%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PHI005^2 : 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 : n003.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 08:43:11 AM UTC 2026 % Result : Theorem 210.46s 210.95s % Output : Proof 210.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PHI005^2 : TPTP v9.2.1. Released v6.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n003.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 12:51:44 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 210.46/210.95 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 210.46/210.95 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 210.46/210.95 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 210.46/210.95 --- Run --ho-elim --full-saturate-quant at 18s... % 210.46/210.95 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 210.46/210.95 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 12s... % 210.46/210.95 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 9s... % 210.46/210.95 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 6s... % 210.46/210.95 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 21s... % 210.46/210.95 % SZS status Theorem % 210.46/210.95 % SZS output start Proof % 210.46/210.95 ( % 210.46/210.95 (declare-sort tptp.mu 0) % 210.46/210.95 (declare-sort $$unsorted 0) % 210.46/210.95 (declare-const tptp.positive (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)) % 210.46/210.95 (declare-const tptp.mbox (-> (-> $$unsorted Bool) $$unsorted Bool)) % 210.46/210.95 (declare-const tptp.essence (-> (-> tptp.mu $$unsorted Bool) tptp.mu $$unsorted Bool)) % 210.46/210.95 (declare-const tptp.mdia (-> (-> $$unsorted Bool) $$unsorted Bool)) % 210.46/210.95 (declare-const tptp.rel (-> $$unsorted $$unsorted Bool)) % 210.46/210.95 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 210.46/210.95 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 210.46/210.95 (define tptp.mfalse () (lambda (@list (@var "W" $$unsorted)) false)) % 210.46/210.95 (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)))))) % 210.46/210.95 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 210.46/210.95 (define tptp.mand () (let ((_let_1 (@var "W" $$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))))))) % 210.46/210.95 (define tptp.mimplies () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 210.46/210.95 (define tptp.mimplied () (let ((_let_1 (@var "W" $$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))))))) % 210.46/210.95 (define tptp.mequiv () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 210.46/210.95 (define tptp.mxor () (let ((_let_1 (@var "W" $$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))))))))) % 210.46/210.95 (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))))))) % 210.46/210.95 (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))))))) % 210.46/210.95 (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))))))) % 210.46/210.95 (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))))))) % 210.46/210.95 (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))))))) % 210.46/210.95 (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))))))) % 210.46/210.95 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 210.46/210.95 (define tptp.mdia_generic () (let ((_let_1 (@var "V" $$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))))))))) % 210.46/210.95 (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)))))) % 210.46/210.95 (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))))))) % 210.46/210.95 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 210.46/210.95 (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)))))) % 210.46/210.95 (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))))))) % 210.46/210.95 (define @t1 () (= tptp.mbox (_ tptp.mbox_generic tptp.rel))) % 210.46/210.95 (define @t2 () (= tptp.mdia (_ tptp.mdia_generic tptp.rel))) % 210.46/210.95 (define @t3 () (@var "__flatten_var_0" $$unsorted)) % 210.46/210.95 (define @t4 () (@var "X" tptp.mu)) % 210.46/210.95 (define @t5 () (_ tptp.god @t4)) % 210.46/210.95 (define @t6 () (@list @t4 @t3)) % 210.46/210.95 (define @t7 () (lambda @t6 (_ @t5 @t3))) % 210.46/210.95 (define @t8 () (_ tptp.mexists_ind @t7)) % 210.46/210.95 (define @t9 () (lambda @t6 (_ (_ (_ tptp.mimplies @t5) (_ (_ tptp.essence tptp.god) @t4)) @t3))) % 210.46/210.95 (define @t10 () (not (_ tptp.mvalid (_ tptp.mbox @t8)))) % 210.46/210.95 (define @t11 () (@var "Y" tptp.mu)) % 210.46/210.95 (define @t12 () (@var "W" $$unsorted)) % 210.46/210.95 (define @t13 () (lambda (@list @t4 @t11 @t12) (= @t4 @t11))) % 210.46/210.95 (define @t14 () (@list @t12)) % 210.46/210.95 (define @t15 () (lambda @t14 true)) % 210.46/210.95 (define @t16 () (lambda @t14 false)) % 210.46/210.95 (define @t17 () (@var "Phi" (-> $$unsorted Bool))) % 210.46/210.95 (define @t18 () (_ @t17 @t12)) % 210.46/210.95 (define @t19 () (not @t18)) % 210.46/210.95 (define @t20 () (@list @t17 @t12)) % 210.46/210.95 (define @t21 () (lambda @t20 @t19)) % 210.46/210.95 (define @t22 () (@var "Psi" (-> $$unsorted Bool))) % 210.46/210.95 (define @t23 () (_ @t22 @t12)) % 210.46/210.95 (define @t24 () (@list @t17 @t22 @t12)) % 210.46/210.95 (define @t25 () (lambda @t24 (or @t18 @t23))) % 210.46/210.95 (define @t26 () (lambda @t24 (and @t18 @t23))) % 210.46/210.95 (define @t27 () (lambda @t24 (=> @t18 @t23))) % 210.46/210.95 (define @t28 () (lambda @t24 (=> @t23 @t18))) % 210.46/210.95 (define @t29 () (lambda @t24 (= @t18 @t23))) % 210.46/210.95 (define @t30 () (lambda @t24 (or (and @t18 (not @t23)) (and @t19 @t23)))) % 210.46/210.95 (define @t31 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 210.46/210.95 (define @t32 () (_ @t31 @t4)) % 210.46/210.95 (define @t33 () (_ @t32 @t12)) % 210.46/210.95 (define @t34 () (@list @t4)) % 210.46/210.95 (define @t35 () (forall @t34 @t33)) % 210.46/210.95 (define @t36 () (@list @t31 @t12)) % 210.46/210.95 (define @t37 () (lambda @t36 @t35)) % 210.46/210.95 (define @t38 () (@var "X" (-> tptp.mu $$unsorted Bool))) % 210.46/210.95 (define @t39 () (@var "Phi" (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool))) % 210.46/210.95 (define @t40 () (_ (_ @t39 @t38) @t12)) % 210.46/210.95 (define @t41 () (@list @t38)) % 210.46/210.95 (define @t42 () (forall @t41 @t40)) % 210.46/210.95 (define @t43 () (@list @t39 @t12)) % 210.46/210.95 (define @t44 () (lambda @t43 @t42)) % 210.46/210.95 (define @t45 () (@var "P" (-> $$unsorted Bool))) % 210.46/210.95 (define @t46 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 210.46/210.95 (define @t47 () (_ (_ @t46 @t45) @t12)) % 210.46/210.95 (define @t48 () (@list @t45)) % 210.46/210.95 (define @t49 () (@list @t46 @t12)) % 210.46/210.95 (define @t50 () (lambda @t49 (forall @t48 @t47))) % 210.46/210.95 (define @t51 () (exists @t34 @t33)) % 210.46/210.95 (define @t52 () (lambda @t36 @t51)) % 210.46/210.95 (define @t53 () (lambda @t43 (exists @t41 @t40))) % 210.46/210.95 (define @t54 () (lambda @t49 (exists @t48 @t47))) % 210.46/210.95 (define @t55 () (@var "V" $$unsorted)) % 210.46/210.95 (define @t56 () (_ @t17 @t55)) % 210.46/210.95 (define @t57 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 210.46/210.95 (define @t58 () (_ (_ @t57 @t12) @t55)) % 210.46/210.95 (define @t59 () (not @t58)) % 210.46/210.95 (define @t60 () (or @t59 @t56)) % 210.46/210.95 (define @t61 () (@list @t55)) % 210.46/210.95 (define @t62 () (forall @t61 @t60)) % 210.46/210.95 (define @t63 () (@list @t57 @t17 @t12)) % 210.46/210.95 (define @t64 () (lambda @t63 @t62)) % 210.46/210.95 (define @t65 () (and @t58 @t56)) % 210.46/210.95 (define @t66 () (exists @t61 @t65)) % 210.46/210.95 (define @t67 () (lambda @t63 @t66)) % 210.46/210.95 (define @t68 () (forall @t14 @t18)) % 210.46/210.95 (define @t69 () (@list @t17)) % 210.46/210.95 (define @t70 () (lambda @t69 @t68)) % 210.46/210.95 (define @t71 () (lambda @t69 (forall @t14 @t19))) % 210.46/210.95 (define @t72 () (@var "S" $$unsorted)) % 210.46/210.95 (define @t73 () (@var "T" $$unsorted)) % 210.46/210.95 (define @t74 () (_ (_ @t57 @t73) @t72)) % 210.46/210.95 (define @t75 () (_ (_ @t57 @t72) @t73)) % 210.46/210.95 (define @t76 () (@list @t72 @t73)) % 210.46/210.95 (define @t77 () (forall @t76 (=> @t75 @t74))) % 210.46/210.95 (define @t78 () (@list @t57)) % 210.46/210.95 (define @t79 () (lambda @t78 @t77)) % 210.46/210.95 (define @t80 () (_ tptp.positive @t31)) % 210.46/210.95 (define @t81 () (@list @t31 @t3)) % 210.46/210.95 (define @t82 () (lambda @t81 (_ (_ (_ tptp.mimplies @t80) @t32) @t3))) % 210.46/210.95 (define @t83 () (lambda @t6 (_ (_ tptp.mforall_indset @t82) @t3))) % 210.46/210.95 (define @t84 () (lambda (@list @t11 @t3) (_ (_ @t31 @t11) @t3))) % 210.46/210.95 (define @t85 () (_ (_ tptp.essence @t31) @t4)) % 210.46/210.95 (define @t86 () (lambda @t81 (_ (_ (_ tptp.mimplies @t85) (_ tptp.mbox (_ tptp.mexists_ind @t84))) @t3))) % 210.46/210.95 (define @t87 () (lambda @t6 (_ (_ tptp.mforall_indset @t86) @t3))) % 210.46/210.95 (define @t88 () (@var "BOUND_VARIABLE_8066" $$unsorted)) % 210.46/210.95 (define @t89 () (@var "BOUND_VARIABLE_8086" tptp.mu)) % 210.46/210.95 (define @t90 () (_ @t38 @t89 @t88)) % 210.46/210.95 (define @t91 () (tptp.positive @t38 @t88)) % 210.46/210.95 (define @t92 () (not @t91)) % 210.46/210.95 (define @t93 () (or @t92 @t90)) % 210.46/210.95 (define @t94 () (forall @t41 @t93)) % 210.46/210.95 (define @t95 () (@list @t89 @t88)) % 210.46/210.95 (define @t96 () (lambda @t95 @t94)) % 210.46/210.95 (define @t97 () (tptp.essence @t96 @t4 @t12)) % 210.46/210.95 (define @t98 () (_ @t38 @t4 @t12)) % 210.46/210.95 (define @t99 () (tptp.positive @t38 @t12)) % 210.46/210.95 (define @t100 () (not @t99)) % 210.46/210.95 (define @t101 () (or @t100 @t98)) % 210.46/210.95 (define @t102 () (forall @t41 @t101)) % 210.46/210.95 (define @t103 () (not @t102)) % 210.46/210.95 (define @t104 () (or @t103 @t97)) % 210.46/210.95 (define @t105 () (forall (@list @t12 @t4) @t104)) % 210.46/210.95 (define @t106 () (forall @t34 @t104)) % 210.46/210.95 (define @t107 () (lambda @t14 @t106)) % 210.46/210.95 (define @t108 () (_ @t107 @t12)) % 210.46/210.95 (define @t109 () (forall @t14 @t108)) % 210.46/210.95 (define @t110 () (_ @t17 @t12)) % 210.46/210.95 (define @t111 () (lambda @t69 (forall @t14 @t110))) % 210.46/210.95 (define @t112 () (_ tptp.positive @t38)) % 210.46/210.95 (define @t113 () (lambda @t95 (forall @t41 (or (not (_ @t112 @t88)) (_ (_ @t38 @t89) @t88))))) % 210.46/210.95 (define @t114 () (_ (_ tptp.essence @t96) @t4)) % 210.46/210.95 (define @t115 () (_ @t114 @t12)) % 210.46/210.95 (define @t116 () (or @t103 @t115)) % 210.46/210.95 (define @t117 () (=> @t102 @t115)) % 210.46/210.95 (define @t118 () (forall @t41 (or (not (tptp.positive @t38 @t3)) (_ @t38 @t4 @t3)))) % 210.46/210.95 (define @t119 () (lambda @t6 (=> @t118 (_ @t114 @t3)))) % 210.46/210.95 (define @t120 () (_ @t119 @t4 @t12)) % 210.46/210.95 (define @t121 () (forall @t34 @t120)) % 210.46/210.95 (define @t122 () (lambda @t14 @t121)) % 210.46/210.95 (define @t123 () (_ @t31 @t4 @t12)) % 210.46/210.95 (define @t124 () (lambda @t36 (forall @t34 @t123))) % 210.46/210.95 (define @t125 () (_ (_ tptp.essence (lambda (@list @t4 @t88) (forall @t41 (or @t92 (_ @t38 @t4 @t88))))) @t4)) % 210.46/210.95 (define @t126 () (=> @t118 (_ @t125 @t3))) % 210.46/210.95 (define @t127 () (lambda @t6 @t118)) % 210.46/210.95 (define @t128 () (_ (_ tptp.essence @t127) @t4)) % 210.46/210.95 (define @t129 () (=> @t102 (_ @t128 @t12))) % 210.46/210.95 (define @t130 () (lambda @t14 @t129)) % 210.46/210.95 (define @t131 () (@list @t22 @t12)) % 210.46/210.95 (define @t132 () (lambda (@list @t3) @t118)) % 210.46/210.95 (define @t133 () (_ @t132 @t12)) % 210.46/210.95 (define @t134 () (=> @t133 @t23)) % 210.46/210.95 (define @t135 () (lambda @t131 @t134)) % 210.46/210.95 (define @t136 () (_ @t127 @t4)) % 210.46/210.95 (define @t137 () (_ @t38 @t4)) % 210.46/210.95 (define @t138 () (_ @t137 @t12)) % 210.46/210.95 (define @t139 () (_ @t112 @t12)) % 210.46/210.95 (define @t140 () (not @t139)) % 210.46/210.95 (define @t141 () (or @t140 @t138)) % 210.46/210.95 (define @t142 () (forall @t41 @t141)) % 210.46/210.95 (define @t143 () (=> @t139 @t138)) % 210.46/210.95 (define @t144 () (=> (_ @t80 @t3) (_ @t32 @t3))) % 210.46/210.95 (define @t145 () (lambda @t81 @t144)) % 210.46/210.95 (define @t146 () (_ @t145 @t38 @t12)) % 210.46/210.95 (define @t147 () (forall @t41 @t146)) % 210.46/210.95 (define @t148 () (lambda @t14 @t147)) % 210.46/210.95 (define @t149 () (_ @t39 @t38 @t12)) % 210.46/210.95 (define @t150 () (lambda @t43 (forall @t41 @t149))) % 210.46/210.95 (define @t151 () (_ @t80 @t12)) % 210.46/210.95 (define @t152 () (lambda @t14 (=> @t151 @t33))) % 210.46/210.95 (define @t153 () (lambda @t131 (=> @t151 @t23))) % 210.46/210.95 (define @t154 () (_ @t27 @t80)) % 210.46/210.95 (define @t155 () (@var "BOUND_VARIABLE_8204" tptp.mu)) % 210.46/210.95 (define @t156 () (not (tptp.positive @t38 @t55))) % 210.46/210.95 (define @t157 () (not (forall @t41 (or @t156 (_ @t38 @t155 @t55))))) % 210.46/210.95 (define @t158 () (not (tptp.rel @t12 @t55))) % 210.46/210.95 (define @t159 () (or @t158 @t157)) % 210.46/210.95 (define @t160 () (@list @t55 @t155)) % 210.46/210.95 (define @t161 () (@list @t155)) % 210.46/210.95 (define @t162 () (forall @t161 @t159)) % 210.46/210.95 (define @t163 () (forall @t161 @t157)) % 210.46/210.95 (define @t164 () (or @t158 @t163)) % 210.46/210.95 (define @t165 () (forall @t34 (not (forall @t41 (or @t156 (_ @t38 @t4 @t55)))))) % 210.46/210.95 (define @t166 () (not @t165)) % 210.46/210.95 (define @t167 () (@var "BOUND_VARIABLE_8028" $$unsorted)) % 210.46/210.95 (define @t168 () (_ @t38 @t4 @t167)) % 210.46/210.95 (define @t169 () (tptp.positive @t38 @t167)) % 210.46/210.95 (define @t170 () (not @t169)) % 210.46/210.95 (define @t171 () (or @t170 @t168)) % 210.46/210.95 (define @t172 () (forall @t41 @t171)) % 210.46/210.95 (define @t173 () (not @t172)) % 210.46/210.95 (define @t174 () (forall @t34 @t173)) % 210.46/210.95 (define @t175 () (not @t174)) % 210.46/210.95 (define @t176 () (@list @t167)) % 210.46/210.95 (define @t177 () (lambda @t176 @t175)) % 210.46/210.95 (define @t178 () (_ @t177 @t55)) % 210.46/210.95 (define @t179 () (not @t178)) % 210.46/210.95 (define @t180 () (or @t158 @t179)) % 210.46/210.95 (define @t181 () (forall @t61 @t180)) % 210.46/210.95 (define @t182 () (not @t181)) % 210.46/210.95 (define @t183 () (_ @t17 @t55)) % 210.46/210.95 (define @t184 () (not @t183)) % 210.46/210.95 (define @t185 () (lambda @t20 (not (forall @t61 (or @t158 @t184))))) % 210.46/210.95 (define @t186 () (_ @t185 @t177 @t12)) % 210.46/210.95 (define @t187 () (_ @t57 @t12 @t55)) % 210.46/210.95 (define @t188 () (not @t187)) % 210.46/210.95 (define @t189 () (_ (lambda @t63 (not (forall @t61 (or @t188 @t184)))) tptp.rel)) % 210.46/210.95 (define @t190 () (not @t56)) % 210.46/210.95 (define @t191 () (or @t59 @t190)) % 210.46/210.95 (define @t192 () (forall @t61 (not @t65))) % 210.46/210.95 (define @t193 () (not @t192)) % 210.46/210.95 (define @t194 () (tptp.mdia @t177 @t12)) % 210.46/210.95 (define @t195 () (lambda @t176 (not (forall @t34 (not (forall @t41 (or (not (_ @t112 @t167)) (_ @t137 @t167)))))))) % 210.46/210.95 (define @t196 () (_ (_ tptp.mdia @t177) @t12)) % 210.46/210.95 (define @t197 () (forall @t34 @t103)) % 210.46/210.95 (define @t198 () (not @t197)) % 210.46/210.95 (define @t199 () (lambda @t14 @t198)) % 210.46/210.95 (define @t200 () (@list @t12)) % 210.46/210.95 (define @t201 () (_ tptp.mdia @t199)) % 210.46/210.95 (define @t202 () (_ @t201 @t12)) % 210.46/210.95 (define @t203 () (lambda @t14 (not (forall @t34 (not @t142))))) % 210.46/210.95 (define @t204 () (_ tptp.mdia @t203)) % 210.46/210.95 (define @t205 () (_ @t201 @t12)) % 210.46/210.95 (define @t206 () (forall @t14 @t205)) % 210.46/210.95 (define @t207 () (_ @t127 @t4 @t12)) % 210.46/210.95 (define @t208 () (not @t207)) % 210.46/210.95 (define @t209 () (forall @t34 @t208)) % 210.46/210.95 (define @t210 () (not @t209)) % 210.46/210.95 (define @t211 () (lambda @t14 @t210)) % 210.46/210.95 (define @t212 () (not (forall @t34 (not @t123)))) % 210.46/210.95 (define @t213 () (lambda @t36 @t212)) % 210.46/210.95 (define @t214 () (lambda @t6 (_ @t136 @t3))) % 210.46/210.95 (define @t215 () (not @t33)) % 210.46/210.95 (define @t216 () (forall @t34 @t215)) % 210.46/210.95 (define @t217 () (not @t216)) % 210.46/210.95 (define @t218 () (or @t158 @t166)) % 210.46/210.95 (define @t219 () (forall (@list @t12 @t55) @t218)) % 210.46/210.95 (define @t220 () (@quantifiers_skolemize @t219 1)) % 210.46/210.95 (define @t221 () (forall @t160 (or (not (tptp.rel @t220 @t55)) @t157))) % 210.46/210.95 (define @t222 () (@quantifiers_skolemize @t221 0)) % 210.46/210.95 (define @t223 () (@quantifiers_skolemize @t221 1)) % 210.46/210.95 (define @t224 () (forall @t41 (or (not (tptp.positive @t38 @t222)) (_ @t38 @t223 @t222)))) % 210.46/210.95 (define @t225 () (not @t224)) % 210.46/210.95 (define @t226 () (tptp.rel @t220 @t222)) % 210.46/210.95 (define @t227 () (not @t226)) % 210.46/210.95 (define @t228 () (or @t227 @t225)) % 210.46/210.95 (define @t229 () (@list true)) % 210.46/210.95 (define @t230 () (@list @t228)) % 210.46/210.95 (define @t231 () (@var "BOUND_VARIABLE_8167" $$unsorted)) % 210.46/210.95 (define @t232 () (@var "BOUND_VARIABLE_7979" tptp.mu)) % 210.46/210.95 (define @t233 () (@list @t232)) % 210.46/210.95 (define @t234 () (not (forall @t233 (not (_ @t38 @t232 @t231))))) % 210.46/210.95 (define @t235 () (@list @t38 @t231)) % 210.46/210.95 (define @t236 () (forall @t235 (or (not (tptp.essence @t38 @t223 @t222)) (not (tptp.rel @t222 @t231)) @t234))) % 210.46/210.95 (define @t237 () (not (tptp.rel @t3 @t231))) % 210.46/210.95 (define @t238 () (tptp.essence @t38 @t4 @t3)) % 210.46/210.95 (define @t239 () (not @t238)) % 210.46/210.95 (define @t240 () (or @t239 @t237 @t234)) % 210.46/210.95 (define @t241 () (lambda @t6 (forall @t235 @t240))) % 210.46/210.95 (define @t242 () (@purify @t241)) % 210.46/210.95 (define @t243 () (tptp.positive @t241 @t222)) % 210.46/210.95 (define @t244 () (not @t243)) % 210.46/210.95 (define @t245 () (or @t244 @t236)) % 210.46/210.95 (define @t246 () (_ @t241 @t223 @t222)) % 210.46/210.95 (define @t247 () (or @t244 @t246)) % 210.46/210.95 (define @t248 () (tptp.positive @t242 @t222)) % 210.46/210.95 (define @t249 () (not @t248)) % 210.46/210.95 (define @t250 () (or @t249 @t236)) % 210.46/210.95 (define @t251 () (@list false)) % 210.46/210.95 (define @t252 () (or @t237 @t234)) % 210.46/210.95 (define @t253 () (or @t239 @t252)) % 210.46/210.95 (define @t254 () (forall @t235 @t253)) % 210.46/210.95 (define @t255 () (@list @t231)) % 210.46/210.95 (define @t256 () (forall @t255 @t253)) % 210.46/210.95 (define @t257 () (forall @t255 @t252)) % 210.46/210.95 (define @t258 () (or @t239 @t257)) % 210.46/210.95 (define @t259 () (not (forall @t233 (not (_ @t38 @t232 @t55))))) % 210.46/210.95 (define @t260 () (not (tptp.rel @t3 @t55))) % 210.46/210.95 (define @t261 () (@var "BOUND_VARIABLE_7823" $$unsorted)) % 210.46/210.95 (define @t262 () (_ @t38 @t232 @t261)) % 210.46/210.95 (define @t263 () (not @t262)) % 210.46/210.95 (define @t264 () (forall @t233 @t263)) % 210.46/210.95 (define @t265 () (not @t264)) % 210.46/210.95 (define @t266 () (@list @t261)) % 210.46/210.95 (define @t267 () (lambda @t266 @t265)) % 210.46/210.95 (define @t268 () (_ @t267 @t55)) % 210.46/210.95 (define @t269 () (or @t260 @t268)) % 210.46/210.95 (define @t270 () (forall @t61 @t269)) % 210.46/210.95 (define @t271 () (lambda @t20 (forall @t61 (or @t158 @t183)))) % 210.46/210.95 (define @t272 () (_ @t271 @t267 @t3)) % 210.46/210.95 (define @t273 () (or @t239 @t272)) % 210.46/210.95 (define @t274 () (forall @t41 @t273)) % 210.46/210.95 (define @t275 () (lambda @t6 @t274)) % 210.46/210.95 (define @t276 () (tptp.positive @t275 @t12)) % 210.46/210.95 (define @t277 () (_ (lambda @t63 (forall @t61 (or @t188 @t183))) tptp.rel)) % 210.46/210.95 (define @t278 () (tptp.mbox @t267 @t3)) % 210.46/210.95 (define @t279 () (or @t239 @t278)) % 210.46/210.95 (define @t280 () (forall @t41 @t279)) % 210.46/210.95 (define @t281 () (lambda @t6 @t280)) % 210.46/210.95 (define @t282 () (tptp.positive @t281 @t12)) % 210.46/210.95 (define @t283 () (lambda @t266 (not (forall @t233 (not (_ (_ @t38 @t232) @t261)))))) % 210.46/210.95 (define @t284 () (_ (_ tptp.essence @t38) @t4)) % 210.46/210.95 (define @t285 () (lambda @t6 (forall @t41 (or (not (_ @t284 @t3)) (_ (_ tptp.mbox @t283) @t3))))) % 210.46/210.95 (define @t286 () (_ tptp.positive @t281)) % 210.46/210.95 (define @t287 () (_ @t286 @t12)) % 210.46/210.95 (define @t288 () (_ tptp.positive @t285)) % 210.46/210.95 (define @t289 () (_ @t286 @t12)) % 210.46/210.95 (define @t290 () (forall @t14 @t289)) % 210.46/210.95 (define @t291 () (_ @t38 @t4 @t261)) % 210.46/210.95 (define @t292 () (not @t291)) % 210.46/210.95 (define @t293 () (forall @t34 @t292)) % 210.46/210.95 (define @t294 () (not @t293)) % 210.46/210.95 (define @t295 () (lambda @t266 @t294)) % 210.46/210.95 (define @t296 () (forall @t41 (or @t239 (tptp.mbox @t295 @t3)))) % 210.46/210.95 (define @t297 () (tptp.mbox @t295 @t12)) % 210.46/210.95 (define @t298 () (tptp.essence @t38 @t4 @t12)) % 210.46/210.95 (define @t299 () (lambda @t266 (not (forall @t34 (not (_ @t137 @t261)))))) % 210.46/210.95 (define @t300 () (_ (_ tptp.mbox @t295) @t12)) % 210.46/210.95 (define @t301 () (_ @t284 @t12)) % 210.46/210.95 (define @t302 () (not @t301)) % 210.46/210.95 (define @t303 () (or @t302 @t300)) % 210.46/210.95 (define @t304 () (=> @t301 @t300)) % 210.46/210.95 (define @t305 () (_ tptp.mbox (lambda @t266 (not (forall @t34 (not (_ @t31 @t4 @t261))))))) % 210.46/210.95 (define @t306 () (=> (_ @t85 @t3) (_ @t305 @t3))) % 210.46/210.95 (define @t307 () (lambda @t81 @t306)) % 210.46/210.95 (define @t308 () (_ @t307 @t38 @t12)) % 210.46/210.95 (define @t309 () (forall @t41 @t308)) % 210.46/210.95 (define @t310 () (lambda @t14 @t309)) % 210.46/210.95 (define @t311 () (_ @t85 @t12)) % 210.46/210.95 (define @t312 () (lambda @t14 (=> @t311 (_ @t305 @t12)))) % 210.46/210.95 (define @t313 () (_ tptp.mbox (lambda @t14 @t212))) % 210.46/210.95 (define @t314 () (lambda @t14 (=> @t311 (_ @t313 @t12)))) % 210.46/210.95 (define @t315 () (lambda @t131 (=> @t311 @t23))) % 210.46/210.95 (define @t316 () (_ @t84 @t4 @t12)) % 210.46/210.95 (define @t317 () (not @t316)) % 210.46/210.95 (define @t318 () (forall @t34 @t317)) % 210.46/210.95 (define @t319 () (not @t318)) % 210.46/210.95 (define @t320 () (lambda @t14 @t319)) % 210.46/210.95 (define @t321 () (_ @t213 @t84)) % 210.46/210.95 (define @t322 () (_ @t27 @t85)) % 210.46/210.95 (define @t323 () (forall @t14 (tptp.positive @t241 @t12))) % 210.46/210.95 (define @t324 () (@list false false)) % 210.46/210.95 (define @t325 () (not (tptp.positive @t38 @t220))) % 210.46/210.95 (define @t326 () (forall @t41 (or @t325 (_ @t38 @t232 @t220)))) % 210.46/210.95 (define @t327 () (forall @t233 (not @t326))) % 210.46/210.95 (define @t328 () (not @t327)) % 210.46/210.95 (define @t329 () (tptp.rel @t222 @t220)) % 210.46/210.95 (define @t330 () (not @t329)) % 210.46/210.95 (define @t331 () (@purify @t96)) % 210.46/210.95 (define @t332 () (tptp.essence @t96 @t223 @t222)) % 210.46/210.95 (define @t333 () (not @t332)) % 210.46/210.95 (define @t334 () (or @t333 @t330 @t328)) % 210.46/210.95 (define @t335 () (_ @t96 @t232 @t220)) % 210.46/210.95 (define @t336 () (not @t335)) % 210.46/210.95 (define @t337 () (forall @t233 @t336)) % 210.46/210.95 (define @t338 () (not @t337)) % 210.46/210.95 (define @t339 () (or @t333 @t330 @t338)) % 210.46/210.95 (define @t340 () (tptp.essence @t331 @t223 @t222)) % 210.46/210.95 (define @t341 () (not @t340)) % 210.46/210.95 (define @t342 () (or @t341 @t330 @t328)) % 210.46/210.95 (define @t343 () (@var "BOUND_VARIABLE_8129" $$unsorted)) % 210.46/210.95 (define @t344 () (_ @t38 @t4 @t343)) % 210.46/210.95 (define @t345 () (tptp.positive @t38 @t343)) % 210.46/210.95 (define @t346 () (not @t345)) % 210.46/210.95 (define @t347 () (or @t346 @t344)) % 210.46/210.95 (define @t348 () (forall @t41 @t347)) % 210.46/210.95 (define @t349 () (not @t348)) % 210.46/210.95 (define @t350 () (forall @t34 @t349)) % 210.46/210.95 (define @t351 () (not @t350)) % 210.46/210.95 (define @t352 () (@list @t343)) % 210.46/210.95 (define @t353 () (lambda @t352 @t351)) % 210.46/210.95 (define @t354 () (_ @t353 @t55)) % 210.46/210.95 (define @t355 () (or @t158 @t354)) % 210.46/210.95 (define @t356 () (forall @t61 @t355)) % 210.46/210.95 (define @t357 () (_ @t271 @t353 @t12)) % 210.46/210.95 (define @t358 () (forall @t14 @t357)) % 210.46/210.95 (define @t359 () (tptp.mbox @t353 @t12)) % 210.46/210.95 (define @t360 () (forall @t14 @t359)) % 210.46/210.95 (define @t361 () (lambda @t352 (not (forall @t34 (not (forall @t41 (or (not (_ @t112 @t343)) (_ @t137 @t343)))))))) % 210.46/210.95 (define @t362 () (_ (_ tptp.mbox @t353) @t12)) % 210.46/210.95 (define @t363 () (_ tptp.mbox @t199)) % 210.46/210.95 (define @t364 () (_ @t363 @t12)) % 210.46/210.95 (define @t365 () (_ tptp.mbox @t203)) % 210.46/210.95 (define @t366 () (_ @t363 @t12)) % 210.46/210.95 (define @t367 () (forall @t14 @t366)) % 210.46/210.95 (define @t368 () (forall @t34 (not (forall @t41 (or @t325 (_ @t38 @t4 @t220)))))) % 210.46/210.95 (define @t369 () (not @t368)) % 210.46/210.95 (define @t370 () (or (not (tptp.rel (@quantifiers_skolemize @t219 0) @t220)) @t369)) % 210.46/210.95 (define @t371 () (@var "BOUND_VARIABLE_13021" tptp.mu)) % 210.46/210.95 (define @t372 () (@var "BOUND_VARIABLE_13022" (-> tptp.mu $$unsorted Bool))) % 210.46/210.95 (define @t373 () (@list @t371 @t372)) % 210.46/210.95 (define @t374 () (_ @t57 @t73 @t72)) % 210.46/210.95 (define @t375 () (_ @t57 @t72 @t73)) % 210.46/210.95 (define @t376 () (not @t75)) % 210.46/210.95 (define @t377 () (or @t376 @t74)) % 210.46/210.95 (define @t378 () (or @t227 @t329)) % 210.46/210.95 (define @t379 () (or @t225 @t340)) % 210.46/210.95 (define @t380 () (not @t379)) % 210.46/210.95 (define @t381 () (or @t225 @t332)) % 210.46/210.95 (assume @p1 @t1) % 210.46/210.95 (assume @p2 @t2) % 210.46/210.95 (assume @p3 (_ tptp.msymmetric tptp.rel)) % 210.46/210.95 (assume @p4 (_ tptp.mvalid (_ tptp.positive tptp.necessary_existence))) % 210.46/210.95 (assume @p5 (_ tptp.mvalid (_ tptp.mdia @t8))) % 210.46/210.95 (assume @p6 (_ tptp.mvalid (_ tptp.mforall_ind @t9))) % 210.46/210.95 (assume @p7 @t10) % 210.46/210.95 (assume @p8 true) % 210.46/210.95 (step @p9 (= tptp.meq_ind @t13) :rule refl :args (@t13)) % 210.46/210.95 (step @p10 (= tptp.mtrue @t15) :rule refl :args (@t15)) % 210.46/210.95 (step @p11 (= tptp.mfalse @t16) :rule refl :args (@t16)) % 210.46/210.95 (step @p12 (= tptp.mnot @t21) :rule refl :args (@t21)) % 210.46/210.95 (step @p13 (= tptp.mor @t25) :rule refl :args (@t25)) % 210.46/210.95 (step @p14 (= tptp.mand @t26) :rule refl :args (@t26)) % 210.46/210.95 (step @p15 (= tptp.mimplies @t27) :rule refl :args (@t27)) % 210.46/210.95 (step @p16 (= tptp.mimplied @t28) :rule refl :args (@t28)) % 210.46/210.95 (step @p17 (= tptp.mequiv @t29) :rule refl :args (@t29)) % 210.46/210.95 (step @p18 (= tptp.mxor @t30) :rule refl :args (@t30)) % 210.46/210.95 (step @p19 (= tptp.mforall_ind @t37) :rule refl :args (@t37)) % 210.46/210.95 (step @p20 (= tptp.mforall_indset @t44) :rule refl :args (@t44)) % 210.46/210.95 (step @p21 (= tptp.mforall_prop @t50) :rule refl :args (@t50)) % 210.46/210.95 (step @p22 (= tptp.mexists_ind @t52) :rule refl :args (@t52)) % 210.46/210.95 (step @p23 (= tptp.mexists_indset @t53) :rule refl :args (@t53)) % 210.46/210.95 (step @p24 (= tptp.mexists_prop @t54) :rule refl :args (@t54)) % 210.46/210.95 (step @p25 (= tptp.mbox_generic @t64) :rule refl :args (@t64)) % 210.46/210.95 (step @p26 (= tptp.mdia_generic @t67) :rule refl :args (@t67)) % 210.46/210.95 (step @p27 (= tptp.mvalid @t70) :rule refl :args (@t70)) % 210.46/210.95 (step @p28 (= tptp.minvalid @t71) :rule refl :args (@t71)) % 210.46/210.95 (step @p29 (= tptp.msymmetric @t79) :rule refl :args (@t79)) % 210.46/210.95 (step @p30 (= tptp.god @t83) :rule refl :args (@t83)) % 210.46/210.95 (step @p31 (= tptp.necessary_existence @t87) :rule refl :args (@t87)) % 210.46/210.95 (step @p32 :rule quant-merge-prenex :args ((= (forall @t14 @t106) @t105))) % 210.46/210.95 (step @p33 :rule beta-reduce :args ((= @t108 @t106))) % 210.46/210.95 (step @p34 :rule cong :premises (@p33) :args (@t109)) % 210.46/210.95 (step @p35 :rule trans :premises (@p34 @p32)) % 210.46/210.95 (step @p36 :rule beta-reduce :args ((= (_ @t111 @t107) @t109))) % 210.46/210.95 (step @p37 :rule trans :premises (@p36 @p35)) % 210.46/210.95 (step @p38 :rule refl :args ((tptp.essence @t113 @t4 @t12))) % 210.46/210.95 (step @p39 :rule refl :args (@t12)) % 210.46/210.95 (step @p40 :rule refl :args (@t4)) % 210.46/210.95 (step @p41 :rule refl :args (@t90)) % 210.46/210.95 (step @p42 :rule refl :args (@t91)) % 210.46/210.95 (step @p43 :rule cong :premises (@p42) :args (@t92)) % 210.46/210.95 (step @p44 :rule nary_cong :premises (@p43 @p41) :args (@t93)) % 210.46/210.95 (step @p45 :rule cong :premises (@p44) :args (@t94)) % 210.46/210.95 (step @p46 :rule cong :premises (@p45) :args (@t96)) % 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210.46/210.95 (step @p277 :rule cong :premises (@p276) :args (@t199)) % 210.46/210.95 (step @p278 :rule ho_cong :premises (@p258 @p277)) % 210.46/210.95 (step @p279 :rule ho_cong :premises (@p278 @p39)) % 210.46/210.95 (step @p280 :rule refl :args ((_ @t204 @t12))) % 210.46/210.95 (step @p281 :rule ho_cong :premises (@p278 @p39)) % 210.46/210.95 (step @p282 :rule trans :premises (@p281 @p280)) % 210.46/210.95 (step @p283 :rule cong :premises (@p282 @p279) :args ((= @t205 @t202))) % 210.46/210.95 (step @p284 :rule symm :premises (@p283)) % 210.46/210.95 (step @p285 :rule refl :args ((_ @t204 @t12))) % 210.46/210.95 (step @p286 :rule eq_resolve :premises (@p285 @p284)) % 210.46/210.95 (step @p287 :rule cong :premises (@p286) :args (@t206)) % 210.46/210.95 (step @p288 :rule trans :premises (@p287 @p270)) % 210.46/210.95 (step @p289 :rule beta-reduce :args ((= (_ @t111 @t201) @t206))) % 210.46/210.95 (step @p290 :rule trans :premises (@p289 @p288)) % 210.46/210.95 (step @p291 :rule beta-reduce :args ((= @t207 @t102))) % 210.46/210.95 (step @p292 :rule cong :premises (@p291) :args (@t208)) % 210.46/210.95 (step @p293 :rule cong :premises (@p292) :args (@t209)) % 210.46/210.95 (step @p294 :rule cong :premises (@p293) :args (@t210)) % 210.46/210.95 (step @p295 :rule cong :premises (@p294) :args (@t211)) % 210.46/210.95 (step @p296 :rule beta-reduce :args ((= (_ @t213 @t127) @t211))) % 210.46/210.95 (step @p297 :rule trans :premises (@p296 @p295)) % 210.46/210.95 (step @p298 :rule beta-reduce :args ((= (_ @t132 @t3) @t118))) % 210.46/210.95 (step @p299 :rule ho_cong :premises (@p90 @p81)) % 210.46/210.95 (step @p300 :rule trans :premises (@p299 @p298)) % 210.46/210.95 (step @p301 :rule cong :premises (@p300) :args (@t214)) % 210.46/210.95 (step @p302 :rule refl :args (@t213)) % 210.46/210.95 (step @p303 :rule ho_cong :premises (@p302 @p301)) % 210.46/210.95 (step @p304 :rule trans :premises (@p303 @p297)) % 210.46/210.95 (step @p305 :rule ho_cong :premises (@p214 @p304)) % 210.46/210.95 (step @p306 :rule ho_cong :premises (@p103 @p305)) % 210.46/210.95 (step @p307 :rule trans :premises (@p306 @p290)) % 210.46/210.95 (step @p308 :rule ho_cong :premises (@p165 @p81)) % 210.46/210.95 (step @p309 :rule cong :premises (@p308) :args (@t7)) % 210.46/210.95 (step @p310 :rule cong :premises (@p174) :args (@t215)) % 210.46/210.95 (step @p311 :rule cong :premises (@p310) :args (@t216)) % 210.46/210.95 (step @p312 :rule cong :premises (@p311) :args (@t217)) % 210.46/210.95 (step @p313 :rule exists-elim :args ((= @t51 @t217))) % 210.46/210.95 (step @p314 :rule trans :premises (@p313 @p312)) % 210.46/210.95 (step @p315 :rule cong :premises (@p314) :args (@t52)) % 210.46/210.95 (step @p316 :rule trans :premises (@p22 @p315)) % 210.46/210.95 (step @p317 :rule ho_cong :premises (@p316 @p309)) % 210.46/210.95 (step @p318 :rule ho_cong :premises (@p214 @p317)) % 210.46/210.95 (step @p319 :rule ho_cong :premises (@p186 @p318)) % 210.46/210.95 (step @p320 :rule trans :premises (@p319 @p307)) % 210.46/210.95 (step @p321 :rule trans :premises (@p320 @p245)) % 210.46/210.95 (step @p322 :rule eq_resolve :premises (@p5 @p321)) % 210.46/210.95 (step @p323 :rule instantiate :premises (@p322) :args ((@list @t220))) % 210.46/210.95 (step @p324 :rule skolemize :premises (@p323)) % 210.46/210.95 (step @p325 :rule bool-double-not-elim :args (@t224)) % 210.46/210.95 (step @p326 :rule refl :args (@t228)) % 210.46/210.95 (step @p327 :rule nary_cong :premises (@p326 @p325) :args ((or @t228 (not @t225)))) % 210.46/210.95 (step @p328 :rule cnf_or_neg :args (@t228 1)) % 210.46/210.95 (step @p329 :rule eq_resolve :premises (@p328 @p327)) % 210.46/210.95 (step @p330 :rule reordering :premises (@p329) :args ((or @t224 @t228))) % 210.46/210.95 (step @p331 :rule chain_m_resolution :premises (@p330 @p324) :args (@t224 @t229 @t230)) % 210.46/210.95 (step @p332 :rule refl :args (@t236)) % 210.46/210.95 (step @p333 :rule refl :args (@t222)) % 210.46/210.95 (step @p334 :rule eq-refl :args (@t241)) % 210.46/210.95 (step @p335 :rule skolem_intro :args (@t242)) % 210.46/210.95 (step @p336 :rule refl :args (@t241)) % 210.46/210.95 (step @p337 :rule cong :premises (@p336 @p335) :args ((= @t241 @t242))) % 210.46/210.95 (step @p338 :rule trans :premises (@p337 @p334)) % 210.46/210.95 (step @p339 :rule true_elim :premises (@p338)) % 210.46/210.95 (step @p340 :rule cong :premises (@p339 @p333) :args (@t243)) % 210.46/210.95 (step @p341 :rule cong :premises (@p340) :args (@t244)) % 210.46/210.95 (step @p342 :rule nary_cong :premises (@p341 @p332) :args (@t245)) % 210.46/210.95 (step @p343 :rule refl :args (@t224)) % 210.46/210.95 (step @p344 :rule cong :premises (@p343 @p342) :args ((=> @t224 @t245))) % 210.46/210.95 (step @p345 :rule beta-reduce :args ((= @t246 @t236))) % 210.46/210.95 (step @p346 :rule refl :args (@t244)) % 210.46/210.95 (step @p347 :rule nary_cong :premises (@p346 @p345) :args (@t247)) % 210.46/210.95 (step @p348 :rule cong :premises (@p343 @p347) :args ((=> @t224 @t247))) % 210.46/210.95 (assume-push @p677 @t224) % 210.46/210.95 (step @p350 :rule instantiate :premises (@p331) :args ((@list @t241))) % 210.46/210.95 (step-pop @p678 :rule scope :premises (@p350)) % 210.46/210.95 (step @p351 :rule process_scope :premises (@p678) :args (@t247)) % 210.46/210.95 (step @p353 :rule eq_resolve :premises (@p351 @p348)) % 210.46/210.95 (step @p354 :rule eq_resolve :premises (@p353 @p344)) % 210.46/210.95 (step @p355 :rule implies_elim :premises (@p354)) % 210.46/210.95 (step @p356 :rule chain_m_resolution :premises (@p355 @p331) :args (@t250 @t251 (@list @t224))) % 210.46/210.95 (step @p357 :rule aci_norm :args ((= @t253 @t240))) % 210.46/210.95 (step @p358 :rule cong :premises (@p357) :args (@t254)) % 210.46/210.95 (step @p359 :rule quant-merge-prenex :args ((= (forall @t41 @t256) @t254))) % 210.46/210.95 (step @p360 :rule alpha_equiv :args (@t257 (@list @t231) (@list @t55))) % 210.46/210.95 (step @p361 :rule refl :args (@t239)) % 210.46/210.95 (step @p362 :rule nary_cong :premises (@p361 @p360) :args (@t258)) % 210.46/210.95 (step @p363 :rule quant-miniscope-or :args ((= @t256 @t258))) % 210.46/210.95 (step @p364 :rule trans :premises (@p363 @p362)) % 210.46/210.95 (step @p365 :rule symm :premises (@p364)) % 210.46/210.95 (step @p366 :rule cong :premises (@p365) :args ((forall @t41 (or @t239 (forall @t61 (or @t260 @t259)))))) % 210.46/210.95 (step @p367 :rule trans :premises (@p366 @p359)) % 210.46/210.95 (step @p368 :rule trans :premises (@p367 @p358)) % 210.46/210.95 (step @p369 :rule beta-reduce :args ((= @t268 @t259))) % 210.46/210.95 (step @p370 :rule refl :args (@t260)) % 210.46/210.95 (step @p371 :rule nary_cong :premises (@p370 @p369) :args (@t269)) % 210.46/210.95 (step @p372 :rule cong :premises (@p371) :args (@t270)) % 210.46/210.95 (step @p373 :rule beta-reduce :args ((= @t272 @t270))) % 210.46/210.95 (step @p374 :rule trans :premises (@p373 @p372)) % 210.46/210.95 (step @p375 :rule refl :args (@t239)) % 210.46/210.95 (step @p376 :rule nary_cong :premises (@p375 @p374) :args (@t273)) % 210.46/210.95 (step @p377 :rule cong :premises (@p376) :args (@t274)) % 210.46/210.95 (step @p378 :rule trans :premises (@p377 @p368)) % 210.46/210.95 (step @p379 :rule cong :premises (@p378) :args (@t275)) % 210.46/210.95 (step @p380 :rule cong :premises (@p379 @p211) :args (@t276)) % 210.46/210.95 (step @p381 :rule cong :premises (@p380) :args ((forall @t14 @t276))) % 210.46/210.95 (step @p382 :rule refl :args (@t267)) % 210.46/210.95 (step @p383 :rule beta-reduce :args ((= @t277 @t271))) % 210.46/210.95 (step @p384 :rule refl :args (tptp.mbox)) % 210.46/210.95 (step @p385 :rule cong :premises (@p384 @p383) :args ((= tptp.mbox @t277))) % 210.46/210.95 (step @p386 :rule nary_cong :premises (@p228 @p221) :args (@t60)) % 210.46/210.95 (step @p387 :rule cong :premises (@p386) :args (@t62)) % 210.46/210.95 (step @p388 :rule cong :premises (@p387) :args (@t64)) % 210.46/210.95 (step @p389 :rule trans :premises (@p25 @p388)) % 210.46/210.95 (step @p390 :rule ho_cong :premises (@p389 @p216)) % 210.46/210.95 (step @p391 :rule cong :premises (@p384 @p390) :args (@t1)) % 210.46/210.95 (step @p392 :rule trans :premises (@p391 @p385)) % 210.46/210.95 (step @p393 :rule eq_resolve :premises (@p1 @p392)) % 210.46/210.95 (step @p394 :rule ho_cong :premises (@p393 @p382 @p81)) % 210.46/210.95 (step @p395 :rule nary_cong :premises (@p375 @p394) :args (@t279)) % 210.46/210.95 (step @p396 :rule cong :premises (@p395) :args (@t280)) % 210.46/210.95 (step @p397 :rule cong :premises (@p396) :args (@t281)) % 210.46/210.95 (step @p398 :rule cong :premises (@p397 @p211) :args (@t282)) % 210.46/210.95 (step @p399 :rule cong :premises (@p398) :args ((forall @t14 @t282))) % 210.46/210.95 (step @p400 :rule trans :premises (@p399 @p381)) % 210.46/210.95 (step @p401 :rule refl :args ((tptp.positive @t285 @t12))) % 210.46/210.95 (step @p402 :rule refl :args ((tptp.mbox @t283 @t3))) % 210.46/210.95 (step @p403 :rule refl :args (@t262)) % 210.46/210.95 (step @p404 :rule cong :premises (@p403) :args (@t263)) % 210.46/210.95 (step @p405 :rule cong :premises (@p404) :args (@t264)) % 210.46/210.95 (step @p406 :rule cong :premises (@p405) :args (@t265)) % 210.46/210.95 (step @p407 :rule cong :premises (@p406) :args (@t267)) % 210.46/210.95 (step @p408 :rule cong :premises (@p407 @p71) :args (@t278)) % 210.46/210.95 (step @p409 :rule trans :premises (@p408 @p402)) % 210.46/210.95 (step @p410 :rule refl :args (@t238)) % 210.46/210.95 (step @p411 :rule cong :premises (@p410) :args (@t239)) % 210.46/210.95 (step @p412 :rule nary_cong :premises (@p411 @p409) :args (@t279)) % 210.46/210.95 (step @p413 :rule cong :premises (@p412) :args (@t280)) % 210.46/210.95 (step @p414 :rule cong :premises (@p413) :args (@t281)) % 210.46/210.95 (step @p415 :rule cong :premises (@p414 @p39) :args (@t282)) % 210.46/210.95 (step @p416 :rule trans :premises (@p415 @p401)) % 210.46/210.95 (step @p417 :rule refl :args (tptp.positive)) % 210.46/210.95 (step @p418 :rule ho_cong :premises (@p417 @p414)) % 210.46/210.95 (step @p419 :rule ho_cong :premises (@p418 @p39)) % 210.46/210.95 (step @p420 :rule cong :premises (@p419 @p416) :args ((= @t287 @t282))) % 210.46/210.95 (step @p421 :rule symm :premises (@p420)) % 210.46/210.95 (step @p422 :rule refl :args ((_ @t288 @t12))) % 210.46/210.95 (step @p423 :rule eq_resolve :premises (@p422 @p421)) % 210.46/210.95 (step @p424 :rule cong :premises (@p423) :args ((forall @t14 @t287))) % 210.46/210.95 (step @p425 :rule refl :args ((_ @t288 @t12))) % 210.46/210.95 (step @p426 :rule ho_cong :premises (@p418 @p39)) % 210.46/210.95 (step @p427 :rule trans :premises (@p426 @p425)) % 210.46/210.95 (step @p428 :rule cong :premises (@p427 @p419) :args ((= @t289 @t287))) % 210.46/210.95 (step @p429 :rule symm :premises (@p428)) % 210.46/210.95 (step @p430 :rule eq_resolve :premises (@p422 @p429)) % 210.46/210.95 (step @p431 :rule cong :premises (@p430) :args (@t290)) % 210.46/210.95 (step @p432 :rule trans :premises (@p431 @p424)) % 210.46/210.95 (step @p433 :rule beta-reduce :args ((= (_ @t111 @t286) @t290))) % 210.46/210.95 (step @p434 :rule trans :premises (@p433 @p432)) % 210.46/210.95 ; trust TRUST_THEORY_REWRITE % 210.46/210.95 (step @p435 :rule trust :premises () :args ((= (lambda @t6 @t296) @t281))) % 210.46/210.95 (step @p436 :rule refl :args (tptp.positive)) % 210.46/210.95 (step @p437 :rule ho_cong :premises (@p436 @p435)) % 210.46/210.95 (step @p438 :rule ho_cong :premises (@p103 @p437)) % 210.46/210.95 (step @p439 :rule trans :premises (@p438 @p434)) % 210.46/210.95 (step @p440 :rule beta-reduce :args ((= (_ (lambda @t14 (forall @t41 (or (not @t298) @t297))) @t3) @t296))) % 210.46/210.95 (step @p441 :rule refl :args ((tptp.mbox @t299 @t12))) % 210.46/210.95 (step @p442 :rule refl :args (@t291)) % 210.46/210.95 (step @p443 :rule cong :premises (@p442) :args (@t292)) % 210.46/210.95 (step @p444 :rule cong :premises (@p443) :args (@t293)) % 210.46/210.95 (step @p445 :rule cong :premises (@p444) :args (@t294)) % 210.46/210.95 (step @p446 :rule cong :premises (@p445) :args (@t295)) % 210.46/210.95 (step @p447 :rule cong :premises (@p446 @p39) :args (@t297)) % 210.46/210.95 (step @p448 :rule trans :premises (@p447 @p441)) % 210.46/210.95 (step @p449 :rule refl :args (tptp.mbox)) % 210.46/210.95 (step @p450 :rule ho_cong :premises (@p449 @p446)) % 210.46/210.95 (step @p451 :rule ho_cong :premises (@p450 @p39)) % 210.46/210.95 (step @p452 :rule cong :premises (@p451 @p448) :args ((= @t300 @t297))) % 210.46/210.95 (step @p453 :rule symm :premises (@p452)) % 210.46/210.95 (step @p454 :rule refl :args ((_ (_ tptp.mbox @t299) @t12))) % 210.46/210.95 (step @p455 :rule eq_resolve :premises (@p454 @p453)) % 210.46/210.95 (step @p456 :rule refl :args (@t298)) % 210.46/210.95 (step @p457 :rule refl :args (@t301)) % 210.46/210.95 (step @p458 :rule cong :premises (@p457 @p456) :args ((= @t301 @t298))) % 210.46/210.95 (step @p459 :rule symm :premises (@p458)) % 210.46/210.95 (step @p460 :rule eq_resolve :premises (@p457 @p459)) % 210.46/210.95 (step @p461 :rule cong :premises (@p460) :args (@t302)) % 210.46/210.95 (step @p462 :rule nary_cong :premises (@p461 @p455) :args (@t303)) % 210.46/210.95 (step @p463 :rule cong :premises (@p462) :args ((forall @t41 @t303))) % 210.46/210.95 (step @p464 :rule bool-impl-elim :args (@t301 @t300)) % 210.46/210.95 (step @p465 :rule cong :premises (@p464) :args ((forall @t41 @t304))) % 210.46/210.95 (step @p466 :rule trans :premises (@p465 @p463)) % 210.46/210.95 (step @p467 :rule beta-reduce :args ((= @t308 @t304))) % 210.46/210.95 (step @p468 :rule cong :premises (@p467) :args (@t309)) % 210.46/210.95 (step @p469 :rule trans :premises (@p468 @p466)) % 210.46/210.95 (step @p470 :rule cong :premises (@p469) :args (@t310)) % 210.46/210.95 (step @p471 :rule beta-reduce :args ((= (_ @t150 @t307) @t310))) % 210.46/210.95 (step @p472 :rule trans :premises (@p471 @p470)) % 210.46/210.95 (step @p473 :rule beta-reduce :args ((= (_ @t312 @t3) @t306))) % 210.46/210.95 ; trust TRUST_THEORY_REWRITE % 210.46/210.95 (step @p474 :rule trust :premises () :args ((= @t314 @t312))) % 210.46/210.95 (step @p475 :rule beta-reduce :args ((= (_ @t315 @t313) @t314))) % 210.46/210.95 (step @p476 :rule trans :premises (@p475 @p474)) % 210.46/210.95 (step @p477 :rule beta-reduce :args ((= @t316 @t33))) % 210.46/210.95 (step @p478 :rule cong :premises (@p477) :args (@t317)) % 210.46/210.95 (step @p479 :rule cong :premises (@p478) :args (@t318)) % 210.46/210.95 (step @p480 :rule trans :premises (@p479 @p311)) % 210.46/210.95 (step @p481 :rule cong :premises (@p480) :args (@t319)) % 210.46/210.95 (step @p482 :rule cong :premises (@p481) :args (@t320)) % 210.46/210.95 (step @p483 :rule beta-reduce :args ((= @t321 @t320))) % 210.46/210.95 (step @p484 :rule trans :premises (@p483 @p482)) % 210.46/210.95 (step @p485 :rule ho_cong :premises (@p384 @p484)) % 210.46/210.95 (step @p486 :rule beta-reduce :args ((= @t322 @t315))) % 210.46/210.95 (step @p487 :rule ho_cong :premises (@p486 @p485)) % 210.46/210.95 (step @p488 :rule trans :premises (@p487 @p476)) % 210.46/210.95 (step @p489 :rule ho_cong :premises (@p488 @p81)) % 210.46/210.95 (step @p490 :rule trans :premises (@p489 @p473)) % 210.46/210.95 (step @p491 :rule cong :premises (@p490) :args ((lambda @t81 (_ (_ @t322 (_ tptp.mbox @t321)) @t3)))) % 210.46/210.95 (step @p492 :rule ho_cong :premises (@p139 @p491)) % 210.46/210.95 (step @p493 :rule trans :premises (@p492 @p472)) % 210.46/210.95 (step @p494 :rule ho_cong :premises (@p493 @p81)) % 210.46/210.95 (step @p495 :rule trans :premises (@p494 @p440)) % 210.46/210.95 (step @p496 :rule refl :args (@t84)) % 210.46/210.95 (step @p497 :rule ho_cong :premises (@p316 @p496)) % 210.46/210.95 (step @p498 :rule ho_cong :premises (@p384 @p497)) % 210.46/210.95 (step @p499 :rule refl :args (@t85)) % 210.46/210.95 (step @p500 :rule ho_cong :premises (@p15 @p499)) % 210.46/210.95 (step @p501 :rule ho_cong :premises (@p500 @p498)) % 210.46/210.95 (step @p502 :rule ho_cong :premises (@p501 @p81)) % 210.46/210.95 (step @p503 :rule cong :premises (@p502) :args (@t86)) % 210.46/210.95 (step @p504 :rule ho_cong :premises (@p156 @p503)) % 210.46/210.95 (step @p505 :rule ho_cong :premises (@p504 @p81)) % 210.46/210.95 (step @p506 :rule trans :premises (@p505 @p495)) % 210.46/210.95 (step @p507 :rule cong :premises (@p506) :args (@t87)) % 210.46/210.95 (step @p508 :rule trans :premises (@p31 @p507)) % 210.46/210.95 (step @p509 :rule ho_cong :premises (@p436 @p508)) % 210.46/210.95 (step @p510 :rule ho_cong :premises (@p186 @p509)) % 210.46/210.95 (step @p511 :rule trans :premises (@p510 @p439)) % 210.46/210.95 (step @p512 :rule trans :premises (@p511 @p400)) % 210.46/210.95 (step @p513 :rule eq_resolve :premises (@p4 @p512)) % 210.46/210.95 (step @p514 :rule refl :args (@t323)) % 210.46/210.95 (step @p515 :rule cong :premises (@p514 @p340) :args ((=> @t323 @t243))) % 210.46/210.95 (assume-push @p679 @t323) % 210.46/210.95 (step @p517 :rule instantiate :premises (@p513) :args ((@list @t222))) % 210.46/210.95 (step-pop @p680 :rule scope :premises (@p517)) % 210.46/210.95 (step @p518 :rule process_scope :premises (@p680) :args (@t243)) % 210.46/210.95 (step @p520 :rule eq_resolve :premises (@p518 @p515)) % 210.46/210.95 (step @p521 :rule implies_elim :premises (@p520)) % 210.46/210.95 (step @p522 :rule chain_m_resolution :premises (@p521 @p513) :args (@t248 @t251 (@list @t323))) % 210.46/210.95 (step @p523 :rule cnf_or_pos :args (@t250)) % 210.46/210.95 (step @p524 :rule reordering :premises (@p523) :args ((or @t236 @t249 (not @t250)))) % 210.46/210.95 (step @p525 :rule chain_m_resolution :premises (@p524 @p522 @p356) :args (@t236 @t324 (@list @t248 @t250))) % 210.46/210.95 (step @p526 :rule refl :args (@t328)) % 210.46/210.95 (step @p527 :rule refl :args (@t330)) % 210.46/210.95 (step @p528 :rule refl :args (@t223)) % 210.46/210.95 (step @p529 :rule eq-refl :args (@t96)) % 210.46/210.95 (step @p530 :rule skolem_intro :args (@t331)) % 210.46/210.95 (step @p531 :rule refl :args (@t96)) % 210.46/210.95 (step @p532 :rule cong :premises (@p531 @p530) :args ((= @t96 @t331))) % 210.46/210.95 (step @p533 :rule trans :premises (@p532 @p529)) % 210.46/210.95 (step @p534 :rule true_elim :premises (@p533)) % 210.46/210.95 (step @p535 :rule cong :premises (@p534 @p528 @p333) :args (@t332)) % 210.46/210.95 (step @p536 :rule cong :premises (@p535) :args (@t333)) % 210.46/210.95 (step @p537 :rule nary_cong :premises (@p536 @p527 @p526) :args (@t334)) % 210.46/210.95 (step @p538 :rule cong :premises (@p332 @p537) :args ((=> @t236 @t334))) % 210.46/210.95 (step @p539 :rule beta-reduce :args ((= @t335 @t326))) % 210.46/210.95 (step @p540 :rule cong :premises (@p539) :args (@t336)) % 210.46/210.95 (step @p541 :rule cong :premises (@p540) :args (@t337)) % 210.46/210.95 (step @p542 :rule cong :premises (@p541) :args (@t338)) % 210.46/210.95 (step @p543 :rule refl :args (@t333)) % 210.46/210.95 (step @p544 :rule nary_cong :premises (@p543 @p527 @p542) :args (@t339)) % 210.46/210.95 (step @p545 :rule cong :premises (@p332 @p544) :args ((=> @t236 @t339))) % 210.46/210.95 (assume-push @p681 @t236) % 210.46/210.95 (step @p547 :rule instantiate :premises (@p525) :args ((@list @t96 @t220))) % 210.46/210.95 (step-pop @p682 :rule scope :premises (@p547)) % 210.46/210.95 (step @p548 :rule process_scope :premises (@p682) :args (@t339)) % 210.46/210.95 (step @p550 :rule eq_resolve :premises (@p548 @p545)) % 210.46/210.95 (step @p551 :rule eq_resolve :premises (@p550 @p538)) % 210.46/210.95 (step @p552 :rule implies_elim :premises (@p551)) % 210.46/210.95 (step @p553 :rule chain_m_resolution :premises (@p552 @p525) :args (@t342 @t251 (@list @t236))) % 210.46/210.95 (step @p554 :rule quant-merge-prenex :args ((= (forall @t14 (forall @t61 @t218)) @t219))) % 210.46/210.95 (step @p555 :rule beta-reduce :args ((= @t354 @t166))) % 210.46/210.95 (step @p556 :rule nary_cong :premises (@p203 @p555) :args (@t355)) % 210.46/210.95 (step @p557 :rule cong :premises (@p556) :args (@t356)) % 210.46/210.95 (step @p558 :rule beta-reduce :args ((= @t357 @t356))) % 210.46/210.95 (step @p559 :rule trans :premises (@p558 @p557)) % 210.46/210.95 (step @p560 :rule cong :premises (@p559) :args (@t358)) % 210.46/210.95 (step @p561 :rule trans :premises (@p560 @p554)) % 210.46/210.95 (step @p562 :rule cong :premises (@p561) :args ((not @t358))) % 210.46/210.95 (step @p563 :rule refl :args (@t353)) % 210.46/210.95 (step @p564 :rule ho_cong :premises (@p393 @p563 @p211)) % 210.46/210.95 (step @p565 :rule cong :premises (@p564) :args (@t360)) % 210.46/210.95 (step @p566 :rule cong :premises (@p565) :args ((not @t360))) % 210.46/210.95 (step @p567 :rule trans :premises (@p566 @p562)) % 210.46/210.95 (step @p568 :rule refl :args ((tptp.mbox @t361 @t12))) % 210.46/210.95 (step @p569 :rule refl :args (@t344)) % 210.46/210.95 (step @p570 :rule refl :args (@t345)) % 210.46/210.95 (step @p571 :rule cong :premises (@p570) :args (@t346)) % 210.46/210.95 (step @p572 :rule nary_cong :premises (@p571 @p569) :args (@t347)) % 210.46/210.95 (step @p573 :rule cong :premises (@p572) :args (@t348)) % 210.46/210.95 (step @p574 :rule cong :premises (@p573) :args (@t349)) % 210.46/210.95 (step @p575 :rule cong :premises (@p574) :args (@t350)) % 210.46/210.95 (step @p576 :rule cong :premises (@p575) :args (@t351)) % 210.46/210.95 (step @p577 :rule cong :premises (@p576) :args (@t353)) % 210.46/210.95 (step @p578 :rule cong :premises (@p577 @p39) :args (@t359)) % 210.46/210.95 (step @p579 :rule trans :premises (@p578 @p568)) % 210.46/210.95 (step @p580 :rule ho_cong :premises (@p449 @p577)) % 210.46/210.95 (step @p581 :rule ho_cong :premises (@p580 @p39)) % 210.46/210.95 (step @p582 :rule cong :premises (@p581 @p579) :args ((= @t362 @t359))) % 210.46/210.95 (step @p583 :rule symm :premises (@p582)) % 210.46/210.95 (step @p584 :rule refl :args ((_ (_ tptp.mbox @t361) @t12))) % 210.46/210.95 (step @p585 :rule eq_resolve :premises (@p584 @p583)) % 210.46/210.95 (step @p586 :rule cong :premises (@p585) :args ((forall @t14 @t362))) % 210.46/210.95 (step @p587 :rule alpha_equiv :args (@t199 @t200 (@list @t343))) % 210.46/210.95 (step @p588 :rule ho_cong :premises (@p449 @p587)) % 210.46/210.95 (step @p589 :rule ho_cong :premises (@p588 @p39)) % 210.46/210.95 (step @p590 :rule cong :premises (@p589) :args ((forall @t14 @t364))) % 210.46/210.95 (step @p591 :rule trans :premises (@p590 @p586)) % 210.46/210.95 (step @p592 :rule ho_cong :premises (@p449 @p277)) % 210.46/210.95 (step @p593 :rule ho_cong :premises (@p592 @p39)) % 210.46/210.95 (step @p594 :rule refl :args ((_ @t365 @t12))) % 210.46/210.95 (step @p595 :rule ho_cong :premises (@p592 @p39)) % 210.46/210.95 (step @p596 :rule trans :premises (@p595 @p594)) % 210.46/210.95 (step @p597 :rule cong :premises (@p596 @p593) :args ((= @t366 @t364))) % 210.46/210.95 (step @p598 :rule symm :premises (@p597)) % 210.46/210.95 (step @p599 :rule refl :args ((_ @t365 @t12))) % 210.46/210.95 (step @p600 :rule eq_resolve :premises (@p599 @p598)) % 210.46/210.95 (step @p601 :rule cong :premises (@p600) :args (@t367)) % 210.46/210.95 (step @p602 :rule trans :premises (@p601 @p591)) % 210.46/210.95 (step @p603 :rule beta-reduce :args ((= (_ @t111 @t363) @t367))) % 210.46/210.95 (step @p604 :rule trans :premises (@p603 @p602)) % 210.46/210.95 (step @p605 :rule ho_cong :premises (@p384 @p304)) % 210.46/210.95 (step @p606 :rule ho_cong :premises (@p103 @p605)) % 210.46/210.95 (step @p607 :rule trans :premises (@p606 @p604)) % 210.46/210.95 (step @p608 :rule cong :premises (@p607) :args ((not (_ @t111 (_ tptp.mbox (_ @t213 @t214)))))) % 210.46/210.95 (step @p609 :rule ho_cong :premises (@p384 @p317)) % 210.46/210.95 (step @p610 :rule ho_cong :premises (@p186 @p609)) % 210.46/210.95 (step @p611 :rule cong :premises (@p610) :args (@t10)) % 210.46/210.95 (step @p612 :rule trans :premises (@p611 @p608)) % 210.46/210.95 (step @p613 :rule trans :premises (@p612 @p567)) % 210.46/210.95 (step @p614 :rule eq_resolve :premises (@p7 @p613)) % 210.46/210.95 (step @p615 :rule skolemize :premises (@p614)) % 210.46/210.95 (step @p616 :rule bool-double-not-elim :args (@t368)) % 210.46/210.95 (step @p617 :rule refl :args (@t370)) % 210.46/210.95 (step @p618 :rule nary_cong :premises (@p617 @p616) :args ((or @t370 (not @t369)))) % 210.46/210.95 (step @p619 :rule cnf_or_neg :args (@t370 1)) % 210.46/210.95 (step @p620 :rule eq_resolve :premises (@p619 @p618)) % 210.46/210.95 (step @p621 :rule reordering :premises (@p620) :args ((or @t368 @t370))) % 210.46/210.95 (step @p622 :rule chain_m_resolution :premises (@p621 @p615) :args (@t368 @t229 (@list @t370))) % 210.46/210.95 (step @p623 :rule alpha_equiv :args ((forall (@list @t371) (not (forall (@list @t372) (or (not (tptp.positive @t372 @t220)) (_ @t372 @t371 @t220))))) @t373 (@list @t232 @t38))) % 210.46/210.95 (step @p624 :rule alpha_equiv :args (@t368 (@list @t4 @t38) @t373)) % 210.46/210.95 (step @p625 :rule trans :premises (@p624 @p623)) % 210.46/210.95 (step @p626 :rule equiv_elim1 :premises (@p625)) % 210.46/210.95 (step @p627 :rule chain_m_resolution :premises (@p626 @p622) :args (@t327 @t251 (@list @t368))) % 210.46/210.95 (step @p628 :rule beta-reduce :args ((= (_ (lambda @t78 (forall @t76 (or (not @t375) @t374))) tptp.rel) (forall @t76 (or (not (tptp.rel @t72 @t73)) (tptp.rel @t73 @t72)))))) % 210.46/210.95 (step @p629 :rule refl :args (@t374)) % 210.46/210.95 (step @p630 :rule refl :args (@t74)) % 210.46/210.95 (step @p631 :rule cong :premises (@p630 @p629) :args ((= @t74 @t374))) % 210.46/210.95 (step @p632 :rule symm :premises (@p631)) % 210.46/210.95 (step @p633 :rule eq_resolve :premises (@p630 @p632)) % 210.46/210.95 (step @p634 :rule refl :args (@t375)) % 210.46/210.95 (step @p635 :rule refl :args (@t75)) % 210.46/210.95 (step @p636 :rule cong :premises (@p635 @p634) :args ((= @t75 @t375))) % 210.46/210.95 (step @p637 :rule symm :premises (@p636)) % 210.46/210.95 (step @p638 :rule eq_resolve :premises (@p635 @p637)) % 210.46/210.95 (step @p639 :rule cong :premises (@p638) :args (@t376)) % 210.46/210.95 (step @p640 :rule nary_cong :premises (@p639 @p633) :args (@t377)) % 210.46/210.95 (step @p641 :rule cong :premises (@p640) :args ((forall @t76 @t377))) % 210.46/210.95 (step @p642 :rule bool-impl-elim :args (@t75 @t74)) % 210.46/210.95 (step @p643 :rule cong :premises (@p642) :args (@t77)) % 210.46/210.95 (step @p644 :rule trans :premises (@p643 @p641)) % 210.46/210.95 (step @p645 :rule cong :premises (@p644) :args (@t79)) % 210.46/210.95 (step @p646 :rule trans :premises (@p29 @p645)) % 210.46/210.95 (step @p647 :rule ho_cong :premises (@p646 @p216)) % 210.46/210.95 (step @p648 :rule trans :premises (@p647 @p628)) % 210.46/210.95 (step @p649 :rule eq_resolve :premises (@p3 @p648)) % 210.46/210.95 (step @p650 :rule instantiate :premises (@p649) :args ((@list @t220 @t222))) % 210.46/210.95 (step @p651 :rule bool-double-not-elim :args (@t226)) % 210.46/210.95 (step @p652 :rule nary_cong :premises (@p326 @p651) :args ((or @t228 (not @t227)))) % 210.46/210.95 (step @p653 :rule cnf_or_neg :args (@t228 0)) % 210.46/210.95 (step @p654 :rule eq_resolve :premises (@p653 @p652)) % 210.46/210.95 (step @p655 :rule reordering :premises (@p654) :args ((or @t226 @t228))) % 210.46/210.95 (step @p656 :rule chain_m_resolution :premises (@p655 @p324) :args (@t226 @t229 @t230)) % 210.46/210.95 (step @p657 :rule cnf_or_pos :args (@t378)) % 210.46/210.95 (step @p658 :rule reordering :premises (@p657) :args ((or @t227 @t329 (not @t378)))) % 210.46/210.95 (step @p659 :rule chain_m_resolution :premises (@p658 @p656 @p650) :args (@t329 @t324 (@list @t226 @t378))) % 210.46/210.95 (step @p660 :rule cnf_or_pos :args (@t342)) % 210.46/210.95 (step @p661 :rule reordering :premises (@p660) :args ((or @t330 @t328 @t341 (not @t342)))) % 210.46/210.95 (step @p662 :rule chain_m_resolution :premises (@p661 @p659 @p627 @p553) :args (@t341 (@list false false false) (@list @t329 @t327 @t342))) % 210.46/210.95 (step @p663 :rule cnf_or_pos :args (@t379)) % 210.46/210.95 (step @p664 :rule reordering :premises (@p663) :args ((or @t225 @t340 @t380))) % 210.46/210.95 (step @p665 :rule chain_m_resolution :premises (@p664 @p331 @p662) :args (@t380 (@list false true) (@list @t224 @t340))) % 210.46/210.95 (step @p666 :rule refl :args (@t225)) % 210.46/210.95 (step @p667 :rule nary_cong :premises (@p666 @p535) :args (@t381)) % 210.46/210.95 (step @p668 :rule refl :args (@t105)) % 210.46/210.95 (step @p669 :rule cong :premises (@p668 @p667) :args ((=> @t105 @t381))) % 210.46/210.95 (assume-push @p683 @t105) % 210.46/210.95 (step @p671 :rule instantiate :premises (@p189) :args ((@list @t222 @t223))) % 210.46/210.95 (step-pop @p684 :rule scope :premises (@p671)) % 210.46/210.95 (step @p672 :rule process_scope :premises (@p684) :args (@t381)) % 210.46/210.95 (step @p674 :rule eq_resolve :premises (@p672 @p669)) % 210.46/210.95 (step @p675 :rule implies_elim :premises (@p674)) % 210.46/210.95 (step @p676 false :rule chain_m_resolution :premises (@p675 @p665 @p189) :args (false (@list true false) (@list @t379 @t105))) % 210.46/210.95 ) % 210.46/210.95 % SZS output end Proof % 210.46/210.95 % cvc5 exiting %------------------------------------------------------------------------------