%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PHI043^1 : TPTP v9.2.1. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n001.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 08:43:16 AM UTC 2026 % Result : Theorem 0.54s 0.73s % Output : Proof 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PHI043^1 : TPTP v9.2.1. Released v7.5.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n001.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Tue Jun 2 12:55:05 EDT 2026 % 0.19/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.54/0.73 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.54/0.73 % SZS status Theorem % 0.54/0.73 % SZS output start Proof % 0.54/0.73 ( % 0.54/0.73 (declare-sort $$unsorted 0) % 0.54/0.73 (declare-sort tptp.mu 0) % 0.54/0.73 (declare-const tptp.p (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)) % 0.54/0.73 (declare-const tptp.mdia (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.54/0.73 (declare-const tptp.mbox (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.54/0.73 (declare-const tptp.rel (-> $$unsorted $$unsorted Bool)) % 0.54/0.73 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.54/0.73 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.54/0.73 (define tptp.mfalse () (lambda (@list (@var "W" $$unsorted)) false)) % 0.54/0.73 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.54/0.73 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.54/0.73 (define tptp.mand () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.54/0.73 (define tptp.mimplies () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.54/0.73 (define tptp.mimplied () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.54/0.73 (define tptp.mequiv () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.54/0.73 (define tptp.mxor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.54/0.73 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.54/0.73 (define tptp.mforall_indset () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" (-> tptp.mu $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.54/0.73 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.54/0.73 (define tptp.mexists_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.54/0.73 (define tptp.mexists_indset () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" (-> tptp.mu $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.54/0.73 (define tptp.mexists_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.54/0.73 (define tptp.mbox_generic () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.54/0.73 (define tptp.mdia_generic () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.54/0.73 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.54/0.73 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.54/0.73 (define @t1 () (= tptp.mbox (_ tptp.mbox_generic tptp.rel))) % 0.54/0.73 (define @t2 () (= tptp.mdia (_ tptp.mdia_generic tptp.rel))) % 0.54/0.73 (define @t3 () (@var "X" tptp.mu)) % 0.54/0.73 (define @t4 () (not (= @t3 @t3))) % 0.54/0.73 (define @t5 () (@var "W" $$unsorted)) % 0.54/0.73 (define @t6 () (@list @t3 @t5)) % 0.54/0.73 (define @t7 () (lambda @t6 @t4)) % 0.54/0.73 (define @t8 () (_ tptp.p @t7)) % 0.54/0.73 (define @t9 () (@var "__flatten_var_0" $$unsorted)) % 0.54/0.73 (define @t10 () (@var "Psi" (-> tptp.mu $$unsorted Bool))) % 0.54/0.73 (define @t11 () (_ tptp.p @t10)) % 0.54/0.73 (define @t12 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.54/0.73 (define @t13 () (_ tptp.p @t12)) % 0.54/0.73 (define @t14 () (_ @t10 @t3)) % 0.54/0.73 (define @t15 () (_ @t12 @t3)) % 0.54/0.73 (define @t16 () (@list @t3 @t9)) % 0.54/0.73 (define @t17 () (lambda @t16 (_ (_ (_ tptp.mequiv @t15) @t14) @t9))) % 0.54/0.73 (define @t18 () (@list @t10 @t9)) % 0.54/0.73 (define @t19 () (lambda @t18 (_ (_ (_ tptp.mimplies (_ tptp.mbox (_ tptp.mforall_ind @t17))) (_ (_ tptp.mequiv @t13) @t11)) @t9))) % 0.54/0.73 (define @t20 () (@list @t12 @t9)) % 0.54/0.73 (define @t21 () (lambda @t20 (_ (_ tptp.mforall_indset @t19) @t9))) % 0.54/0.73 (define @t22 () (_ @t15 @t9)) % 0.54/0.73 (define @t23 () (lambda @t16 @t22)) % 0.54/0.73 (define @t24 () (lambda @t20 (_ (_ (_ tptp.mimplies @t13) (_ tptp.mdia (_ tptp.mexists_ind @t23))) @t9))) % 0.54/0.73 (define @t25 () (not (_ tptp.mvalid (_ tptp.mforall_indset @t24)))) % 0.54/0.73 (define @t26 () (@var "Y" tptp.mu)) % 0.54/0.73 (define @t27 () (lambda (@list @t3 @t26 @t5) (= @t3 @t26))) % 0.54/0.73 (define @t28 () (@list @t5)) % 0.54/0.73 (define @t29 () (lambda @t28 true)) % 0.54/0.73 (define @t30 () (lambda @t28 false)) % 0.54/0.73 (define @t31 () (@var "Phi" (-> $$unsorted Bool))) % 0.54/0.73 (define @t32 () (_ @t31 @t5)) % 0.54/0.73 (define @t33 () (not @t32)) % 0.54/0.73 (define @t34 () (@list @t31 @t5)) % 0.54/0.73 (define @t35 () (lambda @t34 @t33)) % 0.54/0.73 (define @t36 () (@var "Psi" (-> $$unsorted Bool))) % 0.54/0.73 (define @t37 () (_ @t36 @t5)) % 0.54/0.73 (define @t38 () (@list @t31 @t36 @t5)) % 0.54/0.73 (define @t39 () (lambda @t38 (or @t32 @t37))) % 0.54/0.73 (define @t40 () (lambda @t38 (and @t32 @t37))) % 0.54/0.73 (define @t41 () (lambda @t38 (=> @t32 @t37))) % 0.54/0.73 (define @t42 () (lambda @t38 (=> @t37 @t32))) % 0.54/0.73 (define @t43 () (lambda @t38 (= @t32 @t37))) % 0.54/0.73 (define @t44 () (lambda @t38 (or (and @t32 (not @t37)) (and @t33 @t37)))) % 0.54/0.73 (define @t45 () (_ @t15 @t5)) % 0.54/0.73 (define @t46 () (@list @t3)) % 0.54/0.73 (define @t47 () (forall @t46 @t45)) % 0.54/0.73 (define @t48 () (@list @t12 @t5)) % 0.54/0.73 (define @t49 () (lambda @t48 @t47)) % 0.54/0.73 (define @t50 () (@var "X" (-> tptp.mu $$unsorted Bool))) % 0.54/0.73 (define @t51 () (@var "Phi" (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool))) % 0.54/0.73 (define @t52 () (_ (_ @t51 @t50) @t5)) % 0.54/0.73 (define @t53 () (@list @t50)) % 0.54/0.73 (define @t54 () (forall @t53 @t52)) % 0.54/0.73 (define @t55 () (@list @t51 @t5)) % 0.54/0.73 (define @t56 () (lambda @t55 @t54)) % 0.54/0.73 (define @t57 () (@var "P" (-> $$unsorted Bool))) % 0.54/0.73 (define @t58 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.54/0.73 (define @t59 () (_ (_ @t58 @t57) @t5)) % 0.54/0.73 (define @t60 () (@list @t57)) % 0.54/0.73 (define @t61 () (@list @t58 @t5)) % 0.54/0.73 (define @t62 () (lambda @t61 (forall @t60 @t59))) % 0.54/0.73 (define @t63 () (exists @t46 @t45)) % 0.54/0.73 (define @t64 () (lambda @t48 @t63)) % 0.54/0.73 (define @t65 () (lambda @t55 (exists @t53 @t52))) % 0.54/0.73 (define @t66 () (lambda @t61 (exists @t60 @t59))) % 0.54/0.73 (define @t67 () (@var "V" $$unsorted)) % 0.54/0.73 (define @t68 () (_ @t31 @t67)) % 0.54/0.73 (define @t69 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.54/0.73 (define @t70 () (_ (_ @t69 @t5) @t67)) % 0.54/0.73 (define @t71 () (not @t70)) % 0.54/0.73 (define @t72 () (or @t71 @t68)) % 0.54/0.73 (define @t73 () (@list @t67)) % 0.54/0.73 (define @t74 () (forall @t73 @t72)) % 0.54/0.73 (define @t75 () (@list @t69 @t31 @t5)) % 0.54/0.73 (define @t76 () (lambda @t75 @t74)) % 0.54/0.73 (define @t77 () (and @t70 @t68)) % 0.54/0.73 (define @t78 () (exists @t73 @t77)) % 0.54/0.73 (define @t79 () (lambda @t75 @t78)) % 0.54/0.73 (define @t80 () (forall @t28 @t32)) % 0.54/0.73 (define @t81 () (@list @t31)) % 0.54/0.73 (define @t82 () (lambda @t81 @t80)) % 0.54/0.73 (define @t83 () (lambda @t81 (forall @t28 @t33))) % 0.54/0.73 (define @t84 () (@var "BOUND_VARIABLE_8085" tptp.mu)) % 0.54/0.73 (define @t85 () (not (_ @t50 @t84 @t67))) % 0.54/0.73 (define @t86 () (not (tptp.rel @t5 @t67))) % 0.54/0.73 (define @t87 () (or @t86 @t85)) % 0.54/0.73 (define @t88 () (@list @t67 @t84)) % 0.54/0.73 (define @t89 () (forall @t88 @t87)) % 0.54/0.73 (define @t90 () (@list @t84)) % 0.54/0.73 (define @t91 () (forall @t90 @t87)) % 0.54/0.73 (define @t92 () (forall @t90 @t85)) % 0.54/0.73 (define @t93 () (@list @t3)) % 0.54/0.73 (define @t94 () (or @t86 @t92)) % 0.54/0.73 (define @t95 () (_ @t50 @t3 @t67)) % 0.54/0.73 (define @t96 () (forall @t46 (not @t95))) % 0.54/0.73 (define @t97 () (@var "BOUND_VARIABLE_7999" $$unsorted)) % 0.54/0.73 (define @t98 () (_ @t50 @t3 @t97)) % 0.54/0.73 (define @t99 () (not @t98)) % 0.54/0.73 (define @t100 () (forall @t46 @t99)) % 0.54/0.73 (define @t101 () (not @t100)) % 0.54/0.73 (define @t102 () (@list @t97)) % 0.54/0.73 (define @t103 () (lambda @t102 @t101)) % 0.54/0.73 (define @t104 () (_ @t103 @t67)) % 0.54/0.73 (define @t105 () (not @t104)) % 0.54/0.73 (define @t106 () (or @t86 @t105)) % 0.54/0.73 (define @t107 () (forall @t73 @t106)) % 0.54/0.73 (define @t108 () (not @t107)) % 0.54/0.73 (define @t109 () (_ @t31 @t67)) % 0.54/0.73 (define @t110 () (not @t109)) % 0.54/0.73 (define @t111 () (lambda @t34 (not (forall @t73 (or @t86 @t110))))) % 0.54/0.73 (define @t112 () (_ @t111 @t103 @t5)) % 0.54/0.73 (define @t113 () (tptp.p @t50 @t5)) % 0.54/0.73 (define @t114 () (not @t113)) % 0.54/0.73 (define @t115 () (or @t114 @t112)) % 0.54/0.73 (define @t116 () (@list @t5 @t50)) % 0.54/0.73 (define @t117 () (forall @t116 @t115)) % 0.54/0.73 (define @t118 () (_ @t69 @t5 @t67)) % 0.54/0.73 (define @t119 () (not @t118)) % 0.54/0.73 (define @t120 () (_ (lambda @t75 (not (forall @t73 (or @t119 @t110)))) tptp.rel)) % 0.54/0.73 (define @t121 () (not @t68)) % 0.54/0.73 (define @t122 () (or @t71 @t121)) % 0.54/0.73 (define @t123 () (forall @t73 (not @t77))) % 0.54/0.73 (define @t124 () (not @t123)) % 0.54/0.73 (define @t125 () (tptp.mdia @t103 @t5)) % 0.54/0.73 (define @t126 () (or @t114 @t125)) % 0.54/0.73 (define @t127 () (forall @t116 @t126)) % 0.54/0.73 (define @t128 () (forall @t53 @t126)) % 0.54/0.73 (define @t129 () (lambda @t28 @t128)) % 0.54/0.73 (define @t130 () (_ @t129 @t5)) % 0.54/0.73 (define @t131 () (forall @t28 @t130)) % 0.54/0.73 (define @t132 () (_ @t31 @t5)) % 0.54/0.73 (define @t133 () (lambda @t81 (forall @t28 @t132))) % 0.54/0.73 (define @t134 () (_ @t50 @t3)) % 0.54/0.73 (define @t135 () (lambda @t102 (not (forall @t46 (not (_ @t134 @t97)))))) % 0.54/0.73 (define @t136 () (_ (_ tptp.mdia @t103) @t5)) % 0.54/0.73 (define @t137 () (_ (_ tptp.p @t50) @t5)) % 0.54/0.73 (define @t138 () (not @t137)) % 0.54/0.73 (define @t139 () (or @t138 @t136)) % 0.54/0.73 (define @t140 () (=> @t137 @t136)) % 0.54/0.73 (define @t141 () (_ tptp.mdia (lambda @t102 (not (forall @t46 (not (_ @t12 @t3 @t97))))))) % 0.54/0.73 (define @t142 () (_ @t13 @t9)) % 0.54/0.73 (define @t143 () (=> @t142 (_ @t141 @t9))) % 0.54/0.73 (define @t144 () (lambda @t20 @t143)) % 0.54/0.73 (define @t145 () (_ @t144 @t50 @t5)) % 0.54/0.73 (define @t146 () (forall @t53 @t145)) % 0.54/0.73 (define @t147 () (lambda @t28 @t146)) % 0.54/0.73 (define @t148 () (_ @t51 @t50 @t5)) % 0.54/0.73 (define @t149 () (lambda @t55 (forall @t53 @t148))) % 0.54/0.73 (define @t150 () (_ @t13 @t5)) % 0.54/0.73 (define @t151 () (lambda @t28 (=> @t150 (_ @t141 @t5)))) % 0.54/0.73 (define @t152 () (_ @t12 @t3 @t5)) % 0.54/0.73 (define @t153 () (not (forall @t46 (not @t152)))) % 0.54/0.73 (define @t154 () (_ tptp.mdia (lambda @t28 @t153))) % 0.54/0.73 (define @t155 () (lambda @t28 (=> @t150 (_ @t154 @t5)))) % 0.54/0.73 (define @t156 () (@list @t36 @t5)) % 0.54/0.73 (define @t157 () (lambda @t156 (=> @t150 @t37))) % 0.54/0.73 (define @t158 () (not @t45)) % 0.54/0.73 (define @t159 () (forall @t46 @t158)) % 0.54/0.73 (define @t160 () (_ @t23 @t3 @t5)) % 0.54/0.73 (define @t161 () (not @t160)) % 0.54/0.73 (define @t162 () (forall @t46 @t161)) % 0.54/0.73 (define @t163 () (not @t162)) % 0.54/0.73 (define @t164 () (lambda @t28 @t163)) % 0.54/0.73 (define @t165 () (_ (lambda @t48 @t153) @t23)) % 0.54/0.73 (define @t166 () (_ @t41 @t13)) % 0.54/0.73 (define @t167 () (lambda @t20 (_ (_ @t166 (_ tptp.mdia @t165)) @t9))) % 0.54/0.73 (define @t168 () (not @t159)) % 0.54/0.73 (define @t169 () (forall @t116 (or @t114 (not @t89)))) % 0.54/0.73 (define @t170 () (@quantifiers_skolemize @t169 1)) % 0.54/0.73 (define @t171 () (@quantifiers_skolemize @t169 0)) % 0.54/0.73 (define @t172 () (not (tptp.rel @t171 @t67))) % 0.54/0.73 (define @t173 () (forall @t88 (or @t172 (not (_ @t170 @t84 @t67))))) % 0.54/0.73 (define @t174 () (not @t173)) % 0.54/0.73 (define @t175 () (tptp.p @t170 @t171)) % 0.54/0.73 (define @t176 () (not @t175)) % 0.54/0.73 (define @t177 () (or @t176 @t174)) % 0.54/0.73 (define @t178 () (@list true)) % 0.54/0.73 (define @t179 () (@list @t177)) % 0.54/0.73 (define @t180 () (@var "BOUND_VARIABLE_7940" (-> tptp.mu $$unsorted Bool))) % 0.54/0.73 (define @t181 () (= @t113 (tptp.p @t180 @t5))) % 0.54/0.73 (define @t182 () (@var "BOUND_VARIABLE_8058" tptp.mu)) % 0.54/0.73 (define @t183 () (= (_ @t50 @t182 @t67) (_ @t180 @t182 @t67))) % 0.54/0.73 (define @t184 () (or @t86 @t183)) % 0.54/0.73 (define @t185 () (@list @t67 @t182)) % 0.54/0.73 (define @t186 () (@list @t182)) % 0.54/0.73 (define @t187 () (forall @t186 @t184)) % 0.54/0.73 (define @t188 () (forall @t186 @t183)) % 0.54/0.73 (define @t189 () (or @t86 @t188)) % 0.54/0.73 (define @t190 () (forall @t46 (= @t95 (_ @t180 @t3 @t67)))) % 0.54/0.73 (define @t191 () (@var "BOUND_VARIABLE_7861" $$unsorted)) % 0.54/0.73 (define @t192 () (_ @t180 @t3 @t191)) % 0.54/0.73 (define @t193 () (_ @t50 @t3 @t191)) % 0.54/0.73 (define @t194 () (@list @t191)) % 0.54/0.73 (define @t195 () (lambda @t194 (forall @t46 (= @t193 @t192)))) % 0.54/0.73 (define @t196 () (_ @t195 @t67)) % 0.54/0.73 (define @t197 () (or @t86 @t196)) % 0.54/0.73 (define @t198 () (forall @t73 @t197)) % 0.54/0.73 (define @t199 () (lambda @t34 (forall @t73 (or @t86 @t109)))) % 0.54/0.73 (define @t200 () (_ @t199 @t195 @t5)) % 0.54/0.73 (define @t201 () (not @t200)) % 0.54/0.73 (define @t202 () (or @t201 @t181)) % 0.54/0.73 (define @t203 () (@list @t5 @t50 @t180)) % 0.54/0.73 (define @t204 () (_ (lambda @t75 (forall @t73 (or @t119 @t109))) tptp.rel)) % 0.54/0.73 (define @t205 () (not (tptp.mbox @t195 @t5))) % 0.54/0.73 (define @t206 () (or @t205 @t181)) % 0.54/0.73 (define @t207 () (forall @t203 @t206)) % 0.54/0.73 (define @t208 () (forall (@list @t50 @t180) @t206)) % 0.54/0.73 (define @t209 () (lambda @t28 @t208)) % 0.54/0.73 (define @t210 () (_ @t209 @t5)) % 0.54/0.73 (define @t211 () (forall @t28 @t210)) % 0.54/0.73 (define @t212 () (@list @t180)) % 0.54/0.73 (define @t213 () (forall @t212 @t206)) % 0.54/0.73 (define @t214 () (tptp.p @t12 @t9)) % 0.54/0.73 (define @t215 () (_ @t12 @t3 @t191)) % 0.54/0.73 (define @t216 () (= @t215 @t193)) % 0.54/0.73 (define @t217 () (forall @t46 @t216)) % 0.54/0.73 (define @t218 () (lambda @t194 @t217)) % 0.54/0.73 (define @t219 () (forall @t53 (or (not (tptp.mbox @t218 @t9)) (= @t214 (tptp.p @t50 @t9))))) % 0.54/0.73 (define @t220 () (lambda @t20 @t219)) % 0.54/0.73 (define @t221 () (forall @t53 (_ @t220 @t50 @t5))) % 0.54/0.73 (define @t222 () (lambda @t28 @t221)) % 0.54/0.73 (define @t223 () (tptp.p @t12 @t5)) % 0.54/0.73 (define @t224 () (tptp.mbox @t218 @t5)) % 0.54/0.73 (define @t225 () (= @t150 @t137)) % 0.54/0.73 (define @t226 () (lambda @t194 (forall @t46 (= (_ @t15 @t191) (_ @t134 @t191))))) % 0.54/0.73 (define @t227 () (_ (_ tptp.mbox @t218) @t5)) % 0.54/0.73 (define @t228 () (not @t227)) % 0.54/0.73 (define @t229 () (or @t228 @t225)) % 0.54/0.73 (define @t230 () (=> @t227 @t225)) % 0.54/0.73 (define @t231 () (_ tptp.mbox (lambda @t194 (forall @t46 (= @t215 (_ @t10 @t3 @t191)))))) % 0.54/0.73 (define @t232 () (=> (_ @t231 @t9) (= @t142 (_ @t11 @t9)))) % 0.54/0.73 (define @t233 () (lambda @t18 @t232)) % 0.54/0.73 (define @t234 () (_ @t233 @t50 @t5)) % 0.54/0.73 (define @t235 () (forall @t53 @t234)) % 0.54/0.73 (define @t236 () (lambda @t28 @t235)) % 0.54/0.73 (define @t237 () (_ @t11 @t5)) % 0.54/0.73 (define @t238 () (= @t150 @t237)) % 0.54/0.73 (define @t239 () (_ @t231 @t5)) % 0.54/0.73 (define @t240 () (lambda @t28 @t238)) % 0.54/0.73 (define @t241 () (_ @t240 @t5)) % 0.54/0.73 (define @t242 () (=> @t239 @t241)) % 0.54/0.73 (define @t243 () (lambda @t28 @t242)) % 0.54/0.73 (define @t244 () (lambda @t156 (=> @t239 @t37))) % 0.54/0.73 (define @t245 () (lambda @t28 (= @t237 @t150))) % 0.54/0.73 (define @t246 () (lambda @t156 (= @t150 @t37))) % 0.54/0.73 (define @t247 () (_ @t43 @t13)) % 0.54/0.73 (define @t248 () (_ @t10 @t3 @t5)) % 0.54/0.73 (define @t249 () (_ tptp.mbox (lambda @t28 (forall @t46 (= @t152 @t248))))) % 0.54/0.73 (define @t250 () (lambda @t156 (=> (_ @t249 @t5) @t37))) % 0.54/0.73 (define @t251 () (_ @t14 @t5)) % 0.54/0.73 (define @t252 () (= @t45 @t251)) % 0.54/0.73 (define @t253 () (= @t22 (_ @t14 @t9))) % 0.54/0.73 (define @t254 () (lambda @t16 @t253)) % 0.54/0.73 (define @t255 () (_ @t254 @t3 @t5)) % 0.54/0.73 (define @t256 () (forall @t46 @t255)) % 0.54/0.73 (define @t257 () (lambda @t28 @t256)) % 0.54/0.73 (define @t258 () (lambda @t48 (forall @t46 @t152))) % 0.54/0.73 (define @t259 () (lambda @t28 (= @t251 @t45))) % 0.54/0.73 (define @t260 () (lambda @t156 (= @t45 @t37))) % 0.54/0.73 (define @t261 () (_ @t43 @t15)) % 0.54/0.73 (define @t262 () (lambda @t16 (_ (_ @t261 @t14) @t9))) % 0.54/0.73 (define @t263 () (lambda @t18 (_ (_ (_ @t41 (_ tptp.mbox (_ @t258 @t262))) (_ @t247 @t11)) @t9))) % 0.54/0.73 (define @t264 () (@var "BOUND_VARIABLE_8244" $$unsorted)) % 0.54/0.73 (define @t265 () (@var "BOUND_VARIABLE_8242" tptp.mu)) % 0.54/0.73 (define @t266 () (lambda (@list @t265 @t264) false)) % 0.54/0.73 (define @t267 () (@purify @t266)) % 0.54/0.73 (define @t268 () (tptp.p @t266 @t5)) % 0.54/0.73 (define @t269 () (_ tptp.p @t266)) % 0.54/0.73 (define @t270 () (_ @t269 @t5)) % 0.54/0.73 (define @t271 () (not @t270)) % 0.54/0.73 (define @t272 () (lambda @t28 @t271)) % 0.54/0.73 (define @t273 () (_ @t272 @t5)) % 0.54/0.73 (define @t274 () (forall @t28 @t273)) % 0.54/0.73 (define @t275 () (tptp.p @t266 @t171)) % 0.54/0.73 (define @t276 () (not @t275)) % 0.54/0.73 (define @t277 () (forall @t28 (not @t268))) % 0.54/0.73 (define @t278 () (tptp.p @t267 @t171)) % 0.54/0.73 (define @t279 () (= @t175 @t278)) % 0.54/0.73 (define @t280 () (not @t279)) % 0.54/0.73 (define @t281 () (forall @t185 (or @t172 (= (_ @t170 @t182 @t67) (_ @t267 @t182 @t67))))) % 0.54/0.73 (define @t282 () (not @t281)) % 0.54/0.73 (define @t283 () (or @t282 @t279)) % 0.54/0.73 (define @t284 () (@list true false)) % 0.54/0.73 (define @t285 () (@quantifiers_skolemize @t281 0)) % 0.54/0.73 (define @t286 () (@quantifiers_skolemize @t281 1)) % 0.54/0.73 (define @t287 () (_ @t170 @t286 @t285)) % 0.54/0.73 (define @t288 () (not (tptp.rel @t171 @t285))) % 0.54/0.73 (define @t289 () (or @t288 (not @t287))) % 0.54/0.73 (define @t290 () (not @t289)) % 0.54/0.73 (define @t291 () (_ @t266 @t286 @t285)) % 0.54/0.73 (define @t292 () (_ @t267 @t286 @t285)) % 0.54/0.73 (define @t293 () (= @t287 @t292)) % 0.54/0.73 (define @t294 () (or @t288 @t293)) % 0.54/0.73 (define @t295 () (not @t294)) % 0.54/0.73 (assume @p1 @t1) % 0.54/0.73 (assume @p2 @t2) % 0.54/0.73 (assume @p3 (_ tptp.mvalid (_ tptp.mnot @t8))) % 0.54/0.73 (assume @p4 (_ tptp.mvalid (_ tptp.mforall_indset @t21))) % 0.54/0.73 (assume @p5 @t25) % 0.54/0.73 (assume @p6 true) % 0.54/0.73 (step @p7 (= tptp.meq_ind @t27) :rule refl :args (@t27)) % 0.54/0.73 (step @p8 (= tptp.mtrue @t29) :rule refl :args (@t29)) % 0.54/0.73 (step @p9 (= tptp.mfalse @t30) :rule refl :args (@t30)) % 0.54/0.73 (step @p10 (= tptp.mnot @t35) :rule refl :args (@t35)) % 0.54/0.73 (step @p11 (= tptp.mor @t39) :rule refl :args (@t39)) % 0.54/0.73 (step @p12 (= tptp.mand @t40) :rule refl :args (@t40)) % 0.54/0.73 (step @p13 (= tptp.mimplies @t41) :rule refl :args (@t41)) % 0.54/0.73 (step @p14 (= tptp.mimplied @t42) :rule refl :args (@t42)) % 0.54/0.73 (step @p15 (= tptp.mequiv @t43) :rule refl :args (@t43)) % 0.54/0.73 (step @p16 (= tptp.mxor @t44) :rule refl :args (@t44)) % 0.54/0.73 (step @p17 (= tptp.mforall_ind @t49) :rule refl :args (@t49)) % 0.54/0.73 (step @p18 (= tptp.mforall_indset @t56) :rule refl :args (@t56)) % 0.54/0.73 (step @p19 (= tptp.mforall_prop @t62) :rule refl :args (@t62)) % 0.54/0.73 (step @p20 (= tptp.mexists_ind @t64) :rule refl :args (@t64)) % 0.54/0.73 (step @p21 (= tptp.mexists_indset @t65) :rule refl :args (@t65)) % 0.54/0.73 (step @p22 (= tptp.mexists_prop @t66) :rule refl :args (@t66)) % 0.54/0.73 (step @p23 (= tptp.mbox_generic @t76) :rule refl :args (@t76)) % 0.54/0.73 (step @p24 (= tptp.mdia_generic @t79) :rule refl :args (@t79)) % 0.54/0.73 (step @p25 (= tptp.mvalid @t82) :rule refl :args (@t82)) % 0.54/0.73 (step @p26 (= tptp.minvalid @t83) :rule refl :args (@t83)) % 0.54/0.73 (step @p27 :rule quant-merge-prenex :args ((= (forall @t73 @t91) @t89))) % 0.54/0.73 (step @p28 :rule alpha_equiv :args (@t92 (@list @t84) @t93)) % 0.54/0.73 (step @p29 :rule refl :args (@t86)) % 0.54/0.73 (step @p30 :rule nary_cong :premises (@p29 @p28) :args (@t94)) % 0.54/0.73 (step @p31 :rule quant-miniscope-or :args ((= @t91 @t94))) % 0.54/0.73 (step @p32 :rule trans :premises (@p31 @p30)) % 0.54/0.73 (step @p33 :rule symm :premises (@p32)) % 0.54/0.73 (step @p34 :rule cong :premises (@p33) :args ((forall @t73 (or @t86 @t96)))) % 0.54/0.73 (step @p35 :rule trans :premises (@p34 @p27)) % 0.54/0.73 (step @p36 :rule bool-double-not-elim :args (@t96)) % 0.54/0.73 (step @p37 :rule beta-reduce :args ((= @t104 (not @t96)))) % 0.54/0.73 (step @p38 :rule cong :premises (@p37) :args (@t105)) % 0.54/0.73 (step @p39 :rule trans :premises (@p38 @p36)) % 0.54/0.73 (step @p40 :rule refl :args (@t86)) % 0.54/0.73 (step @p41 :rule nary_cong :premises (@p40 @p39) :args (@t106)) % 0.54/0.73 (step @p42 :rule cong :premises (@p41) :args (@t107)) % 0.54/0.73 (step @p43 :rule trans :premises (@p42 @p35)) % 0.54/0.73 (step @p44 :rule cong :premises (@p43) :args (@t108)) % 0.54/0.73 (step @p45 :rule beta-reduce :args ((= @t112 @t108))) % 0.54/0.73 (step @p46 :rule trans :premises (@p45 @p44)) % 0.54/0.73 (step @p47 :rule refl :args (@t114)) % 0.54/0.73 (step @p48 :rule nary_cong :premises (@p47 @p46) :args (@t115)) % 0.54/0.73 (step @p49 :rule cong :premises (@p48) :args (@t117)) % 0.54/0.73 (step @p50 :rule cong :premises (@p49) :args ((not @t117))) % 0.54/0.73 (step @p51 :rule refl :args (@t5)) % 0.54/0.73 (step @p52 :rule refl :args (@t103)) % 0.54/0.73 (step @p53 :rule beta-reduce :args ((= @t120 @t111))) % 0.54/0.73 (step @p54 :rule refl :args (tptp.mdia)) % 0.54/0.73 (step @p55 :rule cong :premises (@p54 @p53) :args ((= tptp.mdia @t120))) % 0.54/0.73 (step @p56 :rule refl :args (tptp.rel)) % 0.54/0.73 (step @p57 :rule refl :args (@t109)) % 0.54/0.73 (step @p58 :rule refl :args (@t68)) % 0.54/0.73 (step @p59 :rule cong :premises (@p58 @p57) :args ((= @t68 @t109))) % 0.54/0.73 (step @p60 :rule symm :premises (@p59)) % 0.54/0.73 (step @p61 :rule eq_resolve :premises (@p58 @p60)) % 0.54/0.73 (step @p62 :rule cong :premises (@p61) :args (@t121)) % 0.54/0.73 (step @p63 :rule refl :args (@t118)) % 0.54/0.73 (step @p64 :rule refl :args (@t70)) % 0.54/0.73 (step @p65 :rule cong :premises (@p64 @p63) :args ((= @t70 @t118))) % 0.54/0.73 (step @p66 :rule symm :premises (@p65)) % 0.54/0.73 (step @p67 :rule eq_resolve :premises (@p64 @p66)) % 0.54/0.73 (step @p68 :rule cong :premises (@p67) :args (@t71)) % 0.54/0.73 (step @p69 :rule nary_cong :premises (@p68 @p62) :args (@t122)) % 0.54/0.73 (step @p70 :rule cong :premises (@p69) :args ((forall @t73 @t122))) % 0.54/0.73 (step @p71 :rule bool-and-de-morgan :args (@t70 @t68 true)) % 0.54/0.73 (step @p72 :rule cong :premises (@p71) :args (@t123)) % 0.54/0.73 (step @p73 :rule trans :premises (@p72 @p70)) % 0.54/0.73 (step @p74 :rule cong :premises (@p73) :args (@t124)) % 0.54/0.73 (step @p75 :rule exists-elim :args ((= @t78 @t124))) % 0.54/0.73 (step @p76 :rule trans :premises (@p75 @p74)) % 0.54/0.73 (step @p77 :rule cong :premises (@p76) :args (@t79)) % 0.54/0.73 (step @p78 :rule trans :premises (@p24 @p77)) % 0.54/0.73 (step @p79 :rule ho_cong :premises (@p78 @p56)) % 0.54/0.73 (step @p80 :rule cong :premises (@p54 @p79) :args (@t2)) % 0.54/0.73 (step @p81 :rule trans :premises (@p80 @p55)) % 0.54/0.73 (step @p82 :rule eq_resolve :premises (@p2 @p81)) % 0.54/0.73 (step @p83 :rule ho_cong :premises (@p82 @p52 @p51)) % 0.54/0.73 (step @p84 :rule nary_cong :premises (@p47 @p83) :args (@t126)) % 0.54/0.73 (step @p85 :rule cong :premises (@p84) :args (@t127)) % 0.54/0.73 (step @p86 :rule cong :premises (@p85) :args ((not @t127))) % 0.54/0.73 (step @p87 :rule trans :premises (@p86 @p50)) % 0.54/0.73 (step @p88 :rule quant-merge-prenex :args ((= (forall @t28 @t128) @t127))) % 0.54/0.73 (step @p89 :rule beta-reduce :args ((= @t130 @t128))) % 0.54/0.73 (step @p90 :rule cong :premises (@p89) :args (@t131)) % 0.54/0.73 (step @p91 :rule trans :premises (@p90 @p88)) % 0.54/0.73 (step @p92 :rule beta-reduce :args ((= (_ @t133 @t129) @t131))) % 0.54/0.73 (step @p93 :rule trans :premises (@p92 @p91)) % 0.54/0.73 (step @p94 :rule refl :args ((tptp.mdia @t135 @t5))) % 0.54/0.73 (step @p95 :rule refl :args (@t5)) % 0.54/0.73 (step @p96 :rule refl :args (@t98)) % 0.54/0.73 (step @p97 :rule cong :premises (@p96) :args (@t99)) % 0.54/0.73 (step @p98 :rule cong :premises (@p97) :args (@t100)) % 0.54/0.73 (step @p99 :rule cong :premises (@p98) :args (@t101)) % 0.54/0.73 (step @p100 :rule cong :premises (@p99) :args (@t103)) % 0.54/0.73 (step @p101 :rule cong :premises (@p100 @p95) :args (@t125)) % 0.54/0.73 (step @p102 :rule trans :premises (@p101 @p94)) % 0.54/0.73 (step @p103 :rule refl :args (tptp.mdia)) % 0.54/0.73 (step @p104 :rule ho_cong :premises (@p103 @p100)) % 0.54/0.73 (step @p105 :rule ho_cong :premises (@p104 @p95)) % 0.54/0.73 (step @p106 :rule cong :premises (@p105 @p102) :args ((= @t136 @t125))) % 0.54/0.73 (step @p107 :rule symm :premises (@p106)) % 0.54/0.73 (step @p108 :rule refl :args ((_ (_ tptp.mdia @t135) @t5))) % 0.54/0.73 (step 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(step @p124 :rule cong :premises (@p123) :args (@t147)) % 0.54/0.73 (step @p125 :rule beta-reduce :args ((= (_ @t149 @t144) @t147))) % 0.54/0.73 (step @p126 :rule trans :premises (@p125 @p124)) % 0.54/0.73 (step @p127 :rule beta-reduce :args ((= (_ @t151 @t9) @t143))) % 0.54/0.73 (step @p128 :rule refl :args (@t9)) % 0.54/0.73 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 0.54/0.73 ; trust TRUST_THEORY_REWRITE % 0.54/0.73 (step @p129 :rule trust :premises () :args ((= @t155 @t151))) % 0.54/0.73 (step @p130 :rule beta-reduce :args ((= (_ @t157 @t154) @t155))) % 0.54/0.73 (step @p131 :rule trans :premises (@p130 @p129)) % 0.54/0.73 (step @p132 :rule refl :args (@t152)) % 0.54/0.73 (step @p133 :rule refl :args (@t45)) % 0.54/0.73 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t45 @t152))) % 0.54/0.73 (step @p135 :rule symm :premises (@p134)) % 0.54/0.73 (step @p136 :rule eq_resolve :premises (@p133 @p135)) % 0.54/0.73 (step @p137 :rule cong :premises (@p136) :args 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(step @p345 :rule ho_cong :premises (@p344 @p343)) % 0.54/0.73 (step @p346 :rule trans :premises (@p345 @p311)) % 0.54/0.73 (step @p347 :rule ho_cong :premises (@p346 @p308)) % 0.54/0.73 (step @p348 :rule trans :premises (@p347 @p297)) % 0.54/0.73 (step @p349 :rule ho_cong :premises (@p348 @p128)) % 0.54/0.73 (step @p350 :rule trans :premises (@p349 @p291)) % 0.54/0.73 (step @p351 :rule cong :premises (@p350) :args (@t263)) % 0.54/0.73 (step @p352 :rule ho_cong :premises (@p154 @p351)) % 0.54/0.73 (step @p353 :rule trans :premises (@p352 @p290)) % 0.54/0.73 (step @p354 :rule ho_cong :premises (@p353 @p128)) % 0.54/0.73 (step @p355 :rule trans :premises (@p354 @p257)) % 0.54/0.73 (step @p356 :rule cong :premises (@p355) :args ((lambda @t20 (_ (_ @t149 @t263) @t9)))) % 0.54/0.73 (step @p357 :rule ho_cong :premises (@p154 @p356)) % 0.54/0.73 (step @p358 :rule trans :premises (@p357 @p256)) % 0.54/0.73 (step @p359 :rule ho_cong :premises (@p157 @p358)) % 0.54/0.73 (step @p360 :rule trans :premises (@p359 @p244)) % 0.54/0.73 (step @p361 :rule ho_cong :premises (@p15 @p169)) % 0.54/0.73 (step @p362 :rule ho_cong :premises (@p361 @p302)) % 0.54/0.73 (step @p363 :rule refl :args (@t15)) % 0.54/0.73 (step @p364 :rule ho_cong :premises (@p15 @p363)) % 0.54/0.73 (step @p365 :rule ho_cong :premises (@p364 @p330)) % 0.54/0.73 (step @p366 :rule ho_cong :premises (@p365 @p128)) % 0.54/0.73 (step @p367 :rule cong :premises (@p366) :args (@t17)) % 0.54/0.73 (step @p368 :rule cong :premises (@p136) :args (@t47)) % 0.54/0.73 (step @p369 :rule cong :premises (@p368) :args (@t49)) % 0.54/0.73 (step @p370 :rule trans :premises (@p17 @p369)) % 0.54/0.73 (step @p371 :rule ho_cong :premises (@p370 @p367)) % 0.54/0.73 (step @p372 :rule ho_cong :premises (@p224 @p371)) % 0.54/0.73 (step @p373 :rule ho_cong :premises (@p13 @p372)) % 0.54/0.73 (step @p374 :rule ho_cong :premises (@p373 @p362)) % 0.54/0.73 (step @p375 :rule ho_cong :premises (@p374 @p128)) % 0.54/0.73 (step @p376 :rule cong :premises (@p375) :args (@t19)) % 0.54/0.73 (step @p377 :rule ho_cong :premises (@p181 @p376)) % 0.54/0.73 (step @p378 :rule ho_cong :premises (@p377 @p128)) % 0.54/0.73 (step @p379 :rule cong :premises (@p378) :args (@t21)) % 0.54/0.73 (step @p380 :rule ho_cong :premises (@p181 @p379)) % 0.54/0.73 (step @p381 :rule ho_cong :premises (@p190 @p380)) % 0.54/0.73 (step @p382 :rule trans :premises (@p381 @p360)) % 0.54/0.73 (step @p383 :rule trans :premises (@p382 @p238)) % 0.54/0.73 (step @p384 :rule eq_resolve :premises (@p4 @p383)) % 0.54/0.73 (step @p385 :rule instantiate :premises (@p384) :args ((@list @t171 @t170 @t267))) % 0.54/0.73 (step @p386 :rule refl :args (@t268)) % 0.54/0.73 (step @p387 :rule refl :args (@t266)) % 0.54/0.73 (step @p388 :rule cong :premises (@p387 @p95) :args (@t268)) % 0.54/0.73 (step @p389 :rule trans :premises (@p388 @p386)) % 0.54/0.73 (step @p390 :rule refl :args (tptp.p)) % 0.54/0.73 (step @p391 :rule ho_cong :premises (@p390 @p387)) % 0.54/0.73 (step @p392 :rule ho_cong :premises (@p391 @p95)) % 0.54/0.73 (step @p393 :rule cong :premises (@p392 @p389) :args ((= @t270 @t268))) % 0.54/0.73 (step @p394 :rule symm :premises (@p393)) % 0.54/0.73 (step @p395 :rule refl :args ((_ (_ tptp.p @t266) @t5))) % 0.54/0.73 (step @p396 :rule eq_resolve :premises (@p395 @p394)) % 0.54/0.73 (step @p397 :rule cong :premises (@p396) :args (@t271)) % 0.54/0.73 (step @p398 :rule cong :premises (@p397) :args ((forall @t28 @t271))) % 0.54/0.73 (step @p399 :rule beta-reduce :args ((= @t273 @t271))) % 0.54/0.73 (step @p400 :rule cong :premises (@p399) :args (@t274)) % 0.54/0.73 (step @p401 :rule trans :premises (@p400 @p398)) % 0.54/0.73 (step @p402 :rule beta-reduce :args ((= (_ @t133 @t272) @t274))) % 0.54/0.73 (step @p403 :rule trans :premises (@p402 @p401)) % 0.54/0.73 (step @p404 :rule beta-reduce :args ((= (_ @t35 @t269) @t272))) % 0.54/0.73 (step @p405 :rule symm :premises (@p387)) % 0.54/0.73 (step @p406 :rule alpha_equiv :args ((lambda @t6 false) (@list @t3 @t5) (@list @t265 @t264))) % 0.54/0.73 (step @p407 :rule trans :premises (@p406 @p405)) % 0.54/0.73 (step @p408 :rule evaluate :args ((not true))) % 0.54/0.73 (step @p409 :rule eq-refl :args (@t3)) % 0.54/0.73 (step @p410 :rule cong :premises (@p409) :args (@t4)) % 0.54/0.73 (step @p411 :rule trans :premises (@p410 @p408)) % 0.54/0.73 (step @p412 :rule cong :premises (@p411) :args (@t7)) % 0.54/0.73 (step @p413 :rule trans :premises (@p412 @p407)) % 0.54/0.73 (step @p414 :rule refl :args (tptp.p)) % 0.54/0.73 (step @p415 :rule ho_cong :premises (@p414 @p413)) % 0.54/0.73 (step @p416 :rule refl :args (@t35)) % 0.54/0.73 (step @p417 :rule ho_cong :premises (@p416 @p415)) % 0.54/0.73 (step @p418 :rule trans :premises (@p417 @p404)) % 0.54/0.73 (step @p419 :rule ho_cong :premises (@p157 @p418)) % 0.54/0.73 (step @p420 :rule trans :premises (@p419 @p403)) % 0.54/0.73 (step @p421 :rule refl :args (@t8)) % 0.54/0.73 (step @p422 :rule ho_cong :premises (@p10 @p421)) % 0.54/0.73 (step @p423 :rule ho_cong :premises (@p190 @p422)) % 0.54/0.73 (step @p424 :rule trans :premises (@p423 @p420)) % 0.54/0.73 (step @p425 :rule eq_resolve :premises (@p3 @p424)) % 0.54/0.73 (step @p426 :rule refl :args (@t171)) % 0.54/0.73 (step @p427 :rule eq-refl :args (@t266)) % 0.54/0.73 (step @p428 :rule refl :args (@t266)) % 0.54/0.73 (step @p429 :rule cong :premises (@p428 @p405) :args ((= @t266 @t266))) % 0.54/0.73 (step @p430 :rule trans :premises (@p429 @p427)) % 0.54/0.73 (step @p431 :rule skolem_intro :args (@t267)) % 0.54/0.73 (step @p432 :rule cong :premises (@p428 @p431) :args ((= @t266 @t267))) % 0.54/0.73 (step @p433 :rule trans :premises (@p432 @p430)) % 0.54/0.73 (step @p434 :rule true_elim :premises (@p433)) % 0.54/0.73 (step @p435 :rule cong :premises (@p434 @p426) :args (@t275)) % 0.54/0.73 (step @p436 :rule cong :premises (@p435) :args (@t276)) % 0.54/0.73 (step @p437 :rule refl :args (@t277)) % 0.54/0.73 (step @p438 :rule cong :premises (@p437 @p436) :args ((=> @t277 @t276))) % 0.54/0.73 (assume-push @p495 @t277) % 0.54/0.73 (step @p440 :rule instantiate :premises (@p425) :args ((@list @t171))) % 0.54/0.73 (step-pop @p496 :rule scope :premises (@p440)) % 0.54/0.73 (step @p441 :rule process_scope :premises (@p496) :args (@t276)) % 0.54/0.73 (step @p443 :rule eq_resolve :premises (@p441 @p438)) % 0.54/0.73 (step @p444 :rule implies_elim :premises (@p443)) % 0.54/0.73 (step @p445 :rule chain_m_resolution :premises (@p444 @p425) :args ((not @t278) (@list false) (@list @t277))) % 0.54/0.73 (step @p446 :rule bool-double-not-elim :args (@t175)) % 0.54/0.73 (step @p447 :rule nary_cong :premises (@p198 @p446) :args ((or @t177 (not @t176)))) % 0.54/0.73 (step @p448 :rule cnf_or_neg :args (@t177 0)) % 0.54/0.73 (step @p449 :rule eq_resolve :premises (@p448 @p447)) % 0.54/0.73 (step @p450 :rule reordering :premises (@p449) :args ((or @t175 @t177))) % 0.54/0.73 (step @p451 :rule chain_m_resolution :premises (@p450 @p196) :args (@t175 @t178 @t179)) % 0.54/0.73 (step @p452 :rule cnf_equiv_pos1 :args (@t279)) % 0.54/0.73 (step @p453 :rule reordering :premises (@p452) :args ((or @t176 @t278 @t280))) % 0.54/0.73 (step @p454 :rule chain_m_resolution :premises (@p453 @p451 @p445) :args (@t280 (@list false true) (@list @t175 @t278))) % 0.54/0.73 (step @p455 :rule cnf_or_pos :args (@t283)) % 0.54/0.73 (step @p456 :rule reordering :premises (@p455) :args ((or @t282 @t279 (not @t283)))) % 0.54/0.73 (step @p457 :rule chain_m_resolution :premises (@p456 @p454 @p385) :args (@t282 @t284 (@list @t279 @t283))) % 0.54/0.73 (step @p458 :rule refl :args (@t290)) % 0.54/0.73 (step @p459 :rule bool-double-not-elim :args (@t281)) % 0.54/0.73 (step @p460 :rule nary_cong :premises (@p459 @p458) :args ((or (not @t282) @t290))) % 0.54/0.73 (step @p461 :rule bool-eq-false :args (@t287)) % 0.54/0.73 (step @p462 :rule evaluate :args ((not false))) % 0.54/0.73 (step @p463 :rule beta-reduce :args ((= @t291 false))) % 0.54/0.73 (step @p464 :rule cong :premises (@p463) :args ((not @t291))) % 0.54/0.73 (step @p465 :rule trans :premises (@p464 @p462)) % 0.54/0.73 (step @p466 :rule refl :args (@t285)) % 0.54/0.73 (step @p467 :rule refl :args (@t286)) % 0.54/0.73 (step @p468 :rule ho_cong :premises (@p431 @p467 @p466)) % 0.54/0.73 (step @p469 :rule cong :premises (@p468) :args ((not @t292))) % 0.54/0.73 (step @p470 :rule bool-eq-false :args (@t292)) % 0.54/0.73 (step @p471 :rule trans :premises (@p470 @p469 @p465)) % 0.54/0.73 (step @p472 :rule true_elim :premises (@p471)) % 0.54/0.73 (step @p473 :rule refl :args (@t287)) % 0.54/0.73 (step @p474 :rule cong :premises (@p473 @p472) :args (@t293)) % 0.54/0.73 (step @p475 :rule trans :premises (@p474 @p461)) % 0.54/0.73 (step @p476 :rule refl :args (@t288)) % 0.54/0.73 (step @p477 :rule nary_cong :premises (@p476 @p475) :args (@t294)) % 0.54/0.73 (step @p478 :rule cong :premises (@p477) :args (@t295)) % 0.54/0.73 (step @p479 :rule refl :args (@t282)) % 0.54/0.73 (step @p480 :rule cong :premises (@p479 @p478) :args ((=> @t282 @t295))) % 0.54/0.73 (assume-push @p497 @t282) % 0.54/0.73 (step @p482 :rule skolemize :premises (@p457)) % 0.54/0.73 (step-pop @p498 :rule scope :premises (@p482)) % 0.54/0.73 (step @p483 :rule process_scope :premises (@p498) :args (@t295)) % 0.54/0.73 (step @p485 :rule eq_resolve :premises (@p483 @p480)) % 0.54/0.73 (step @p486 :rule implies_elim :premises (@p485)) % 0.54/0.73 (step @p487 :rule eq_resolve :premises (@p486 @p460)) % 0.54/0.73 (step @p488 :rule chain_m_resolution :premises (@p487 @p457) :args (@t290 @t178 (@list @t281))) % 0.54/0.73 (assume-push @p499 @t173) % 0.54/0.73 (step @p490 :rule instantiate :premises (@p203) :args ((@list @t285 @t286))) % 0.54/0.73 (step-pop @p500 :rule scope :premises (@p490)) % 0.54/0.73 (step @p491 :rule process_scope :premises (@p500) :args (@t289)) % 0.54/0.73 (step @p493 :rule implies_elim :premises (@p491)) % 0.54/0.73 (step @p494 false :rule chain_m_resolution :premises (@p493 @p488 @p203) :args (false @t284 (@list @t289 @t173))) % 0.54/0.73 ) % 0.54/0.73 % SZS output end Proof % 0.54/0.73 % cvc5 exiting %------------------------------------------------------------------------------