p525)) % 3.33/3.62 (step-pop @p526 :rule scope :premises (@p51)) % 3.33/3.62 (step @p52 :rule process_scope :premises (@p526) :args (@t104)) % 3.33/3.62 (step @p54 :rule implies_elim :premises (@p52)) % 3.33/3.62 (step @p55 :rule eq_resolve :premises (@p54 @p49)) % 3.33/3.62 (step @p56 :rule bool-double-not-elim :args (@t101)) % 3.33/3.62 (step @p57 :rule refl :args (@t103)) % 3.33/3.62 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or @t103 (not @t102)))) % 3.33/3.62 (step @p59 :rule cnf_or_neg :args (@t103 0)) % 3.33/3.62 (step @p60 :rule eq_resolve :premises (@p59 @p58)) % 3.33/3.62 (step @p61 :rule reordering :premises (@p60) :args ((or @t101 @t103))) % 3.33/3.62 (step @p62 :rule bool-double-not-elim :args (@t99)) % 3.33/3.62 (step @p63 :rule nary_cong :premises (@p57 @p62) :args ((or @t103 (not @t100)))) % 3.33/3.62 (step @p64 :rule cnf_or_neg :args (@t103 1)) % 3.33/3.62 (step @p65 :rule eq_resolve :premises (@p64 @p63)) % 3.33/3.62 (step @p66 :rule reordering :premises (@p65) :args ((or @t99 @t103))) % 3.33/3.62 (step @p67 :rule cnf_or_neg :args (@t103 3)) % 3.33/3.62 (step @p68 :rule refl :args (@t68)) % 3.33/3.62 (step @p69 :rule refl :args (@t10)) % 3.33/3.62 (step @p70 :rule cong :premises (@p69 @p68) :args ((= @t10 @t68))) % 3.33/3.62 (step @p71 :rule symm :premises (@p70)) % 3.33/3.62 (step @p72 :rule eq_resolve :premises (@p69 @p71)) % 3.33/3.62 (step @p73 :rule refl :args (@t105)) % 3.33/3.62 (step @p74 :rule refl :args (@t11)) % 3.33/3.62 (step @p75 :rule cong :premises (@p74 @p73) :args ((= @t11 @t105))) % 3.33/3.62 (step @p76 :rule symm :premises (@p75)) % 3.33/3.62 (step @p77 :rule eq_resolve :premises (@p74 @p76)) % 3.33/3.62 (step @p78 :rule cong :premises (@p77) :args (@t106)) % 3.33/3.62 (step @p79 :rule refl :args (@t107)) % 3.33/3.62 (step @p80 :rule refl :args (@t7)) % 3.33/3.62 (step @p81 :rule cong :premises (@p80 @p79) :args ((= @t7 @t107))) % 3.33/3.62 (step @p82 :rule symm :premises (@p81)) % 3.33/3.62 (step @p83 :rule eq_resolve :premises (@p80 @p82)) % 3.33/3.62 (step @p84 :rule cong :premises (@p83) :args (@t108)) % 3.33/3.62 (step @p85 :rule nary_cong :premises (@p84 @p78 @p72) :args (@t109)) % 3.33/3.62 (step @p86 :rule cong :premises (@p85) :args ((forall @t13 @t109))) % 3.33/3.62 (step @p87 :rule aci_norm :args ((= (or (or @t108 @t106) @t10) @t109))) % 3.33/3.62 (step @p88 :rule bool-and-de-morgan :args (@t7 @t11 true)) % 3.33/3.62 (step @p89 :rule nary_cong :premises (@p88 @p69) :args ((or (not @t12) @t10))) % 3.33/3.62 (step @p90 :rule trans :premises (@p89 @p87)) % 3.33/3.62 (step @p91 :rule bool-impl-elim :args (@t12 @t10)) % 3.33/3.62 (step @p92 :rule trans :premises (@p91 @p90)) % 3.33/3.62 (step @p93 :rule cong :premises (@p92) :args (@t14)) % 3.33/3.62 (step @p94 :rule trans :premises (@p93 @p86)) % 3.33/3.62 (step @p95 :rule eq_resolve :premises (@p3 @p94)) % 3.33/3.62 (step @p96 :rule instantiate :premises (@p95) :args ((@list @t98 @t76 @t88))) % 3.33/3.62 (step @p97 :rule cnf_or_pos :args (@t110)) % 3.33/3.62 (step @p98 :rule reordering :premises (@p97) :args ((or @t102 @t100 @t92 (not @t110)))) % 3.33/3.62 (step @p99 :rule instantiate :premises (@p43) :args ((@list @t111 @t96))) % 3.33/3.62 (step @p100 :rule cnf_or_pos :args (@t114)) % 3.33/3.62 (step @p101 :rule reordering :premises (@p100) :args ((or @t97 @t113 (not @t114)))) % 3.33/3.62 (step @p102 :rule cnf_or_pos :args (@t94)) % 3.33/3.62 (step @p103 :rule reordering :premises (@p102) :args ((or @t93 @t91 (not @t94)))) % 3.33/3.62 (assume-push @p527 @t115) % 3.33/3.62 (step @p105 :rule instantiate :premises (@p527) :args ((@list @t96))) % 3.33/3.62 (step-pop @p528 :rule scope :premises (@p105)) % 3.33/3.62 (step @p106 :rule process_scope :premises (@p528) :args (@t114)) % 3.33/3.62 (step @p108 :rule implies_elim :premises (@p106)) % 3.33/3.62 (step @p109 :rule refl :args (@t118)) % 3.33/3.62 (step @p110 :rule bool-double-not-elim :args (@t90)) % 3.33/3.62 (step @p111 :rule nary_cong :premises (@p110 @p109) :args ((or (not @t91) @t118))) % 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false false true true false false false false false) (@list @t117 @t115 @t90 @t114 @t112 @t92 @t110 @t97 @t99 @t101 @t103 @t83 @t85 @t94 @t87 @t79 @t77))) % 3.33/3.62 (step @p125 :rule refl :args (@t119)) % 3.33/3.62 (step @p126 :rule bool-double-not-elim :args (@t75)) % 3.33/3.62 (step @p127 :rule nary_cong :premises (@p126 @p125) :args ((or (not @t120) @t119))) % 3.33/3.62 (assume-push @p531 @t120) % 3.33/3.62 (step @p129 :rule skolemize :premises (@p531)) % 3.33/3.62 (step-pop @p532 :rule scope :premises (@p129)) % 3.33/3.62 (step @p130 :rule process_scope :premises (@p532) :args (@t119)) % 3.33/3.62 (step @p132 :rule implies_elim :premises (@p130)) % 3.33/3.62 (step @p133 :rule eq_resolve :premises (@p132 @p127)) % 3.33/3.62 (step @p134 :rule chain_m_resolution :premises (@p133 @p124) :args (@t75 @t121 (@list @t82))) % 3.33/3.62 (step @p135 :rule beta-reduce :args ((= @t140 (and @t75 @t133)))) % 3.33/3.62 (step @p136 :rule beta-reduce :args ((= (_ @t27 @t139) @t140))) % 3.33/3.62 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@p276) :args (@t280)) % 3.33/3.62 (step @p340 :rule cong :premises (@p339) :args (@t281)) % 3.33/3.62 (step @p341 :rule beta-reduce :args ((= (_ @t34 @t278) @t281))) % 3.33/3.62 (step @p342 :rule trans :premises (@p341 @p340)) % 3.33/3.62 (step @p343 :rule aci_norm :args ((= (or @t134 (or @t73 @t70)) @t137))) % 3.33/3.62 (step @p344 :rule bool-impl-elim :args (@t72 @t70)) % 3.33/3.62 (step @p345 :rule nary_cong :premises (@p149 @p344) :args (@t283)) % 3.33/3.62 (step @p346 :rule trans :premises (@p345 @p343)) % 3.33/3.62 (step @p347 :rule cong :premises (@p346) :args ((forall @t39 @t283))) % 3.33/3.62 (step @p348 :rule beta-reduce :args ((= (_ (lambda @t9 (=> (forall @t71 (or (not (tptp.mrel @t2 @t58)) @t60)) (not (forall @t8 (or @t165 (not (forall @t67 (or (not (tptp.mrel @t2 @t63)) @t66)))))))) @t1) @t282))) % 3.33/3.62 (step @p349 :rule alpha_equiv :args (@t170 @t168 (@list @t63))) % 3.33/3.62 (step @p350 :rule cong :premises (@p349) :args (@t171)) % 3.33/3.62 (step @p351 :rule nary_cong :premises (@p172 @p350) :args (@t172)) % 3.33/3.62 (step @p352 :rule cong :premises (@p351) :args (@t173)) % 3.33/3.62 (step @p353 :rule cong :premises (@p352) :args (@t174)) % 3.33/3.62 (step @p354 :rule alpha_equiv :args (@t167 @t168 (@list @t58))) % 3.33/3.62 (step @p355 :rule cong :premises (@p354 @p353) :args (@t284)) % 3.33/3.62 (step @p356 :rule cong :premises (@p355) :args (@t285)) % 3.33/3.62 (step @p357 :rule ho_cong :premises (@p356 @p168)) % 3.33/3.62 (step @p358 :rule trans :premises (@p357 @p348)) % 3.33/3.62 (step @p359 :rule nary_cong :premises (@p180 @p358) :args (@t286)) % 3.33/3.62 (step @p360 :rule cong :premises (@p359) :args (@t287)) % 3.33/3.62 (step @p361 :rule trans :premises (@p360 @p347)) % 3.33/3.62 (step @p362 :rule cong :premises (@p361) :args (@t288)) % 3.33/3.62 (step @p363 :rule beta-reduce :args ((= (_ @t181 @t285) @t288))) % 3.33/3.62 (step @p364 :rule trans :premises (@p363 @p362)) % 3.33/3.62 (step @p365 :rule refl :args (@t167)) % 3.33/3.62 (step @p366 :rule cong :premises (@p365 @p277) :args (@t289)) % 3.33/3.62 (step @p367 :rule cong :premises (@p366) :args (@t290)) % 3.33/3.62 (step @p368 :rule beta-reduce :args ((= (_ (lambda @t145 (=> @t167 @t32)) @t244) @t290))) % 3.33/3.62 (step @p369 :rule trans :premises (@p368 @p367)) % 3.33/3.62 (step @p370 :rule cong :premises (@p187 @p276) :args (@t291)) % 3.33/3.62 (step @p371 :rule cong :premises (@p370) :args (@t292)) % 3.33/3.62 (step @p372 :rule beta-reduce :args ((= (_ @t36 @t182) @t292))) % 3.33/3.62 (step @p373 :rule trans :premises (@p372 @p371)) % 3.33/3.62 (step @p374 :rule ho_cong :premises (@p331 @p275)) % 3.33/3.62 (step @p375 :rule trans :premises (@p374 @p373)) % 3.33/3.62 (step @p376 :rule ho_cong :premises (@p375 @p330)) % 3.33/3.62 (step @p377 :rule trans :premises (@p376 @p369)) % 3.33/3.62 (step @p378 :rule ho_cong :premises (@p268 @p377)) % 3.33/3.62 (step @p379 :rule trans :premises (@p378 @p364)) % 3.33/3.62 (step @p380 :rule refl :args (@t34)) % 3.33/3.62 (step @p381 :rule ho_cong :premises (@p380 @p379)) % 3.33/3.62 (step @p382 :rule trans :premises (@p381 @p342)) % 3.33/3.62 (step @p383 :rule ho_cong :premises (@p382 @p337)) % 3.33/3.62 (step @p384 :rule trans :premises (@p383 @p143)) % 3.33/3.62 (step @p385 :rule refl :args (@t27)) % 3.33/3.62 (step @p386 :rule ho_cong :premises (@p385 @p384)) % 3.33/3.62 (step @p387 :rule trans :premises (@p386 @p137)) % 3.33/3.62 (step @p388 :rule cong :premises (@p387) :args ((not (_ @t27 (_ (_ @t34 (_ @t181 (_ (_ @t36 @t293) @t294))) (_ @t181 (_ (_ @t36 @t294) @t293))))))) % 3.33/3.62 (step @p389 :rule refl :args (@t16)) % 3.33/3.62 (step @p390 :rule refl :args (@t180)) % 3.33/3.62 (step @p391 :rule refl :args (@t38)) % 3.33/3.62 (step @p392 :rule cong :premises (@p391 @p390) :args ((= @t38 @t180))) % 3.33/3.62 (step @p393 :rule symm :premises (@p392)) % 3.33/3.62 (step @p394 :rule eq_resolve :premises (@p391 @p393)) % 3.33/3.62 (step @p395 :rule cong :premises (@p41) :args (@t295)) % 3.33/3.62 (step @p396 :rule nary_cong :premises (@p395 @p394) :args (@t296)) % 3.33/3.62 (step @p397 :rule cong :premises (@p396) :args ((forall @t39 @t296))) % 3.33/3.62 (step @p398 :rule bool-impl-elim :args (@t3 @t38)) % 3.33/3.62 (step @p399 :rule cong :premises (@p398) :args (@t40)) % 3.33/3.62 (step @p400 :rule trans :premises (@p399 @p397)) % 3.33/3.62 (step @p401 :rule cong :premises (@p400) :args (@t42)) % 3.33/3.62 (step @p402 :rule trans :premises (@p12 @p401)) % 3.33/3.62 (step @p403 :rule ho_cong :premises (@p402 @p389)) % 3.33/3.62 (step @p404 :rule ho_cong :premises (@p403 @p247)) % 3.33/3.62 (step @p405 :rule cong :premises (@p404) :args (@t18)) % 3.33/3.62 (step @p406 :rule refl :args (@t234)) % 3.33/3.62 (step @p407 :rule refl :args (@t45)) % 3.33/3.62 (step @p408 :rule cong :premises (@p407 @p406) :args ((= @t45 @t234))) % 3.33/3.62 (step @p409 :rule symm :premises (@p408)) % 3.33/3.62 (step @p410 :rule eq_resolve :premises (@p407 @p409)) % 3.33/3.62 (step @p411 :rule nary_cong :premises (@p84 @p410) :args (@t297)) % 3.33/3.62 (step @p412 :rule cong :premises (@p411) :args ((forall @t8 @t297))) % 3.33/3.62 (step @p413 :rule bool-impl-elim :args (@t7 @t45)) % 3.33/3.62 (step @p414 :rule cong :premises (@p413) :args (@t46)) % 3.33/3.62 (step @p415 :rule trans :premises (@p414 @p412)) % 3.33/3.62 (step @p416 :rule cong :premises (@p415) :args (@t48)) % 3.33/3.62 (step @p417 :rule trans :premises (@p14 @p416)) % 3.33/3.62 (step @p418 :rule ho_cong :premises (@p417 @p405)) % 3.33/3.62 (step @p419 :rule ho_cong :premises (@p402 @p418)) % 3.33/3.62 (step @p420 :rule ho_cong :premises (@p7 @p419)) % 3.33/3.62 (step @p421 :rule ho_cong :premises (@p402 @p420)) % 3.33/3.62 (step @p422 :rule refl :args (@t21)) % 3.33/3.62 (step @p423 :rule ho_cong :premises (@p402 @p422)) % 3.33/3.62 (step @p424 :rule ho_cong :premises (@p7 @p423)) % 3.33/3.62 (step @p425 :rule ho_cong :premises (@p402 @p424)) % 3.33/3.62 (step @p426 :rule ho_cong :premises (@p425 @p247)) % 3.33/3.62 (step @p427 :rule cong :premises (@p426) :args (@t23)) % 3.33/3.62 (step @p428 :rule cong :premises (@p410) :args (@t298)) % 3.33/3.62 (step @p429 :rule nary_cong :premises (@p84 @p428) :args (@t299)) % 3.33/3.62 (step @p430 :rule cong :premises (@p429) :args ((forall @t8 @t299))) % 3.33/3.62 (step @p431 :rule bool-and-de-morgan :args (@t7 @t45 true)) % 3.33/3.62 (step @p432 :rule cong :premises (@p431) :args (@t300)) % 3.33/3.62 (step @p433 :rule trans :premises (@p432 @p430)) % 3.33/3.62 (step @p434 :rule cong :premises (@p433) :args (@t301)) % 3.33/3.62 (step @p435 :rule exists-elim :args ((= @t50 @t301))) % 3.33/3.62 (step @p436 :rule trans :premises (@p435 @p434)) % 3.33/3.62 (step @p437 :rule cong :premises (@p436) :args (@t51)) % 3.33/3.62 (step @p438 :rule trans :premises (@p15 @p437)) % 3.33/3.62 (step @p439 :rule ho_cong :premises (@p438 @p427)) % 3.33/3.62 (step @p440 :rule ho_cong :premises (@p10 @p439)) % 3.33/3.62 (step @p441 :rule ho_cong :premises (@p440 @p421)) % 3.33/3.62 (step @p442 :rule ho_cong :premises (@p402 @p441)) % 3.33/3.62 (step @p443 :rule ho_cong :premises (@p10 @p421)) % 3.33/3.62 (step @p444 :rule ho_cong :premises (@p443 @p439)) % 3.33/3.62 (step @p445 :rule ho_cong :premises (@p402 @p444)) % 3.33/3.62 (step @p446 :rule ho_cong :premises (@p8 @p445)) % 3.33/3.62 (step @p447 :rule ho_cong :premises (@p446 @p442)) % 3.33/3.62 (step @p448 :rule ho_cong :premises (@p6 @p447)) % 3.33/3.62 (step @p449 :rule cong :premises (@p448) :args (@t25)) % 3.33/3.62 (step @p450 :rule trans :premises (@p449 @p388)) % 3.33/3.62 (step @p451 :rule eq_resolve :premises (@p4 @p450)) % 3.33/3.62 (step @p452 :rule not_and :premises (@p451)) % 3.33/3.62 (step @p453 :rule chain_m_resolution :premises (@p452 @p134) :args (@t302 @t121 (@list @t75))) % 3.33/3.62 (step @p454 :rule refl :args (@t316)) % 3.33/3.62 (step @p455 :rule bool-double-not-elim :args (@t133)) % 3.33/3.62 (step @p456 :rule nary_cong :premises (@p455 @p454) :args ((or (not @t302) @t316))) % 3.33/3.62 (assume-push @p533 @t302) % 3.33/3.62 (step @p458 :rule skolemize :premises (@p533)) % 3.33/3.62 (step-pop @p534 :rule scope :premises (@p458)) % 3.33/3.62 (step @p459 :rule process_scope :premises (@p534) :args (@t316)) % 3.33/3.62 (step @p461 :rule implies_elim :premises (@p459)) % 3.33/3.62 (step @p462 :rule eq_resolve :premises (@p461 @p456)) % 3.33/3.62 (step @p463 :rule chain_m_resolution :premises (@p462 @p453) :args (@t316 @t317 (@list @t133))) % 3.33/3.62 (step @p464 :rule bool-double-not-elim :args (@t304)) % 3.33/3.62 (step @p465 :rule refl :args (@t315)) % 3.33/3.62 (step @p466 :rule nary_cong :premises (@p465 @p464) :args ((or @t315 (not @t305)))) % 3.33/3.62 (step @p467 :rule cnf_or_neg :args (@t315 4)) % 3.33/3.62 (step @p468 :rule eq_resolve :premises (@p467 @p466)) % 3.33/3.62 (step @p469 :rule reordering :premises (@p468) :args ((or @t304 @t315))) % 3.33/3.62 (step @p470 :rule chain_m_resolution :premises (@p469 @p463) :args (@t304 @t317 @t318)) % 3.33/3.62 (step @p471 :rule instantiate :premises (@p43) :args ((@list @t306 @t320))) % 3.33/3.62 (step @p472 :rule bool-double-not-elim :args (@t311)) % 3.33/3.62 (step @p473 :rule nary_cong :premises (@p465 @p472) :args ((or @t315 (not @t312)))) % 3.33/3.62 (step @p474 :rule cnf_or_neg :args (@t315 2)) % 3.33/3.62 (step @p475 :rule eq_resolve :premises (@p474 @p473)) % 3.33/3.62 (step @p476 :rule reordering :premises (@p475) :args ((or @t311 @t315))) % 3.33/3.62 (step @p477 :rule chain_m_resolution :premises (@p476 @p463) :args (@t311 @t317 @t318)) % 3.33/3.62 (assume-push @p535 @t311) % 3.33/3.62 (step @p479 :rule instantiate :premises (@p535) :args ((@list @t303))) % 3.33/3.62 (step-pop @p536 :rule scope :premises (@p479)) % 3.33/3.62 (step @p480 :rule process_scope :premises (@p536) :args (@t322)) % 3.33/3.62 (step @p482 :rule implies_elim :premises (@p480)) % 3.33/3.62 (step @p483 :rule chain_m_resolution :premises (@p482 @p477) :args (@t322 @t121 (@list @t311))) % 3.33/3.62 (step @p484 :rule bool-double-not-elim :args (@t307)) % 3.33/3.62 (step @p485 :rule nary_cong :premises (@p465 @p484) :args ((or @t315 (not @t308)))) % 3.33/3.62 (step @p486 :rule cnf_or_neg :args (@t315 3)) % 3.33/3.62 (step @p487 :rule eq_resolve :premises (@p486 @p485)) % 3.33/3.62 (step @p488 :rule reordering :premises (@p487) :args ((or @t307 @t315))) % 3.33/3.62 (step @p489 :rule chain_m_resolution :premises (@p488 @p463) :args (@t307 @t317 @t318)) % 3.33/3.62 (step @p490 :rule cnf_or_pos :args (@t322)) % 3.33/3.62 (step @p491 :rule reordering :premises (@p490) :args ((or @t308 @t321 (not @t322)))) % 3.33/3.62 (step @p492 :rule chain_m_resolution :premises (@p491 @p489 @p483) :args (@t321 (@list false false) (@list @t307 @t322))) % 3.33/3.62 (step @p493 :rule refl :args (@t325)) % 3.33/3.62 (step @p494 :rule bool-double-not-elim :args (@t319)) % 3.33/3.63 (step @p495 :rule nary_cong :premises (@p494 @p493) :args ((or (not @t321) @t325))) % 3.33/3.63 (assume-push @p537 @t321) % 3.33/3.63 (step @p497 :rule skolemize :premises (@p537)) % 3.33/3.63 (step-pop @p538 :rule scope :premises (@p497)) % 3.33/3.63 (step @p498 :rule process_scope :premises (@p538) :args (@t325)) % 3.33/3.63 (step @p500 :rule implies_elim :premises (@p498)) % 3.33/3.63 (step @p501 :rule eq_resolve :premises (@p500 @p495)) % 3.33/3.63 (step @p502 :rule chain_m_resolution :premises (@p501 @p492) :args (@t325 @t317 (@list @t319))) % 3.33/3.63 (step @p503 :rule cnf_or_neg :args (@t324 1)) % 3.33/3.63 (step @p504 :rule chain_m_resolution :premises (@p503 @p502) :args ((not @t323) @t317 (@list @t324))) % 3.33/3.63 (step @p505 :rule instantiate :premises (@p43) :args ((@list @t303 @t306))) % 3.33/3.63 (step @p506 :rule bool-double-not-elim :args (@t313)) % 3.33/3.63 (step @p507 :rule nary_cong :premises (@p465 @p506) :args ((or @t315 (not @t314)))) % 3.33/3.63 (step @p508 :rule cnf_or_neg :args (@t315 1)) % 3.33/3.63 (step @p509 :rule eq_resolve :premises (@p508 @p507)) % 3.33/3.63 (step @p510 :rule reordering :premises (@p509) :args ((or @t313 @t315))) % 3.33/3.63 (step @p511 :rule chain_m_resolution :premises (@p510 @p463) :args (@t313 @t317 @t318)) % 3.33/3.63 (step @p512 :rule cnf_or_pos :args (@t330)) % 3.33/3.63 (step @p513 :rule reordering :premises (@p512) :args ((or @t314 @t329 @t323 @t327 @t331))) % 3.33/3.63 (step @p514 :rule chain_m_resolution :premises (@p513 @p511 @p505 @p504 @p471) :args (@t331 (@list false false true false) (@list @t313 @t328 @t323 @t326))) % 3.33/3.63 (assume-push @p539 @t304) % 3.33/3.63 (step @p516 :rule instantiate :premises (@p539) :args ((@list @t306 @t309 @t320))) % 3.33/3.63 (step-pop @p540 :rule scope :premises (@p516)) % 3.33/3.63 (step @p517 :rule process_scope :premises (@p540) :args (@t330)) % 3.33/3.63 (step @p519 :rule implies_elim :premises (@p517)) % 3.33/3.63 (step @p520 false :rule chain_m_resolution :premises (@p519 @p514 @p470) :args (false (@list true false) (@list @t330 @t304))) % 3.33/3.63 ) % 3.33/3.63 % SZS output end Proof % 3.33/3.63 % cvc5 exiting %------------------------------------------------------------------------------