%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PHI002^1 : TPTP v9.2.1. Released v6.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n011.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 0.46s 0.63s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PHI002^1 : TPTP v9.2.1. Released v6.1.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n011.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 12:50:50 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.49 %----Proving TH0 % 0.46/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.46/0.63 % SZS status Theorem % 0.46/0.63 % SZS output start Proof % 0.46/0.63 ( % 0.46/0.63 (declare-sort tptp.mu 0) % 0.46/0.63 (declare-sort $$unsorted 0) % 0.46/0.63 (declare-const tptp.positive (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)) % 0.46/0.63 (declare-const tptp.mbox (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.46/0.63 (declare-const tptp.mdia (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.46/0.63 (declare-const tptp.rel (-> $$unsorted $$unsorted Bool)) % 0.46/0.63 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.46/0.63 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.46/0.63 (define tptp.mfalse () (lambda (@list (@var "W" $$unsorted)) false)) % 0.46/0.63 (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)))))) % 0.46/0.63 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.46/0.63 (define tptp.mand () (let ((_let_1 (@var "W" $$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))))))) % 0.46/0.63 (define tptp.mimplies () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.46/0.63 (define tptp.mimplied () (let ((_let_1 (@var "W" $$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))))))) % 0.46/0.63 (define tptp.mequiv () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.46/0.63 (define tptp.mxor () (let ((_let_1 (@var "W" $$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))))))))) % 0.46/0.63 (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))))))) % 0.46/0.63 (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))))))) % 0.46/0.63 (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))))))) % 0.46/0.63 (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))))))) % 0.46/0.63 (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))))))) % 0.46/0.63 (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))))))) % 0.46/0.63 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.46/0.63 (define tptp.mdia_generic () (let ((_let_1 (@var "V" $$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))))))))) % 0.46/0.63 (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)))))) % 0.46/0.63 (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))))))) % 0.46/0.63 (define tptp.god () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mforall_indset (lambda (@list _let_3 _let_1) (_ (_ (_ tptp.mimplies (_ tptp.positive _let_3)) (_ _let_3 _let_2)) _let_1))) _let_1)))))) % 0.46/0.63 (define tptp.essence () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Y" tptp.mu))) (let ((_let_3 (@var "Psi" (-> tptp.mu $$unsorted Bool)))) (let ((_let_4 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (let ((_let_5 (@var "X" tptp.mu))) (lambda (@list _let_4 _let_5 _let_1) (_ (_ (_ tptp.mand (_ _let_4 _let_5)) (_ tptp.mforall_indset (lambda (@list _let_3 _let_1) (_ (_ (_ tptp.mimplies (_ _let_3 _let_5)) (_ tptp.mbox (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ (_ tptp.mimplies (_ _let_4 _let_2)) (_ _let_3 _let_2)) _let_1))))) _let_1)))) _let_1)))))))) % 0.46/0.63 (define tptp.necessary_existence () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Y" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (let ((_let_4 (@var "X" tptp.mu))) (lambda (@list _let_4 _let_1) (_ (_ tptp.mforall_indset (lambda (@list _let_3 _let_1) (_ (_ (_ tptp.mimplies (_ (_ tptp.essence _let_3) _let_4)) (_ tptp.mbox (_ tptp.mexists_ind (lambda (@list _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))) _let_1))) _let_1))))))) % 0.46/0.63 (define @t1 () (= tptp.mbox (_ tptp.mbox_generic tptp.rel))) % 0.46/0.63 (define @t2 () (= tptp.mdia (_ tptp.mdia_generic tptp.rel))) % 0.46/0.63 (define @t3 () (@var "__flatten_var_0" $$unsorted)) % 0.46/0.63 (define @t4 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.46/0.63 (define @t5 () (_ tptp.positive @t4)) % 0.46/0.63 (define @t6 () (@var "X" tptp.mu)) % 0.46/0.63 (define @t7 () (_ @t4 @t6)) % 0.46/0.63 (define @t8 () (@list @t6 @t3)) % 0.46/0.63 (define @t9 () (lambda @t8 (_ (_ tptp.mnot @t7) @t3))) % 0.46/0.63 (define @t10 () (@list @t4 @t3)) % 0.46/0.63 (define @t11 () (lambda @t10 (_ (_ (_ tptp.mequiv (_ tptp.positive @t9)) (_ tptp.mnot @t5)) @t3))) % 0.46/0.63 (define @t12 () (@var "Psi" (-> tptp.mu $$unsorted Bool))) % 0.46/0.63 (define @t13 () (_ tptp.positive @t12)) % 0.46/0.63 (define @t14 () (_ @t12 @t6)) % 0.46/0.63 (define @t15 () (lambda @t8 (_ (_ (_ tptp.mimplies @t7) @t14) @t3))) % 0.46/0.63 (define @t16 () (@list @t12 @t3)) % 0.46/0.63 (define @t17 () (lambda @t16 (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t5) (_ tptp.mbox (_ tptp.mforall_ind @t15)))) @t13) @t3))) % 0.46/0.63 (define @t18 () (lambda @t10 (_ (_ tptp.mforall_indset @t17) @t3))) % 0.46/0.63 (define @t19 () (_ tptp.mimplies @t5)) % 0.46/0.63 (define @t20 () (_ @t7 @t3)) % 0.46/0.63 (define @t21 () (lambda @t8 @t20)) % 0.46/0.63 (define @t22 () (lambda @t10 (_ (_ @t19 (_ tptp.mdia (_ tptp.mexists_ind @t21))) @t3))) % 0.46/0.63 (define @t23 () (not (_ tptp.mvalid (_ tptp.mforall_indset @t22)))) % 0.46/0.63 (define @t24 () (@var "Y" tptp.mu)) % 0.46/0.63 (define @t25 () (@var "W" $$unsorted)) % 0.46/0.63 (define @t26 () (lambda (@list @t6 @t24 @t25) (= @t6 @t24))) % 0.46/0.63 (define @t27 () (@list @t25)) % 0.46/0.63 (define @t28 () (lambda @t27 true)) % 0.46/0.63 (define @t29 () (lambda @t27 false)) % 0.46/0.63 (define @t30 () (@var "Phi" (-> $$unsorted Bool))) % 0.46/0.63 (define @t31 () (_ @t30 @t25)) % 0.46/0.63 (define @t32 () (not @t31)) % 0.46/0.63 (define @t33 () (@list @t30 @t25)) % 0.46/0.63 (define @t34 () (lambda @t33 @t32)) % 0.46/0.63 (define @t35 () (@var "Psi" (-> $$unsorted Bool))) % 0.46/0.63 (define @t36 () (_ @t35 @t25)) % 0.46/0.63 (define @t37 () (@list @t30 @t35 @t25)) % 0.46/0.63 (define @t38 () (lambda @t37 (or @t31 @t36))) % 0.46/0.63 (define @t39 () (lambda @t37 (and @t31 @t36))) % 0.46/0.63 (define @t40 () (lambda @t37 (=> @t31 @t36))) % 0.46/0.63 (define @t41 () (lambda @t37 (=> @t36 @t31))) % 0.46/0.63 (define @t42 () (lambda @t37 (= @t31 @t36))) % 0.46/0.63 (define @t43 () (lambda @t37 (or (and @t31 (not @t36)) (and @t32 @t36)))) % 0.46/0.63 (define @t44 () (_ @t7 @t25)) % 0.46/0.63 (define @t45 () (@list @t6)) % 0.46/0.63 (define @t46 () (forall @t45 @t44)) % 0.46/0.63 (define @t47 () (@list @t4 @t25)) % 0.46/0.63 (define @t48 () (lambda @t47 @t46)) % 0.46/0.63 (define @t49 () (@var "X" (-> tptp.mu $$unsorted Bool))) % 0.46/0.63 (define @t50 () (@var "Phi" (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool))) % 0.46/0.63 (define @t51 () (_ (_ @t50 @t49) @t25)) % 0.46/0.63 (define @t52 () (@list @t49)) % 0.46/0.63 (define @t53 () (forall @t52 @t51)) % 0.46/0.63 (define @t54 () (@list @t50 @t25)) % 0.46/0.63 (define @t55 () (lambda @t54 @t53)) % 0.46/0.63 (define @t56 () (@var "P" (-> $$unsorted Bool))) % 0.46/0.63 (define @t57 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.46/0.63 (define @t58 () (_ (_ @t57 @t56) @t25)) % 0.46/0.63 (define @t59 () (@list @t56)) % 0.46/0.63 (define @t60 () (@list @t57 @t25)) % 0.46/0.63 (define @t61 () (lambda @t60 (forall @t59 @t58))) % 0.46/0.63 (define @t62 () (exists @t45 @t44)) % 0.46/0.63 (define @t63 () (lambda @t47 @t62)) % 0.46/0.63 (define @t64 () (lambda @t54 (exists @t52 @t51))) % 0.46/0.63 (define @t65 () (lambda @t60 (exists @t59 @t58))) % 0.46/0.63 (define @t66 () (@var "V" $$unsorted)) % 0.46/0.63 (define @t67 () (_ @t30 @t66)) % 0.46/0.63 (define @t68 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.46/0.63 (define @t69 () (_ (_ @t68 @t25) @t66)) % 0.46/0.63 (define @t70 () (not @t69)) % 0.46/0.63 (define @t71 () (or @t70 @t67)) % 0.46/0.63 (define @t72 () (@list @t66)) % 0.46/0.63 (define @t73 () (forall @t72 @t71)) % 0.46/0.63 (define @t74 () (@list @t68 @t30 @t25)) % 0.46/0.63 (define @t75 () (lambda @t74 @t73)) % 0.46/0.63 (define @t76 () (and @t69 @t67)) % 0.46/0.63 (define @t77 () (exists @t72 @t76)) % 0.46/0.63 (define @t78 () (lambda @t74 @t77)) % 0.46/0.63 (define @t79 () (forall @t27 @t31)) % 0.46/0.63 (define @t80 () (@list @t30)) % 0.46/0.63 (define @t81 () (lambda @t80 @t79)) % 0.46/0.63 (define @t82 () (lambda @t80 (forall @t27 @t32))) % 0.46/0.63 (define @t83 () (lambda @t8 (_ (_ tptp.mforall_indset (lambda @t10 (_ (_ @t19 @t7) @t3))) @t3))) % 0.46/0.63 (define @t84 () (_ @t4 @t24)) % 0.46/0.63 (define @t85 () (@list @t24 @t3)) % 0.46/0.63 (define @t86 () (lambda (@list @t4 @t6 @t3) (_ (_ (_ tptp.mand @t7) (_ tptp.mforall_indset (lambda @t16 (_ (_ (_ tptp.mimplies @t14) (_ tptp.mbox (_ tptp.mforall_ind (lambda @t85 (_ (_ (_ tptp.mimplies @t84) (_ @t12 @t24)) @t3))))) @t3)))) @t3))) % 0.46/0.63 (define @t87 () (lambda @t8 (_ (_ tptp.mforall_indset (lambda @t10 (_ (_ (_ tptp.mimplies (_ (_ tptp.essence @t4) @t6)) (_ tptp.mbox (_ tptp.mexists_ind (lambda @t85 (_ @t84 @t3))))) @t3))) @t3))) % 0.46/0.63 (define @t88 () (@var "BOUND_VARIABLE_8674" tptp.mu)) % 0.46/0.63 (define @t89 () (not (_ @t49 @t88 @t66))) % 0.46/0.63 (define @t90 () (not (tptp.rel @t25 @t66))) % 0.46/0.63 (define @t91 () (or @t90 @t89)) % 0.46/0.63 (define @t92 () (@list @t66 @t88)) % 0.46/0.63 (define @t93 () (forall @t92 @t91)) % 0.46/0.63 (define @t94 () (@list @t88)) % 0.46/0.63 (define @t95 () (forall @t94 @t91)) % 0.46/0.63 (define @t96 () (forall @t94 @t89)) % 0.46/0.63 (define @t97 () (@list @t6)) % 0.46/0.63 (define @t98 () (or @t90 @t96)) % 0.46/0.63 (define @t99 () (not (_ @t49 @t6 @t66))) % 0.46/0.63 (define @t100 () (forall @t45 @t99)) % 0.46/0.63 (define @t101 () (@var "BOUND_VARIABLE_8481" $$unsorted)) % 0.46/0.63 (define @t102 () (_ @t49 @t6 @t101)) % 0.46/0.63 (define @t103 () (not @t102)) % 0.46/0.63 (define @t104 () (forall @t45 @t103)) % 0.46/0.63 (define @t105 () (not @t104)) % 0.46/0.63 (define @t106 () (@list @t101)) % 0.46/0.63 (define @t107 () (lambda @t106 @t105)) % 0.46/0.63 (define @t108 () (_ @t107 @t66)) % 0.46/0.63 (define @t109 () (not @t108)) % 0.46/0.63 (define @t110 () (or @t90 @t109)) % 0.46/0.63 (define @t111 () (forall @t72 @t110)) % 0.46/0.63 (define @t112 () (not @t111)) % 0.46/0.63 (define @t113 () (_ @t30 @t66)) % 0.46/0.63 (define @t114 () (not @t113)) % 0.46/0.63 (define @t115 () (lambda @t33 (not (forall @t72 (or @t90 @t114))))) % 0.46/0.63 (define @t116 () (_ @t115 @t107 @t25)) % 0.46/0.63 (define @t117 () (tptp.positive @t49 @t25)) % 0.46/0.63 (define @t118 () (not @t117)) % 0.46/0.63 (define @t119 () (or @t118 @t116)) % 0.46/0.63 (define @t120 () (@list @t25 @t49)) % 0.46/0.63 (define @t121 () (forall @t120 @t119)) % 0.46/0.63 (define @t122 () (_ @t68 @t25 @t66)) % 0.46/0.63 (define @t123 () (not @t122)) % 0.46/0.63 (define @t124 () (_ (lambda @t74 (not (forall @t72 (or @t123 @t114)))) tptp.rel)) % 0.46/0.63 (define @t125 () (not @t67)) % 0.46/0.63 (define @t126 () (or @t70 @t125)) % 0.46/0.63 (define @t127 () (forall @t72 (not @t76))) % 0.46/0.63 (define @t128 () (not @t127)) % 0.46/0.63 (define @t129 () (tptp.mdia @t107 @t25)) % 0.46/0.63 (define @t130 () (or @t118 @t129)) % 0.46/0.63 (define @t131 () (forall @t120 @t130)) % 0.46/0.63 (define @t132 () (forall @t52 @t130)) % 0.46/0.63 (define @t133 () (lambda @t27 @t132)) % 0.46/0.63 (define @t134 () (_ @t133 @t25)) % 0.46/0.63 (define @t135 () (forall @t27 @t134)) % 0.46/0.63 (define @t136 () (_ @t30 @t25)) % 0.46/0.63 (define @t137 () (lambda @t80 (forall @t27 @t136))) % 0.46/0.63 (define @t138 () (_ @t49 @t6)) % 0.46/0.63 (define @t139 () (lambda @t106 (not (forall @t45 (not (_ @t138 @t101)))))) % 0.46/0.63 (define @t140 () (_ (_ tptp.mdia @t107) @t25)) % 0.46/0.63 (define @t141 () (_ (_ tptp.positive @t49) @t25)) % 0.46/0.63 (define @t142 () (not @t141)) % 0.46/0.63 (define @t143 () (or @t142 @t140)) % 0.46/0.63 (define @t144 () (=> @t141 @t140)) % 0.46/0.63 (define @t145 () (_ tptp.mdia (lambda @t106 (not (forall @t45 (not (_ @t4 @t6 @t101))))))) % 0.46/0.63 (define @t146 () (_ @t5 @t3)) % 0.46/0.63 (define @t147 () (=> @t146 (_ @t145 @t3))) % 0.46/0.63 (define @t148 () (lambda @t10 @t147)) % 0.46/0.63 (define @t149 () (_ @t148 @t49 @t25)) % 0.46/0.63 (define @t150 () (forall @t52 @t149)) % 0.46/0.63 (define @t151 () (lambda @t27 @t150)) % 0.46/0.63 (define @t152 () (_ @t50 @t49 @t25)) % 0.46/0.63 (define @t153 () (lambda @t54 (forall @t52 @t152))) % 0.46/0.63 (define @t154 () (_ @t5 @t25)) % 0.46/0.63 (define @t155 () (lambda @t27 (=> @t154 (_ @t145 @t25)))) % 0.46/0.63 (define @t156 () (_ @t4 @t6 @t25)) % 0.46/0.63 (define @t157 () (not @t156)) % 0.46/0.63 (define @t158 () (not (forall @t45 @t157))) % 0.46/0.63 (define @t159 () (_ tptp.mdia (lambda @t27 @t158))) % 0.46/0.63 (define @t160 () (lambda @t27 (=> @t154 (_ @t159 @t25)))) % 0.46/0.63 (define @t161 () (@list @t35 @t25)) % 0.46/0.63 (define @t162 () (lambda @t161 (=> @t154 @t36))) % 0.46/0.63 (define @t163 () (not @t44)) % 0.46/0.63 (define @t164 () (forall @t45 @t163)) % 0.46/0.63 (define @t165 () (_ @t21 @t6 @t25)) % 0.46/0.63 (define @t166 () (not @t165)) % 0.46/0.63 (define @t167 () (forall @t45 @t166)) % 0.46/0.63 (define @t168 () (not @t167)) % 0.46/0.63 (define @t169 () (lambda @t27 @t168)) % 0.46/0.63 (define @t170 () (_ (lambda @t47 @t158) @t21)) % 0.46/0.63 (define @t171 () (_ @t40 @t5)) % 0.46/0.63 (define @t172 () (lambda @t10 (_ (_ @t171 (_ tptp.mdia @t170)) @t3))) % 0.46/0.63 (define @t173 () (not @t164)) % 0.46/0.63 (define @t174 () (forall @t120 (or @t118 (not @t93)))) % 0.46/0.63 (define @t175 () (@quantifiers_skolemize @t174 1)) % 0.46/0.63 (define @t176 () (@quantifiers_skolemize @t174 0)) % 0.46/0.63 (define @t177 () (not (tptp.rel @t176 @t66))) % 0.46/0.63 (define @t178 () (forall @t92 (or @t177 (not (_ @t175 @t88 @t66))))) % 0.46/0.63 (define @t179 () (not @t178)) % 0.46/0.63 (define @t180 () (tptp.positive @t175 @t176)) % 0.46/0.63 (define @t181 () (not @t180)) % 0.46/0.63 (define @t182 () (or @t181 @t179)) % 0.46/0.63 (define @t183 () (@list true)) % 0.46/0.63 (define @t184 () (@list @t182)) % 0.46/0.63 (define @t185 () (@var "BOUND_VARIABLE_8359" (-> tptp.mu $$unsorted Bool))) % 0.46/0.63 (define @t186 () (tptp.positive @t185 @t25)) % 0.46/0.63 (define @t187 () (@var "BOUND_VARIABLE_8538" tptp.mu)) % 0.46/0.63 (define @t188 () (_ @t185 @t187 @t66)) % 0.46/0.63 (define @t189 () (not (_ @t49 @t187 @t66))) % 0.46/0.63 (define @t190 () (or @t189 @t188)) % 0.46/0.63 (define @t191 () (or @t90 @t190)) % 0.46/0.63 (define @t192 () (@list @t66 @t187)) % 0.46/0.63 (define @t193 () (forall @t192 @t191)) % 0.46/0.63 (define @t194 () (@list @t187)) % 0.46/0.63 (define @t195 () (forall @t194 @t191)) % 0.46/0.63 (define @t196 () (forall @t194 @t190)) % 0.46/0.63 (define @t197 () (or @t90 @t196)) % 0.46/0.63 (define @t198 () (forall @t45 (or @t99 (_ @t185 @t6 @t66)))) % 0.46/0.63 (define @t199 () (@var "BOUND_VARIABLE_8262" $$unsorted)) % 0.46/0.63 (define @t200 () (_ @t49 @t6 @t199)) % 0.46/0.63 (define @t201 () (not @t200)) % 0.46/0.63 (define @t202 () (@list @t199)) % 0.46/0.63 (define @t203 () (lambda @t202 (forall @t45 (or @t201 (_ @t185 @t6 @t199))))) % 0.46/0.63 (define @t204 () (_ @t203 @t66)) % 0.46/0.63 (define @t205 () (or @t90 @t204)) % 0.46/0.63 (define @t206 () (forall @t72 @t205)) % 0.46/0.63 (define @t207 () (lambda @t33 (forall @t72 (or @t90 @t113)))) % 0.46/0.63 (define @t208 () (_ @t207 @t203 @t25)) % 0.46/0.63 (define @t209 () (not @t208)) % 0.46/0.63 (define @t210 () (or @t118 @t209 @t186)) % 0.46/0.63 (define @t211 () (@list @t25 @t49 @t185)) % 0.46/0.63 (define @t212 () (_ (lambda @t74 (forall @t72 (or @t123 @t113))) tptp.rel)) % 0.46/0.63 (define @t213 () (not (tptp.mbox @t203 @t25))) % 0.46/0.63 (define @t214 () (or @t118 @t213 @t186)) % 0.46/0.63 (define @t215 () (forall @t211 @t214)) % 0.46/0.63 (define @t216 () (@list @t49 @t185)) % 0.46/0.63 (define @t217 () (forall @t216 @t214)) % 0.46/0.63 (define @t218 () (lambda @t27 @t217)) % 0.46/0.63 (define @t219 () (_ @t218 @t25)) % 0.46/0.63 (define @t220 () (forall @t27 @t219)) % 0.46/0.63 (define @t221 () (or @t213 @t186)) % 0.46/0.63 (define @t222 () (or @t118 @t221)) % 0.46/0.63 (define @t223 () (forall @t216 @t222)) % 0.46/0.63 (define @t224 () (@list @t185)) % 0.46/0.63 (define @t225 () (forall @t224 @t222)) % 0.46/0.63 (define @t226 () (forall @t224 @t221)) % 0.46/0.63 (define @t227 () (@var "BOUND_VARIABLE_8331" (-> tptp.mu $$unsorted Bool))) % 0.46/0.63 (define @t228 () (@list @t227)) % 0.46/0.63 (define @t229 () (or @t118 @t226)) % 0.46/0.63 (define @t230 () (_ @t227 @t6 @t199)) % 0.46/0.63 (define @t231 () (@list @t227)) % 0.46/0.63 (define @t232 () (forall @t231 (or (not (tptp.mbox (lambda @t202 (forall @t45 (or @t201 @t230))) @t25)) (tptp.positive @t227 @t25)))) % 0.46/0.63 (define @t233 () (or @t142 @t232)) % 0.46/0.63 (define @t234 () (_ @t4 @t6 @t199)) % 0.46/0.63 (define @t235 () (not @t234)) % 0.46/0.63 (define @t236 () (not @t146)) % 0.46/0.63 (define @t237 () (or @t235 @t200)) % 0.46/0.63 (define @t238 () (forall @t45 @t237)) % 0.46/0.63 (define @t239 () (lambda @t202 @t238)) % 0.46/0.63 (define @t240 () (forall @t52 (or (not (tptp.mbox @t239 @t3)) (tptp.positive @t49 @t3)))) % 0.46/0.63 (define @t241 () (or @t236 @t240)) % 0.46/0.63 (define @t242 () (lambda @t10 @t241)) % 0.46/0.63 (define @t243 () (forall @t52 (_ @t242 @t49 @t25))) % 0.46/0.63 (define @t244 () (lambda @t27 @t243)) % 0.46/0.63 (define @t245 () (tptp.mbox @t239 @t25)) % 0.46/0.63 (define @t246 () (not @t154)) % 0.46/0.63 (define @t247 () (lambda @t202 (forall @t45 (or (not (_ @t7 @t199)) (_ @t138 @t199))))) % 0.46/0.63 (define @t248 () (_ (_ tptp.mbox @t239) @t25)) % 0.46/0.63 (define @t249 () (not @t248)) % 0.46/0.63 (define @t250 () (or @t249 @t141)) % 0.46/0.63 (define @t251 () (forall @t52 @t250)) % 0.46/0.63 (define @t252 () (or @t246 @t251)) % 0.46/0.63 (define @t253 () (or @t246 @t250)) % 0.46/0.63 (define @t254 () (or @t246 @t249 @t141)) % 0.46/0.63 (define @t255 () (and @t154 @t248)) % 0.46/0.63 (define @t256 () (=> @t255 @t141)) % 0.46/0.63 (define @t257 () (_ tptp.mbox (lambda @t202 (forall @t45 (or @t235 (_ @t12 @t6 @t199)))))) % 0.46/0.63 (define @t258 () (=> (and @t146 (_ @t257 @t3)) (_ @t13 @t3))) % 0.46/0.63 (define @t259 () (lambda @t16 @t258)) % 0.46/0.63 (define @t260 () (_ @t259 @t49 @t25)) % 0.46/0.63 (define @t261 () (forall @t52 @t260)) % 0.46/0.63 (define @t262 () (lambda @t27 @t261)) % 0.46/0.63 (define @t263 () (and @t154 (_ @t257 @t25))) % 0.46/0.63 (define @t264 () (lambda @t27 (=> @t263 (_ @t13 @t25)))) % 0.46/0.63 (define @t265 () (lambda @t27 @t263)) % 0.46/0.63 (define @t266 () (_ @t265 @t25)) % 0.46/0.63 (define @t267 () (=> @t266 @t36)) % 0.46/0.63 (define @t268 () (lambda @t161 @t267)) % 0.46/0.63 (define @t269 () (_ @t12 @t6 @t25)) % 0.46/0.63 (define @t270 () (_ tptp.mbox (lambda @t27 (forall @t45 (or @t157 @t269))))) % 0.46/0.63 (define @t271 () (lambda @t27 (and @t154 (_ @t270 @t25)))) % 0.46/0.63 (define @t272 () (lambda @t161 (and @t154 @t36))) % 0.46/0.63 (define @t273 () (_ @t14 @t25)) % 0.46/0.63 (define @t274 () (or @t163 @t273)) % 0.46/0.63 (define @t275 () (=> @t44 @t273)) % 0.46/0.63 (define @t276 () (=> @t20 (_ @t14 @t3))) % 0.46/0.63 (define @t277 () (lambda @t8 @t276)) % 0.46/0.63 (define @t278 () (_ @t277 @t6 @t25)) % 0.46/0.63 (define @t279 () (forall @t45 @t278)) % 0.46/0.63 (define @t280 () (lambda @t27 @t279)) % 0.46/0.63 (define @t281 () (lambda @t47 (forall @t45 @t156))) % 0.46/0.63 (define @t282 () (lambda @t27 @t275)) % 0.46/0.63 (define @t283 () (lambda @t161 (=> @t44 @t36))) % 0.46/0.63 (define @t284 () (_ @t40 @t7)) % 0.46/0.63 (define @t285 () (lambda @t8 (_ (_ @t284 @t14) @t3))) % 0.46/0.63 (define @t286 () (_ @t39 @t5)) % 0.46/0.63 (define @t287 () (lambda @t16 (_ (_ (_ @t40 (_ @t286 (_ tptp.mbox (_ @t281 @t285)))) @t13) @t3))) % 0.46/0.63 (define @t288 () (@var "BOUND_VARIABLE_8179" $$unsorted)) % 0.46/0.63 (define @t289 () (@list @t6 @t288)) % 0.46/0.63 (define @t290 () (lambda @t289 (not (_ @t175 @t6 @t288)))) % 0.46/0.63 (define @t291 () (@purify @t290)) % 0.46/0.63 (define @t292 () (_ @t49 @t6 @t288)) % 0.46/0.63 (define @t293 () (not @t292)) % 0.46/0.63 (define @t294 () (lambda @t289 @t293)) % 0.46/0.63 (define @t295 () (tptp.positive @t294 @t25)) % 0.46/0.63 (define @t296 () (= @t118 @t295)) % 0.46/0.63 (define @t297 () (forall @t120 @t296)) % 0.46/0.63 (define @t298 () (forall @t52 @t296)) % 0.46/0.63 (define @t299 () (lambda @t27 @t298)) % 0.46/0.63 (define @t300 () (_ @t299 @t25)) % 0.46/0.63 (define @t301 () (forall @t27 @t300)) % 0.46/0.63 (define @t302 () (_ @t138 @t288)) % 0.46/0.63 (define @t303 () (not @t302)) % 0.46/0.63 (define @t304 () (lambda @t289 @t303)) % 0.46/0.63 (define @t305 () (_ (_ tptp.positive @t304) @t25)) % 0.46/0.63 (define @t306 () (= @t142 @t305)) % 0.46/0.63 (define @t307 () (_ tptp.positive (lambda @t289 (not (_ @t7 @t288))))) % 0.46/0.63 (define @t308 () (= @t236 (_ @t307 @t3))) % 0.46/0.63 (define @t309 () (lambda @t10 @t308)) % 0.46/0.63 (define @t310 () (_ @t309 @t49 @t25)) % 0.46/0.63 (define @t311 () (forall @t52 @t310)) % 0.46/0.63 (define @t312 () (lambda @t27 @t311)) % 0.46/0.63 (define @t313 () (_ @t307 @t25)) % 0.46/0.63 (define @t314 () (not @t20)) % 0.46/0.63 (define @t315 () (lambda @t8 @t314)) % 0.46/0.63 (define @t316 () (_ tptp.positive @t315)) % 0.46/0.63 (define @t317 () (_ @t316 @t25)) % 0.46/0.63 (define @t318 () (= @t317 @t246)) % 0.46/0.63 (define @t319 () (lambda @t27 @t246)) % 0.46/0.63 (define @t320 () (_ @t319 @t25)) % 0.46/0.63 (define @t321 () (lambda @t27 (= @t320 @t317))) % 0.46/0.63 (define @t322 () (_ @t34 @t5)) % 0.46/0.63 (define @t323 () (lambda @t161 (= @t317 @t36))) % 0.46/0.63 (define @t324 () (lambda @t27 @t163)) % 0.46/0.63 (define @t325 () (_ @t34 @t7)) % 0.46/0.63 (define @t326 () (lambda @t8 (_ @t325 @t3))) % 0.46/0.63 (define @t327 () (tptp.positive @t290 @t176)) % 0.46/0.63 (define @t328 () (= @t181 @t327)) % 0.46/0.63 (define @t329 () (tptp.positive @t291 @t176)) % 0.46/0.63 (define @t330 () (= @t181 @t329)) % 0.46/0.63 (define @t331 () (not @t329)) % 0.46/0.63 (define @t332 () (@list false false)) % 0.46/0.63 (define @t333 () (forall @t192 (or @t177 (not (_ @t175 @t187 @t66)) (_ @t291 @t187 @t66)))) % 0.46/0.63 (define @t334 () (not @t333)) % 0.46/0.63 (define @t335 () (or @t181 @t334 @t329)) % 0.46/0.63 (define @t336 () (@quantifiers_skolemize @t333 0)) % 0.46/0.63 (define @t337 () (@quantifiers_skolemize @t333 1)) % 0.46/0.63 (define @t338 () (_ @t175 @t337 @t336)) % 0.46/0.63 (define @t339 () (not @t338)) % 0.46/0.63 (define @t340 () (tptp.rel @t176 @t336)) % 0.46/0.63 (define @t341 () (not @t340)) % 0.46/0.63 (define @t342 () (or @t341 @t339 (_ @t291 @t337 @t336))) % 0.46/0.63 (define @t343 () (@list @t342)) % 0.46/0.63 (define @t344 () (or @t341 @t339)) % 0.46/0.63 (define @t345 () (not @t344)) % 0.46/0.63 (assume @p1 @t1) % 0.46/0.63 (assume @p2 @t2) % 0.46/0.63 (assume @p3 (_ tptp.mvalid (_ tptp.mforall_indset @t11))) % 0.46/0.63 (assume @p4 (_ tptp.mvalid (_ tptp.mforall_indset @t18))) % 0.46/0.63 (assume @p5 (_ tptp.mvalid (_ tptp.positive tptp.god))) % 0.46/0.63 (assume @p6 (_ tptp.mvalid (_ tptp.mforall_indset (lambda @t10 (_ (_ @t19 (_ tptp.mbox @t5)) @t3))))) % 0.46/0.63 (assume @p7 (_ tptp.mvalid (_ tptp.positive tptp.necessary_existence))) % 0.46/0.63 (assume @p8 @t23) % 0.46/0.63 (assume @p9 true) % 0.46/0.63 (step @p10 (= tptp.meq_ind @t26) :rule refl :args (@t26)) % 0.46/0.63 (step @p11 (= tptp.mtrue @t28) :rule refl :args (@t28)) % 0.46/0.63 (step @p12 (= tptp.mfalse @t29) :rule refl :args (@t29)) % 0.46/0.63 (step @p13 (= tptp.mnot @t34) :rule refl :args (@t34)) % 0.46/0.63 (step @p14 (= tptp.mor @t38) :rule refl :args (@t38)) % 0.46/0.63 (step @p15 (= tptp.mand @t39) :rule refl :args (@t39)) % 0.46/0.63 (step @p16 (= tptp.mimplies @t40) :rule refl :args (@t40)) % 0.46/0.63 (step @p17 (= tptp.mimplied @t41) :rule refl :args (@t41)) % 0.46/0.63 (step @p18 (= tptp.mequiv @t42) :rule refl :args (@t42)) % 0.46/0.63 (step @p19 (= tptp.mxor @t43) :rule refl :args (@t43)) % 0.46/0.63 (step @p20 (= tptp.mforall_ind @t48) :rule refl :args (@t48)) % 0.46/0.63 (step @p21 (= tptp.mforall_indset @t55) :rule refl :args (@t55)) % 0.46/0.63 (step @p22 (= tptp.mforall_prop @t61) :rule refl :args (@t61)) % 0.46/0.63 (step @p23 (= tptp.mexists_ind @t63) :rule refl :args (@t63)) % 0.46/0.63 (step @p24 (= tptp.mexists_indset @t64) :rule refl :args (@t64)) % 0.46/0.63 (step @p25 (= tptp.mexists_prop @t65) :rule refl :args (@t65)) % 0.46/0.63 (step @p26 (= tptp.mbox_generic @t75) :rule refl :args (@t75)) % 0.46/0.63 (step @p27 (= tptp.mdia_generic @t78) :rule refl :args (@t78)) % 0.46/0.63 (step @p28 (= tptp.mvalid @t81) :rule refl :args (@t81)) % 0.46/0.63 (step @p29 (= tptp.minvalid @t82) :rule refl :args (@t82)) % 0.46/0.63 (step @p30 (= tptp.god @t83) :rule refl :args (@t83)) % 0.46/0.63 (step @p31 (= tptp.essence @t86) :rule refl :args (@t86)) % 0.46/0.63 (step @p32 (= tptp.necessary_existence @t87) :rule refl :args (@t87)) % 0.46/0.63 (step @p33 :rule quant-merge-prenex :args ((= (forall @t72 @t95) @t93))) % 0.46/0.63 (step @p34 :rule alpha_equiv :args (@t96 (@list @t88) @t97)) % 0.46/0.63 (step @p35 :rule refl :args (@t90)) % 0.46/0.63 (step @p36 :rule nary_cong :premises (@p35 @p34) :args (@t98)) % 0.46/0.63 (step @p37 :rule quant-miniscope-or :args ((= @t95 @t98))) % 0.46/0.63 (step @p38 :rule trans :premises (@p37 @p36)) % 0.46/0.63 (step @p39 :rule symm :premises (@p38)) % 0.46/0.63 (step @p40 :rule cong :premises (@p39) :args ((forall @t72 (or @t90 @t100)))) % 0.46/0.63 (step @p41 :rule trans :premises (@p40 @p33)) % 0.46/0.63 (step @p42 :rule bool-double-not-elim :args (@t100)) % 0.46/0.63 (step @p43 :rule beta-reduce :args ((= @t108 (not @t100)))) % 0.46/0.63 (step @p44 :rule cong :premises (@p43) :args (@t109)) % 0.46/0.63 (step @p45 :rule trans :premises (@p44 @p42)) % 0.46/0.63 (step @p46 :rule refl :args (@t90)) % 0.46/0.63 (step @p47 :rule nary_cong :premises (@p46 @p45) :args (@t110)) % 0.46/0.63 (step @p48 :rule cong :premises (@p47) :args (@t111)) % 0.46/0.63 (step @p49 :rule trans :premises (@p48 @p41)) % 0.46/0.63 (step @p50 :rule cong :premises (@p49) :args (@t112)) % 0.46/0.63 (step @p51 :rule beta-reduce :args ((= @t116 @t112))) % 0.46/0.63 (step @p52 :rule trans :premises (@p51 @p50)) % 0.46/0.63 (step @p53 :rule refl :args (@t118)) % 0.46/0.63 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t119)) % 0.46/0.63 (step @p55 :rule cong :premises (@p54) :args (@t121)) % 0.46/0.63 (step @p56 :rule cong :premises (@p55) :args ((not @t121))) % 0.46/0.63 (step @p57 :rule refl :args (@t25)) % 0.46/0.63 (step @p58 :rule refl :args (@t107)) % 0.46/0.63 (step @p59 :rule beta-reduce :args ((= @t124 @t115))) % 0.46/0.63 (step @p60 :rule refl :args (tptp.mdia)) % 0.46/0.63 (step @p61 :rule cong :premises (@p60 @p59) :args ((= tptp.mdia @t124))) % 0.46/0.63 (step @p62 :rule refl :args (tptp.rel)) % 0.46/0.63 (step @p63 :rule refl :args (@t113)) % 0.46/0.63 (step @p64 :rule refl :args (@t67)) % 0.46/0.63 (step @p65 :rule cong :premises (@p64 @p63) :args ((= @t67 @t113))) % 0.46/0.63 (step @p66 :rule symm :premises (@p65)) % 0.46/0.63 (step @p67 :rule eq_resolve :premises (@p64 @p66)) % 0.46/0.63 (step @p68 :rule cong :premises (@p67) :args (@t125)) % 0.46/0.63 (step @p69 :rule refl :args (@t122)) % 0.46/0.63 (step @p70 :rule refl :args (@t69)) % 0.46/0.63 (step @p71 :rule cong :premises (@p70 @p69) :args ((= @t69 @t122))) % 0.46/0.63 (step @p72 :rule symm :premises (@p71)) % 0.46/0.63 (step @p73 :rule eq_resolve :premises (@p70 @p72)) % 0.46/0.63 (step @p74 :rule cong :premises (@p73) :args (@t70)) % 0.46/0.63 (step @p75 :rule nary_cong :premises (@p74 @p68) :args (@t126)) % 0.46/0.63 (step @p76 :rule cong :premises (@p75) :args ((forall @t72 @t126))) % 0.46/0.63 (step @p77 :rule bool-and-de-morgan :args (@t69 @t67 true)) % 0.46/0.63 (step @p78 :rule cong :premises (@p77) :args (@t127)) % 0.46/0.63 (step @p79 :rule trans :premises (@p78 @p76)) % 0.46/0.63 (step @p80 :rule cong :premises (@p79) :args (@t128)) % 0.46/0.63 (step @p81 :rule exists-elim :args ((= @t77 @t128))) % 0.46/0.63 (step @p82 :rule trans :premises (@p81 @p80)) % 0.46/0.63 (step @p83 :rule cong :premises (@p82) :args (@t78)) % 0.46/0.63 (step @p84 :rule trans :premises (@p27 @p83)) % 0.46/0.63 (step @p85 :rule ho_cong :premises (@p84 @p62)) % 0.46/0.63 (step @p86 :rule cong :premises (@p60 @p85) :args (@t2)) % 0.46/0.63 (step @p87 :rule trans :premises (@p86 @p61)) % 0.46/0.63 (step @p88 :rule eq_resolve :premises (@p2 @p87)) % 0.46/0.63 (step @p89 :rule ho_cong :premises (@p88 @p58 @p57)) % 0.46/0.63 (step @p90 :rule nary_cong :premises (@p53 @p89) :args (@t130)) % 0.46/0.63 (step @p91 :rule cong :premises (@p90) :args (@t131)) % 0.46/0.63 (step @p92 :rule cong :premises (@p91) :args ((not @t131))) % 0.46/0.63 (step @p93 :rule trans :premises (@p92 @p56)) % 0.46/0.63 (step @p94 :rule quant-merge-prenex :args ((= (forall @t27 @t132) @t131))) % 0.46/0.63 (step @p95 :rule beta-reduce :args ((= @t134 @t132))) % 0.46/0.63 (step @p96 :rule cong :premises (@p95) :args (@t135)) % 0.46/0.63 (step @p97 :rule trans :premises (@p96 @p94)) % 0.46/0.63 (step @p98 :rule beta-reduce :args ((= (_ @t137 @t133) @t135))) % 0.46/0.63 (step @p99 :rule trans :premises (@p98 @p97)) % 0.46/0.63 (step @p100 :rule refl :args ((tptp.mdia @t139 @t25))) % 0.46/0.63 (step @p101 :rule refl :args (@t25)) % 0.46/0.63 (step @p102 :rule refl :args (@t102)) % 0.46/0.63 (step @p103 :rule cong :premises (@p102) :args (@t103)) % 0.46/0.63 (step @p104 :rule cong :premises (@p103) :args (@t104)) % 0.46/0.63 (step @p105 :rule cong :premises (@p104) :args (@t105)) % 0.46/0.63 (step @p106 :rule cong :premises (@p105) :args (@t107)) % 0.46/0.63 (step @p107 :rule cong :premises (@p106 @p101) :args (@t129)) % 0.46/0.63 (step @p108 :rule trans :premises (@p107 @p100)) % 0.46/0.63 (step @p109 :rule refl :args (tptp.mdia)) % 0.46/0.63 (step @p110 :rule ho_cong :premises (@p109 @p106)) % 0.46/0.63 (step @p111 :rule ho_cong :premises (@p110 @p101)) % 0.46/0.63 (step @p112 :rule cong :premises (@p111 @p108) :args ((= @t140 @t129))) % 0.46/0.63 (step @p113 :rule symm :premises (@p112)) % 0.46/0.63 (step @p114 :rule refl :args ((_ (_ tptp.mdia @t139) @t25))) % 0.46/0.63 (step @p115 :rule eq_resolve :premises (@p114 @p113)) % 0.46/0.63 (step @p116 :rule refl :args (@t117)) % 0.46/0.63 (step @p117 :rule refl :args (@t141)) % 0.46/0.63 (step @p118 :rule cong :premises (@p117 @p116) :args ((= @t141 @t117))) % 0.46/0.63 (step @p119 :rule symm :premises (@p118)) % 0.46/0.63 (step @p120 :rule eq_resolve :premises (@p117 @p119)) % 0.46/0.63 (step @p121 :rule cong :premises (@p120) :args (@t142)) % 0.46/0.63 (step @p122 :rule nary_cong :premises (@p121 @p115) :args (@t143)) % 0.46/0.63 (step @p123 :rule cong :premises (@p122) :args ((forall @t52 @t143))) % 0.46/0.63 (step @p124 :rule bool-impl-elim :args (@t141 @t140)) % 0.46/0.63 (step @p125 :rule cong :premises (@p124) :args ((forall @t52 @t144))) % 0.46/0.63 (step @p126 :rule trans :premises (@p125 @p123)) % 0.46/0.63 (step @p127 :rule beta-reduce :args ((= @t149 @t144))) % 0.46/0.63 (step @p128 :rule cong :premises (@p127) :args (@t150)) % 0.46/0.63 (step @p129 :rule trans :premises (@p128 @p126)) % 0.46/0.63 (step @p130 :rule cong :premises (@p129) :args (@t151)) % 0.46/0.63 (step @p131 :rule beta-reduce :args ((= (_ @t153 @t148) @t151))) % 0.46/0.63 (step @p132 :rule trans :premises (@p131 @p130)) % 0.46/0.63 (step @p133 :rule beta-reduce :args ((= (_ @t155 @t3) @t147))) % 0.46/0.63 (step @p134 :rule refl :args (@t3)) % 0.46/0.63 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 0.46/0.63 ; trust TRUST_THEORY_REWRITE % 0.46/0.63 (step @p135 :rule trust :premises () :args ((= @t160 @t155))) % 0.46/0.63 (step @p136 :rule beta-reduce :args ((= (_ @t162 @t159) @t160))) % 0.46/0.63 (step @p137 :rule trans :premises (@p136 @p135)) % 0.46/0.63 (step @p138 :rule refl :args (@t156)) % 0.46/0.63 (step @p139 :rule refl :args (@t44)) % 0.46/0.63 (step @p140 :rule cong :premises (@p139 @p138) :args ((= @t44 @t156))) % 0.46/0.63 (step @p141 :rule symm :premises (@p140)) % 0.46/0.63 (step @p142 :rule eq_resolve :premises (@p139 @p141)) % 0.46/0.63 (step @p143 :rule cong :premises (@p142) :args (@t163)) % 0.46/0.63 (step @p144 :rule cong :premises (@p143) :args (@t164)) % 0.46/0.63 (step @p145 :rule beta-reduce :args ((= @t165 @t44))) % 0.46/0.63 (step @p146 :rule cong :premises (@p145) :args (@t166)) % 0.46/0.63 (step @p147 :rule cong :premises (@p146) :args (@t167)) % 0.46/0.63 (step @p148 :rule trans :premises (@p147 @p144)) % 0.46/0.63 (step @p149 :rule cong :premises (@p148) :args (@t168)) % 0.46/0.63 (step @p150 :rule cong :premises (@p149) :args (@t169)) % 0.46/0.63 (step @p151 :rule beta-reduce :args ((= @t170 @t169))) % 0.46/0.63 (step @p152 :rule trans :premises (@p151 @p150)) % 0.46/0.63 (step @p153 :rule ho_cong :premises (@p60 @p152)) % 0.46/0.63 (step @p154 :rule beta-reduce :args ((= @t171 @t162))) % 0.46/0.63 (step @p155 :rule ho_cong :premises (@p154 @p153)) % 0.46/0.63 (step @p156 :rule trans :premises (@p155 @p137)) % 0.46/0.63 (step @p157 :rule ho_cong :premises (@p156 @p134)) % 0.46/0.63 (step @p158 :rule trans :premises (@p157 @p133)) % 0.46/0.63 (step @p159 :rule cong :premises (@p158) :args (@t172)) % 0.46/0.63 (step @p160 :rule refl :args (@t153)) % 0.46/0.63 (step @p161 :rule ho_cong :premises (@p160 @p159)) % 0.46/0.63 (step @p162 :rule trans :premises (@p161 @p132)) % 0.46/0.63 (step @p163 :rule refl :args (@t137)) % 0.46/0.63 (step @p164 :rule ho_cong :premises (@p163 @p162)) % 0.46/0.63 (step @p165 :rule trans :premises (@p164 @p99)) % 0.46/0.63 (step @p166 :rule cong :premises (@p165) :args ((not (_ @t137 (_ @t153 @t172))))) % 0.46/0.63 (step @p167 :rule refl :args (@t21)) % 0.46/0.63 (step @p168 :rule cong :premises (@p144) :args (@t173)) % 0.46/0.63 (step @p169 :rule exists-elim :args ((= @t62 @t173))) % 0.46/0.63 (step @p170 :rule trans :premises (@p169 @p168)) % 0.46/0.63 (step @p171 :rule cong :premises (@p170) :args (@t63)) % 0.46/0.63 (step @p172 :rule trans :premises (@p23 @p171)) % 0.46/0.63 (step @p173 :rule ho_cong :premises (@p172 @p167)) % 0.46/0.63 (step @p174 :rule ho_cong :premises (@p60 @p173)) % 0.46/0.63 (step @p175 :rule refl :args (@t5)) % 0.46/0.63 (step @p176 :rule ho_cong :premises (@p16 @p175)) % 0.46/0.63 (step @p177 :rule ho_cong :premises (@p176 @p174)) % 0.46/0.63 (step @p178 :rule ho_cong :premises (@p177 @p134)) % 0.46/0.63 (step @p179 :rule cong :premises (@p178) :args (@t22)) % 0.46/0.63 (step @p180 :rule refl :args (@t152)) % 0.46/0.63 (step @p181 :rule refl :args (@t51)) % 0.46/0.63 (step @p182 :rule cong :premises (@p181 @p180) :args ((= @t51 @t152))) % 0.46/0.63 (step @p183 :rule symm :premises (@p182)) % 0.46/0.63 (step @p184 :rule eq_resolve :premises (@p181 @p183)) % 0.46/0.63 (step @p185 :rule cong :premises (@p184) :args (@t53)) % 0.46/0.63 (step @p186 :rule cong :premises (@p185) :args (@t55)) % 0.46/0.63 (step @p187 :rule trans :premises (@p21 @p186)) % 0.46/0.63 (step @p188 :rule ho_cong :premises (@p187 @p179)) % 0.46/0.63 (step @p189 :rule refl :args (@t136)) % 0.46/0.63 (step @p190 :rule refl :args (@t31)) % 0.46/0.63 (step @p191 :rule cong :premises (@p190 @p189) :args ((= @t31 @t136))) % 0.46/0.63 (step @p192 :rule symm :premises (@p191)) % 0.46/0.63 (step @p193 :rule eq_resolve :premises (@p190 @p192)) % 0.46/0.63 (step @p194 :rule cong :premises (@p193) :args (@t79)) % 0.46/0.63 (step @p195 :rule cong :premises (@p194) :args (@t81)) % 0.46/0.63 (step @p196 :rule trans :premises (@p28 @p195)) % 0.46/0.63 (step @p197 :rule ho_cong :premises (@p196 @p188)) % 0.46/0.63 (step @p198 :rule cong :premises (@p197) :args (@t23)) % 0.46/0.63 (step @p199 :rule trans :premises (@p198 @p166)) % 0.46/0.63 (step @p200 :rule trans :premises (@p199 @p93)) % 0.46/0.63 (step @p201 :rule eq_resolve :premises (@p8 @p200)) % 0.46/0.63 (step @p202 :rule skolemize :premises (@p201)) % 0.46/0.63 (step @p203 :rule bool-double-not-elim :args (@t178)) % 0.46/0.63 (step @p204 :rule refl :args (@t182)) % 0.46/0.63 (step @p205 :rule nary_cong :premises (@p204 @p203) :args ((or @t182 (not @t179)))) % 0.46/0.63 (step @p206 :rule cnf_or_neg :args (@t182 1)) % 0.46/0.63 (step @p207 :rule eq_resolve :premises (@p206 @p205)) % 0.46/0.63 (step @p208 :rule reordering :premises (@p207) :args ((or @t178 @t182))) % 0.46/0.63 (step @p209 :rule chain_m_resolution :premises (@p208 @p202) :args (@t178 @t183 @t184)) % 0.46/0.63 (step @p210 :rule refl :args (@t186)) % 0.46/0.63 (step @p211 :rule aci_norm :args ((= @t191 (or @t90 @t189 @t188)))) % 0.46/0.63 (step @p212 :rule cong :premises (@p211) :args (@t193)) % 0.46/0.63 (step @p213 :rule quant-merge-prenex :args ((= (forall @t72 @t195) @t193))) % 0.46/0.63 (step @p214 :rule alpha_equiv :args (@t196 (@list @t187) @t97)) % 0.46/0.63 (step @p215 :rule nary_cong :premises (@p35 @p214) :args (@t197)) % 0.46/0.63 (step @p216 :rule quant-miniscope-or :args ((= @t195 @t197))) % 0.46/0.63 (step @p217 :rule trans :premises (@p216 @p215)) % 0.46/0.63 (step @p218 :rule symm :premises (@p217)) % 0.46/0.63 (step @p219 :rule cong :premises (@p218) :args ((forall @t72 (or @t90 @t198)))) % 0.46/0.63 (step @p220 :rule trans :premises (@p219 @p213)) % 0.46/0.63 (step @p221 :rule trans :premises (@p220 @p212)) % 0.46/0.63 (step @p222 :rule beta-reduce :args ((= @t204 @t198))) % 0.46/0.63 (step @p223 :rule nary_cong :premises (@p46 @p222) :args (@t205)) % 0.46/0.63 (step @p224 :rule cong :premises (@p223) :args (@t206)) % 0.46/0.63 (step @p225 :rule trans :premises (@p224 @p221)) % 0.46/0.63 (step @p226 :rule beta-reduce :args ((= @t208 @t206))) % 0.46/0.63 (step @p227 :rule trans :premises (@p226 @p225)) % 0.46/0.63 (step @p228 :rule cong :premises (@p227) :args (@t209)) % 0.46/0.63 (step @p229 :rule nary_cong :premises (@p53 @p228 @p210) :args (@t210)) % 0.46/0.63 (step @p230 :rule cong :premises (@p229) :args ((forall @t211 @t210))) % 0.46/0.63 (step @p231 :rule refl :args (@t203)) % 0.46/0.63 (step @p232 :rule beta-reduce :args ((= @t212 @t207))) % 0.46/0.63 (step @p233 :rule refl :args (tptp.mbox)) % 0.46/0.63 (step @p234 :rule cong :premises (@p233 @p232) :args ((= tptp.mbox @t212))) % 0.46/0.63 (step @p235 :rule nary_cong :premises (@p74 @p67) :args (@t71)) % 0.46/0.63 (step @p236 :rule cong :premises (@p235) :args (@t73)) % 0.46/0.63 (step @p237 :rule cong :premises (@p236) :args (@t75)) % 0.46/0.63 (step @p238 :rule trans :premises (@p26 @p237)) % 0.46/0.63 (step @p239 :rule ho_cong :premises (@p238 @p62)) % 0.46/0.63 (step @p240 :rule cong :premises (@p233 @p239) :args (@t1)) % 0.46/0.63 (step @p241 :rule trans :premises (@p240 @p234)) % 0.46/0.63 (step @p242 :rule eq_resolve :premises (@p1 @p241)) % 0.46/0.63 (step @p243 :rule ho_cong :premises (@p242 @p231 @p57)) % 0.46/0.63 (step @p244 :rule cong :premises (@p243) :args (@t213)) % 0.46/0.63 (step @p245 :rule nary_cong :premises (@p53 @p244 @p210) :args (@t214)) % 0.46/0.63 (step @p246 :rule cong :premises (@p245) :args (@t215)) % 0.46/0.63 (step @p247 :rule trans :premises (@p246 @p230)) % 0.46/0.63 (step @p248 :rule quant-merge-prenex :args ((= (forall @t27 @t217) @t215))) % 0.46/0.63 (step @p249 :rule beta-reduce :args ((= @t219 @t217))) % 0.46/0.63 (step @p250 :rule cong :premises (@p249) :args (@t220)) % 0.46/0.63 (step @p251 :rule trans :premises (@p250 @p248)) % 0.46/0.63 (step @p252 :rule beta-reduce :args ((= (_ @t137 @t218) @t220))) % 0.46/0.63 (step @p253 :rule trans :premises (@p252 @p251)) % 0.46/0.63 (step @p254 :rule aci_norm :args ((= @t222 @t214))) % 0.46/0.63 (step @p255 :rule cong :premises (@p254) :args (@t223)) % 0.46/0.63 (step @p256 :rule quant-merge-prenex :args ((= (forall @t52 @t225) @t223))) % 0.46/0.63 (step @p257 :rule alpha_equiv :args (@t226 (@list @t185) @t228)) % 0.46/0.63 (step @p258 :rule refl :args (@t118)) % 0.46/0.63 (step @p259 :rule nary_cong :premises (@p258 @p257) :args (@t229)) % 0.46/0.63 (step @p260 :rule quant-miniscope-or :args ((= @t225 @t229))) % 0.46/0.63 (step @p261 :rule trans :premises (@p260 @p259)) % 0.46/0.63 (step @p262 :rule symm :premises (@p261)) % 0.46/0.63 (step @p263 :rule cong :premises (@p262) :args ((forall @t52 (or @t118 @t232)))) % 0.46/0.63 (step @p264 :rule trans :premises (@p263 @p256)) % 0.46/0.63 (step @p265 :rule trans :premises (@p264 @p255)) % 0.46/0.63 (step @p266 :rule refl :args (@t232)) % 0.46/0.63 (step @p267 :rule nary_cong :premises (@p121 @p266) :args (@t233)) % 0.46/0.63 (step @p268 :rule cong :premises (@p267) :args ((forall @t52 @t233))) % 0.46/0.63 (step @p269 :rule trans :premises (@p268 @p265)) % 0.46/0.63 (step @p270 :rule beta-reduce :args ((= (_ (lambda @t10 (or @t236 (forall @t231 (or (not (tptp.mbox (lambda @t202 (forall @t45 (or @t235 @t230))) @t3)) (tptp.positive @t227 @t3))))) @t49 @t25) @t233))) % 0.46/0.63 (step @p271 :rule refl :args (@t49)) % 0.46/0.63 (step @p272 :rule alpha_equiv :args (@t240 (@list @t49) @t228)) % 0.46/0.63 (step @p273 :rule refl :args (@t236)) % 0.46/0.63 (step @p274 :rule nary_cong :premises (@p273 @p272) :args (@t241)) % 0.46/0.63 (step @p275 :rule cong :premises (@p274) :args (@t242)) % 0.46/0.63 (step @p276 :rule ho_cong :premises (@p275 @p271 @p101)) % 0.46/0.63 (step @p277 :rule trans :premises (@p276 @p270)) % 0.46/0.63 (step @p278 :rule cong :premises (@p277) :args (@t243)) % 0.46/0.63 (step @p279 :rule trans :premises (@p278 @p269)) % 0.46/0.63 (step @p280 :rule cong :premises (@p279) :args (@t244)) % 0.46/0.63 (step @p281 :rule beta-reduce :args ((= (_ @t153 @t242) @t244))) % 0.46/0.63 (step @p282 :rule trans :premises (@p281 @p280)) % 0.46/0.63 (step @p283 :rule beta-reduce :args ((= (_ (lambda @t27 (or @t246 (forall @t52 (or (not @t245) @t117)))) @t3) @t241))) % 0.46/0.63 (step @p284 :rule refl :args ((tptp.mbox @t247 @t25))) % 0.46/0.63 (step @p285 :rule refl :args (@t200)) % 0.46/0.63 (step @p286 :rule refl :args (@t234)) % 0.46/0.63 (step @p287 :rule cong :premises (@p286) :args (@t235)) % 0.46/0.63 (step @p288 :rule nary_cong :premises (@p287 @p285) :args (@t237)) % 0.46/0.63 (step @p289 :rule cong :premises (@p288) :args (@t238)) % 0.46/0.63 (step @p290 :rule cong :premises (@p289) :args (@t239)) % 0.46/0.63 (step @p291 :rule cong :premises (@p290 @p101) :args (@t245)) % 0.46/0.63 (step @p292 :rule trans :premises (@p291 @p284)) % 0.46/0.63 (step @p293 :rule refl :args (tptp.mbox)) % 0.46/0.63 (step @p294 :rule ho_cong :premises (@p293 @p290)) % 0.46/0.63 (step @p295 :rule ho_cong :premises (@p294 @p101)) % 0.46/0.63 (step @p296 :rule cong :premises (@p295 @p292) :args ((= @t248 @t245))) % 0.46/0.63 (step @p297 :rule symm :premises (@p296)) % 0.46/0.63 (step @p298 :rule refl :args ((_ (_ tptp.mbox @t247) @t25))) % 0.46/0.63 (step @p299 :rule eq_resolve :premises (@p298 @p297)) % 0.46/0.63 (step @p300 :rule cong :premises (@p299) :args (@t249)) % 0.46/0.63 (step @p301 :rule nary_cong :premises (@p300 @p120) :args (@t250)) % 0.46/0.63 (step @p302 :rule cong :premises (@p301) :args (@t251)) % 0.46/0.63 (step @p303 :rule refl :args (@t246)) % 0.46/0.63 (step @p304 :rule nary_cong :premises (@p303 @p302) :args (@t252)) % 0.46/0.63 (step @p305 :rule quant-miniscope-or :args ((= (forall @t52 @t253) @t252))) % 0.46/0.63 (step @p306 :rule aci_norm :args ((= @t254 @t253))) % 0.46/0.63 (step @p307 :rule cong :premises (@p306) :args ((forall @t52 @t254))) % 0.46/0.63 (step @p308 :rule trans :premises (@p307 @p305)) % 0.46/0.63 (step @p309 :rule trans :premises (@p308 @p304)) % 0.46/0.63 (step @p310 :rule aci_norm :args ((= (or (or @t246 @t249) @t141) @t254))) % 0.46/0.63 (step @p311 :rule bool-and-de-morgan :args (@t154 @t248 true)) % 0.46/0.63 (step @p312 :rule nary_cong :premises (@p311 @p117) :args ((or (not @t255) @t141))) % 0.46/0.63 (step @p313 :rule trans :premises (@p312 @p310)) % 0.46/0.63 (step @p314 :rule bool-impl-elim :args (@t255 @t141)) % 0.46/0.63 (step @p315 :rule trans :premises (@p314 @p313)) % 0.46/0.63 (step @p316 :rule cong :premises (@p315) :args ((forall @t52 @t256))) % 0.46/0.63 (step @p317 :rule trans :premises (@p316 @p309)) % 0.46/0.63 (step @p318 :rule beta-reduce :args ((= @t260 @t256))) % 0.46/0.63 (step @p319 :rule cong :premises (@p318) :args (@t261)) % 0.46/0.63 (step @p320 :rule trans :premises (@p319 @p317)) % 0.46/0.63 (step @p321 :rule cong :premises (@p320) :args (@t262)) % 0.46/0.63 (step @p322 :rule beta-reduce :args ((= (_ @t153 @t259) @t262))) % 0.46/0.63 (step @p323 :rule trans :premises (@p322 @p321)) % 0.46/0.63 (step @p324 :rule beta-reduce :args ((= (_ @t264 @t3) @t258))) % 0.46/0.63 (step @p325 :rule beta-reduce :args ((= (_ (lambda @t161 (=> @t263 @t36)) @t13) @t264))) % 0.46/0.63 (step @p326 :rule refl :args (@t13)) % 0.46/0.63 (step @p327 :rule refl :args (@t36)) % 0.46/0.63 (step @p328 :rule beta-reduce :args ((= @t266 @t263))) % 0.46/0.63 (step @p329 :rule cong :premises (@p328 @p327) :args (@t267)) % 0.46/0.63 (step @p330 :rule cong :premises (@p329) :args (@t268)) % 0.46/0.63 (step @p331 :rule beta-reduce :args ((= (_ @t40 @t265) @t268))) % 0.46/0.63 (step @p332 :rule trans :premises (@p331 @p330)) % 0.46/0.63 ; trust TRUST_THEORY_REWRITE % 0.46/0.63 (step @p333 :rule trust :premises () :args ((= @t271 @t265))) % 0.46/0.63 (step @p334 :rule beta-reduce :args ((= (_ @t272 @t270) @t271))) % 0.46/0.63 (step @p335 :rule trans :premises (@p334 @p333)) % 0.46/0.63 (step @p336 :rule refl :args (@t269)) % 0.46/0.63 (step @p337 :rule refl :args (@t273)) % 0.46/0.63 (step @p338 :rule cong :premises (@p337 @p336) :args ((= @t273 @t269))) % 0.46/0.63 (step @p339 :rule symm :premises (@p338)) % 0.46/0.63 (step @p340 :rule eq_resolve :premises (@p337 @p339)) % 0.46/0.63 (step @p341 :rule nary_cong :premises (@p143 @p340) :args (@t274)) % 0.46/0.63 (step @p342 :rule cong :premises (@p341) :args ((forall @t45 @t274))) % 0.46/0.63 (step @p343 :rule bool-impl-elim :args (@t44 @t273)) % 0.46/0.63 (step @p344 :rule cong :premises (@p343) :args ((forall @t45 @t275))) % 0.46/0.63 (step @p345 :rule trans :premises (@p344 @p342)) % 0.46/0.63 (step @p346 :rule beta-reduce :args ((= @t278 @t275))) % 0.46/0.63 (step @p347 :rule cong :premises (@p346) :args (@t279)) % 0.46/0.63 (step @p348 :rule trans :premises (@p347 @p345)) % 0.46/0.63 (step @p349 :rule cong :premises (@p348) :args (@t280)) % 0.46/0.63 (step @p350 :rule beta-reduce :args ((= (_ @t281 @t277) @t280))) % 0.46/0.63 (step @p351 :rule trans :premises (@p350 @p349)) % 0.46/0.63 (step @p352 :rule beta-reduce :args ((= (_ @t282 @t3) @t276))) % 0.46/0.63 (step @p353 :rule beta-reduce :args ((= (_ @t283 @t14) @t282))) % 0.46/0.63 (step @p354 :rule refl :args (@t14)) % 0.46/0.63 (step @p355 :rule beta-reduce :args ((= @t284 @t283))) % 0.46/0.63 (step @p356 :rule ho_cong :premises (@p355 @p354)) % 0.46/0.63 (step @p357 :rule trans :premises (@p356 @p353)) % 0.46/0.63 (step @p358 :rule ho_cong :premises (@p357 @p134)) % 0.46/0.63 (step @p359 :rule trans :premises (@p358 @p352)) % 0.46/0.63 (step @p360 :rule cong :premises (@p359) :args (@t285)) % 0.46/0.63 (step @p361 :rule refl :args (@t281)) % 0.46/0.63 (step @p362 :rule ho_cong :premises (@p361 @p360)) % 0.46/0.63 (step @p363 :rule trans :premises (@p362 @p351)) % 0.46/0.63 (step @p364 :rule ho_cong :premises (@p233 @p363)) % 0.46/0.63 (step @p365 :rule beta-reduce :args ((= @t286 @t272))) % 0.46/0.63 (step @p366 :rule ho_cong :premises (@p365 @p364)) % 0.46/0.63 (step @p367 :rule trans :premises (@p366 @p335)) % 0.46/0.63 (step @p368 :rule refl :args (@t40)) % 0.46/0.63 (step @p369 :rule ho_cong :premises (@p368 @p367)) % 0.46/0.63 (step @p370 :rule trans :premises (@p369 @p332)) % 0.46/0.63 (step @p371 :rule ho_cong :premises (@p370 @p326)) % 0.46/0.63 (step @p372 :rule trans :premises (@p371 @p325)) % 0.46/0.63 (step @p373 :rule ho_cong :premises (@p372 @p134)) % 0.46/0.63 (step @p374 :rule trans :premises (@p373 @p324)) % 0.46/0.63 (step @p375 :rule cong :premises (@p374) :args (@t287)) % 0.46/0.63 (step @p376 :rule ho_cong :premises (@p160 @p375)) % 0.46/0.63 (step @p377 :rule trans :premises (@p376 @p323)) % 0.46/0.63 (step @p378 :rule ho_cong :premises (@p377 @p134)) % 0.46/0.63 (step @p379 :rule trans :premises (@p378 @p283)) % 0.46/0.63 (step @p380 :rule cong :premises (@p379) :args ((lambda @t10 (_ (_ @t153 @t287) @t3)))) % 0.46/0.63 (step @p381 :rule ho_cong :premises (@p160 @p380)) % 0.46/0.63 (step @p382 :rule trans :premises (@p381 @p282)) % 0.46/0.63 (step @p383 :rule ho_cong :premises (@p163 @p382)) % 0.46/0.63 (step @p384 :rule trans :premises (@p383 @p253)) % 0.46/0.63 (step @p385 :rule refl :args (@t7)) % 0.46/0.63 (step @p386 :rule ho_cong :premises (@p16 @p385)) % 0.46/0.63 (step @p387 :rule ho_cong :premises (@p386 @p354)) % 0.46/0.63 (step @p388 :rule ho_cong :premises (@p387 @p134)) % 0.46/0.63 (step @p389 :rule cong :premises (@p388) :args (@t15)) % 0.46/0.63 (step @p390 :rule cong :premises (@p142) :args (@t46)) % 0.46/0.63 (step @p391 :rule cong :premises (@p390) :args (@t48)) % 0.46/0.63 (step @p392 :rule trans :premises (@p20 @p391)) % 0.46/0.63 (step @p393 :rule ho_cong :premises (@p392 @p389)) % 0.46/0.63 (step @p394 :rule ho_cong :premises (@p233 @p393)) % 0.46/0.63 (step @p395 :rule ho_cong :premises (@p15 @p175)) % 0.46/0.63 (step @p396 :rule ho_cong :premises (@p395 @p394)) % 0.46/0.63 (step @p397 :rule ho_cong :premises (@p16 @p396)) % 0.46/0.63 (step @p398 :rule ho_cong :premises (@p397 @p326)) % 0.46/0.63 (step @p399 :rule ho_cong :premises (@p398 @p134)) % 0.46/0.63 (step @p400 :rule cong :premises (@p399) :args (@t17)) % 0.46/0.63 (step @p401 :rule ho_cong :premises (@p187 @p400)) % 0.46/0.63 (step @p402 :rule ho_cong :premises (@p401 @p134)) % 0.46/0.63 (step @p403 :rule cong :premises (@p402) :args (@t18)) % 0.46/0.63 (step @p404 :rule ho_cong :premises (@p187 @p403)) % 0.46/0.63 (step @p405 :rule ho_cong :premises (@p196 @p404)) % 0.46/0.63 (step @p406 :rule trans :premises (@p405 @p384)) % 0.46/0.63 (step @p407 :rule trans :premises (@p406 @p247)) % 0.46/0.63 (step @p408 :rule eq_resolve :premises (@p4 @p407)) % 0.46/0.63 (step @p409 :rule instantiate :premises (@p408) :args ((@list @t176 @t175 @t291))) % 0.46/0.63 (step @p410 :rule quant-merge-prenex :args ((= (forall @t27 @t298) @t297))) % 0.46/0.63 (step @p411 :rule beta-reduce :args ((= @t300 @t298))) % 0.46/0.63 (step @p412 :rule cong :premises (@p411) :args (@t301)) % 0.46/0.63 (step @p413 :rule trans :premises (@p412 @p410)) % 0.46/0.63 (step @p414 :rule beta-reduce :args ((= (_ @t137 @t299) @t301))) % 0.46/0.63 (step @p415 :rule trans :premises (@p414 @p413)) % 0.46/0.63 (step @p416 :rule refl :args ((tptp.positive @t304 @t25))) % 0.46/0.63 (step @p417 :rule refl :args (@t292)) % 0.46/0.63 (step @p418 :rule cong :premises (@p417) :args (@t293)) % 0.46/0.63 (step @p419 :rule cong :premises (@p418) :args (@t294)) % 0.46/0.63 (step @p420 :rule cong :premises (@p419 @p101) :args (@t295)) % 0.46/0.63 (step @p421 :rule trans :premises (@p420 @p416)) % 0.46/0.63 (step @p422 :rule refl :args (tptp.positive)) % 0.46/0.63 (step @p423 :rule ho_cong :premises (@p422 @p419)) % 0.46/0.63 (step @p424 :rule ho_cong :premises (@p423 @p101)) % 0.46/0.63 (step @p425 :rule cong :premises (@p424 @p421) :args ((= (_ (_ tptp.positive @t294) @t25) @t295))) % 0.46/0.63 (step @p426 :rule symm :premises (@p425)) % 0.46/0.63 (step @p427 :rule refl :args (@t305)) % 0.46/0.63 (step @p428 :rule eq_resolve :premises (@p427 @p426)) % 0.46/0.63 (step @p429 :rule refl :args (@t302)) % 0.46/0.63 (step @p430 :rule cong :premises (@p429 @p417) :args ((= @t302 @t292))) % 0.46/0.63 (step @p431 :rule symm :premises (@p430)) % 0.46/0.63 (step @p432 :rule eq_resolve :premises (@p429 @p431)) % 0.46/0.63 (step @p433 :rule cong :premises (@p432) :args (@t303)) % 0.46/0.63 (step @p434 :rule cong :premises (@p433) :args (@t304)) % 0.46/0.63 (step @p435 :rule ho_cong :premises (@p422 @p434)) % 0.46/0.63 (step @p436 :rule ho_cong :premises (@p435 @p101)) % 0.46/0.63 (step @p437 :rule trans :premises (@p436 @p428)) % 0.46/0.63 (step @p438 :rule cong :premises (@p121 @p437) :args (@t306)) % 0.46/0.63 (step @p439 :rule cong :premises (@p438) :args ((forall @t52 @t306))) % 0.46/0.63 (step @p440 :rule beta-reduce :args ((= @t310 @t306))) % 0.46/0.63 (step @p441 :rule cong :premises (@p440) :args (@t311)) % 0.46/0.63 (step @p442 :rule trans :premises (@p441 @p439)) % 0.46/0.63 (step @p443 :rule cong :premises (@p442) :args (@t312)) % 0.46/0.63 (step @p444 :rule beta-reduce :args ((= (_ @t153 @t309) @t312))) % 0.46/0.63 (step @p445 :rule trans :premises (@p444 @p443)) % 0.46/0.63 (step @p446 :rule beta-reduce :args ((= (_ (lambda @t27 (= @t246 @t313)) @t3) @t308))) % 0.46/0.63 (step @p447 :rule eq-symm :args (@t313 @t246)) % 0.46/0.63 (step @p448 :rule cong :premises (@p447) :args ((lambda @t27 (= @t313 @t246)))) % 0.46/0.63 (step @p449 :rule ho_cong :premises (@p448 @p134)) % 0.46/0.63 (step @p450 :rule trans :premises (@p449 @p446)) % 0.46/0.63 (step @p451 :rule refl :args (@t3)) % 0.46/0.63 (step @p452 :rule refl :args (@t246)) % 0.46/0.63 (step @p453 :rule alpha_equiv :args (@t315 (@list @t3) (@list @t288))) % 0.46/0.63 (step @p454 :rule ho_cong :premises (@p422 @p453)) % 0.46/0.63 (step @p455 :rule ho_cong :premises (@p454 @p101)) % 0.46/0.63 (step @p456 :rule cong :premises (@p455 @p452) :args (@t318)) % 0.46/0.63 (step @p457 :rule cong :premises (@p456) :args ((lambda @t27 @t318))) % 0.46/0.63 (step @p458 :rule ho_cong :premises (@p457 @p451)) % 0.46/0.63 (step @p459 :rule trans :premises (@p458 @p450)) % 0.46/0.63 (step @p460 :rule beta-reduce :args ((= @t320 @t246))) % 0.46/0.63 (step @p461 :rule refl :args (@t317)) % 0.46/0.63 (step @p462 :rule cong :premises (@p461 @p460) :args ((= @t317 @t320))) % 0.46/0.63 (step @p463 :rule eq-symm :args (@t320 @t317)) % 0.46/0.63 (step @p464 :rule trans :premises (@p463 @p462)) % 0.46/0.63 (step @p465 :rule cong :premises (@p464) :args (@t321)) % 0.46/0.63 (step @p466 :rule beta-reduce :args ((= (_ (lambda @t161 (= @t36 @t317)) @t319) @t321))) % 0.46/0.63 (step @p467 :rule trans :premises (@p466 @p465)) % 0.46/0.63 (step @p468 :rule beta-reduce :args ((= @t322 @t319))) % 0.46/0.63 (step @p469 :rule eq-symm :args (@t317 @t36)) % 0.46/0.63 (step @p470 :rule cong :premises (@p469) :args (@t323)) % 0.46/0.63 (step @p471 :rule beta-reduce :args ((= (_ @t42 @t316) @t323))) % 0.46/0.63 (step @p472 :rule trans :premises (@p471 @p470)) % 0.46/0.63 (step @p473 :rule beta-reduce :args ((= (_ @t324 @t3) @t314))) % 0.46/0.63 (step @p474 :rule beta-reduce :args ((= @t325 @t324))) % 0.46/0.63 (step @p475 :rule ho_cong :premises (@p474 @p134)) % 0.46/0.63 (step @p476 :rule trans :premises (@p475 @p473)) % 0.46/0.63 (step @p477 :rule cong :premises (@p476) :args (@t326)) % 0.46/0.63 (step @p478 :rule refl :args (tptp.positive)) % 0.46/0.63 (step @p479 :rule ho_cong :premises (@p478 @p477)) % 0.46/0.63 (step @p480 :rule refl :args (@t42)) % 0.46/0.63 (step @p481 :rule ho_cong :premises (@p480 @p479)) % 0.46/0.63 (step @p482 :rule trans :premises (@p481 @p472)) % 0.46/0.63 (step @p483 :rule ho_cong :premises (@p482 @p468)) % 0.46/0.63 (step @p484 :rule trans :premises (@p483 @p467)) % 0.46/0.63 (step @p485 :rule ho_cong :premises (@p484 @p134)) % 0.46/0.63 (step @p486 :rule trans :premises (@p485 @p459)) % 0.46/0.63 (step @p487 :rule cong :premises (@p486) :args ((lambda @t10 (_ (_ (_ @t42 (_ tptp.positive @t326)) @t322) @t3)))) % 0.46/0.63 (step @p488 :rule ho_cong :premises (@p160 @p487)) % 0.46/0.63 (step @p489 :rule trans :premises (@p488 @p445)) % 0.46/0.63 (step @p490 :rule ho_cong :premises (@p163 @p489)) % 0.46/0.63 (step @p491 :rule trans :premises (@p490 @p415)) % 0.46/0.63 (step @p492 :rule ho_cong :premises (@p13 @p175)) % 0.46/0.63 (step @p493 :rule ho_cong :premises (@p13 @p385)) % 0.46/0.63 (step @p494 :rule ho_cong :premises (@p493 @p134)) % 0.46/0.63 (step @p495 :rule cong :premises (@p494) :args (@t9)) % 0.46/0.63 (step @p496 :rule ho_cong :premises (@p478 @p495)) % 0.46/0.63 (step @p497 :rule ho_cong :premises (@p18 @p496)) % 0.46/0.63 (step @p498 :rule ho_cong :premises (@p497 @p492)) % 0.46/0.63 (step @p499 :rule ho_cong :premises (@p498 @p134)) % 0.46/0.63 (step @p500 :rule cong :premises (@p499) :args (@t11)) % 0.46/0.63 (step @p501 :rule ho_cong :premises (@p187 @p500)) % 0.46/0.63 (step @p502 :rule ho_cong :premises (@p196 @p501)) % 0.46/0.63 (step @p503 :rule trans :premises (@p502 @p491)) % 0.46/0.63 (step @p504 :rule eq_resolve :premises (@p3 @p503)) % 0.46/0.63 (step @p505 :rule refl :args (@t176)) % 0.46/0.63 (step @p506 :rule eq-refl :args (@t290)) % 0.46/0.63 (step @p507 :rule skolem_intro :args (@t291)) % 0.46/0.63 (step @p508 :rule refl :args (@t290)) % 0.46/0.63 (step @p509 :rule cong :premises (@p508 @p507) :args ((= @t290 @t291))) % 0.46/0.63 (step @p510 :rule trans :premises (@p509 @p506)) % 0.46/0.63 (step @p511 :rule true_elim :premises (@p510)) % 0.46/0.63 (step @p512 :rule cong :premises (@p511 @p505) :args (@t327)) % 0.46/0.63 (step @p513 :rule refl :args (@t181)) % 0.46/0.63 (step @p514 :rule cong :premises (@p513 @p512) :args (@t328)) % 0.46/0.63 (step @p515 :rule refl :args (@t297)) % 0.46/0.63 (step @p516 :rule cong :premises (@p515 @p514) :args ((=> @t297 @t328))) % 0.46/0.63 (assume-push @p559 @t297) % 0.46/0.63 (step @p518 :rule instantiate :premises (@p504) :args ((@list @t176 @t175))) % 0.46/0.63 (step-pop @p560 :rule scope :premises (@p518)) % 0.46/0.63 (step @p519 :rule process_scope :premises (@p560) :args (@t328)) % 0.46/0.63 (step @p521 :rule eq_resolve :premises (@p519 @p516)) % 0.46/0.63 (step @p522 :rule implies_elim :premises (@p521)) % 0.46/0.63 (step @p523 :rule chain_m_resolution :premises (@p522 @p504) :args (@t330 (@list false) (@list @t297))) % 0.46/0.63 (step @p524 :rule bool-double-not-elim :args (@t180)) % 0.46/0.63 (step @p525 :rule nary_cong :premises (@p204 @p524) :args ((or @t182 (not @t181)))) % 0.46/0.63 (step @p526 :rule cnf_or_neg :args (@t182 0)) % 0.46/0.63 (step @p527 :rule eq_resolve :premises (@p526 @p525)) % 0.46/0.63 (step @p528 :rule reordering :premises (@p527) :args ((or @t180 @t182))) % 0.46/0.63 (step @p529 :rule chain_m_resolution :premises (@p528 @p202) :args (@t180 @t183 @t184)) % 0.46/0.63 (step @p530 :rule cnf_equiv_pos2 :args (@t330)) % 0.46/0.63 (step @p531 :rule reordering :premises (@p530) :args ((or @t181 @t331 (not @t330)))) % 0.46/0.63 (step @p532 :rule chain_m_resolution :premises (@p531 @p529 @p523) :args (@t331 @t332 (@list @t180 @t330))) % 0.46/0.63 (step @p533 :rule cnf_or_pos :args (@t335)) % 0.46/0.63 (step @p534 :rule reordering :premises (@p533) :args ((or @t181 @t329 @t334 (not @t335)))) % 0.46/0.63 (step @p535 :rule chain_m_resolution :premises (@p534 @p529 @p532 @p409) :args (@t334 (@list false true false) (@list @t180 @t329 @t335))) % 0.46/0.63 (step @p536 :rule skolemize :premises (@p535)) % 0.46/0.63 (step @p537 :rule bool-double-not-elim :args (@t338)) % 0.46/0.63 (step @p538 :rule refl :args (@t342)) % 0.46/0.63 (step @p539 :rule nary_cong :premises (@p538 @p537) :args ((or @t342 (not @t339)))) % 0.46/0.63 (step @p540 :rule cnf_or_neg :args (@t342 1)) % 0.46/0.63 (step @p541 :rule eq_resolve :premises (@p540 @p539)) % 0.46/0.63 (step @p542 :rule reordering :premises (@p541) :args ((or @t338 @t342))) % 0.46/0.63 (step @p543 :rule chain_m_resolution :premises (@p542 @p536) :args (@t338 @t183 @t343)) % 0.46/0.63 (step @p544 :rule bool-double-not-elim :args (@t340)) % 0.46/0.63 (step @p545 :rule nary_cong :premises (@p538 @p544) :args ((or @t342 (not @t341)))) % 0.46/0.63 (step @p546 :rule cnf_or_neg :args (@t342 0)) % 0.46/0.63 (step @p547 :rule eq_resolve :premises (@p546 @p545)) % 0.46/0.63 (step @p548 :rule reordering :premises (@p547) :args ((or @t340 @t342))) % 0.46/0.63 (step @p549 :rule chain_m_resolution :premises (@p548 @p536) :args (@t340 @t183 @t343)) % 0.46/0.63 (step @p550 :rule cnf_or_pos :args (@t344)) % 0.46/0.63 (step @p551 :rule reordering :premises (@p550) :args ((or @t341 @t339 @t345))) % 0.46/0.63 (step @p552 :rule chain_m_resolution :premises (@p551 @p549 @p543) :args (@t345 @t332 (@list @t340 @t338))) % 0.46/0.63 (assume-push @p561 @t178) % 0.46/0.63 (step @p554 :rule instantiate :premises (@p209) :args ((@list @t336 @t337))) % 0.46/0.63 (step-pop @p562 :rule scope :premises (@p554)) % 0.46/0.63 (step @p555 :rule process_scope :premises (@p562) :args (@t344)) % 0.46/0.63 (step @p557 :rule implies_elim :premises (@p555)) % 0.46/0.63 (step @p558 false :rule chain_m_resolution :premises (@p557 @p552 @p209) :args (false (@list true false) (@list @t344 @t178))) % 0.46/0.63 ) % 0.46/0.63 % SZS output end Proof % 0.46/0.63 % cvc5 exiting %------------------------------------------------------------------------------