%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PHI002^2 : TPTP v9.2.1. Released v6.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:43:10 AM UTC 2026 % Result : Theorem 0.44s 0.63s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PHI002^2 : TPTP v9.2.1. Released v6.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n021.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 12:52:35 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.44/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.44/0.63 % SZS status Theorem % 0.44/0.63 % SZS output start Proof % 0.44/0.63 ( % 0.44/0.63 (declare-sort $$unsorted 0) % 0.44/0.63 (declare-sort tptp.mu 0) % 0.44/0.63 (declare-const tptp.rel (-> $$unsorted $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.mbox (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.mdia (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.positive (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)) % 0.44/0.63 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.44/0.63 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.44/0.63 (define tptp.mfalse () (lambda (@list (@var "W" $$unsorted)) false)) % 0.44/0.63 (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)))))) % 0.44/0.63 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.63 (define tptp.mand () (let ((_let_1 (@var "W" $$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))))))) % 0.44/0.63 (define tptp.mimplies () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.63 (define tptp.mimplied () (let ((_let_1 (@var "W" $$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))))))) % 0.44/0.63 (define tptp.mequiv () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.63 (define tptp.mxor () (let ((_let_1 (@var "W" $$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))))))))) % 0.44/0.63 (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))))))) % 0.44/0.63 (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))))))) % 0.44/0.63 (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))))))) % 0.44/0.63 (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))))))) % 0.44/0.63 (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))))))) % 0.44/0.63 (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))))))) % 0.44/0.63 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.44/0.63 (define tptp.mdia_generic () (let ((_let_1 (@var "V" $$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))))))))) % 0.44/0.63 (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)))))) % 0.44/0.63 (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))))))) % 0.44/0.63 (define @t1 () (= tptp.mbox (_ tptp.mbox_generic tptp.rel))) % 0.44/0.63 (define @t2 () (= tptp.mdia (_ tptp.mdia_generic tptp.rel))) % 0.44/0.63 (define @t3 () (@var "__flatten_var_0" $$unsorted)) % 0.44/0.63 (define @t4 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.44/0.63 (define @t5 () (_ tptp.positive @t4)) % 0.44/0.63 (define @t6 () (@var "X" tptp.mu)) % 0.44/0.63 (define @t7 () (_ @t4 @t6)) % 0.44/0.63 (define @t8 () (@list @t6 @t3)) % 0.44/0.63 (define @t9 () (lambda @t8 (_ (_ tptp.mnot @t7) @t3))) % 0.44/0.63 (define @t10 () (@list @t4 @t3)) % 0.44/0.63 (define @t11 () (lambda @t10 (_ (_ (_ tptp.mequiv (_ tptp.positive @t9)) (_ tptp.mnot @t5)) @t3))) % 0.44/0.63 (define @t12 () (@var "Psi" (-> tptp.mu $$unsorted Bool))) % 0.44/0.63 (define @t13 () (_ tptp.positive @t12)) % 0.44/0.63 (define @t14 () (_ @t12 @t6)) % 0.44/0.63 (define @t15 () (lambda @t8 (_ (_ (_ tptp.mimplies @t7) @t14) @t3))) % 0.44/0.63 (define @t16 () (@list @t12 @t3)) % 0.44/0.63 (define @t17 () (lambda @t16 (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t5) (_ tptp.mbox (_ tptp.mforall_ind @t15)))) @t13) @t3))) % 0.44/0.63 (define @t18 () (lambda @t10 (_ (_ tptp.mforall_indset @t17) @t3))) % 0.44/0.63 (define @t19 () (_ @t7 @t3)) % 0.44/0.63 (define @t20 () (lambda @t8 @t19)) % 0.44/0.63 (define @t21 () (lambda @t10 (_ (_ (_ tptp.mimplies @t5) (_ tptp.mdia (_ tptp.mexists_ind @t20))) @t3))) % 0.44/0.63 (define @t22 () (not (_ tptp.mvalid (_ tptp.mforall_indset @t21)))) % 0.44/0.63 (define @t23 () (@var "Y" tptp.mu)) % 0.44/0.63 (define @t24 () (@var "W" $$unsorted)) % 0.44/0.63 (define @t25 () (lambda (@list @t6 @t23 @t24) (= @t6 @t23))) % 0.44/0.63 (define @t26 () (@list @t24)) % 0.44/0.63 (define @t27 () (lambda @t26 true)) % 0.44/0.63 (define @t28 () (lambda @t26 false)) % 0.44/0.63 (define @t29 () (@var "Phi" (-> $$unsorted Bool))) % 0.44/0.63 (define @t30 () (_ @t29 @t24)) % 0.44/0.63 (define @t31 () (not @t30)) % 0.44/0.63 (define @t32 () (@list @t29 @t24)) % 0.44/0.63 (define @t33 () (lambda @t32 @t31)) % 0.44/0.63 (define @t34 () (@var "Psi" (-> $$unsorted Bool))) % 0.44/0.63 (define @t35 () (_ @t34 @t24)) % 0.44/0.63 (define @t36 () (@list @t29 @t34 @t24)) % 0.44/0.63 (define @t37 () (lambda @t36 (or @t30 @t35))) % 0.44/0.63 (define @t38 () (lambda @t36 (and @t30 @t35))) % 0.44/0.63 (define @t39 () (lambda @t36 (=> @t30 @t35))) % 0.44/0.63 (define @t40 () (lambda @t36 (=> @t35 @t30))) % 0.44/0.63 (define @t41 () (lambda @t36 (= @t30 @t35))) % 0.44/0.63 (define @t42 () (lambda @t36 (or (and @t30 (not @t35)) (and @t31 @t35)))) % 0.44/0.63 (define @t43 () (_ @t7 @t24)) % 0.44/0.63 (define @t44 () (@list @t6)) % 0.44/0.63 (define @t45 () (forall @t44 @t43)) % 0.44/0.63 (define @t46 () (@list @t4 @t24)) % 0.44/0.63 (define @t47 () (lambda @t46 @t45)) % 0.44/0.63 (define @t48 () (@var "X" (-> tptp.mu $$unsorted Bool))) % 0.44/0.63 (define @t49 () (@var "Phi" (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool))) % 0.44/0.63 (define @t50 () (_ (_ @t49 @t48) @t24)) % 0.44/0.63 (define @t51 () (@list @t48)) % 0.44/0.63 (define @t52 () (forall @t51 @t50)) % 0.44/0.63 (define @t53 () (@list @t49 @t24)) % 0.44/0.63 (define @t54 () (lambda @t53 @t52)) % 0.44/0.63 (define @t55 () (@var "P" (-> $$unsorted Bool))) % 0.44/0.63 (define @t56 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.44/0.63 (define @t57 () (_ (_ @t56 @t55) @t24)) % 0.44/0.63 (define @t58 () (@list @t55)) % 0.44/0.63 (define @t59 () (@list @t56 @t24)) % 0.44/0.63 (define @t60 () (lambda @t59 (forall @t58 @t57))) % 0.44/0.63 (define @t61 () (exists @t44 @t43)) % 0.44/0.63 (define @t62 () (lambda @t46 @t61)) % 0.44/0.63 (define @t63 () (lambda @t53 (exists @t51 @t50))) % 0.44/0.63 (define @t64 () (lambda @t59 (exists @t58 @t57))) % 0.44/0.63 (define @t65 () (@var "V" $$unsorted)) % 0.44/0.63 (define @t66 () (_ @t29 @t65)) % 0.44/0.63 (define @t67 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.44/0.63 (define @t68 () (_ (_ @t67 @t24) @t65)) % 0.44/0.63 (define @t69 () (not @t68)) % 0.44/0.63 (define @t70 () (or @t69 @t66)) % 0.44/0.63 (define @t71 () (@list @t65)) % 0.44/0.63 (define @t72 () (forall @t71 @t70)) % 0.44/0.63 (define @t73 () (@list @t67 @t29 @t24)) % 0.44/0.63 (define @t74 () (lambda @t73 @t72)) % 0.44/0.63 (define @t75 () (and @t68 @t66)) % 0.44/0.63 (define @t76 () (exists @t71 @t75)) % 0.44/0.63 (define @t77 () (lambda @t73 @t76)) % 0.44/0.63 (define @t78 () (forall @t26 @t30)) % 0.44/0.63 (define @t79 () (@list @t29)) % 0.44/0.63 (define @t80 () (lambda @t79 @t78)) % 0.44/0.63 (define @t81 () (lambda @t79 (forall @t26 @t31))) % 0.44/0.63 (define @t82 () (@var "BOUND_VARIABLE_8165" tptp.mu)) % 0.44/0.63 (define @t83 () (not (_ @t48 @t82 @t65))) % 0.44/0.63 (define @t84 () (not (tptp.rel @t24 @t65))) % 0.44/0.63 (define @t85 () (or @t84 @t83)) % 0.44/0.63 (define @t86 () (@list @t65 @t82)) % 0.44/0.63 (define @t87 () (forall @t86 @t85)) % 0.44/0.63 (define @t88 () (@list @t82)) % 0.44/0.63 (define @t89 () (forall @t88 @t85)) % 0.44/0.63 (define @t90 () (forall @t88 @t83)) % 0.44/0.63 (define @t91 () (@list @t6)) % 0.44/0.63 (define @t92 () (or @t84 @t90)) % 0.44/0.63 (define @t93 () (not (_ @t48 @t6 @t65))) % 0.44/0.63 (define @t94 () (forall @t44 @t93)) % 0.44/0.63 (define @t95 () (@var "BOUND_VARIABLE_8079" $$unsorted)) % 0.44/0.63 (define @t96 () (_ @t48 @t6 @t95)) % 0.44/0.63 (define @t97 () (not @t96)) % 0.44/0.63 (define @t98 () (forall @t44 @t97)) % 0.44/0.63 (define @t99 () (not @t98)) % 0.44/0.63 (define @t100 () (@list @t95)) % 0.44/0.63 (define @t101 () (lambda @t100 @t99)) % 0.44/0.63 (define @t102 () (_ @t101 @t65)) % 0.44/0.63 (define @t103 () (not @t102)) % 0.44/0.63 (define @t104 () (or @t84 @t103)) % 0.44/0.63 (define @t105 () (forall @t71 @t104)) % 0.44/0.63 (define @t106 () (not @t105)) % 0.44/0.63 (define @t107 () (_ @t29 @t65)) % 0.44/0.63 (define @t108 () (not @t107)) % 0.44/0.63 (define @t109 () (lambda @t32 (not (forall @t71 (or @t84 @t108))))) % 0.44/0.63 (define @t110 () (_ @t109 @t101 @t24)) % 0.44/0.63 (define @t111 () (tptp.positive @t48 @t24)) % 0.44/0.63 (define @t112 () (not @t111)) % 0.44/0.63 (define @t113 () (or @t112 @t110)) % 0.44/0.63 (define @t114 () (@list @t24 @t48)) % 0.44/0.63 (define @t115 () (forall @t114 @t113)) % 0.44/0.63 (define @t116 () (_ @t67 @t24 @t65)) % 0.44/0.63 (define @t117 () (not @t116)) % 0.44/0.63 (define @t118 () (_ (lambda @t73 (not (forall @t71 (or @t117 @t108)))) tptp.rel)) % 0.44/0.63 (define @t119 () (not @t66)) % 0.44/0.63 (define @t120 () (or @t69 @t119)) % 0.44/0.63 (define @t121 () (forall @t71 (not @t75))) % 0.44/0.63 (define @t122 () (not @t121)) % 0.44/0.63 (define @t123 () (tptp.mdia @t101 @t24)) % 0.44/0.63 (define @t124 () (or @t112 @t123)) % 0.44/0.63 (define @t125 () (forall @t114 @t124)) % 0.44/0.63 (define @t126 () (forall @t51 @t124)) % 0.44/0.63 (define @t127 () (lambda @t26 @t126)) % 0.44/0.63 (define @t128 () (_ @t127 @t24)) % 0.44/0.63 (define @t129 () (forall @t26 @t128)) % 0.44/0.63 (define @t130 () (_ @t29 @t24)) % 0.44/0.63 (define @t131 () (lambda @t79 (forall @t26 @t130))) % 0.44/0.63 (define @t132 () (_ @t48 @t6)) % 0.44/0.63 (define @t133 () (lambda @t100 (not (forall @t44 (not (_ @t132 @t95)))))) % 0.44/0.63 (define @t134 () (_ (_ tptp.mdia @t101) @t24)) % 0.44/0.63 (define @t135 () (_ (_ tptp.positive @t48) @t24)) % 0.44/0.63 (define @t136 () (not @t135)) % 0.44/0.63 (define @t137 () (or @t136 @t134)) % 0.44/0.63 (define @t138 () (=> @t135 @t134)) % 0.44/0.63 (define @t139 () (_ tptp.mdia (lambda @t100 (not (forall @t44 (not (_ @t4 @t6 @t95))))))) % 0.44/0.63 (define @t140 () (_ @t5 @t3)) % 0.44/0.63 (define @t141 () (=> @t140 (_ @t139 @t3))) % 0.44/0.63 (define @t142 () (lambda @t10 @t141)) % 0.44/0.63 (define @t143 () (_ @t142 @t48 @t24)) % 0.44/0.63 (define @t144 () (forall @t51 @t143)) % 0.44/0.63 (define @t145 () (lambda @t26 @t144)) % 0.44/0.63 (define @t146 () (_ @t49 @t48 @t24)) % 0.44/0.63 (define @t147 () (lambda @t53 (forall @t51 @t146))) % 0.44/0.63 (define @t148 () (_ @t5 @t24)) % 0.44/0.63 (define @t149 () (lambda @t26 (=> @t148 (_ @t139 @t24)))) % 0.44/0.63 (define @t150 () (_ @t4 @t6 @t24)) % 0.44/0.63 (define @t151 () (not @t150)) % 0.44/0.63 (define @t152 () (not (forall @t44 @t151))) % 0.44/0.63 (define @t153 () (_ tptp.mdia (lambda @t26 @t152))) % 0.44/0.63 (define @t154 () (lambda @t26 (=> @t148 (_ @t153 @t24)))) % 0.44/0.63 (define @t155 () (@list @t34 @t24)) % 0.44/0.63 (define @t156 () (lambda @t155 (=> @t148 @t35))) % 0.44/0.63 (define @t157 () (not @t43)) % 0.44/0.63 (define @t158 () (forall @t44 @t157)) % 0.44/0.63 (define @t159 () (_ @t20 @t6 @t24)) % 0.44/0.63 (define @t160 () (not @t159)) % 0.44/0.63 (define @t161 () (forall @t44 @t160)) % 0.44/0.63 (define @t162 () (not @t161)) % 0.44/0.63 (define @t163 () (lambda @t26 @t162)) % 0.44/0.63 (define @t164 () (_ (lambda @t46 @t152) @t20)) % 0.44/0.63 (define @t165 () (_ @t39 @t5)) % 0.44/0.63 (define @t166 () (lambda @t10 (_ (_ @t165 (_ tptp.mdia @t164)) @t3))) % 0.44/0.63 (define @t167 () (not @t158)) % 0.44/0.63 (define @t168 () (forall @t114 (or @t112 (not @t87)))) % 0.44/0.63 (define @t169 () (@quantifiers_skolemize @t168 1)) % 0.44/0.63 (define @t170 () (@quantifiers_skolemize @t168 0)) % 0.44/0.63 (define @t171 () (not (tptp.rel @t170 @t65))) % 0.44/0.63 (define @t172 () (forall @t86 (or @t171 (not (_ @t169 @t82 @t65))))) % 0.44/0.63 (define @t173 () (not @t172)) % 0.44/0.63 (define @t174 () (tptp.positive @t169 @t170)) % 0.44/0.63 (define @t175 () (not @t174)) % 0.44/0.63 (define @t176 () (or @t175 @t173)) % 0.44/0.63 (define @t177 () (@list true)) % 0.44/0.63 (define @t178 () (@list @t176)) % 0.44/0.63 (define @t179 () (@var "BOUND_VARIABLE_8032" (-> tptp.mu $$unsorted Bool))) % 0.44/0.63 (define @t180 () (tptp.positive @t179 @t24)) % 0.44/0.63 (define @t181 () (@var "BOUND_VARIABLE_8136" tptp.mu)) % 0.44/0.63 (define @t182 () (_ @t179 @t181 @t65)) % 0.44/0.63 (define @t183 () (not (_ @t48 @t181 @t65))) % 0.44/0.63 (define @t184 () (or @t183 @t182)) % 0.44/0.63 (define @t185 () (or @t84 @t184)) % 0.44/0.63 (define @t186 () (@list @t65 @t181)) % 0.44/0.63 (define @t187 () (forall @t186 @t185)) % 0.44/0.63 (define @t188 () (@list @t181)) % 0.44/0.63 (define @t189 () (forall @t188 @t185)) % 0.44/0.63 (define @t190 () (forall @t188 @t184)) % 0.44/0.63 (define @t191 () (or @t84 @t190)) % 0.44/0.63 (define @t192 () (forall @t44 (or @t93 (_ @t179 @t6 @t65)))) % 0.44/0.63 (define @t193 () (@var "BOUND_VARIABLE_7934" $$unsorted)) % 0.44/0.63 (define @t194 () (_ @t48 @t6 @t193)) % 0.44/0.63 (define @t195 () (not @t194)) % 0.44/0.63 (define @t196 () (@list @t193)) % 0.44/0.63 (define @t197 () (lambda @t196 (forall @t44 (or @t195 (_ @t179 @t6 @t193))))) % 0.44/0.63 (define @t198 () (_ @t197 @t65)) % 0.44/0.63 (define @t199 () (or @t84 @t198)) % 0.44/0.63 (define @t200 () (forall @t71 @t199)) % 0.44/0.63 (define @t201 () (lambda @t32 (forall @t71 (or @t84 @t107)))) % 0.44/0.63 (define @t202 () (_ @t201 @t197 @t24)) % 0.44/0.63 (define @t203 () (not @t202)) % 0.44/0.63 (define @t204 () (or @t112 @t203 @t180)) % 0.44/0.63 (define @t205 () (@list @t24 @t48 @t179)) % 0.44/0.63 (define @t206 () (_ (lambda @t73 (forall @t71 (or @t117 @t107))) tptp.rel)) % 0.44/0.63 (define @t207 () (not (tptp.mbox @t197 @t24))) % 0.44/0.63 (define @t208 () (or @t112 @t207 @t180)) % 0.44/0.63 (define @t209 () (forall @t205 @t208)) % 0.44/0.63 (define @t210 () (@list @t48 @t179)) % 0.44/0.63 (define @t211 () (forall @t210 @t208)) % 0.44/0.63 (define @t212 () (lambda @t26 @t211)) % 0.44/0.63 (define @t213 () (_ @t212 @t24)) % 0.44/0.63 (define @t214 () (forall @t26 @t213)) % 0.44/0.63 (define @t215 () (or @t207 @t180)) % 0.44/0.63 (define @t216 () (or @t112 @t215)) % 0.44/0.63 (define @t217 () (forall @t210 @t216)) % 0.44/0.63 (define @t218 () (@list @t179)) % 0.44/0.63 (define @t219 () (forall @t218 @t216)) % 0.44/0.63 (define @t220 () (forall @t218 @t215)) % 0.44/0.63 (define @t221 () (@var "BOUND_VARIABLE_8004" (-> tptp.mu $$unsorted Bool))) % 0.44/0.63 (define @t222 () (@list @t221)) % 0.44/0.63 (define @t223 () (or @t112 @t220)) % 0.44/0.63 (define @t224 () (_ @t221 @t6 @t193)) % 0.44/0.63 (define @t225 () (@list @t221)) % 0.44/0.63 (define @t226 () (forall @t225 (or (not (tptp.mbox (lambda @t196 (forall @t44 (or @t195 @t224))) @t24)) (tptp.positive @t221 @t24)))) % 0.44/0.63 (define @t227 () (or @t136 @t226)) % 0.44/0.63 (define @t228 () (_ @t4 @t6 @t193)) % 0.44/0.63 (define @t229 () (not @t228)) % 0.44/0.63 (define @t230 () (not @t140)) % 0.44/0.63 (define @t231 () (or @t229 @t194)) % 0.44/0.63 (define @t232 () (forall @t44 @t231)) % 0.44/0.63 (define @t233 () (lambda @t196 @t232)) % 0.44/0.63 (define @t234 () (forall @t51 (or (not (tptp.mbox @t233 @t3)) (tptp.positive @t48 @t3)))) % 0.44/0.63 (define @t235 () (or @t230 @t234)) % 0.44/0.63 (define @t236 () (lambda @t10 @t235)) % 0.44/0.63 (define @t237 () (forall @t51 (_ @t236 @t48 @t24))) % 0.44/0.63 (define @t238 () (lambda @t26 @t237)) % 0.44/0.63 (define @t239 () (tptp.mbox @t233 @t24)) % 0.44/0.63 (define @t240 () (not @t148)) % 0.44/0.63 (define @t241 () (lambda @t196 (forall @t44 (or (not (_ @t7 @t193)) (_ @t132 @t193))))) % 0.44/0.63 (define @t242 () (_ (_ tptp.mbox @t233) @t24)) % 0.44/0.63 (define @t243 () (not @t242)) % 0.44/0.63 (define @t244 () (or @t243 @t135)) % 0.44/0.63 (define @t245 () (forall @t51 @t244)) % 0.44/0.63 (define @t246 () (or @t240 @t245)) % 0.44/0.63 (define @t247 () (or @t240 @t244)) % 0.44/0.63 (define @t248 () (or @t240 @t243 @t135)) % 0.44/0.63 (define @t249 () (and @t148 @t242)) % 0.44/0.63 (define @t250 () (=> @t249 @t135)) % 0.44/0.63 (define @t251 () (_ tptp.mbox (lambda @t196 (forall @t44 (or @t229 (_ @t12 @t6 @t193)))))) % 0.44/0.63 (define @t252 () (=> (and @t140 (_ @t251 @t3)) (_ @t13 @t3))) % 0.44/0.63 (define @t253 () (lambda @t16 @t252)) % 0.44/0.63 (define @t254 () (_ @t253 @t48 @t24)) % 0.44/0.63 (define @t255 () (forall @t51 @t254)) % 0.44/0.63 (define @t256 () (lambda @t26 @t255)) % 0.44/0.63 (define @t257 () (and @t148 (_ @t251 @t24))) % 0.44/0.63 (define @t258 () (lambda @t26 (=> @t257 (_ @t13 @t24)))) % 0.44/0.63 (define @t259 () (lambda @t26 @t257)) % 0.44/0.63 (define @t260 () (_ @t259 @t24)) % 0.44/0.63 (define @t261 () (=> @t260 @t35)) % 0.44/0.63 (define @t262 () (lambda @t155 @t261)) % 0.44/0.63 (define @t263 () (_ @t12 @t6 @t24)) % 0.44/0.63 (define @t264 () (_ tptp.mbox (lambda @t26 (forall @t44 (or @t151 @t263))))) % 0.44/0.63 (define @t265 () (lambda @t26 (and @t148 (_ @t264 @t24)))) % 0.44/0.63 (define @t266 () (lambda @t155 (and @t148 @t35))) % 0.44/0.63 (define @t267 () (_ @t14 @t24)) % 0.44/0.63 (define @t268 () (or @t157 @t267)) % 0.44/0.63 (define @t269 () (=> @t43 @t267)) % 0.44/0.63 (define @t270 () (=> @t19 (_ @t14 @t3))) % 0.44/0.63 (define @t271 () (lambda @t8 @t270)) % 0.44/0.63 (define @t272 () (_ @t271 @t6 @t24)) % 0.44/0.63 (define @t273 () (forall @t44 @t272)) % 0.44/0.63 (define @t274 () (lambda @t26 @t273)) % 0.44/0.63 (define @t275 () (lambda @t46 (forall @t44 @t150))) % 0.44/0.63 (define @t276 () (lambda @t26 @t269)) % 0.44/0.63 (define @t277 () (lambda @t155 (=> @t43 @t35))) % 0.44/0.63 (define @t278 () (_ @t39 @t7)) % 0.44/0.63 (define @t279 () (lambda @t8 (_ (_ @t278 @t14) @t3))) % 0.44/0.63 (define @t280 () (_ @t38 @t5)) % 0.44/0.63 (define @t281 () (lambda @t16 (_ (_ (_ @t39 (_ @t280 (_ tptp.mbox (_ @t275 @t279)))) @t13) @t3))) % 0.44/0.63 (define @t282 () (@var "BOUND_VARIABLE_7829" $$unsorted)) % 0.44/0.63 (define @t283 () (@list @t6 @t282)) % 0.44/0.63 (define @t284 () (lambda @t283 (not (_ @t169 @t6 @t282)))) % 0.44/0.63 (define @t285 () (@purify @t284)) % 0.44/0.63 (define @t286 () (_ @t48 @t6 @t282)) % 0.44/0.63 (define @t287 () (not @t286)) % 0.44/0.63 (define @t288 () (lambda @t283 @t287)) % 0.44/0.63 (define @t289 () (tptp.positive @t288 @t24)) % 0.44/0.63 (define @t290 () (= @t112 @t289)) % 0.44/0.63 (define @t291 () (forall @t114 @t290)) % 0.44/0.63 (define @t292 () (forall @t51 @t290)) % 0.44/0.63 (define @t293 () (lambda @t26 @t292)) % 0.44/0.63 (define @t294 () (_ @t293 @t24)) % 0.44/0.63 (define @t295 () (forall @t26 @t294)) % 0.44/0.63 (define @t296 () (_ @t132 @t282)) % 0.44/0.63 (define @t297 () (not @t296)) % 0.44/0.63 (define @t298 () (lambda @t283 @t297)) % 0.44/0.63 (define @t299 () (_ (_ tptp.positive @t298) @t24)) % 0.44/0.63 (define @t300 () (= @t136 @t299)) % 0.44/0.63 (define @t301 () (_ tptp.positive (lambda @t283 (not (_ @t7 @t282))))) % 0.44/0.63 (define @t302 () (= @t230 (_ @t301 @t3))) % 0.44/0.63 (define @t303 () (lambda @t10 @t302)) % 0.44/0.63 (define @t304 () (_ @t303 @t48 @t24)) % 0.44/0.63 (define @t305 () (forall @t51 @t304)) % 0.44/0.63 (define @t306 () (lambda @t26 @t305)) % 0.44/0.63 (define @t307 () (_ @t301 @t24)) % 0.44/0.63 (define @t308 () (not @t19)) % 0.44/0.63 (define @t309 () (lambda @t8 @t308)) % 0.44/0.63 (define @t310 () (_ tptp.positive @t309)) % 0.44/0.63 (define @t311 () (_ @t310 @t24)) % 0.44/0.63 (define @t312 () (= @t311 @t240)) % 0.44/0.63 (define @t313 () (lambda @t26 @t240)) % 0.44/0.63 (define @t314 () (_ @t313 @t24)) % 0.44/0.63 (define @t315 () (lambda @t26 (= @t314 @t311))) % 0.44/0.63 (define @t316 () (_ @t33 @t5)) % 0.44/0.63 (define @t317 () (lambda @t155 (= @t311 @t35))) % 0.44/0.63 (define @t318 () (lambda @t26 @t157)) % 0.44/0.63 (define @t319 () (_ @t33 @t7)) % 0.44/0.63 (define @t320 () (lambda @t8 (_ @t319 @t3))) % 0.44/0.63 (define @t321 () (tptp.positive @t284 @t170)) % 0.44/0.63 (define @t322 () (= @t175 @t321)) % 0.44/0.63 (define @t323 () (tptp.positive @t285 @t170)) % 0.44/0.63 (define @t324 () (= @t175 @t323)) % 0.44/0.63 (define @t325 () (not @t323)) % 0.44/0.63 (define @t326 () (@list false false)) % 0.44/0.63 (define @t327 () (forall @t186 (or @t171 (not (_ @t169 @t181 @t65)) (_ @t285 @t181 @t65)))) % 0.44/0.63 (define @t328 () (not @t327)) % 0.44/0.63 (define @t329 () (or @t175 @t328 @t323)) % 0.44/0.63 (define @t330 () (@quantifiers_skolemize @t327 0)) % 0.44/0.63 (define @t331 () (@quantifiers_skolemize @t327 1)) % 0.44/0.63 (define @t332 () (_ @t169 @t331 @t330)) % 0.44/0.63 (define @t333 () (not @t332)) % 0.44/0.63 (define @t334 () (tptp.rel @t170 @t330)) % 0.44/0.63 (define @t335 () (not @t334)) % 0.44/0.63 (define @t336 () (or @t335 @t333 (_ @t285 @t331 @t330))) % 0.44/0.63 (define @t337 () (@list @t336)) % 0.44/0.63 (define @t338 () (or @t335 @t333)) % 0.44/0.63 (define @t339 () (not @t338)) % 0.44/0.63 (assume @p1 @t1) % 0.44/0.63 (assume @p2 @t2) % 0.44/0.63 (assume @p3 (_ tptp.mvalid (_ tptp.mforall_indset @t11))) % 0.44/0.63 (assume @p4 (_ tptp.mvalid (_ tptp.mforall_indset @t18))) % 0.44/0.63 (assume @p5 @t22) % 0.44/0.63 (assume @p6 true) % 0.44/0.63 (step @p7 (= tptp.meq_ind @t25) :rule refl :args (@t25)) % 0.44/0.63 (step @p8 (= tptp.mtrue @t27) :rule refl :args (@t27)) % 0.44/0.63 (step @p9 (= tptp.mfalse @t28) :rule refl :args (@t28)) % 0.44/0.63 (step @p10 (= tptp.mnot @t33) :rule refl :args (@t33)) % 0.44/0.63 (step @p11 (= tptp.mor @t37) :rule refl :args (@t37)) % 0.44/0.63 (step @p12 (= tptp.mand @t38) :rule refl :args (@t38)) % 0.44/0.63 (step @p13 (= tptp.mimplies @t39) :rule refl :args (@t39)) % 0.44/0.63 (step @p14 (= tptp.mimplied @t40) :rule refl :args (@t40)) % 0.44/0.63 (step @p15 (= tptp.mequiv @t41) :rule refl :args (@t41)) % 0.44/0.63 (step @p16 (= tptp.mxor @t42) :rule refl :args (@t42)) % 0.44/0.63 (step @p17 (= tptp.mforall_ind @t47) :rule refl :args (@t47)) % 0.44/0.63 (step @p18 (= tptp.mforall_indset @t54) :rule refl :args (@t54)) % 0.44/0.63 (step @p19 (= tptp.mforall_prop @t60) :rule refl :args (@t60)) % 0.44/0.63 (step @p20 (= tptp.mexists_ind @t62) :rule refl :args (@t62)) % 0.44/0.63 (step @p21 (= tptp.mexists_indset @t63) :rule refl :args (@t63)) % 0.44/0.63 (step @p22 (= tptp.mexists_prop @t64) :rule refl :args (@t64)) % 0.44/0.63 (step @p23 (= tptp.mbox_generic @t74) :rule refl :args (@t74)) % 0.44/0.63 (step @p24 (= tptp.mdia_generic @t77) :rule refl :args (@t77)) % 0.44/0.63 (step @p25 (= tptp.mvalid @t80) :rule refl :args (@t80)) % 0.44/0.63 (step @p26 (= tptp.minvalid @t81) :rule refl :args (@t81)) % 0.44/0.63 (step @p27 :rule quant-merge-prenex :args ((= (forall @t71 @t89) @t87))) % 0.44/0.63 (step @p28 :rule alpha_equiv :args (@t90 (@list @t82) @t91)) % 0.44/0.63 (step @p29 :rule refl :args (@t84)) % 0.44/0.63 (step @p30 :rule nary_cong :premises (@p29 @p28) :args (@t92)) % 0.44/0.63 (step @p31 :rule quant-miniscope-or :args ((= @t89 @t92))) % 0.44/0.63 (step @p32 :rule trans :premises (@p31 @p30)) % 0.44/0.63 (step @p33 :rule symm :premises (@p32)) % 0.44/0.63 (step @p34 :rule cong :premises (@p33) :args ((forall @t71 (or @t84 @t94)))) % 0.44/0.63 (step @p35 :rule trans :premises (@p34 @p27)) % 0.44/0.63 (step @p36 :rule bool-double-not-elim :args (@t94)) % 0.44/0.63 (step @p37 :rule beta-reduce :args ((= @t102 (not @t94)))) % 0.44/0.63 (step @p38 :rule cong :premises (@p37) :args (@t103)) % 0.44/0.63 (step @p39 :rule trans :premises (@p38 @p36)) % 0.44/0.63 (step @p40 :rule refl :args (@t84)) % 0.44/0.63 (step @p41 :rule nary_cong :premises (@p40 @p39) :args (@t104)) % 0.44/0.63 (step @p42 :rule cong :premises (@p41) :args (@t105)) % 0.44/0.63 (step @p43 :rule trans :premises (@p42 @p35)) % 0.44/0.63 (step @p44 :rule cong :premises (@p43) :args (@t106)) % 0.44/0.63 (step @p45 :rule beta-reduce :args ((= @t110 @t106))) % 0.44/0.63 (step @p46 :rule trans :premises (@p45 @p44)) % 0.44/0.63 (step @p47 :rule refl :args (@t112)) % 0.44/0.63 (step @p48 :rule nary_cong :premises (@p47 @p46) :args (@t113)) % 0.44/0.63 (step @p49 :rule cong :premises (@p48) :args (@t115)) % 0.44/0.63 (step @p50 :rule cong :premises (@p49) :args ((not @t115))) % 0.44/0.63 (step @p51 :rule refl :args (@t24)) % 0.44/0.63 (step @p52 :rule refl :args (@t101)) % 0.44/0.63 (step @p53 :rule beta-reduce :args ((= @t118 @t109))) % 0.44/0.63 (step @p54 :rule refl :args (tptp.mdia)) % 0.44/0.63 (step @p55 :rule cong :premises (@p54 @p53) :args ((= tptp.mdia @t118))) % 0.44/0.63 (step @p56 :rule refl :args (tptp.rel)) % 0.44/0.63 (step @p57 :rule refl :args (@t107)) % 0.44/0.63 (step @p58 :rule refl :args (@t66)) % 0.44/0.63 (step @p59 :rule cong :premises (@p58 @p57) :args ((= @t66 @t107))) % 0.44/0.63 (step @p60 :rule symm :premises (@p59)) % 0.44/0.63 (step @p61 :rule eq_resolve :premises (@p58 @p60)) % 0.44/0.63 (step @p62 :rule cong :premises (@p61) :args (@t119)) % 0.44/0.63 (step @p63 :rule refl :args (@t116)) % 0.44/0.63 (step @p64 :rule refl :args (@t68)) % 0.44/0.63 (step @p65 :rule cong :premises (@p64 @p63) :args ((= @t68 @t116))) % 0.44/0.63 (step @p66 :rule symm :premises (@p65)) % 0.44/0.63 (step @p67 :rule eq_resolve :premises (@p64 @p66)) % 0.44/0.63 (step @p68 :rule cong :premises (@p67) :args (@t69)) % 0.44/0.63 (step @p69 :rule nary_cong :premises (@p68 @p62) :args (@t120)) % 0.44/0.63 (step @p70 :rule cong :premises (@p69) :args ((forall @t71 @t120))) % 0.44/0.63 (step @p71 :rule bool-and-de-morgan :args (@t68 @t66 true)) % 0.44/0.63 (step @p72 :rule cong :premises (@p71) :args (@t121)) % 0.44/0.63 (step @p73 :rule trans :premises (@p72 @p70)) % 0.44/0.63 (step @p74 :rule cong :premises (@p73) :args (@t122)) % 0.44/0.63 (step @p75 :rule exists-elim :args ((= @t76 @t122))) % 0.44/0.63 (step @p76 :rule trans :premises (@p75 @p74)) % 0.44/0.63 (step @p77 :rule cong :premises (@p76) :args (@t77)) % 0.44/0.63 (step @p78 :rule trans :premises (@p24 @p77)) % 0.44/0.63 (step @p79 :rule ho_cong :premises (@p78 @p56)) % 0.44/0.63 (step @p80 :rule cong :premises (@p54 @p79) :args (@t2)) % 0.44/0.63 (step @p81 :rule trans :premises (@p80 @p55)) % 0.44/0.63 (step @p82 :rule eq_resolve :premises (@p2 @p81)) % 0.44/0.63 (step @p83 :rule ho_cong :premises (@p82 @p52 @p51)) % 0.44/0.63 (step @p84 :rule nary_cong :premises (@p47 @p83) :args (@t124)) % 0.44/0.63 (step @p85 :rule cong :premises (@p84) :args (@t125)) % 0.44/0.63 (step @p86 :rule cong :premises (@p85) :args ((not @t125))) % 0.44/0.63 (step @p87 :rule trans :premises (@p86 @p50)) % 0.44/0.63 (step @p88 :rule quant-merge-prenex :args ((= (forall @t26 @t126) @t125))) % 0.44/0.63 (step @p89 :rule beta-reduce :args ((= @t128 @t126))) % 0.44/0.63 (step @p90 :rule cong :premises (@p89) :args (@t129)) % 0.44/0.63 (step @p91 :rule trans :premises (@p90 @p88)) % 0.44/0.63 (step @p92 :rule beta-reduce :args ((= (_ @t131 @t127) @t129))) % 0.44/0.63 (step @p93 :rule trans :premises (@p92 @p91)) % 0.44/0.63 (step @p94 :rule refl :args ((tptp.mdia @t133 @t24))) % 0.44/0.63 (step @p95 :rule refl :args (@t24)) % 0.44/0.63 (step @p96 :rule refl :args (@t96)) % 0.44/0.63 (step @p97 :rule cong :premises (@p96) :args (@t97)) % 0.44/0.63 (step @p98 :rule cong :premises (@p97) :args (@t98)) % 0.44/0.63 (step @p99 :rule cong :premises (@p98) :args (@t99)) % 0.44/0.63 (step @p100 :rule cong :premises (@p99) :args (@t101)) % 0.44/0.63 (step @p101 :rule cong :premises (@p100 @p95) :args (@t123)) % 0.44/0.63 (step @p102 :rule trans :premises (@p101 @p94)) % 0.44/0.63 (step @p103 :rule refl :args (tptp.mdia)) % 0.44/0.63 (step @p104 :rule ho_cong :premises (@p103 @p100)) % 0.44/0.63 (step @p105 :rule ho_cong :premises (@p104 @p95)) % 0.44/0.63 (step @p106 :rule cong :premises (@p105 @p102) :args ((= @t134 @t123))) % 0.44/0.63 (step @p107 :rule symm :premises (@p106)) % 0.44/0.63 (step @p108 :rule refl :args ((_ (_ tptp.mdia @t133) @t24))) % 0.44/0.63 (step @p109 :rule eq_resolve :premises (@p108 @p107)) % 0.44/0.63 (step @p110 :rule refl :args (@t111)) % 0.44/0.63 (step @p111 :rule refl :args (@t135)) % 0.44/0.63 (step @p112 :rule cong :premises (@p111 @p110) :args ((= @t135 @t111))) % 0.44/0.63 (step @p113 :rule symm :premises (@p112)) % 0.44/0.63 (step @p114 :rule eq_resolve :premises (@p111 @p113)) % 0.44/0.63 (step @p115 :rule cong :premises (@p114) :args (@t136)) % 0.44/0.63 (step @p116 :rule nary_cong :premises (@p115 @p109) :args (@t137)) % 0.44/0.63 (step @p117 :rule cong :premises (@p116) :args ((forall @t51 @t137))) % 0.44/0.63 (step @p118 :rule bool-impl-elim :args (@t135 @t134)) % 0.44/0.63 (step @p119 :rule cong :premises (@p118) :args ((forall @t51 @t138))) % 0.44/0.63 (step @p120 :rule trans :premises (@p119 @p117)) % 0.44/0.63 (step @p121 :rule beta-reduce :args ((= @t143 @t138))) % 0.44/0.63 (step @p122 :rule cong :premises (@p121) :args (@t144)) % 0.44/0.63 (step @p123 :rule trans :premises (@p122 @p120)) % 0.44/0.63 (step @p124 :rule cong :premises (@p123) :args (@t145)) % 0.44/0.63 (step @p125 :rule beta-reduce :args ((= (_ @t147 @t142) @t145))) % 0.44/0.63 (step @p126 :rule trans :premises (@p125 @p124)) % 0.44/0.63 (step @p127 :rule beta-reduce :args ((= (_ @t149 @t3) @t141))) % 0.44/0.63 (step @p128 :rule refl :args (@t3)) % 0.44/0.63 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 0.44/0.63 ; trust TRUST_THEORY_REWRITE % 0.44/0.63 (step @p129 :rule trust :premises () :args ((= @t154 @t149))) % 0.44/0.63 (step @p130 :rule beta-reduce :args ((= (_ @t156 @t153) @t154))) % 0.44/0.63 (step @p131 :rule trans :premises (@p130 @p129)) % 0.44/0.63 (step @p132 :rule refl :args (@t150)) % 0.44/0.63 (step @p133 :rule refl :args (@t43)) % 0.44/0.63 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t43 @t150))) % 0.44/0.63 (step @p135 :rule symm :premises (@p134)) % 0.44/0.63 (step @p136 :rule eq_resolve :premises (@p133 @p135)) % 0.44/0.63 (step @p137 :rule cong :premises (@p136) :args (@t157)) % 0.44/0.63 (step @p138 :rule cong :premises (@p137) :args (@t158)) % 0.44/0.63 (step @p139 :rule beta-reduce :args ((= @t159 @t43))) % 0.44/0.63 (step @p140 :rule cong :premises (@p139) :args (@t160)) % 0.44/0.63 (step @p141 :rule cong :premises (@p140) :args (@t161)) % 0.44/0.63 (step @p142 :rule trans :premises (@p141 @p138)) % 0.44/0.63 (step @p143 :rule cong :premises (@p142) :args (@t162)) % 0.44/0.63 (step @p144 :rule cong :premises (@p143) :args (@t163)) % 0.44/0.63 (step @p145 :rule beta-reduce :args ((= @t164 @t163))) % 0.44/0.63 (step @p146 :rule trans :premises (@p145 @p144)) % 0.44/0.63 (step @p147 :rule ho_cong :premises (@p54 @p146)) % 0.44/0.63 (step @p148 :rule beta-reduce :args ((= @t165 @t156))) % 0.44/0.63 (step @p149 :rule ho_cong :premises (@p148 @p147)) % 0.44/0.63 (step @p150 :rule trans :premises (@p149 @p131)) % 0.44/0.63 (step @p151 :rule ho_cong :premises (@p150 @p128)) % 0.44/0.63 (step @p152 :rule trans :premises (@p151 @p127)) % 0.44/0.63 (step @p153 :rule cong :premises (@p152) :args (@t166)) % 0.44/0.63 (step @p154 :rule refl :args (@t147)) % 0.44/0.63 (step @p155 :rule ho_cong :premises (@p154 @p153)) % 0.44/0.63 (step @p156 :rule trans :premises (@p155 @p126)) % 0.44/0.63 (step @p157 :rule refl :args (@t131)) % 0.44/0.63 (step @p158 :rule ho_cong :premises (@p157 @p156)) % 0.44/0.63 (step @p159 :rule trans :premises (@p158 @p93)) % 0.44/0.63 (step @p160 :rule cong :premises (@p159) :args ((not (_ @t131 (_ @t147 @t166))))) % 0.44/0.63 (step @p161 :rule refl :args (@t20)) % 0.44/0.63 (step @p162 :rule cong :premises (@p138) :args (@t167)) % 0.44/0.63 (step @p163 :rule exists-elim :args ((= @t61 @t167))) % 0.44/0.63 (step @p164 :rule trans :premises (@p163 @p162)) % 0.44/0.63 (step @p165 :rule cong :premises (@p164) :args (@t62)) % 0.44/0.63 (step @p166 :rule trans :premises (@p20 @p165)) % 0.44/0.63 (step @p167 :rule ho_cong :premises (@p166 @p161)) % 0.44/0.63 (step @p168 :rule ho_cong :premises (@p54 @p167)) % 0.44/0.63 (step @p169 :rule refl :args (@t5)) % 0.44/0.63 (step @p170 :rule ho_cong :premises (@p13 @p169)) % 0.44/0.63 (step @p171 :rule ho_cong :premises (@p170 @p168)) % 0.44/0.63 (step @p172 :rule ho_cong :premises (@p171 @p128)) % 0.44/0.63 (step @p173 :rule cong :premises (@p172) :args (@t21)) % 0.44/0.63 (step @p174 :rule refl :args (@t146)) % 0.44/0.63 (step @p175 :rule refl :args (@t50)) % 0.44/0.63 (step @p176 :rule cong :premises (@p175 @p174) :args ((= @t50 @t146))) % 0.44/0.63 (step @p177 :rule symm :premises (@p176)) % 0.44/0.63 (step @p178 :rule eq_resolve :premises (@p175 @p177)) % 0.44/0.63 (step @p179 :rule cong :premises (@p178) :args (@t52)) % 0.44/0.63 (step @p180 :rule cong :premises (@p179) :args (@t54)) % 0.44/0.63 (step @p181 :rule trans :premises (@p18 @p180)) % 0.44/0.63 (step @p182 :rule ho_cong :premises (@p181 @p173)) % 0.44/0.63 (step @p183 :rule refl :args (@t130)) % 0.44/0.63 (step @p184 :rule refl :args (@t30)) % 0.44/0.63 (step @p185 :rule cong :premises (@p184 @p183) :args ((= @t30 @t130))) % 0.44/0.63 (step @p186 :rule symm :premises (@p185)) % 0.44/0.63 (step @p187 :rule eq_resolve :premises (@p184 @p186)) % 0.44/0.63 (step @p188 :rule cong :premises (@p187) :args (@t78)) % 0.44/0.63 (step @p189 :rule cong :premises (@p188) :args (@t80)) % 0.44/0.63 (step @p190 :rule trans :premises (@p25 @p189)) % 0.44/0.63 (step @p191 :rule ho_cong :premises (@p190 @p182)) % 0.44/0.63 (step @p192 :rule cong :premises (@p191) :args (@t22)) % 0.44/0.63 (step @p193 :rule trans :premises (@p192 @p160)) % 0.44/0.63 (step @p194 :rule trans :premises (@p193 @p87)) % 0.44/0.63 (step @p195 :rule eq_resolve :premises (@p5 @p194)) % 0.44/0.63 (step @p196 :rule skolemize :premises (@p195)) % 0.44/0.63 (step @p197 :rule bool-double-not-elim :args (@t172)) % 0.44/0.63 (step @p198 :rule refl :args (@t176)) % 0.44/0.63 (step @p199 :rule nary_cong :premises (@p198 @p197) :args ((or @t176 (not @t173)))) % 0.44/0.63 (step @p200 :rule cnf_or_neg :args (@t176 1)) % 0.44/0.63 (step @p201 :rule eq_resolve :premises (@p200 @p199)) % 0.44/0.63 (step @p202 :rule reordering :premises (@p201) :args ((or @t172 @t176))) % 0.44/0.63 (step @p203 :rule chain_m_resolution :premises (@p202 @p196) :args (@t172 @t177 @t178)) % 0.44/0.63 (step @p204 :rule refl :args (@t180)) % 0.44/0.63 (step @p205 :rule aci_norm :args ((= @t185 (or @t84 @t183 @t182)))) % 0.44/0.63 (step @p206 :rule cong :premises (@p205) :args (@t187)) % 0.44/0.63 (step @p207 :rule quant-merge-prenex :args ((= (forall @t71 @t189) @t187))) % 0.44/0.63 (step @p208 :rule alpha_equiv :args (@t190 (@list @t181) @t91)) % 0.44/0.63 (step @p209 :rule nary_cong :premises (@p29 @p208) :args (@t191)) % 0.44/0.63 (step @p210 :rule quant-miniscope-or :args ((= @t189 @t191))) % 0.44/0.63 (step @p211 :rule trans :premises (@p210 @p209)) % 0.44/0.63 (step @p212 :rule symm :premises (@p211)) % 0.44/0.63 (step @p213 :rule cong :premises (@p212) :args ((forall @t71 (or @t84 @t192)))) % 0.44/0.63 (step @p214 :rule trans :premises (@p213 @p207)) % 0.44/0.63 (step @p215 :rule trans :premises (@p214 @p206)) % 0.44/0.63 (step @p216 :rule beta-reduce :args ((= @t198 @t192))) % 0.44/0.63 (step @p217 :rule nary_cong :premises (@p40 @p216) :args (@t199)) % 0.44/0.63 (step @p218 :rule cong :premises (@p217) :args (@t200)) % 0.44/0.63 (step @p219 :rule trans :premises (@p218 @p215)) % 0.44/0.63 (step @p220 :rule beta-reduce :args ((= @t202 @t200))) % 0.44/0.63 (step @p221 :rule trans :premises (@p220 @p219)) % 0.44/0.63 (step @p222 :rule cong :premises (@p221) :args (@t203)) % 0.44/0.63 (step @p223 :rule nary_cong :premises (@p47 @p222 @p204) :args (@t204)) % 0.44/0.63 (step @p224 :rule cong :premises (@p223) :args ((forall @t205 @t204))) % 0.44/0.63 (step @p225 :rule refl :args (@t197)) % 0.44/0.63 (step @p226 :rule beta-reduce :args ((= @t206 @t201))) % 0.44/0.63 (step @p227 :rule refl :args (tptp.mbox)) % 0.44/0.63 (step @p228 :rule cong :premises (@p227 @p226) :args ((= tptp.mbox @t206))) % 0.44/0.63 (step @p229 :rule nary_cong :premises (@p68 @p61) :args (@t70)) % 0.44/0.63 (step @p230 :rule cong :premises (@p229) :args (@t72)) % 0.44/0.63 (step @p231 :rule cong :premises (@p230) :args (@t74)) % 0.44/0.63 (step @p232 :rule trans :premises (@p23 @p231)) % 0.44/0.63 (step @p233 :rule ho_cong :premises (@p232 @p56)) % 0.44/0.63 (step @p234 :rule cong :premises (@p227 @p233) :args (@t1)) % 0.44/0.63 (step @p235 :rule trans :premises (@p234 @p228)) % 0.44/0.63 (step @p236 :rule eq_resolve :premises (@p1 @p235)) % 0.44/0.63 (step @p237 :rule ho_cong :premises (@p236 @p225 @p51)) % 0.44/0.63 (step @p238 :rule cong :premises (@p237) :args (@t207)) % 0.44/0.63 (step @p239 :rule nary_cong :premises (@p47 @p238 @p204) :args (@t208)) % 0.44/0.63 (step @p240 :rule cong :premises (@p239) :args (@t209)) % 0.44/0.63 (step @p241 :rule trans :premises (@p240 @p224)) % 0.44/0.63 (step @p242 :rule quant-merge-prenex :args ((= (forall @t26 @t211) @t209))) % 0.44/0.63 (step @p243 :rule beta-reduce :args ((= @t213 @t211))) % 0.44/0.63 (step @p244 :rule cong :premises (@p243) :args (@t214)) % 0.44/0.63 (step @p245 :rule trans :premises (@p244 @p242)) % 0.44/0.63 (step @p246 :rule beta-reduce :args ((= (_ @t131 @t212) @t214))) % 0.44/0.63 (step @p247 :rule trans :premises (@p246 @p245)) % 0.44/0.63 (step @p248 :rule aci_norm :args ((= @t216 @t208))) % 0.44/0.63 (step @p249 :rule cong :premises (@p248) :args (@t217)) % 0.44/0.63 (step @p250 :rule quant-merge-prenex :args ((= (forall @t51 @t219) @t217))) % 0.44/0.63 (step @p251 :rule alpha_equiv :args (@t220 (@list @t179) @t222)) % 0.44/0.63 (step @p252 :rule refl :args (@t112)) % 0.44/0.63 (step @p253 :rule nary_cong :premises (@p252 @p251) :args (@t223)) % 0.44/0.63 (step @p254 :rule quant-miniscope-or :args ((= @t219 @t223))) % 0.44/0.63 (step @p255 :rule trans :premises (@p254 @p253)) % 0.44/0.63 (step @p256 :rule symm :premises (@p255)) % 0.44/0.63 (step @p257 :rule cong :premises (@p256) :args ((forall @t51 (or @t112 @t226)))) % 0.44/0.63 (step @p258 :rule trans :premises (@p257 @p250)) % 0.44/0.63 (step @p259 :rule trans :premises (@p258 @p249)) % 0.44/0.63 (step @p260 :rule refl :args (@t226)) % 0.44/0.63 (step @p261 :rule nary_cong :premises (@p115 @p260) :args (@t227)) % 0.44/0.63 (step @p262 :rule cong :premises (@p261) :args ((forall @t51 @t227))) % 0.44/0.63 (step @p263 :rule trans :premises (@p262 @p259)) % 0.44/0.63 (step @p264 :rule beta-reduce :args ((= (_ (lambda @t10 (or @t230 (forall @t225 (or (not (tptp.mbox (lambda @t196 (forall @t44 (or @t229 @t224))) @t3)) (tptp.positive @t221 @t3))))) @t48 @t24) @t227))) % 0.44/0.63 (step @p265 :rule refl :args (@t48)) % 0.44/0.63 (step @p266 :rule alpha_equiv :args (@t234 (@list @t48) @t222)) % 0.44/0.63 (step @p267 :rule refl :args (@t230)) % 0.44/0.63 (step @p268 :rule nary_cong :premises (@p267 @p266) :args (@t235)) % 0.44/0.63 (step @p269 :rule cong :premises (@p268) :args (@t236)) % 0.44/0.63 (step @p270 :rule ho_cong :premises (@p269 @p265 @p95)) % 0.44/0.63 (step @p271 :rule trans :premises (@p270 @p264)) % 0.44/0.63 (step @p272 :rule cong :premises (@p271) :args (@t237)) % 0.44/0.63 (step @p273 :rule trans :premises (@p272 @p263)) % 0.44/0.63 (step @p274 :rule cong :premises (@p273) :args (@t238)) % 0.44/0.63 (step @p275 :rule beta-reduce :args ((= (_ @t147 @t236) @t238))) % 0.44/0.63 (step @p276 :rule trans :premises (@p275 @p274)) % 0.44/0.63 (step @p277 :rule beta-reduce :args ((= (_ (lambda @t26 (or @t240 (forall @t51 (or (not @t239) @t111)))) @t3) @t235))) % 0.44/0.63 (step @p278 :rule refl :args ((tptp.mbox @t241 @t24))) % 0.44/0.63 (step @p279 :rule refl :args (@t194)) % 0.44/0.63 (step @p280 :rule refl :args (@t228)) % 0.44/0.63 (step @p281 :rule cong :premises (@p280) :args (@t229)) % 0.44/0.63 (step @p282 :rule nary_cong :premises (@p281 @p279) :args (@t231)) % 0.44/0.63 (step @p283 :rule cong :premises (@p282) :args (@t232)) % 0.44/0.63 (step @p284 :rule cong :premises (@p283) :args (@t233)) % 0.44/0.63 (step @p285 :rule cong :premises (@p284 @p95) :args (@t239)) % 0.44/0.63 (step @p286 :rule trans :premises (@p285 @p278)) % 0.44/0.63 (step @p287 :rule refl :args (tptp.mbox)) % 0.44/0.63 (step @p288 :rule ho_cong :premises (@p287 @p284)) % 0.44/0.63 (step @p289 :rule ho_cong :premises (@p288 @p95)) % 0.44/0.63 (step @p290 :rule cong :premises (@p289 @p286) :args ((= @t242 @t239))) % 0.44/0.63 (step @p291 :rule symm :premises (@p290)) % 0.44/0.63 (step @p292 :rule refl :args ((_ (_ tptp.mbox @t241) @t24))) % 0.44/0.63 (step @p293 :rule eq_resolve :premises (@p292 @p291)) % 0.44/0.63 (step @p294 :rule cong :premises (@p293) :args (@t243)) % 0.44/0.63 (step @p295 :rule nary_cong :premises (@p294 @p114) :args (@t244)) % 0.44/0.63 (step @p296 :rule cong :premises (@p295) :args (@t245)) % 0.44/0.63 (step @p297 :rule refl :args (@t240)) % 0.44/0.63 (step @p298 :rule nary_cong :premises (@p297 @p296) :args (@t246)) % 0.44/0.63 (step @p299 :rule quant-miniscope-or :args ((= (forall @t51 @t247) @t246))) % 0.44/0.63 (step @p300 :rule aci_norm :args ((= @t248 @t247))) % 0.44/0.63 (step @p301 :rule cong :premises (@p300) :args ((forall @t51 @t248))) % 0.44/0.63 (step @p302 :rule trans :premises (@p301 @p299)) % 0.44/0.63 (step @p303 :rule trans :premises (@p302 @p298)) % 0.44/0.63 (step @p304 :rule aci_norm :args ((= (or (or @t240 @t243) @t135) @t248))) % 0.44/0.63 (step @p305 :rule bool-and-de-morgan :args (@t148 @t242 true)) % 0.44/0.63 (step @p306 :rule nary_cong :premises (@p305 @p111) :args ((or (not @t249) @t135))) % 0.44/0.63 (step @p307 :rule trans :premises (@p306 @p304)) % 0.44/0.63 (step @p308 :rule bool-impl-elim :args (@t249 @t135)) % 0.44/0.63 (step @p309 :rule trans :premises (@p308 @p307)) % 0.44/0.63 (step @p310 :rule cong :premises (@p309) :args ((forall @t51 @t250))) % 0.44/0.63 (step @p311 :rule trans :premises (@p310 @p303)) % 0.44/0.63 (step @p312 :rule beta-reduce :args ((= @t254 @t250))) % 0.44/0.63 (step @p313 :rule cong :premises (@p312) :args (@t255)) % 0.44/0.63 (step @p314 :rule trans :premises (@p313 @p311)) % 0.44/0.63 (step @p315 :rule cong :premises (@p314) :args (@t256)) % 0.44/0.63 (step @p316 :rule beta-reduce :args ((= (_ @t147 @t253) @t256))) % 0.44/0.63 (step @p317 :rule trans :premises (@p316 @p315)) % 0.44/0.63 (step @p318 :rule beta-reduce :args ((= (_ @t258 @t3) @t252))) % 0.44/0.63 (step @p319 :rule beta-reduce :args ((= (_ (lambda @t155 (=> @t257 @t35)) @t13) @t258))) % 0.44/0.63 (step @p320 :rule refl :args (@t13)) % 0.44/0.63 (step @p321 :rule refl :args (@t35)) % 0.44/0.63 (step @p322 :rule beta-reduce :args ((= @t260 @t257))) % 0.44/0.63 (step @p323 :rule cong :premises (@p322 @p321) :args (@t261)) % 0.44/0.63 (step @p324 :rule cong :premises (@p323) :args (@t262)) % 0.44/0.63 (step @p325 :rule beta-reduce :args ((= (_ @t39 @t259) @t262))) % 0.44/0.63 (step @p326 :rule trans :premises (@p325 @p324)) % 0.44/0.63 ; trust TRUST_THEORY_REWRITE % 0.44/0.63 (step @p327 :rule trust :premises () :args ((= @t265 @t259))) % 0.44/0.63 (step @p328 :rule beta-reduce :args ((= (_ @t266 @t264) @t265))) % 0.44/0.63 (step @p329 :rule trans :premises (@p328 @p327)) % 0.44/0.63 (step @p330 :rule refl :args (@t263)) % 0.44/0.63 (step @p331 :rule refl :args (@t267)) % 0.44/0.63 (step @p332 :rule cong :premises (@p331 @p330) :args ((= @t267 @t263))) % 0.44/0.63 (step @p333 :rule symm :premises (@p332)) % 0.44/0.63 (step @p334 :rule eq_resolve :premises (@p331 @p333)) % 0.44/0.63 (step @p335 :rule nary_cong :premises (@p137 @p334) :args (@t268)) % 0.44/0.63 (step @p336 :rule cong :premises (@p335) :args ((forall @t44 @t268))) % 0.44/0.63 (step @p337 :rule bool-impl-elim :args (@t43 @t267)) % 0.44/0.63 (step @p338 :rule cong :premises (@p337) :args ((forall @t44 @t269))) % 0.44/0.63 (step @p339 :rule trans :premises (@p338 @p336)) % 0.44/0.63 (step @p340 :rule beta-reduce :args ((= @t272 @t269))) % 0.44/0.63 (step @p341 :rule cong :premises (@p340) :args (@t273)) % 0.44/0.63 (step @p342 :rule trans :premises (@p341 @p339)) % 0.44/0.63 (step @p343 :rule cong :premises (@p342) :args (@t274)) % 0.44/0.63 (step @p344 :rule beta-reduce :args ((= (_ @t275 @t271) @t274))) % 0.44/0.63 (step @p345 :rule trans :premises (@p344 @p343)) % 0.44/0.63 (step @p346 :rule beta-reduce :args ((= (_ @t276 @t3) @t270))) % 0.44/0.63 (step @p347 :rule beta-reduce :args ((= (_ @t277 @t14) @t276))) % 0.44/0.63 (step @p348 :rule refl :args (@t14)) % 0.44/0.63 (step @p349 :rule beta-reduce :args ((= @t278 @t277))) % 0.44/0.63 (step @p350 :rule ho_cong :premises (@p349 @p348)) % 0.44/0.63 (step @p351 :rule trans :premises (@p350 @p347)) % 0.44/0.63 (step @p352 :rule ho_cong :premises (@p351 @p128)) % 0.44/0.63 (step @p353 :rule trans :premises (@p352 @p346)) % 0.44/0.63 (step @p354 :rule cong :premises (@p353) :args (@t279)) % 0.44/0.63 (step @p355 :rule refl :args (@t275)) % 0.44/0.63 (step @p356 :rule ho_cong :premises (@p355 @p354)) % 0.44/0.63 (step @p357 :rule trans :premises (@p356 @p345)) % 0.44/0.63 (step @p358 :rule ho_cong :premises (@p227 @p357)) % 0.44/0.63 (step @p359 :rule beta-reduce :args ((= @t280 @t266))) % 0.44/0.63 (step @p360 :rule ho_cong :premises (@p359 @p358)) % 0.44/0.63 (step @p361 :rule trans :premises (@p360 @p329)) % 0.44/0.63 (step @p362 :rule refl :args (@t39)) % 0.44/0.63 (step @p363 :rule ho_cong :premises (@p362 @p361)) % 0.44/0.63 (step @p364 :rule trans :premises (@p363 @p326)) % 0.44/0.63 (step @p365 :rule ho_cong :premises (@p364 @p320)) % 0.44/0.63 (step @p366 :rule trans :premises (@p365 @p319)) % 0.44/0.63 (step @p367 :rule ho_cong :premises (@p366 @p128)) % 0.44/0.63 (step @p368 :rule trans :premises (@p367 @p318)) % 0.44/0.63 (step @p369 :rule cong :premises (@p368) :args (@t281)) % 0.44/0.63 (step @p370 :rule ho_cong :premises (@p154 @p369)) % 0.44/0.63 (step @p371 :rule trans :premises (@p370 @p317)) % 0.44/0.63 (step @p372 :rule ho_cong :premises (@p371 @p128)) % 0.44/0.63 (step @p373 :rule trans :premises (@p372 @p277)) % 0.44/0.63 (step @p374 :rule cong :premises (@p373) :args ((lambda @t10 (_ (_ @t147 @t281) @t3)))) % 0.44/0.63 (step @p375 :rule ho_cong :premises (@p154 @p374)) % 0.44/0.63 (step @p376 :rule trans :premises (@p375 @p276)) % 0.44/0.63 (step @p377 :rule ho_cong :premises (@p157 @p376)) % 0.44/0.63 (step @p378 :rule trans :premises (@p377 @p247)) % 0.44/0.63 (step @p379 :rule refl :args (@t7)) % 0.44/0.63 (step @p380 :rule ho_cong :premises (@p13 @p379)) % 0.44/0.63 (step @p381 :rule ho_cong :premises (@p380 @p348)) % 0.44/0.63 (step @p382 :rule ho_cong :premises (@p381 @p128)) % 0.44/0.63 (step @p383 :rule cong :premises (@p382) :args (@t15)) % 0.44/0.63 (step @p384 :rule cong :premises (@p136) :args (@t45)) % 0.44/0.63 (step @p385 :rule cong :premises (@p384) :args (@t47)) % 0.44/0.63 (step @p386 :rule trans :premises (@p17 @p385)) % 0.44/0.63 (step @p387 :rule ho_cong :premises (@p386 @p383)) % 0.44/0.63 (step @p388 :rule ho_cong :premises (@p227 @p387)) % 0.44/0.63 (step @p389 :rule ho_cong :premises (@p12 @p169)) % 0.44/0.63 (step @p390 :rule ho_cong :premises (@p389 @p388)) % 0.44/0.63 (step @p391 :rule ho_cong :premises (@p13 @p390)) % 0.44/0.63 (step @p392 :rule ho_cong :premises (@p391 @p320)) % 0.44/0.63 (step @p393 :rule ho_cong :premises (@p392 @p128)) % 0.44/0.63 (step @p394 :rule cong :premises (@p393) :args (@t17)) % 0.44/0.63 (step @p395 :rule ho_cong :premises (@p181 @p394)) % 0.44/0.63 (step @p396 :rule ho_cong :premises (@p395 @p128)) % 0.44/0.63 (step @p397 :rule cong :premises (@p396) :args (@t18)) % 0.44/0.63 (step @p398 :rule ho_cong :premises (@p181 @p397)) % 0.44/0.63 (step @p399 :rule ho_cong :premises (@p190 @p398)) % 0.44/0.63 (step @p400 :rule trans :premises (@p399 @p378)) % 0.44/0.63 (step @p401 :rule trans :premises (@p400 @p241)) % 0.44/0.63 (step @p402 :rule eq_resolve :premises (@p4 @p401)) % 0.44/0.63 (step @p403 :rule instantiate :premises (@p402) :args ((@list @t170 @t169 @t285))) % 0.44/0.63 (step @p404 :rule quant-merge-prenex :args ((= (forall @t26 @t292) @t291))) % 0.44/0.63 (step @p405 :rule beta-reduce :args ((= @t294 @t292))) % 0.44/0.63 (step @p406 :rule cong :premises (@p405) :args (@t295)) % 0.44/0.63 (step @p407 :rule trans :premises (@p406 @p404)) % 0.44/0.63 (step @p408 :rule beta-reduce :args ((= (_ @t131 @t293) @t295))) % 0.44/0.63 (step @p409 :rule trans :premises (@p408 @p407)) % 0.44/0.63 (step @p410 :rule refl :args ((tptp.positive @t298 @t24))) % 0.44/0.63 (step @p411 :rule refl :args (@t286)) % 0.44/0.63 (step @p412 :rule cong :premises (@p411) :args (@t287)) % 0.44/0.63 (step @p413 :rule cong :premises (@p412) :args (@t288)) % 0.44/0.63 (step @p414 :rule cong :premises (@p413 @p95) :args (@t289)) % 0.44/0.63 (step @p415 :rule trans :premises (@p414 @p410)) % 0.44/0.63 (step @p416 :rule refl :args (tptp.positive)) % 0.44/0.63 (step @p417 :rule ho_cong :premises (@p416 @p413)) % 0.44/0.63 (step @p418 :rule ho_cong :premises (@p417 @p95)) % 0.44/0.63 (step @p419 :rule cong :premises (@p418 @p415) :args ((= (_ (_ tptp.positive @t288) @t24) @t289))) % 0.44/0.63 (step @p420 :rule symm :premises (@p419)) % 0.44/0.63 (step @p421 :rule refl :args (@t299)) % 0.44/0.63 (step @p422 :rule eq_resolve :premises (@p421 @p420)) % 0.44/0.63 (step @p423 :rule refl :args (@t296)) % 0.44/0.63 (step @p424 :rule cong :premises (@p423 @p411) :args ((= @t296 @t286))) % 0.44/0.63 (step @p425 :rule symm :premises (@p424)) % 0.44/0.63 (step @p426 :rule eq_resolve :premises (@p423 @p425)) % 0.44/0.63 (step @p427 :rule cong :premises (@p426) :args (@t297)) % 0.44/0.63 (step @p428 :rule cong :premises (@p427) :args (@t298)) % 0.44/0.63 (step @p429 :rule ho_cong :premises (@p416 @p428)) % 0.44/0.63 (step @p430 :rule ho_cong :premises (@p429 @p95)) % 0.44/0.63 (step @p431 :rule trans :premises (@p430 @p422)) % 0.44/0.63 (step @p432 :rule cong :premises (@p115 @p431) :args (@t300)) % 0.44/0.63 (step @p433 :rule cong :premises (@p432) :args ((forall @t51 @t300))) % 0.44/0.63 (step @p434 :rule beta-reduce :args ((= @t304 @t300))) % 0.44/0.63 (step @p435 :rule cong :premises (@p434) :args (@t305)) % 0.44/0.63 (step @p436 :rule trans :premises (@p435 @p433)) % 0.44/0.63 (step @p437 :rule cong :premises (@p436) :args (@t306)) % 0.44/0.63 (step @p438 :rule beta-reduce :args ((= (_ @t147 @t303) @t306))) % 0.44/0.63 (step @p439 :rule trans :premises (@p438 @p437)) % 0.44/0.63 (step @p440 :rule beta-reduce :args ((= (_ (lambda @t26 (= @t240 @t307)) @t3) @t302))) % 0.44/0.63 (step @p441 :rule eq-symm :args (@t307 @t240)) % 0.44/0.63 (step @p442 :rule cong :premises (@p441) :args ((lambda @t26 (= @t307 @t240)))) % 0.44/0.63 (step @p443 :rule ho_cong :premises (@p442 @p128)) % 0.44/0.63 (step @p444 :rule trans :premises (@p443 @p440)) % 0.44/0.63 (step @p445 :rule refl :args (@t3)) % 0.44/0.63 (step @p446 :rule refl :args (@t240)) % 0.44/0.63 (step @p447 :rule alpha_equiv :args (@t309 (@list @t3) (@list @t282))) % 0.44/0.63 (step @p448 :rule ho_cong :premises (@p416 @p447)) % 0.44/0.63 (step @p449 :rule ho_cong :premises (@p448 @p95)) % 0.44/0.63 (step @p450 :rule cong :premises (@p449 @p446) :args (@t312)) % 0.44/0.63 (step @p451 :rule cong :premises (@p450) :args ((lambda @t26 @t312))) % 0.44/0.63 (step @p452 :rule ho_cong :premises (@p451 @p445)) % 0.44/0.63 (step @p453 :rule trans :premises (@p452 @p444)) % 0.44/0.63 (step @p454 :rule beta-reduce :args ((= @t314 @t240))) % 0.44/0.63 (step @p455 :rule refl :args (@t311)) % 0.44/0.63 (step @p456 :rule cong :premises (@p455 @p454) :args ((= @t311 @t314))) % 0.44/0.63 (step @p457 :rule eq-symm :args (@t314 @t311)) % 0.44/0.63 (step @p458 :rule trans :premises (@p457 @p456)) % 0.44/0.63 (step @p459 :rule cong :premises (@p458) :args (@t315)) % 0.44/0.63 (step @p460 :rule beta-reduce :args ((= (_ (lambda @t155 (= @t35 @t311)) @t313) @t315))) % 0.44/0.63 (step @p461 :rule trans :premises (@p460 @p459)) % 0.44/0.63 (step @p462 :rule beta-reduce :args ((= @t316 @t313))) % 0.44/0.63 (step @p463 :rule eq-symm :args (@t311 @t35)) % 0.44/0.63 (step @p464 :rule cong :premises (@p463) :args (@t317)) % 0.44/0.63 (step @p465 :rule beta-reduce :args ((= (_ @t41 @t310) @t317))) % 0.44/0.63 (step @p466 :rule trans :premises (@p465 @p464)) % 0.44/0.63 (step @p467 :rule beta-reduce :args ((= (_ @t318 @t3) @t308))) % 0.44/0.63 (step @p468 :rule beta-reduce :args ((= @t319 @t318))) % 0.44/0.63 (step @p469 :rule ho_cong :premises (@p468 @p128)) % 0.44/0.63 (step @p470 :rule trans :premises (@p469 @p467)) % 0.44/0.63 (step @p471 :rule cong :premises (@p470) :args (@t320)) % 0.44/0.63 (step @p472 :rule refl :args (tptp.positive)) % 0.44/0.63 (step @p473 :rule ho_cong :premises (@p472 @p471)) % 0.44/0.63 (step @p474 :rule refl :args (@t41)) % 0.44/0.63 (step @p475 :rule ho_cong :premises (@p474 @p473)) % 0.44/0.63 (step @p476 :rule trans :premises (@p475 @p466)) % 0.44/0.63 (step @p477 :rule ho_cong :premises (@p476 @p462)) % 0.44/0.63 (step @p478 :rule trans :premises (@p477 @p461)) % 0.44/0.63 (step @p479 :rule ho_cong :premises (@p478 @p128)) % 0.44/0.63 (step @p480 :rule trans :premises (@p479 @p453)) % 0.44/0.63 (step @p481 :rule cong :premises (@p480) :args ((lambda @t10 (_ (_ (_ @t41 (_ tptp.positive @t320)) @t316) @t3)))) % 0.44/0.63 (step @p482 :rule ho_cong :premises (@p154 @p481)) % 0.44/0.63 (step @p483 :rule trans :premises (@p482 @p439)) % 0.44/0.63 (step @p484 :rule ho_cong :premises (@p157 @p483)) % 0.44/0.63 (step @p485 :rule trans :premises (@p484 @p409)) % 0.44/0.63 (step @p486 :rule ho_cong :premises (@p10 @p169)) % 0.44/0.63 (step @p487 :rule ho_cong :premises (@p10 @p379)) % 0.44/0.63 (step @p488 :rule ho_cong :premises (@p487 @p128)) % 0.44/0.63 (step @p489 :rule cong :premises (@p488) :args (@t9)) % 0.44/0.63 (step @p490 :rule ho_cong :premises (@p472 @p489)) % 0.44/0.63 (step @p491 :rule ho_cong :premises (@p15 @p490)) % 0.44/0.63 (step @p492 :rule ho_cong :premises (@p491 @p486)) % 0.44/0.63 (step @p493 :rule ho_cong :premises (@p492 @p128)) % 0.44/0.63 (step @p494 :rule cong :premises (@p493) :args (@t11)) % 0.44/0.63 (step @p495 :rule ho_cong :premises (@p181 @p494)) % 0.44/0.63 (step @p496 :rule ho_cong :premises (@p190 @p495)) % 0.44/0.63 (step @p497 :rule trans :premises (@p496 @p485)) % 0.44/0.63 (step @p498 :rule eq_resolve :premises (@p3 @p497)) % 0.44/0.63 (step @p499 :rule refl :args (@t170)) % 0.44/0.63 (step @p500 :rule eq-refl :args (@t284)) % 0.44/0.63 (step @p501 :rule skolem_intro :args (@t285)) % 0.44/0.63 (step @p502 :rule refl :args (@t284)) % 0.44/0.63 (step @p503 :rule cong :premises (@p502 @p501) :args ((= @t284 @t285))) % 0.44/0.63 (step @p504 :rule trans :premises (@p503 @p500)) % 0.44/0.63 (step @p505 :rule true_elim :premises (@p504)) % 0.44/0.63 (step @p506 :rule cong :premises (@p505 @p499) :args (@t321)) % 0.44/0.63 (step @p507 :rule refl :args (@t175)) % 0.44/0.63 (step @p508 :rule cong :premises (@p507 @p506) :args (@t322)) % 0.44/0.63 (step @p509 :rule refl :args (@t291)) % 0.44/0.63 (step @p510 :rule cong :premises (@p509 @p508) :args ((=> @t291 @t322))) % 0.44/0.63 (assume-push @p553 @t291) % 0.44/0.63 (step @p512 :rule instantiate :premises (@p498) :args ((@list @t170 @t169))) % 0.44/0.63 (step-pop @p554 :rule scope :premises (@p512)) % 0.44/0.63 (step @p513 :rule process_scope :premises (@p554) :args (@t322)) % 0.44/0.63 (step @p515 :rule eq_resolve :premises (@p513 @p510)) % 0.44/0.63 (step @p516 :rule implies_elim :premises (@p515)) % 0.44/0.63 (step @p517 :rule chain_m_resolution :premises (@p516 @p498) :args (@t324 (@list false) (@list @t291))) % 0.44/0.63 (step @p518 :rule bool-double-not-elim :args (@t174)) % 0.44/0.63 (step @p519 :rule nary_cong :premises (@p198 @p518) :args ((or @t176 (not @t175)))) % 0.44/0.63 (step @p520 :rule cnf_or_neg :args (@t176 0)) % 0.44/0.63 (step @p521 :rule eq_resolve :premises (@p520 @p519)) % 0.44/0.63 (step @p522 :rule reordering :premises (@p521) :args ((or @t174 @t176))) % 0.44/0.63 (step @p523 :rule chain_m_resolution :premises (@p522 @p196) :args (@t174 @t177 @t178)) % 0.44/0.63 (step @p524 :rule cnf_equiv_pos2 :args (@t324)) % 0.44/0.63 (step @p525 :rule reordering :premises (@p524) :args ((or @t175 @t325 (not @t324)))) % 0.44/0.63 (step @p526 :rule chain_m_resolution :premises (@p525 @p523 @p517) :args (@t325 @t326 (@list @t174 @t324))) % 0.44/0.63 (step @p527 :rule cnf_or_pos :args (@t329)) % 0.44/0.63 (step @p528 :rule reordering :premises (@p527) :args ((or @t175 @t323 @t328 (not @t329)))) % 0.44/0.63 (step @p529 :rule chain_m_resolution :premises (@p528 @p523 @p526 @p403) :args (@t328 (@list false true false) (@list @t174 @t323 @t329))) % 0.44/0.63 (step @p530 :rule skolemize :premises (@p529)) % 0.44/0.63 (step @p531 :rule bool-double-not-elim :args (@t332)) % 0.44/0.63 (step @p532 :rule refl :args (@t336)) % 0.44/0.63 (step @p533 :rule nary_cong :premises (@p532 @p531) :args ((or @t336 (not @t333)))) % 0.44/0.63 (step @p534 :rule cnf_or_neg :args (@t336 1)) % 0.44/0.63 (step @p535 :rule eq_resolve :premises (@p534 @p533)) % 0.44/0.63 (step @p536 :rule reordering :premises (@p535) :args ((or @t332 @t336))) % 0.44/0.63 (step @p537 :rule chain_m_resolution :premises (@p536 @p530) :args (@t332 @t177 @t337)) % 0.44/0.63 (step @p538 :rule bool-double-not-elim :args (@t334)) % 0.44/0.63 (step @p539 :rule nary_cong :premises (@p532 @p538) :args ((or @t336 (not @t335)))) % 0.44/0.63 (step @p540 :rule cnf_or_neg :args (@t336 0)) % 0.44/0.63 (step @p541 :rule eq_resolve :premises (@p540 @p539)) % 0.44/0.63 (step @p542 :rule reordering :premises (@p541) :args ((or @t334 @t336))) % 0.44/0.63 (step @p543 :rule chain_m_resolution :premises (@p542 @p530) :args (@t334 @t177 @t337)) % 0.44/0.63 (step @p544 :rule cnf_or_pos :args (@t338)) % 0.44/0.63 (step @p545 :rule reordering :premises (@p544) :args ((or @t335 @t333 @t339))) % 0.44/0.63 (step @p546 :rule chain_m_resolution :premises (@p545 @p543 @p537) :args (@t339 @t326 (@list @t334 @t332))) % 0.44/0.63 (assume-push @p555 @t172) % 0.44/0.63 (step @p548 :rule instantiate :premises (@p203) :args ((@list @t330 @t331))) % 0.44/0.63 (step-pop @p556 :rule scope :premises (@p548)) % 0.44/0.63 (step @p549 :rule process_scope :premises (@p556) :args (@t338)) % 0.44/0.63 (step @p551 :rule implies_elim :premises (@p549)) % 0.44/0.63 (step @p552 false :rule chain_m_resolution :premises (@p551 @p546 @p203) :args (false (@list true false) (@list @t338 @t172))) % 0.44/0.63 ) % 0.44/0.63 % SZS output end Proof % 0.44/0.63 % cvc5 exiting %------------------------------------------------------------------------------