%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PHI004^1 : TPTP v9.2.1. Released v6.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n020.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 168.93s 169.57s % Output : Proof 168.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : PHI004^1 : TPTP v9.2.1. Released v6.1.0. % 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.33 % Computer : n020.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Jun 2 12:52:10 EDT 2026 % 0.15/0.33 % CPUTime : % 0.30/0.49 %----Proving TH0 % 168.93/169.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 168.93/169.57 --- 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... % 168.93/169.57 --- 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... % 168.93/169.57 --- Run --ho-elim --full-saturate-quant at 18s... % 168.93/169.57 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 168.93/169.57 % SZS status Theorem % 168.93/169.57 % SZS output start Proof % 168.93/169.57 ( % 168.93/169.57 (declare-sort $$unsorted 0) % 168.93/169.57 (declare-sort tptp.mu 0) % 168.93/169.57 (declare-const tptp.positive (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)) % 168.93/169.57 (declare-const tptp.mbox (-> (-> $$unsorted Bool) $$unsorted Bool)) % 168.93/169.57 (declare-const tptp.mdia (-> (-> $$unsorted Bool) $$unsorted Bool)) % 168.93/169.57 (declare-const tptp.rel (-> $$unsorted $$unsorted Bool)) % 168.93/169.57 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 168.93/169.58 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 168.93/169.58 (define tptp.mfalse () (lambda (@list (@var "W" $$unsorted)) false)) % 168.93/169.58 (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)))))) % 168.93/169.58 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 168.93/169.58 (define tptp.mand () (let ((_let_1 (@var "W" $$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))))))) % 168.93/169.58 (define tptp.mimplies () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 168.93/169.58 (define tptp.mimplied () (let ((_let_1 (@var "W" $$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))))))) % 168.93/169.58 (define tptp.mequiv () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 168.93/169.58 (define tptp.mxor () (let ((_let_1 (@var "W" $$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))))))))) % 168.93/169.58 (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))))))) % 168.93/169.58 (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))))))) % 168.93/169.58 (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))))))) % 168.93/169.58 (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))))))) % 168.93/169.58 (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))))))) % 168.93/169.58 (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))))))) % 168.93/169.58 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 168.93/169.58 (define tptp.mdia_generic () (let ((_let_1 (@var "V" $$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))))))))) % 168.93/169.58 (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)))))) % 168.93/169.58 (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))))))) % 168.93/169.58 (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)))))) % 168.93/169.58 (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 $$unsorted Bool)))) (let ((_let_5 (@var "X" tptp.mu))) (lambda (@list _let_4 _let_5 _let_1) (_ (_ (_ tptp.mand (_ _let_4 _let_5)) (_ tptp.mforall_indset (lambda (@list _let_3 _let_1) (_ (_ (_ tptp.mimplies (_ _let_3 _let_5)) (_ tptp.mbox (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ (_ tptp.mimplies (_ _let_4 _let_2)) (_ _let_3 _let_2)) _let_1))))) _let_1)))) _let_1)))))))) % 168.93/169.58 (define tptp.necessary_existence () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Y" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (let ((_let_4 (@var "X" tptp.mu))) (lambda (@list _let_4 _let_1) (_ (_ tptp.mforall_indset (lambda (@list _let_3 _let_1) (_ (_ (_ tptp.mimplies (_ (_ tptp.essence _let_3) _let_4)) (_ tptp.mbox (_ tptp.mexists_ind (lambda (@list _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))) _let_1))) _let_1))))))) % 168.93/169.58 (define @t1 () (= tptp.mbox (_ tptp.mbox_generic tptp.rel))) % 168.93/169.58 (define @t2 () (@var "__flatten_var_0" $$unsorted)) % 168.93/169.58 (define @t3 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 168.93/169.58 (define @t4 () (_ tptp.positive @t3)) % 168.93/169.58 (define @t5 () (@var "X" tptp.mu)) % 168.93/169.58 (define @t6 () (_ @t3 @t5)) % 168.93/169.58 (define @t7 () (@list @t5 @t2)) % 168.93/169.58 (define @t8 () (lambda @t7 (_ (_ tptp.mnot @t6) @t2))) % 168.93/169.58 (define @t9 () (@list @t3 @t2)) % 168.93/169.58 (define @t10 () (lambda @t9 (_ (_ (_ tptp.mequiv (_ tptp.positive @t8)) (_ tptp.mnot @t4)) @t2))) % 168.93/169.58 (define @t11 () (@var "Psi" (-> tptp.mu $$unsorted Bool))) % 168.93/169.58 (define @t12 () (_ @t11 @t5)) % 168.93/169.58 (define @t13 () (@list @t11 @t2)) % 168.93/169.58 (define @t14 () (_ tptp.mbox @t4)) % 168.93/169.58 (define @t15 () (_ tptp.mimplies @t4)) % 168.93/169.58 (define @t16 () (lambda @t9 (_ (_ @t15 @t14) @t2))) % 168.93/169.58 (define @t17 () (lambda @t7 (_ (_ (_ tptp.mimplies (_ tptp.god @t5)) (_ (_ tptp.essence tptp.god) @t5)) @t2))) % 168.93/169.58 (define @t18 () (not (_ tptp.mvalid (_ tptp.mforall_ind @t17)))) % 168.93/169.58 (define @t19 () (@var "Y" tptp.mu)) % 168.93/169.58 (define @t20 () (@var "W" $$unsorted)) % 168.93/169.58 (define @t21 () (lambda (@list @t5 @t19 @t20) (= @t5 @t19))) % 168.93/169.58 (define @t22 () (@list @t20)) % 168.93/169.58 (define @t23 () (lambda @t22 true)) % 168.93/169.58 (define @t24 () (lambda @t22 false)) % 168.93/169.58 (define @t25 () (@var "Phi" (-> $$unsorted Bool))) % 168.93/169.58 (define @t26 () (_ @t25 @t20)) % 168.93/169.58 (define @t27 () (not @t26)) % 168.93/169.58 (define @t28 () (@list @t25 @t20)) % 168.93/169.58 (define @t29 () (lambda @t28 @t27)) % 168.93/169.58 (define @t30 () (@var "Psi" (-> $$unsorted Bool))) % 168.93/169.58 (define @t31 () (_ @t30 @t20)) % 168.93/169.58 (define @t32 () (@list @t25 @t30 @t20)) % 168.93/169.58 (define @t33 () (lambda @t32 (or @t26 @t31))) % 168.93/169.58 (define @t34 () (lambda @t32 (and @t26 @t31))) % 168.93/169.58 (define @t35 () (lambda @t32 (=> @t26 @t31))) % 168.93/169.58 (define @t36 () (lambda @t32 (=> @t31 @t26))) % 168.93/169.58 (define @t37 () (lambda @t32 (= @t26 @t31))) % 168.93/169.58 (define @t38 () (lambda @t32 (or (and @t26 (not @t31)) (and @t27 @t31)))) % 168.93/169.58 (define @t39 () (_ @t6 @t20)) % 168.93/169.58 (define @t40 () (@list @t5)) % 168.93/169.58 (define @t41 () (forall @t40 @t39)) % 168.93/169.58 (define @t42 () (@list @t3 @t20)) % 168.93/169.58 (define @t43 () (lambda @t42 @t41)) % 168.93/169.58 (define @t44 () (@var "X" (-> tptp.mu $$unsorted Bool))) % 168.93/169.58 (define @t45 () (@var "Phi" (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool))) % 168.93/169.58 (define @t46 () (_ (_ @t45 @t44) @t20)) % 168.93/169.58 (define @t47 () (@list @t44)) % 168.93/169.58 (define @t48 () (forall @t47 @t46)) % 168.93/169.58 (define @t49 () (@list @t45 @t20)) % 168.93/169.58 (define @t50 () (lambda @t49 @t48)) % 168.93/169.58 (define @t51 () (@var "P" (-> $$unsorted Bool))) % 168.93/169.58 (define @t52 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 168.93/169.58 (define @t53 () (_ (_ @t52 @t51) @t20)) % 168.93/169.58 (define @t54 () (@list @t51)) % 168.93/169.58 (define @t55 () (@list @t52 @t20)) % 168.93/169.58 (define @t56 () (lambda @t55 (forall @t54 @t53))) % 168.93/169.58 (define @t57 () (lambda @t42 (exists @t40 @t39))) % 168.93/169.58 (define @t58 () (lambda @t49 (exists @t47 @t46))) % 168.93/169.58 (define @t59 () (lambda @t55 (exists @t54 @t53))) % 168.93/169.58 (define @t60 () (@var "V" $$unsorted)) % 168.93/169.58 (define @t61 () (_ @t25 @t60)) % 168.93/169.58 (define @t62 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 168.93/169.58 (define @t63 () (_ (_ @t62 @t20) @t60)) % 168.93/169.58 (define @t64 () (not @t63)) % 168.93/169.58 (define @t65 () (or @t64 @t61)) % 168.93/169.58 (define @t66 () (@list @t60)) % 168.93/169.58 (define @t67 () (forall @t66 @t65)) % 168.93/169.58 (define @t68 () (@list @t62 @t25 @t20)) % 168.93/169.58 (define @t69 () (lambda @t68 @t67)) % 168.93/169.58 (define @t70 () (lambda @t68 (exists @t66 (and @t63 @t61)))) % 168.93/169.58 (define @t71 () (forall @t22 @t26)) % 168.93/169.58 (define @t72 () (@list @t25)) % 168.93/169.58 (define @t73 () (lambda @t72 @t71)) % 168.93/169.58 (define @t74 () (lambda @t72 (forall @t22 @t27))) % 168.93/169.58 (define @t75 () (lambda @t9 (_ (_ @t15 @t6) @t2))) % 168.93/169.58 (define @t76 () (lambda @t7 (_ (_ tptp.mforall_indset @t75) @t2))) % 168.93/169.58 (define @t77 () (_ @t11 @t19)) % 168.93/169.58 (define @t78 () (_ @t3 @t19)) % 168.93/169.58 (define @t79 () (@list @t19 @t2)) % 168.93/169.58 (define @t80 () (lambda @t79 (_ (_ (_ tptp.mimplies @t78) @t77) @t2))) % 168.93/169.58 (define @t81 () (lambda @t13 (_ (_ (_ tptp.mimplies @t12) (_ tptp.mbox (_ tptp.mforall_ind @t80))) @t2))) % 168.93/169.58 (define @t82 () (@list @t3 @t5 @t2)) % 168.93/169.58 (define @t83 () (lambda @t82 (_ (_ (_ tptp.mand @t6) (_ tptp.mforall_indset @t81)) @t2))) % 168.93/169.58 (define @t84 () (_ @t78 @t2)) % 168.93/169.58 (define @t85 () (lambda @t7 (_ (_ tptp.mforall_indset (lambda @t9 (_ (_ (_ tptp.mimplies (_ (_ tptp.essence @t3) @t5)) (_ tptp.mbox (_ tptp.mexists_ind (lambda @t79 @t84)))) @t2))) @t2))) % 168.93/169.58 (define @t86 () (@var "BOUND_VARIABLE_8618" $$unsorted)) % 168.93/169.58 (define @t87 () (@var "BOUND_VARIABLE_8848" (@ho-elim-sort (-> tptp.mu $$unsorted Bool)))) % 168.93/169.58 (define @t88 () (@const 0 (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.mu $$unsorted Bool)) $$unsorted Bool)))) % 168.93/169.58 (define @t89 () (@const 1 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.mu $$unsorted Bool)) $$unsorted Bool)) (@ho-elim-sort (-> tptp.mu $$unsorted Bool)) (@ho-elim-sort (-> $$unsorted Bool))))) % 168.93/169.58 (define @t90 () (_ @t89 @t88 @t87)) % 168.93/169.58 (define @t91 () (@const 2 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))) % 168.93/169.58 (define @t92 () (@const 3 (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 168.93/169.58 (define @t93 () (@const 4 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool))))) % 168.93/169.58 (define @t94 () (_ @t93 @t92 @t20)) % 168.93/169.58 (define @t95 () (not (_ @t91 @t90 @t20))) % 168.93/169.58 (define @t96 () (forall (@list @t20 @t87 @t86) (or @t95 (not (_ @t91 @t94 @t86)) (_ @t91 @t90 @t86)))) % 168.93/169.58 (define @t97 () (tptp.positive @t44 @t86)) % 168.93/169.58 (define @t98 () (not (tptp.rel @t20 @t86))) % 168.93/169.58 (define @t99 () (tptp.positive @t44 @t20)) % 168.93/169.58 (define @t100 () (not @t99)) % 168.93/169.58 (define @t101 () (or @t100 @t98 @t97)) % 168.93/169.58 (define @t102 () (@list @t20 @t44 @t86)) % 168.93/169.58 (define @t103 () (or @t98 @t97)) % 168.93/169.58 (define @t104 () (or @t100 @t103)) % 168.93/169.58 (define @t105 () (forall @t102 @t104)) % 168.93/169.58 (define @t106 () (@list @t86)) % 168.93/169.58 (define @t107 () (forall @t106 @t104)) % 168.93/169.58 (define @t108 () (@list @t20 @t44)) % 168.93/169.58 (define @t109 () (forall @t106 @t103)) % 168.93/169.58 (define @t110 () (or @t100 @t109)) % 168.93/169.58 (define @t111 () (tptp.positive @t44 @t60)) % 168.93/169.58 (define @t112 () (not (tptp.rel @t20 @t60))) % 168.93/169.58 (define @t113 () (_ tptp.positive @t44)) % 168.93/169.58 (define @t114 () (_ @t113 @t60)) % 168.93/169.58 (define @t115 () (or @t112 @t114)) % 168.93/169.58 (define @t116 () (_ @t113 @t60)) % 168.93/169.58 (define @t117 () (or @t112 @t116)) % 168.93/169.58 (define @t118 () (forall @t66 @t117)) % 168.93/169.58 (define @t119 () (_ @t25 @t60)) % 168.93/169.58 (define @t120 () (lambda @t28 (forall @t66 (or @t112 @t119)))) % 168.93/169.58 (define @t121 () (_ @t120 @t113 @t20)) % 168.93/169.58 (define @t122 () (or @t100 @t121)) % 168.93/169.58 (define @t123 () (_ @t62 @t20 @t60)) % 168.93/169.58 (define @t124 () (_ (lambda @t68 (forall @t66 (or (not @t123) @t119))) tptp.rel)) % 168.93/169.58 (define @t125 () (tptp.mbox @t113 @t20)) % 168.93/169.58 (define @t126 () (or @t100 @t125)) % 168.93/169.58 (define @t127 () (forall @t108 @t126)) % 168.93/169.58 (define @t128 () (forall @t47 @t126)) % 168.93/169.58 (define @t129 () (lambda @t22 @t128)) % 168.93/169.58 (define @t130 () (_ @t129 @t20)) % 168.93/169.58 (define @t131 () (forall @t22 @t130)) % 168.93/169.58 (define @t132 () (_ @t25 @t20)) % 168.93/169.58 (define @t133 () (lambda @t72 (forall @t22 @t132))) % 168.93/169.58 (define @t134 () (_ (_ tptp.mbox @t113) @t20)) % 168.93/169.58 (define @t135 () (_ @t113 @t20)) % 168.93/169.58 (define @t136 () (not @t135)) % 168.93/169.58 (define @t137 () (or @t136 @t134)) % 168.93/169.58 (define @t138 () (=> @t135 @t134)) % 168.93/169.58 (define @t139 () (_ @t4 @t2)) % 168.93/169.58 (define @t140 () (=> @t139 (_ @t14 @t2))) % 168.93/169.58 (define @t141 () (lambda @t9 @t140)) % 168.93/169.58 (define @t142 () (_ @t141 @t44 @t20)) % 168.93/169.58 (define @t143 () (forall @t47 @t142)) % 168.93/169.58 (define @t144 () (lambda @t22 @t143)) % 168.93/169.58 (define @t145 () (_ @t45 @t44 @t20)) % 168.93/169.58 (define @t146 () (lambda @t49 (forall @t47 @t145))) % 168.93/169.58 (define @t147 () (_ @t4 @t20)) % 168.93/169.58 (define @t148 () (lambda @t22 (=> @t147 (_ @t14 @t20)))) % 168.93/169.58 (define @t149 () (@list @t30 @t20)) % 168.93/169.58 (define @t150 () (lambda @t149 (=> @t147 @t31))) % 168.93/169.58 (define @t151 () (_ @t35 @t4)) % 168.93/169.58 (define @t152 () (@const 5 (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.mu $$unsorted Bool)) tptp.mu $$unsorted Bool)))) % 168.93/169.58 (define @t153 () (@const 6 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.mu $$unsorted Bool)) tptp.mu $$unsorted Bool)) (@ho-elim-sort (-> tptp.mu $$unsorted Bool)) (@ho-elim-sort (-> tptp.mu $$unsorted Bool))))) % 168.93/169.58 (define @t154 () (_ @t91 (_ @t89 @t88 (_ @t153 @t152 @t87)) @t20)) % 168.93/169.58 (define @t155 () (@list @t20 @t87)) % 168.93/169.58 (define @t156 () (forall @t155 (= @t95 @t154))) % 168.93/169.58 (define @t157 () (@const 7 (-> (-> tptp.mu $$unsorted Bool) tptp.mu $$unsorted Bool))) % 168.93/169.58 (define @t158 () (forall @t108 (= @t100 (tptp.positive (_ @t157 @t44) @t20)))) % 168.93/169.58 (define @t159 () (@var "BOUND_VARIABLE_8181" $$unsorted)) % 168.93/169.58 (define @t160 () (_ @t44 @t5 @t159)) % 168.93/169.58 (define @t161 () (not @t160)) % 168.93/169.58 (define @t162 () (@list @t5 @t159)) % 168.93/169.58 (define @t163 () (lambda @t162 @t161)) % 168.93/169.58 (define @t164 () (tptp.positive @t163 @t20)) % 168.93/169.58 (define @t165 () (= @t100 @t164)) % 168.93/169.58 (define @t166 () (forall @t108 @t165)) % 168.93/169.58 (define @t167 () (forall @t47 @t165)) % 168.93/169.58 (define @t168 () (lambda @t22 @t167)) % 168.93/169.58 (define @t169 () (_ @t168 @t20)) % 168.93/169.58 (define @t170 () (forall @t22 @t169)) % 168.93/169.58 (define @t171 () (_ @t44 @t5)) % 168.93/169.58 (define @t172 () (_ @t171 @t159)) % 168.93/169.58 (define @t173 () (not @t172)) % 168.93/169.58 (define @t174 () (lambda @t162 @t173)) % 168.93/169.58 (define @t175 () (_ (_ tptp.positive @t174) @t20)) % 168.93/169.58 (define @t176 () (= @t136 @t175)) % 168.93/169.58 (define @t177 () (_ tptp.positive (lambda @t162 (not (_ @t6 @t159))))) % 168.93/169.58 (define @t178 () (= (not @t139) (_ @t177 @t2))) % 168.93/169.58 (define @t179 () (lambda @t9 @t178)) % 168.93/169.58 (define @t180 () (_ @t179 @t44 @t20)) % 168.93/169.58 (define @t181 () (forall @t47 @t180)) % 168.93/169.58 (define @t182 () (lambda @t22 @t181)) % 168.93/169.58 (define @t183 () (_ @t177 @t20)) % 168.93/169.58 (define @t184 () (not @t147)) % 168.93/169.58 (define @t185 () (_ @t6 @t2)) % 168.93/169.58 (define @t186 () (not @t185)) % 168.93/169.58 (define @t187 () (lambda @t7 @t186)) % 168.93/169.58 (define @t188 () (_ tptp.positive @t187)) % 168.93/169.58 (define @t189 () (_ @t188 @t20)) % 168.93/169.58 (define @t190 () (= @t189 @t184)) % 168.93/169.58 (define @t191 () (lambda @t22 @t184)) % 168.93/169.58 (define @t192 () (_ @t191 @t20)) % 168.93/169.58 (define @t193 () (lambda @t22 (= @t192 @t189))) % 168.93/169.58 (define @t194 () (_ @t29 @t4)) % 168.93/169.58 (define @t195 () (lambda @t149 (= @t189 @t31))) % 168.93/169.58 (define @t196 () (not @t39)) % 168.93/169.58 (define @t197 () (lambda @t22 @t196)) % 168.93/169.58 (define @t198 () (_ @t29 @t6)) % 168.93/169.58 (define @t199 () (lambda @t7 (_ @t198 @t2))) % 168.93/169.58 (define @t200 () (@var "BOUND_VARIABLE_8748" $$unsorted)) % 168.93/169.58 (define @t201 () (@var "BOUND_VARIABLE_8750" tptp.mu)) % 168.93/169.58 (define @t202 () (@var "BOUND_VARIABLE_8937" (@ho-elim-sort (-> tptp.mu $$unsorted Bool)))) % 168.93/169.58 (define @t203 () (@const 8 (-> (@ho-elim-sort (-> tptp.mu $$unsorted Bool)) tptp.mu (@ho-elim-sort (-> $$unsorted Bool))))) % 168.93/169.58 (define @t204 () (@var "BOUND_VARIABLE_8942" (@ho-elim-sort (-> tptp.mu $$unsorted Bool)))) % 168.93/169.58 (define @t205 () (_ @t89 @t88 @t204)) % 168.93/169.58 (define @t206 () (@list @t204)) % 168.93/169.58 (define @t207 () (@var "BOUND_VARIABLE_8965" (@ho-elim-sort (-> tptp.mu $$unsorted Bool)))) % 168.93/169.58 (define @t208 () (@list @t87)) % 168.93/169.58 (define @t209 () (forall (@list @t20 @t5 @t207 @t202 @t200 @t201) (or (not (forall @t208 (or @t95 (_ @t91 (_ @t203 @t87 @t5) @t20)))) (and (or (not (_ @t91 (_ @t89 @t88 @t207) @t20)) (_ @t91 (_ @t203 @t207 @t5) @t20)) (or (not (_ @t91 (_ @t203 @t202 @t5) @t20)) (not (_ @t91 @t94 @t200)) (not (forall @t206 (or (not (_ @t91 @t205 @t200)) (_ @t91 (_ @t203 @t204 @t201) @t200)))) (_ @t91 (_ @t203 @t202 @t201) @t200)))))) % 168.93/169.58 (define @t210 () (@quantifiers_skolemize @t209 0)) % 168.93/169.58 (define @t211 () (@quantifiers_skolemize @t209 3)) % 168.93/169.58 (define @t212 () (_ @t153 @t152 @t211)) % 168.93/169.58 (define @t213 () (_ @t91 (_ @t89 @t88 @t212) @t210)) % 168.93/169.58 (define @t214 () (_ @t89 @t88 @t211)) % 168.93/169.58 (define @t215 () (_ @t91 @t214 @t210)) % 168.93/169.58 (define @t216 () (not @t215)) % 168.93/169.58 (define @t217 () (forall @t155 (= @t154 @t95))) % 168.93/169.58 (define @t218 () (= @t213 @t216)) % 168.93/169.58 (define @t219 () (= @t216 @t213)) % 168.93/169.58 (define @t220 () (@list false)) % 168.93/169.58 (define @t221 () (@var "BOUND_VARIABLE_8552" (-> tptp.mu $$unsorted Bool))) % 168.93/169.58 (define @t222 () (_ @t221 @t201 @t200)) % 168.93/169.58 (define @t223 () (@var "BOUND_VARIABLE_8505" (-> tptp.mu $$unsorted Bool))) % 168.93/169.58 (define @t224 () (@list @t223)) % 168.93/169.58 (define @t225 () (not (forall @t224 (or (not (tptp.positive @t223 @t200)) (_ @t223 @t201 @t200))))) % 168.93/169.58 (define @t226 () (not (tptp.rel @t20 @t200))) % 168.93/169.58 (define @t227 () (not (_ @t221 @t5 @t20))) % 168.93/169.58 (define @t228 () (or @t227 @t226 @t225 @t222)) % 168.93/169.58 (define @t229 () (@var "BOUND_VARIABLE_8546" (-> tptp.mu $$unsorted Bool))) % 168.93/169.58 (define @t230 () (or (not (tptp.positive @t229 @t20)) (_ @t229 @t5 @t20))) % 168.93/169.58 (define @t231 () (_ @t44 @t5 @t20)) % 168.93/169.58 (define @t232 () (forall @t47 (or @t100 @t231))) % 168.93/169.58 (define @t233 () (not @t232)) % 168.93/169.58 (define @t234 () (@list @t20 @t5 @t229 @t221 @t200 @t201)) % 168.93/169.58 (define @t235 () (or @t226 @t225 @t222)) % 168.93/169.58 (define @t236 () (or @t227 @t235)) % 168.93/169.58 (define @t237 () (and @t230 @t236)) % 168.93/169.58 (define @t238 () (or @t233 @t237)) % 168.93/169.58 (define @t239 () (forall @t234 @t238)) % 168.93/169.58 (define @t240 () (@list @t200 @t201)) % 168.93/169.58 (define @t241 () (forall @t240 @t238)) % 168.93/169.58 (define @t242 () (@list @t20 @t5 @t229 @t221)) % 168.93/169.58 (define @t243 () (forall @t240 @t235)) % 168.93/169.58 (define @t244 () (@var "BOUND_VARIABLE_8731" tptp.mu)) % 168.93/169.58 (define @t245 () (or @t227 @t243)) % 168.93/169.58 (define @t246 () (forall @t240 @t236)) % 168.93/169.58 (define @t247 () (forall @t240 @t230)) % 168.93/169.58 (define @t248 () (and @t247 @t246)) % 168.93/169.58 (define @t249 () (forall @t240 @t237)) % 168.93/169.58 (define @t250 () (or @t233 @t249)) % 168.93/169.58 (define @t251 () (_ @t221 @t244 @t60)) % 168.93/169.58 (define @t252 () (not (tptp.positive @t223 @t60))) % 168.93/169.58 (define @t253 () (not (forall @t224 (or @t252 (_ @t223 @t244 @t60))))) % 168.93/169.58 (define @t254 () (or @t112 @t253 @t251)) % 168.93/169.58 (define @t255 () (@list @t60 @t244)) % 168.93/169.58 (define @t256 () (or @t253 @t251)) % 168.93/169.58 (define @t257 () (or @t112 @t256)) % 168.93/169.58 (define @t258 () (forall @t255 @t257)) % 168.93/169.58 (define @t259 () (@list @t244)) % 168.93/169.58 (define @t260 () (forall @t259 @t257)) % 168.93/169.58 (define @t261 () (forall @t259 @t256)) % 168.93/169.58 (define @t262 () (@var "BOUND_VARIABLE_7948" tptp.mu)) % 168.93/169.58 (define @t263 () (or @t112 @t261)) % 168.93/169.58 (define @t264 () (@list @t262)) % 168.93/169.58 (define @t265 () (forall @t264 (or (not (forall @t224 (or @t252 (_ @t223 @t262 @t60)))) (_ @t221 @t262 @t60)))) % 168.93/169.58 (define @t266 () (@var "BOUND_VARIABLE_7865" $$unsorted)) % 168.93/169.58 (define @t267 () (not (forall @t224 (or (not (tptp.positive @t223 @t266)) (_ @t223 @t262 @t266))))) % 168.93/169.58 (define @t268 () (@list @t266)) % 168.93/169.58 (define @t269 () (lambda @t268 (forall @t264 (or @t267 (_ @t221 @t262 @t266))))) % 168.93/169.58 (define @t270 () (_ @t269 @t60)) % 168.93/169.58 (define @t271 () (or @t112 @t270)) % 168.93/169.58 (define @t272 () (forall @t66 @t271)) % 168.93/169.58 (define @t273 () (_ @t120 @t269 @t20)) % 168.93/169.58 (define @t274 () (or @t227 @t273)) % 168.93/169.58 (define @t275 () (and @t230 @t274)) % 168.93/169.58 (define @t276 () (or @t233 @t275)) % 168.93/169.58 (define @t277 () (forall @t242 @t276)) % 168.93/169.58 (define @t278 () (or @t227 (tptp.mbox @t269 @t20))) % 168.93/169.58 (define @t279 () (and @t230 @t278)) % 168.93/169.58 (define @t280 () (or @t233 @t279)) % 168.93/169.58 (define @t281 () (forall @t242 @t280)) % 168.93/169.58 (define @t282 () (forall (@list @t5 @t229 @t221) @t280)) % 168.93/169.58 (define @t283 () (lambda @t22 @t282)) % 168.93/169.58 (define @t284 () (_ @t283 @t20)) % 168.93/169.58 (define @t285 () (forall @t22 @t284)) % 168.93/169.58 (define @t286 () (@list @t229 @t221)) % 168.93/169.58 (define @t287 () (forall @t286 @t280)) % 168.93/169.58 (define @t288 () (forall (@list @t221) @t278)) % 168.93/169.58 (define @t289 () (@list @t44)) % 168.93/169.58 (define @t290 () (forall @t286 @t278)) % 168.93/169.58 (define @t291 () (forall (@list @t229) @t230)) % 168.93/169.58 (define @t292 () (forall @t286 @t230)) % 168.93/169.58 (define @t293 () (and @t292 @t290)) % 168.93/169.58 (define @t294 () (forall @t286 @t279)) % 168.93/169.58 (define @t295 () (or @t233 @t294)) % 168.93/169.58 (define @t296 () (_ @t44 @t262 @t266)) % 168.93/169.58 (define @t297 () (lambda @t268 (forall @t264 (or @t267 @t296)))) % 168.93/169.58 (define @t298 () (not @t231)) % 168.93/169.58 (define @t299 () (and @t232 (forall @t47 (or @t298 (tptp.mbox @t297 @t20))))) % 168.93/169.58 (define @t300 () (=> @t232 @t299)) % 168.93/169.58 (define @t301 () (_ @t44 @t5 @t2)) % 168.93/169.58 (define @t302 () (not @t301)) % 168.93/169.58 (define @t303 () (forall @t47 (or (not (tptp.positive @t44 @t2)) @t301))) % 168.93/169.58 (define @t304 () (and @t303 (forall @t47 (or @t302 (tptp.mbox @t297 @t2))))) % 168.93/169.58 (define @t305 () (=> @t303 @t304)) % 168.93/169.58 (define @t306 () (lambda @t7 @t305)) % 168.93/169.58 (define @t307 () (_ @t306 @t5 @t20)) % 168.93/169.58 (define @t308 () (forall @t40 @t307)) % 168.93/169.58 (define @t309 () (lambda @t22 @t308)) % 168.93/169.58 (define @t310 () (_ @t3 @t5 @t20)) % 168.93/169.58 (define @t311 () (lambda @t42 (forall @t40 @t310))) % 168.93/169.58 (define @t312 () (@list @t2)) % 168.93/169.58 (define @t313 () (lambda @t312 @t304)) % 168.93/169.58 (define @t314 () (_ @t313 @t20)) % 168.93/169.58 (define @t315 () (=> @t232 @t314)) % 168.93/169.58 (define @t316 () (lambda @t22 @t315)) % 168.93/169.58 (define @t317 () (forall @t47 (or (not (tptp.positive @t44 @t266)) @t296))) % 168.93/169.58 (define @t318 () (not @t317)) % 168.93/169.58 (define @t319 () (or @t318 @t296)) % 168.93/169.58 (define @t320 () (forall @t264 @t319)) % 168.93/169.58 (define @t321 () (lambda @t268 @t320)) % 168.93/169.58 (define @t322 () (tptp.mbox @t321 @t2)) % 168.93/169.58 (define @t323 () (or @t302 @t322)) % 168.93/169.58 (define @t324 () (lambda @t7 @t303)) % 168.93/169.58 (define @t325 () (_ @t324 @t262 @t266)) % 168.93/169.58 (define @t326 () (not @t325)) % 168.93/169.58 (define @t327 () (or @t326 @t296)) % 168.93/169.58 (define @t328 () (forall @t264 @t327)) % 168.93/169.58 (define @t329 () (lambda @t268 @t328)) % 168.93/169.58 (define @t330 () (tptp.mbox @t329 @t2)) % 168.93/169.58 (define @t331 () (or @t302 @t330)) % 168.93/169.58 (define @t332 () (forall @t47 @t331)) % 168.93/169.58 (define @t333 () (lambda @t312 @t303)) % 168.93/169.58 (define @t334 () (_ @t324 @t5)) % 168.93/169.58 (define @t335 () (and (_ @t334 @t2) @t332)) % 168.93/169.58 (define @t336 () (lambda @t7 @t335)) % 168.93/169.58 (define @t337 () (lambda @t82 (and @t185 (forall @t47 (or @t302 (tptp.mbox (lambda @t268 (forall @t264 (or (not (_ @t3 @t262 @t266)) @t296))) @t2)))))) % 168.93/169.58 (define @t338 () (_ @t44 @t5 @t266)) % 168.93/169.58 (define @t339 () (_ @t3 @t5 @t266)) % 168.93/169.58 (define @t340 () (not @t339)) % 168.93/169.58 (define @t341 () (or @t340 @t338)) % 168.93/169.58 (define @t342 () (forall @t40 @t341)) % 168.93/169.58 (define @t343 () (lambda @t268 @t342)) % 168.93/169.58 (define @t344 () (and @t185 (forall @t47 (or @t302 (tptp.mbox @t343 @t2))))) % 168.93/169.58 (define @t345 () (lambda @t82 @t344)) % 168.93/169.58 (define @t346 () (_ @t333 @t20)) % 168.93/169.58 (define @t347 () (=> @t346 @t31)) % 168.93/169.58 (define @t348 () (lambda @t149 @t347)) % 168.93/169.58 (define @t349 () (lambda @t7 (_ (_ (_ @t35 @t334) (_ (_ @t345 @t324) @t5)) @t2))) % 168.93/169.58 (define @t350 () (_ @t171 @t20)) % 168.93/169.58 (define @t351 () (or @t136 @t350)) % 168.93/169.58 (define @t352 () (=> @t135 @t350)) % 168.93/169.58 (define @t353 () (=> @t139 @t185)) % 168.93/169.58 (define @t354 () (lambda @t9 @t353)) % 168.93/169.58 (define @t355 () (_ @t354 @t44 @t20)) % 168.93/169.58 (define @t356 () (forall @t47 @t355)) % 168.93/169.58 (define @t357 () (lambda @t22 @t356)) % 168.93/169.58 (define @t358 () (lambda @t22 (=> @t147 @t39))) % 168.93/169.58 (define @t359 () (tptp.mbox @t343 @t20)) % 168.93/169.58 (define @t360 () (forall @t47 (or @t298 @t359))) % 168.93/169.58 (define @t361 () (lambda @t22 @t360)) % 168.93/169.58 (define @t362 () (_ @t361 @t20)) % 168.93/169.58 (define @t363 () (and @t39 @t362)) % 168.93/169.58 (define @t364 () (lambda @t22 @t363)) % 168.93/169.58 (define @t365 () (lambda @t149 (and @t39 @t31))) % 168.93/169.58 (define @t366 () (lambda @t268 (forall @t40 (or (not (_ @t6 @t266)) (_ @t171 @t266))))) % 168.93/169.58 (define @t367 () (_ (_ tptp.mbox @t343) @t20)) % 168.93/169.58 (define @t368 () (not @t350)) % 168.93/169.58 (define @t369 () (or @t368 @t367)) % 168.93/169.58 (define @t370 () (=> @t350 @t367)) % 168.93/169.58 (define @t371 () (_ tptp.mbox (lambda @t268 (forall @t40 (or @t340 (_ @t11 @t5 @t266)))))) % 168.93/169.58 (define @t372 () (=> (_ @t12 @t2) (_ @t371 @t2))) % 168.93/169.58 (define @t373 () (lambda @t13 @t372)) % 168.93/169.58 (define @t374 () (_ @t373 @t44 @t20)) % 168.93/169.58 (define @t375 () (forall @t47 @t374)) % 168.93/169.58 (define @t376 () (lambda @t22 @t375)) % 168.93/169.58 (define @t377 () (_ @t12 @t20)) % 168.93/169.58 (define @t378 () (lambda @t22 (=> @t377 (_ @t371 @t20)))) % 168.93/169.58 (define @t379 () (_ @t11 @t5 @t20)) % 168.93/169.58 (define @t380 () (_ tptp.mbox (lambda @t22 (forall @t40 (or (not @t310) @t379))))) % 168.93/169.58 (define @t381 () (lambda @t22 (=> @t377 (_ @t380 @t20)))) % 168.93/169.58 (define @t382 () (lambda @t149 (=> @t377 @t31))) % 168.93/169.58 (define @t383 () (or @t196 @t377)) % 168.93/169.58 (define @t384 () (=> @t39 @t377)) % 168.93/169.58 (define @t385 () (=> @t84 (_ @t77 @t2))) % 168.93/169.58 (define @t386 () (lambda @t79 @t385)) % 168.93/169.58 (define @t387 () (_ @t386 @t5 @t20)) % 168.93/169.58 (define @t388 () (forall @t40 @t387)) % 168.93/169.58 (define @t389 () (lambda @t22 @t388)) % 168.93/169.58 (define @t390 () (_ @t78 @t20)) % 168.93/169.58 (define @t391 () (lambda @t22 (=> @t390 (_ @t77 @t20)))) % 168.93/169.58 (define @t392 () (lambda @t149 (=> @t390 @t31))) % 168.93/169.58 (define @t393 () (_ @t35 @t78)) % 168.93/169.58 (define @t394 () (lambda @t79 (_ (_ @t393 @t77) @t2))) % 168.93/169.58 (define @t395 () (_ @t35 @t12)) % 168.93/169.58 (define @t396 () (@quantifiers_skolemize @t209 1)) % 168.93/169.58 (define @t397 () (forall @t208 (or (not (_ @t91 @t90 @t210)) (_ @t91 (_ @t203 @t87 @t396) @t210)))) % 168.93/169.58 (define @t398 () (@quantifiers_skolemize @t209 4)) % 168.93/169.58 (define @t399 () (@quantifiers_skolemize @t209 5)) % 168.93/169.58 (define @t400 () (_ @t91 (_ @t203 @t211 @t399) @t398)) % 168.93/169.58 (define @t401 () (forall @t206 (or (not (_ @t91 @t205 @t398)) (_ @t91 (_ @t203 @t204 @t399) @t398)))) % 168.93/169.58 (define @t402 () (not @t401)) % 168.93/169.58 (define @t403 () (_ @t91 (_ @t93 @t92 @t210) @t398)) % 168.93/169.58 (define @t404 () (not @t403)) % 168.93/169.58 (define @t405 () (_ @t91 (_ @t203 @t211 @t396) @t210)) % 168.93/169.58 (define @t406 () (not @t405)) % 168.93/169.58 (define @t407 () (or @t406 @t404 @t402 @t400)) % 168.93/169.58 (define @t408 () (@quantifiers_skolemize @t209 2)) % 168.93/169.58 (define @t409 () (or (not (_ @t91 (_ @t89 @t88 @t408) @t210)) (_ @t91 (_ @t203 @t408 @t396) @t210))) % 168.93/169.58 (define @t410 () (and @t409 @t407)) % 168.93/169.58 (define @t411 () (not @t397)) % 168.93/169.58 (define @t412 () (or @t411 @t410)) % 168.93/169.58 (define @t413 () (@list true)) % 168.93/169.58 (define @t414 () (@list @t412)) % 168.93/169.58 (define @t415 () (@var "BOUND_VARIABLE_8801" $$unsorted)) % 168.93/169.58 (define @t416 () (@var "BOUND_VARIABLE_8800" tptp.mu)) % 168.93/169.58 (define @t417 () (@var "BOUND_VARIABLE_8990" (@ho-elim-sort (-> tptp.mu $$unsorted Bool)))) % 168.93/169.58 (define @t418 () (not (_ @t91 (_ @t203 @t417 @t416) @t415))) % 168.93/169.58 (define @t419 () (_ @t91 (_ @t203 (_ @t153 @t152 @t417) @t416) @t415)) % 168.93/169.58 (define @t420 () (@list @t417 @t416 @t415)) % 168.93/169.58 (define @t421 () (forall @t420 (= @t418 @t419))) % 168.93/169.58 (define @t422 () (@var "BOUND_VARIABLE_8799" (-> tptp.mu $$unsorted Bool))) % 168.93/169.58 (define @t423 () (forall (@list @t422 @t416 @t415) (= (not (_ @t422 @t416 @t415)) (_ @t157 @t422 @t416 @t415)))) % 168.93/169.58 (define @t424 () (_ @t91 (_ @t203 @t212 @t396) @t210)) % 168.93/169.58 (define @t425 () (forall @t420 (= @t419 @t418))) % 168.93/169.58 (define @t426 () (= @t424 @t406)) % 168.93/169.58 (define @t427 () (= @t406 @t424)) % 168.93/169.58 (define @t428 () (@list true false)) % 168.93/169.58 (define @t429 () (@list @t407)) % 168.93/169.58 (define @t430 () (not @t424)) % 168.93/169.58 (define @t431 () (not @t213)) % 168.93/169.58 (define @t432 () (or @t431 @t424)) % 168.93/169.58 (define @t433 () (not @t219)) % 168.93/169.58 (define @t434 () (_ @t91 @t214 @t398)) % 168.93/169.58 (define @t435 () (not @t434)) % 168.93/169.58 (define @t436 () (or @t435 @t400)) % 168.93/169.58 (define @t437 () (or @t216 @t404 @t434)) % 168.93/169.58 (define @t438 () (not @t437)) % 168.93/169.58 (assume @p1 @t1) % 168.93/169.58 (assume @p2 (= tptp.mdia (_ tptp.mdia_generic tptp.rel))) % 168.93/169.58 (assume @p3 (_ tptp.mvalid (_ tptp.mforall_indset @t10))) % 168.93/169.58 (assume @p4 (_ tptp.mvalid (_ tptp.mforall_indset (lambda @t9 (_ (_ tptp.mforall_indset (lambda @t13 (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t4) (_ tptp.mbox (_ tptp.mforall_ind (lambda @t7 (_ (_ (_ tptp.mimplies @t6) @t12) @t2)))))) (_ tptp.positive @t11)) @t2))) @t2))))) % 168.93/169.58 (assume @p5 (_ tptp.mvalid (_ tptp.positive tptp.god))) % 168.93/169.58 (assume @p6 (_ tptp.mvalid (_ tptp.mforall_indset @t16))) % 168.93/169.58 (assume @p7 (_ tptp.mvalid (_ tptp.positive tptp.necessary_existence))) % 168.93/169.58 (assume @p8 @t18) % 168.93/169.58 (assume @p9 true) % 168.93/169.58 (step @p10 (= tptp.meq_ind @t21) :rule refl :args (@t21)) % 168.93/169.58 (step @p11 (= tptp.mtrue @t23) :rule refl :args (@t23)) % 168.93/169.58 (step @p12 (= tptp.mfalse @t24) :rule refl :args (@t24)) % 168.93/169.58 (step @p13 (= tptp.mnot @t29) :rule refl :args (@t29)) % 168.93/169.58 (step @p14 (= tptp.mor @t33) :rule refl :args (@t33)) % 168.93/169.58 (step @p15 (= tptp.mand @t34) :rule refl :args (@t34)) % 168.93/169.58 (step @p16 (= tptp.mimplies @t35) :rule refl :args (@t35)) % 168.93/169.58 (step @p17 (= tptp.mimplied @t36) :rule refl :args (@t36)) % 168.93/169.58 (step @p18 (= tptp.mequiv @t37) :rule refl :args (@t37)) % 168.93/169.58 (step @p19 (= tptp.mxor @t38) :rule refl :args (@t38)) % 168.93/169.58 (step @p20 (= tptp.mforall_ind @t43) :rule refl :args (@t43)) % 168.93/169.58 (step @p21 (= tptp.mforall_indset @t50) :rule refl :args (@t50)) % 168.93/169.58 (step @p22 (= tptp.mforall_prop @t56) :rule refl :args (@t56)) % 168.93/169.58 (step @p23 (= tptp.mexists_ind @t57) :rule refl :args (@t57)) % 168.93/169.58 (step @p24 (= tptp.mexists_indset @t58) :rule refl :args (@t58)) % 168.93/169.58 (step @p25 (= tptp.mexists_prop @t59) :rule refl :args (@t59)) % 168.93/169.58 (step @p26 (= tptp.mbox_generic @t69) :rule refl :args (@t69)) % 168.93/169.58 (step @p27 (= tptp.mdia_generic @t70) :rule refl :args (@t70)) % 168.93/169.58 (step @p28 (= tptp.mvalid @t73) :rule refl :args (@t73)) % 168.93/169.58 (step @p29 (= tptp.minvalid @t74) :rule refl :args (@t74)) % 168.93/169.58 (step @p30 (= tptp.god @t76) :rule refl :args (@t76)) % 168.93/169.58 (step @p31 (= tptp.essence @t83) :rule refl :args (@t83)) % 168.93/169.58 (step @p32 (= tptp.necessary_existence @t85) :rule refl :args (@t85)) % 168.93/169.58 ; WARNING: add trust step for TRUST % 168.93/169.58 ; trust TRUST PREPROCESS_HO_ELIM % 168.93/169.58 (step @p33 :rule trust :premises () :args ((= (forall @t102 @t101) @t96))) % 168.93/169.58 (step @p34 :rule aci_norm :args ((= @t104 @t101))) % 168.93/169.58 (step @p35 :rule cong :premises (@p34) :args (@t105)) % 168.93/169.58 (step @p36 :rule quant-merge-prenex :args ((= (forall @t108 @t107) @t105))) % 168.93/169.58 (step @p37 :rule alpha_equiv :args (@t109 (@list @t86) (@list @t60))) % 168.93/169.58 (step @p38 :rule refl :args (@t100)) % 168.93/169.58 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t110)) % 168.93/169.58 (step @p40 :rule quant-miniscope-or :args ((= @t107 @t110))) % 168.93/169.58 (step @p41 :rule trans :premises (@p40 @p39)) % 168.93/169.58 (step @p42 :rule symm :premises (@p41)) % 168.93/169.58 (step @p43 :rule cong :premises (@p42) :args ((forall @t108 (or @t100 (forall @t66 (or @t112 @t111)))))) % 168.93/169.58 (step @p44 :rule trans :premises (@p43 @p36)) % 168.93/169.58 (step @p45 :rule trans :premises (@p44 @p35)) % 168.93/169.58 (step @p46 :rule refl :args (@t111)) % 168.93/169.58 (step @p47 :rule refl :args (@t114)) % 168.93/169.58 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t114 @t111))) % 168.93/169.58 (step @p49 :rule symm :premises (@p48)) % 168.93/169.58 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 168.93/169.58 (step @p51 :rule refl :args (@t112)) % 168.93/169.58 (step @p52 :rule nary_cong :premises (@p51 @p50) :args (@t115)) % 168.93/169.58 (step @p53 :rule cong :premises (@p52) :args ((forall @t66 @t115))) % 168.93/169.58 (step @p54 :rule refl :args (@t116)) % 168.93/169.58 (step @p55 :rule refl :args (@t112)) % 168.93/169.58 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t117)) % 168.93/169.58 (step @p57 :rule cong :premises (@p56) :args (@t118)) % 168.93/169.58 (step @p58 :rule trans :premises (@p57 @p53)) % 168.93/169.58 (step @p59 :rule beta-reduce :args ((= @t121 @t118))) % 168.93/169.58 (step @p60 :rule trans :premises (@p59 @p58)) % 168.93/169.58 (step @p61 :rule refl :args (@t100)) % 168.93/169.58 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t122)) % 168.93/169.58 (step @p63 :rule cong :premises (@p62) :args ((forall @t108 @t122))) % 168.93/169.58 (step @p64 :rule trans :premises (@p63 @p45)) % 168.93/169.58 (step @p65 :rule refl :args (@t20)) % 168.93/169.58 (step @p66 :rule refl :args (@t113)) % 168.93/169.58 (step @p67 :rule beta-reduce :args ((= @t124 @t120))) % 168.93/169.58 (step @p68 :rule refl :args (tptp.mbox)) % 168.93/169.58 (step @p69 :rule cong :premises (@p68 @p67) :args ((= tptp.mbox @t124))) % 168.93/169.58 (step @p70 :rule refl :args (tptp.rel)) % 168.93/169.58 (step @p71 :rule refl :args (@t119)) % 168.93/169.58 (step @p72 :rule refl :args (@t61)) % 168.93/169.58 (step @p73 :rule cong :premises (@p72 @p71) :args ((= @t61 @t119))) % 168.93/169.58 (step @p74 :rule symm :premises (@p73)) % 168.93/169.58 (step @p75 :rule eq_resolve :premises (@p72 @p74)) % 168.93/169.58 (step @p76 :rule refl :args (@t123)) % 168.93/169.58 (step @p77 :rule refl :args (@t63)) % 168.93/169.58 (step @p78 :rule cong :premises (@p77 @p76) :args ((= @t63 @t123))) % 168.93/169.58 (step @p79 :rule symm :premises (@p78)) % 168.93/169.58 (step @p80 :rule eq_resolve :premises (@p77 @p79)) % 168.93/169.58 (step @p81 :rule cong :premises (@p80) :args (@t64)) % 168.93/169.58 (step @p82 :rule nary_cong :premises (@p81 @p75) :args (@t65)) % 168.93/169.58 (step @p83 :rule cong :premises (@p82) :args (@t67)) % 168.93/169.58 (step @p84 :rule cong :premises (@p83) :args (@t69)) % 168.93/169.58 (step @p85 :rule trans :premises (@p26 @p84)) % 168.93/169.58 (step @p86 :rule ho_cong :premises (@p85 @p70)) % 168.93/169.58 (step @p87 :rule cong :premises (@p68 @p86) :args (@t1)) % 168.93/169.58 (step @p88 :rule trans :premises (@p87 @p69)) % 168.93/169.58 (step @p89 :rule eq_resolve :premises (@p1 @p88)) % 168.93/169.58 (step @p90 :rule ho_cong :premises (@p89 @p66 @p65)) % 168.93/169.58 (step @p91 :rule nary_cong :premises (@p61 @p90) :args (@t126)) % 168.93/169.58 (step @p92 :rule cong :premises (@p91) :args (@t127)) % 168.93/169.58 (step @p93 :rule trans :premises (@p92 @p64)) % 168.93/169.58 (step @p94 :rule quant-merge-prenex :args ((= (forall @t22 @t128) @t127))) % 168.93/169.58 (step @p95 :rule beta-reduce :args ((= @t130 @t128))) % 168.93/169.58 (step @p96 :rule cong :premises (@p95) :args (@t131)) % 168.93/169.58 (step @p97 :rule trans :premises (@p96 @p94)) % 168.93/169.58 (step @p98 :rule beta-reduce :args ((= (_ @t133 @t129) @t131))) % 168.93/169.58 (step @p99 :rule trans :premises (@p98 @p97)) % 168.93/169.58 (step @p100 :rule refl :args (@t125)) % 168.93/169.58 (step @p101 :rule refl :args (@t134)) % 168.93/169.58 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t134 @t125))) % 168.93/169.58 (step @p103 :rule symm :premises (@p102)) % 168.93/169.58 (step @p104 :rule eq_resolve :premises (@p101 @p103)) % 168.93/169.58 (step @p105 :rule refl :args (@t99)) % 168.93/169.58 (step @p106 :rule refl :args (@t135)) % 168.93/169.58 (step @p107 :rule cong :premises (@p106 @p105) :args ((= @t135 @t99))) % 168.93/169.58 (step @p108 :rule symm :premises (@p107)) % 168.93/169.58 (step @p109 :rule eq_resolve :premises (@p106 @p108)) % 168.93/169.58 (step @p110 :rule cong :premises (@p109) :args (@t136)) % 168.93/169.58 (step @p111 :rule nary_cong :premises (@p110 @p104) :args (@t137)) % 168.93/169.58 (step @p112 :rule cong :premises (@p111) :args ((forall @t47 @t137))) % 168.93/169.58 (step @p113 :rule bool-impl-elim :args (@t135 @t134)) % 168.93/169.58 (step @p114 :rule cong :premises (@p113) :args ((forall @t47 @t138))) % 168.93/169.58 (step @p115 :rule trans :premises (@p114 @p112)) % 168.93/169.58 (step @p116 :rule beta-reduce :args ((= @t142 @t138))) % 168.93/169.58 (step @p117 :rule cong :premises (@p116) :args (@t143)) % 168.93/169.58 (step @p118 :rule trans :premises (@p117 @p115)) % 168.93/169.58 (step @p119 :rule cong :premises (@p118) :args (@t144)) % 168.93/169.58 (step @p120 :rule beta-reduce :args ((= (_ @t146 @t141) @t144))) % 168.93/169.58 (step @p121 :rule trans :premises (@p120 @p119)) % 168.93/169.58 (step @p122 :rule beta-reduce :args ((= (_ @t148 @t2) @t140))) % 168.93/169.58 (step @p123 :rule refl :args (@t2)) % 168.93/169.58 (step @p124 :rule beta-reduce :args ((= (_ @t150 @t14) @t148))) % 168.93/169.58 (step @p125 :rule refl :args (@t14)) % 168.93/169.58 (step @p126 :rule beta-reduce :args ((= @t151 @t150))) % 168.93/169.58 (step @p127 :rule ho_cong :premises (@p126 @p125)) % 168.93/169.58 (step @p128 :rule trans :premises (@p127 @p124)) % 168.93/169.58 (step @p129 :rule ho_cong :premises (@p128 @p123)) % 168.93/169.58 (step @p130 :rule trans :premises (@p129 @p122)) % 168.93/169.58 (step @p131 :rule cong :premises (@p130) :args ((lambda @t9 (_ (_ @t151 @t14) @t2)))) % 168.93/169.58 (step @p132 :rule refl :args (@t146)) % 168.93/169.58 (step @p133 :rule ho_cong :premises (@p132 @p131)) % 168.93/169.58 (step @p134 :rule trans :premises (@p133 @p121)) % 168.93/169.58 (step @p135 :rule refl :args (@t133)) % 168.93/169.58 (step @p136 :rule ho_cong :premises (@p135 @p134)) % 168.93/169.58 (step @p137 :rule trans :premises (@p136 @p99)) % 168.93/169.58 (step @p138 :rule refl :args (@t4)) % 168.93/169.58 (step @p139 :rule ho_cong :premises (@p16 @p138)) % 168.93/169.58 (step @p140 :rule ho_cong :premises (@p139 @p125)) % 168.93/169.58 (step @p141 :rule ho_cong :premises (@p140 @p123)) % 168.93/169.58 (step @p142 :rule cong :premises (@p141) :args (@t16)) % 168.93/169.58 (step @p143 :rule refl :args (@t145)) % 168.93/169.58 (step @p144 :rule refl :args (@t46)) % 168.93/169.58 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t46 @t145))) % 168.93/169.58 (step @p146 :rule symm :premises (@p145)) % 168.93/169.58 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 168.93/169.58 (step @p148 :rule cong :premises (@p147) :args (@t48)) % 168.93/169.58 (step @p149 :rule cong :premises (@p148) :args (@t50)) % 168.93/169.58 (step @p150 :rule trans :premises (@p21 @p149)) % 168.93/169.58 (step @p151 :rule ho_cong :premises (@p150 @p142)) % 168.93/169.58 (step @p152 :rule refl :args (@t132)) % 168.93/169.58 (step @p153 :rule refl :args (@t26)) % 168.93/169.58 (step @p154 :rule cong :premises (@p153 @p152) :args ((= @t26 @t132))) % 168.93/169.58 (step @p155 :rule symm :premises (@p154)) % 168.93/169.58 (step @p156 :rule eq_resolve :premises (@p153 @p155)) % 168.93/169.58 (step @p157 :rule cong :premises (@p156) :args (@t71)) % 168.93/169.58 (step @p158 :rule cong :premises (@p157) :args (@t73)) % 168.93/169.58 (step @p159 :rule trans :premises (@p28 @p158)) % 168.93/169.58 (step @p160 :rule ho_cong :premises (@p159 @p151)) % 168.93/169.58 (step @p161 :rule trans :premises (@p160 @p137)) % 168.93/169.58 (step @p162 :rule trans :premises (@p161 @p93 @p33)) % 168.93/169.58 (step @p163 :rule eq_resolve :premises (@p6 @p162)) % 168.93/169.58 (step @p164 :rule eq-symm :args (@t95 @t154)) % 168.93/169.58 (step @p165 :rule cong :premises (@p164) :args (@t156)) % 168.93/169.58 ; trust TRUST PREPROCESS_HO_ELIM % 168.93/169.58 (step @p166 :rule trust :premises () :args ((= @t158 @t156))) % 168.93/169.58 ; trust TRUST PREPROCESS_HO_ELIM % 168.93/169.58 (step @p167 :rule trust :premises () :args ((= @t166 @t158))) % 168.93/169.58 (step @p168 :rule quant-merge-prenex :args ((= (forall @t22 @t167) @t166))) % 168.93/169.58 (step @p169 :rule beta-reduce :args ((= @t169 @t167))) % 168.93/169.58 (step @p170 :rule cong :premises (@p169) :args (@t170)) % 168.93/169.58 (step @p171 :rule trans :premises (@p170 @p168)) % 168.93/169.58 (step @p172 :rule beta-reduce :args ((= (_ @t133 @t168) @t170))) % 168.93/169.58 (step @p173 :rule trans :premises (@p172 @p171)) % 168.93/169.58 (step @p174 :rule refl :args ((tptp.positive @t174 @t20))) % 168.93/169.58 (step @p175 :rule refl :args (@t20)) % 168.93/169.58 (step @p176 :rule refl :args (@t160)) % 168.93/169.58 (step @p177 :rule cong :premises (@p176) :args (@t161)) % 168.93/169.58 (step @p178 :rule cong :premises (@p177) :args (@t163)) % 168.93/169.58 (step @p179 :rule cong :premises (@p178 @p175) :args (@t164)) % 168.93/169.58 (step @p180 :rule trans :premises (@p179 @p174)) % 168.93/169.58 (step @p181 :rule refl :args (tptp.positive)) % 168.93/169.58 (step @p182 :rule ho_cong :premises (@p181 @p178)) % 168.93/169.58 (step @p183 :rule ho_cong :premises (@p182 @p175)) % 168.93/169.58 (step @p184 :rule cong :premises (@p183 @p180) :args ((= (_ (_ tptp.positive @t163) @t20) @t164))) % 168.93/169.58 (step @p185 :rule symm :premises (@p184)) % 168.93/169.58 (step @p186 :rule refl :args (@t175)) % 168.93/169.58 (step @p187 :rule eq_resolve :premises (@p186 @p185)) % 168.93/169.58 (step @p188 :rule refl :args (@t172)) % 168.93/169.58 (step @p189 :rule cong :premises (@p188 @p176) :args ((= @t172 @t160))) % 168.93/169.58 (step @p190 :rule symm :premises (@p189)) % 168.93/169.58 (step @p191 :rule eq_resolve :premises (@p188 @p190)) % 168.93/169.58 (step @p192 :rule cong :premises (@p191) :args (@t173)) % 168.93/169.58 (step @p193 :rule cong :premises (@p192) :args (@t174)) % 168.93/169.58 (step @p194 :rule ho_cong :premises (@p181 @p193)) % 168.93/169.58 (step @p195 :rule ho_cong :premises (@p194 @p175)) % 168.93/169.58 (step @p196 :rule trans :premises (@p195 @p187)) % 168.93/169.58 (step @p197 :rule cong :premises (@p110 @p196) :args (@t176)) % 168.93/169.58 (step @p198 :rule cong :premises (@p197) :args ((forall @t47 @t176))) % 168.93/169.58 (step @p199 :rule beta-reduce :args ((= @t180 @t176))) % 168.93/169.58 (step @p200 :rule cong :premises (@p199) :args (@t181)) % 168.93/169.58 (step @p201 :rule trans :premises (@p200 @p198)) % 168.93/169.58 (step @p202 :rule cong :premises (@p201) :args (@t182)) % 168.93/169.58 (step @p203 :rule beta-reduce :args ((= (_ @t146 @t179) @t182))) % 168.93/169.58 (step @p204 :rule trans :premises (@p203 @p202)) % 168.93/169.58 (step @p205 :rule beta-reduce :args ((= (_ (lambda @t22 (= @t184 @t183)) @t2) @t178))) % 168.93/169.58 (step @p206 :rule eq-symm :args (@t183 @t184)) % 168.93/169.58 (step @p207 :rule cong :premises (@p206) :args ((lambda @t22 (= @t183 @t184)))) % 168.93/169.58 (step @p208 :rule ho_cong :premises (@p207 @p123)) % 168.93/169.58 (step @p209 :rule trans :premises (@p208 @p205)) % 168.93/169.58 (step @p210 :rule refl :args (@t2)) % 168.93/169.58 (step @p211 :rule refl :args (@t184)) % 168.93/169.58 (step @p212 :rule alpha_equiv :args (@t187 (@list @t2) (@list @t159))) % 168.93/169.58 (step @p213 :rule ho_cong :premises (@p181 @p212)) % 168.93/169.58 (step @p214 :rule ho_cong :premises (@p213 @p175)) % 168.93/169.58 (step @p215 :rule cong :premises (@p214 @p211) :args (@t190)) % 168.93/169.58 (step @p216 :rule cong :premises (@p215) :args ((lambda @t22 @t190))) % 168.93/169.58 (step @p217 :rule ho_cong :premises (@p216 @p210)) % 168.93/169.58 (step @p218 :rule trans :premises (@p217 @p209)) % 168.93/169.58 (step @p219 :rule beta-reduce :args ((= @t192 @t184))) % 168.93/169.58 (step @p220 :rule refl :args (@t189)) % 168.93/169.58 (step @p221 :rule cong :premises (@p220 @p219) :args ((= @t189 @t192))) % 168.93/169.58 (step @p222 :rule eq-symm :args (@t192 @t189)) % 168.93/169.58 (step @p223 :rule trans :premises (@p222 @p221)) % 168.93/169.58 (step @p224 :rule cong :premises (@p223) :args (@t193)) % 168.93/169.58 (step @p225 :rule beta-reduce :args ((= (_ (lambda @t149 (= @t31 @t189)) @t191) @t193))) % 168.93/169.58 (step @p226 :rule trans :premises (@p225 @p224)) % 168.93/169.58 (step @p227 :rule beta-reduce :args ((= @t194 @t191))) % 168.93/169.58 (step @p228 :rule eq-symm :args (@t189 @t31)) % 168.93/169.58 (step @p229 :rule cong :premises (@p228) :args (@t195)) % 168.93/169.58 (step @p230 :rule beta-reduce :args ((= (_ @t37 @t188) @t195))) % 168.93/169.58 (step @p231 :rule trans :premises (@p230 @p229)) % 168.93/169.58 (step @p232 :rule beta-reduce :args ((= (_ @t197 @t2) @t186))) % 168.93/169.58 (step @p233 :rule beta-reduce :args ((= @t198 @t197))) % 168.93/169.58 (step @p234 :rule ho_cong :premises (@p233 @p123)) % 168.93/169.58 (step @p235 :rule trans :premises (@p234 @p232)) % 168.93/169.58 (step @p236 :rule cong :premises (@p235) :args (@t199)) % 168.93/169.58 (step @p237 :rule refl :args (tptp.positive)) % 168.93/169.58 (step @p238 :rule ho_cong :premises (@p237 @p236)) % 168.93/169.58 (step @p239 :rule refl :args (@t37)) % 168.93/169.58 (step @p240 :rule ho_cong :premises (@p239 @p238)) % 168.93/169.58 (step @p241 :rule trans :premises (@p240 @p231)) % 168.93/169.58 (step @p242 :rule ho_cong :premises (@p241 @p227)) % 168.93/169.58 (step @p243 :rule trans :premises (@p242 @p226)) % 168.93/169.58 (step @p244 :rule ho_cong :premises (@p243 @p123)) % 168.93/169.58 (step @p245 :rule trans :premises (@p244 @p218)) % 168.93/169.58 (step @p246 :rule cong :premises (@p245) :args ((lambda @t9 (_ (_ (_ @t37 (_ tptp.positive @t199)) @t194) @t2)))) % 168.93/169.58 (step @p247 :rule ho_cong :premises (@p132 @p246)) % 168.93/169.58 (step @p248 :rule trans :premises (@p247 @p204)) % 168.93/169.58 (step @p249 :rule ho_cong :premises (@p135 @p248)) % 168.93/169.58 (step @p250 :rule trans :premises (@p249 @p173)) % 168.93/169.58 (step @p251 :rule ho_cong :premises (@p13 @p138)) % 168.93/169.58 (step @p252 :rule refl :args (@t6)) % 168.93/169.58 (step @p253 :rule ho_cong :premises (@p13 @p252)) % 168.93/169.58 (step @p254 :rule ho_cong :premises (@p253 @p123)) % 168.93/169.58 (step @p255 :rule cong :premises (@p254) :args (@t8)) % 168.93/169.58 (step @p256 :rule ho_cong :premises (@p237 @p255)) % 168.93/169.58 (step @p257 :rule ho_cong :premises (@p18 @p256)) % 168.93/169.58 (step @p258 :rule ho_cong :premises (@p257 @p251)) % 168.93/169.58 (step @p259 :rule ho_cong :premises (@p258 @p123)) % 168.93/169.58 (step @p260 :rule cong :premises (@p259) :args (@t10)) % 168.93/169.58 (step @p261 :rule ho_cong :premises (@p150 @p260)) % 168.93/169.58 (step @p262 :rule ho_cong :premises (@p159 @p261)) % 168.93/169.58 (step @p263 :rule trans :premises (@p262 @p250)) % 168.93/169.58 (step @p264 :rule trans :premises (@p263 @p167 @p166 @p165)) % 168.93/169.58 (step @p265 :rule eq_resolve :premises (@p3 @p264)) % 168.93/169.58 (step @p266 :rule eq-symm :args (@t213 @t216)) % 168.93/169.58 (step @p267 :rule refl :args (@t217)) % 168.93/169.58 (step @p268 :rule cong :premises (@p267 @p266) :args ((=> @t217 @t218))) % 168.93/169.58 (assume-push @p663 @t217) % 168.93/169.58 (step @p270 :rule instantiate :premises (@p265) :args ((@list @t210 @t211))) % 168.93/169.58 (step-pop @p664 :rule scope :premises (@p270)) % 168.93/169.58 (step @p271 :rule process_scope :premises (@p664) :args (@t218)) % 168.93/169.58 (step @p273 :rule eq_resolve :premises (@p271 @p268)) % 168.93/169.58 (step @p274 :rule implies_elim :premises (@p273)) % 168.93/169.58 (step @p275 :rule chain_m_resolution :premises (@p274 @p265) :args (@t219 @t220 (@list @t217))) % 168.93/169.58 ; trust TRUST PREPROCESS_HO_ELIM % 168.93/169.58 (step @p276 :rule trust :premises () :args ((= (not (forall @t234 (or @t233 (and @t230 @t228)))) (not @t209)))) % 168.93/169.58 (step @p277 :rule aci_norm :args ((= @t236 @t228))) % 168.93/169.58 (step @p278 :rule refl :args (@t230)) % 168.93/169.58 (step @p279 :rule nary_cong :premises (@p278 @p277) :args (@t237)) % 168.93/169.58 (step @p280 :rule refl :args (@t233)) % 168.93/169.58 (step @p281 :rule nary_cong :premises (@p280 @p279) :args (@t238)) % 168.93/169.58 (step @p282 :rule cong :premises (@p281) :args (@t239)) % 168.93/169.58 (step @p283 :rule quant-merge-prenex :args ((= (forall @t242 @t241) @t239))) % 168.93/169.58 (step @p284 :rule alpha_equiv :args (@t243 (@list @t200 @t201) (@list @t60 @t244))) % 168.93/169.58 (step @p285 :rule refl :args (@t227)) % 168.93/169.58 (step @p286 :rule nary_cong :premises (@p285 @p284) :args (@t245)) % 168.93/169.58 (step @p287 :rule quant-miniscope-or :args ((= @t246 @t245))) % 168.93/169.58 (step @p288 :rule trans :premises (@p287 @p286)) % 168.93/169.58 (step @p289 :rule quant-unused-vars :args ((= @t247 @t230))) % 168.93/169.58 (step @p290 :rule nary_cong :premises (@p289 @p288) :args (@t248)) % 168.93/169.58 (step @p291 :rule quant-miniscope-and :args ((= @t249 @t248))) % 168.93/169.58 (step @p292 :rule trans :premises (@p291 @p290)) % 168.93/169.58 (step @p293 :rule refl :args (@t233)) % 168.93/169.58 (step @p294 :rule nary_cong :premises (@p293 @p292) :args (@t250)) % 168.93/169.58 (step @p295 :rule quant-miniscope-or :args ((= @t241 @t250))) % 168.93/169.58 (step @p296 :rule trans :premises (@p295 @p294)) % 168.93/169.58 (step @p297 :rule symm :premises (@p296)) % 168.93/169.58 (step @p298 :rule cong :premises (@p297) :args ((forall @t242 (or @t233 (and @t230 (or @t227 (forall @t255 @t254))))))) % 168.93/169.58 (step @p299 :rule trans :premises (@p298 @p283)) % 168.93/169.58 (step @p300 :rule trans :premises (@p299 @p282)) % 168.93/169.58 (step @p301 :rule aci_norm :args ((= @t257 @t254))) % 168.93/169.58 (step @p302 :rule cong :premises (@p301) :args (@t258)) % 168.93/169.58 (step @p303 :rule quant-merge-prenex :args ((= (forall @t66 @t260) @t258))) % 168.93/169.58 (step @p304 :rule alpha_equiv :args (@t261 (@list @t244) (@list @t262))) % 168.93/169.58 (step @p305 :rule nary_cong :premises (@p51 @p304) :args (@t263)) % 168.93/169.58 (step @p306 :rule quant-miniscope-or :args ((= @t260 @t263))) % 168.93/169.58 (step @p307 :rule trans :premises (@p306 @p305)) % 168.93/169.58 (step @p308 :rule symm :premises (@p307)) % 168.93/169.58 (step @p309 :rule cong :premises (@p308) :args ((forall @t66 (or @t112 @t265)))) % 168.93/169.58 (step @p310 :rule trans :premises (@p309 @p303)) % 168.93/169.58 (step @p311 :rule trans :premises (@p310 @p302)) % 168.93/169.58 (step @p312 :rule beta-reduce :args ((= @t270 @t265))) % 168.93/169.58 (step @p313 :rule nary_cong :premises (@p55 @p312) :args (@t271)) % 168.93/169.58 (step @p314 :rule cong :premises (@p313) :args (@t272)) % 168.93/169.58 (step @p315 :rule trans :premises (@p314 @p311)) % 168.93/169.58 (step @p316 :rule beta-reduce :args ((= @t273 @t272))) % 168.93/169.58 (step @p317 :rule trans :premises (@p316 @p315)) % 168.93/169.58 (step @p318 :rule refl :args (@t227)) % 168.93/169.58 (step @p319 :rule nary_cong :premises (@p318 @p317) :args (@t274)) % 168.93/169.58 (step @p320 :rule nary_cong :premises (@p278 @p319) :args (@t275)) % 168.93/169.58 (step @p321 :rule nary_cong :premises (@p280 @p320) :args (@t276)) % 168.93/169.58 (step @p322 :rule cong :premises (@p321) :args (@t277)) % 168.93/169.58 (step @p323 :rule trans :premises (@p322 @p300)) % 168.93/169.58 (step @p324 :rule cong :premises (@p323) :args ((not @t277))) % 168.93/169.58 (step @p325 :rule refl :args (@t269)) % 168.93/169.58 (step @p326 :rule ho_cong :premises (@p89 @p325 @p65)) % 168.93/169.58 (step @p327 :rule nary_cong :premises (@p318 @p326) :args (@t278)) % 168.93/169.58 (step @p328 :rule nary_cong :premises (@p278 @p327) :args (@t279)) % 168.93/169.58 (step @p329 :rule nary_cong :premises (@p280 @p328) :args (@t280)) % 168.93/169.58 (step @p330 :rule cong :premises (@p329) :args (@t281)) % 168.93/169.58 (step @p331 :rule cong :premises (@p330) :args ((not @t281))) % 168.93/169.58 (step @p332 :rule trans :premises (@p331 @p324)) % 168.93/169.58 (step @p333 :rule quant-merge-prenex :args ((= (forall @t22 @t282) @t281))) % 168.93/169.58 (step @p334 :rule beta-reduce :args ((= @t284 @t282))) % 168.93/169.58 (step @p335 :rule cong :premises (@p334) :args (@t285)) % 168.93/169.58 (step @p336 :rule trans :premises (@p335 @p333)) % 168.93/169.58 (step @p337 :rule beta-reduce :args ((= (_ @t133 @t283) @t285))) % 168.93/169.58 (step @p338 :rule trans :premises (@p337 @p336)) % 168.93/169.58 (step @p339 :rule quant-merge-prenex :args ((= (forall @t40 @t287) @t282))) % 168.93/169.58 (step @p340 :rule alpha_equiv :args (@t288 (@list @t221) @t289)) % 168.93/169.58 (step @p341 :rule quant-unused-vars :args ((= @t290 @t288))) % 168.93/169.58 (step @p342 :rule trans :premises (@p341 @p340)) % 168.93/169.58 (step @p343 :rule alpha_equiv :args (@t291 (@list @t229) @t289)) % 168.93/169.58 (step @p344 :rule quant-unused-vars :args ((= @t292 @t291))) % 168.93/169.58 (step @p345 :rule trans :premises (@p344 @p343)) % 168.93/169.58 (step @p346 :rule nary_cong :premises (@p345 @p342) :args (@t293)) % 168.93/169.58 (step @p347 :rule quant-miniscope-and :args ((= @t294 @t293))) % 168.93/169.58 (step @p348 :rule trans :premises (@p347 @p346)) % 168.93/169.58 (step @p349 :rule nary_cong :premises (@p293 @p348) :args (@t295)) % 168.93/169.58 (step @p350 :rule quant-miniscope-or :args ((= @t287 @t295))) % 168.93/169.58 (step @p351 :rule trans :premises (@p350 @p349)) % 168.93/169.58 (step @p352 :rule symm :premises (@p351)) % 168.93/169.58 (step @p353 :rule cong :premises (@p352) :args ((forall @t40 (or @t233 @t299)))) % 168.93/169.58 (step @p354 :rule trans :premises (@p353 @p339)) % 168.93/169.58 (step @p355 :rule bool-impl-elim :args (@t232 @t299)) % 168.93/169.58 (step @p356 :rule cong :premises (@p355) :args ((forall @t40 @t300))) % 168.93/169.58 (step @p357 :rule trans :premises (@p356 @p354)) % 168.93/169.58 (step @p358 :rule beta-reduce :args ((= @t307 @t300))) % 168.93/169.58 (step @p359 :rule cong :premises (@p358) :args (@t308)) % 168.93/169.58 (step @p360 :rule trans :premises (@p359 @p357)) % 168.93/169.58 (step @p361 :rule cong :premises (@p360) :args (@t309)) % 168.93/169.58 (step @p362 :rule beta-reduce :args ((= (_ @t311 @t306) @t309))) % 168.93/169.58 (step @p363 :rule trans :premises (@p362 @p361)) % 168.93/169.58 (step @p364 :rule beta-reduce :args ((= (_ (lambda @t22 @t300) @t2) @t305))) % 168.93/169.58 (step @p365 :rule beta-reduce :args ((= @t314 @t299))) % 168.93/169.58 (step @p366 :rule refl :args (@t232)) % 168.93/169.58 (step @p367 :rule cong :premises (@p366 @p365) :args (@t315)) % 168.93/169.58 (step @p368 :rule cong :premises (@p367) :args (@t316)) % 168.93/169.58 (step @p369 :rule beta-reduce :args ((= (_ (lambda @t149 (=> @t232 @t31)) @t313) @t316))) % 168.93/169.58 (step @p370 :rule trans :premises (@p369 @p368)) % 168.93/169.58 (step @p371 :rule beta-reduce :args ((= (_ (lambda @t7 @t304) @t5) @t313))) % 168.93/169.58 (step @p372 :rule refl :args (@t5)) % 168.93/169.58 (step @p373 :rule refl :args (@t296)) % 168.93/169.58 (step @p374 :rule alpha_equiv :args (@t317 @t289 (@list @t223))) % 168.93/169.58 (step @p375 :rule cong :premises (@p374) :args (@t318)) % 168.93/169.58 (step @p376 :rule nary_cong :premises (@p375 @p373) :args (@t319)) % 168.93/169.58 (step @p377 :rule cong :premises (@p376) :args (@t320)) % 168.93/169.58 (step @p378 :rule cong :premises (@p377) :args (@t321)) % 168.93/169.58 (step @p379 :rule cong :premises (@p378 @p210) :args (@t322)) % 168.93/169.58 (step @p380 :rule refl :args (@t302)) % 168.93/169.58 (step @p381 :rule nary_cong :premises (@p380 @p379) :args (@t323)) % 168.93/169.58 (step @p382 :rule cong :premises (@p381) :args ((forall @t47 @t323))) % 168.93/169.58 (step @p383 :rule refl :args (@t296)) % 168.93/169.58 (step @p384 :rule beta-reduce :args ((= @t325 @t317))) % 168.93/169.58 (step @p385 :rule cong :premises (@p384) :args (@t326)) % 168.93/169.58 (step @p386 :rule nary_cong :premises (@p385 @p383) :args (@t327)) % 168.93/169.58 (step @p387 :rule cong :premises (@p386) :args (@t328)) % 168.93/169.58 (step @p388 :rule cong :premises (@p387) :args (@t329)) % 168.93/169.58 (step @p389 :rule cong :premises (@p388 @p123) :args (@t330)) % 168.93/169.58 (step @p390 :rule refl :args (@t302)) % 168.93/169.58 (step @p391 :rule nary_cong :premises (@p390 @p389) :args (@t331)) % 168.93/169.58 (step @p392 :rule cong :premises (@p391) :args (@t332)) % 168.93/169.58 (step @p393 :rule trans :premises (@p392 @p382)) % 168.93/169.58 (step @p394 :rule beta-reduce :args ((= (_ @t333 @t2) @t303))) % 168.93/169.58 (step @p395 :rule beta-reduce :args ((= @t334 @t333))) % 168.93/169.58 (step @p396 :rule ho_cong :premises (@p395 @p123)) % 168.93/169.58 (step @p397 :rule trans :premises (@p396 @p394)) % 168.93/169.58 (step @p398 :rule nary_cong :premises (@p397 @p393) :args (@t335)) % 168.93/169.58 (step @p399 :rule cong :premises (@p398) :args (@t336)) % 168.93/169.58 (step @p400 :rule beta-reduce :args ((= (_ @t337 @t324) @t336))) % 168.93/169.58 (step @p401 :rule trans :premises (@p400 @p399)) % 168.93/169.58 (step @p402 :rule refl :args (@t324)) % 168.93/169.58 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 168.93/169.58 ; trust TRUST_THEORY_REWRITE % 168.93/169.58 (step @p403 :rule trust :premises () :args ((= @t345 @t337))) % 168.93/169.58 (step @p404 :rule ho_cong :premises (@p403 @p402)) % 168.93/169.58 (step @p405 :rule trans :premises (@p404 @p401)) % 168.93/169.58 (step @p406 :rule ho_cong :premises (@p405 @p372)) % 168.93/169.58 (step @p407 :rule trans :premises (@p406 @p371)) % 168.93/169.58 (step @p408 :rule refl :args (@t31)) % 168.93/169.58 (step @p409 :rule beta-reduce :args ((= @t346 @t232))) % 168.93/169.58 (step @p410 :rule cong :premises (@p409 @p408) :args (@t347)) % 168.93/169.58 (step @p411 :rule cong :premises (@p410) :args (@t348)) % 168.93/169.58 (step @p412 :rule beta-reduce :args ((= (_ @t35 @t333) @t348))) % 168.93/169.58 (step @p413 :rule trans :premises (@p412 @p411)) % 168.93/169.58 (step @p414 :rule refl :args (@t35)) % 168.93/169.58 (step @p415 :rule ho_cong :premises (@p414 @p395)) % 168.93/169.58 (step @p416 :rule trans :premises (@p415 @p413)) % 168.93/169.58 (step @p417 :rule ho_cong :premises (@p416 @p407)) % 168.93/169.58 (step @p418 :rule trans :premises (@p417 @p370)) % 168.93/169.58 (step @p419 :rule ho_cong :premises (@p418 @p123)) % 168.93/169.58 (step @p420 :rule trans :premises (@p419 @p364)) % 168.93/169.58 (step @p421 :rule cong :premises (@p420) :args (@t349)) % 168.93/169.58 (step @p422 :rule refl :args (@t311)) % 168.93/169.58 (step @p423 :rule ho_cong :premises (@p422 @p421)) % 168.93/169.58 (step @p424 :rule trans :premises (@p423 @p363)) % 168.93/169.58 (step @p425 :rule ho_cong :premises (@p135 @p424)) % 168.93/169.58 (step @p426 :rule trans :premises (@p425 @p338)) % 168.93/169.58 (step @p427 :rule cong :premises (@p426) :args ((not (_ @t133 (_ @t311 @t349))))) % 168.93/169.58 (step @p428 :rule beta-reduce :args ((= (_ (lambda @t22 @t232) @t2) @t303))) % 168.93/169.58 (step @p429 :rule refl :args (@t231)) % 168.93/169.58 (step @p430 :rule refl :args (@t350)) % 168.93/169.58 (step @p431 :rule cong :premises (@p430 @p429) :args ((= @t350 @t231))) % 168.93/169.58 (step @p432 :rule symm :premises (@p431)) % 168.93/169.58 (step @p433 :rule eq_resolve :premises (@p430 @p432)) % 168.93/169.58 (step @p434 :rule nary_cong :premises (@p110 @p433) :args (@t351)) % 168.93/169.58 (step @p435 :rule cong :premises (@p434) :args ((forall @t47 @t351))) % 168.93/169.58 (step @p436 :rule bool-impl-elim :args (@t135 @t350)) % 168.93/169.58 (step @p437 :rule cong :premises (@p436) :args ((forall @t47 @t352))) % 168.93/169.58 (step @p438 :rule trans :premises (@p437 @p435)) % 168.93/169.58 (step @p439 :rule beta-reduce :args ((= @t355 @t352))) % 168.93/169.58 (step @p440 :rule cong :premises (@p439) :args (@t356)) % 168.93/169.58 (step @p441 :rule trans :premises (@p440 @p438)) % 168.93/169.58 (step @p442 :rule cong :premises (@p441) :args (@t357)) % 168.93/169.58 (step @p443 :rule beta-reduce :args ((= (_ @t146 @t354) @t357))) % 168.93/169.58 (step @p444 :rule trans :premises (@p443 @p442)) % 168.93/169.58 (step @p445 :rule beta-reduce :args ((= (_ @t358 @t2) @t353))) % 168.93/169.58 (step @p446 :rule beta-reduce :args ((= (_ @t150 @t6) @t358))) % 168.93/169.58 (step @p447 :rule ho_cong :premises (@p126 @p252)) % 168.93/169.58 (step @p448 :rule trans :premises (@p447 @p446)) % 168.93/169.58 (step @p449 :rule ho_cong :premises (@p448 @p123)) % 168.93/169.58 (step @p450 :rule trans :premises (@p449 @p445)) % 168.93/169.58 (step @p451 :rule cong :premises (@p450) :args ((lambda @t9 (_ (_ @t151 @t6) @t2)))) % 168.93/169.58 (step @p452 :rule ho_cong :premises (@p132 @p451)) % 168.93/169.58 (step @p453 :rule trans :premises (@p452 @p444)) % 168.93/169.58 (step @p454 :rule ho_cong :premises (@p453 @p123)) % 168.93/169.58 (step @p455 :rule trans :premises (@p454 @p428)) % 168.93/169.58 (step @p456 :rule ho_cong :premises (@p139 @p252)) % 168.93/169.58 (step @p457 :rule ho_cong :premises (@p456 @p123)) % 168.93/169.58 (step @p458 :rule cong :premises (@p457) :args (@t75)) % 168.93/169.58 (step @p459 :rule ho_cong :premises (@p150 @p458)) % 168.93/169.58 (step @p460 :rule ho_cong :premises (@p459 @p123)) % 168.93/169.58 (step @p461 :rule trans :premises (@p460 @p455)) % 168.93/169.58 (step @p462 :rule cong :premises (@p461) :args (@t76)) % 168.93/169.58 (step @p463 :rule trans :premises (@p30 @p462)) % 168.93/169.58 (step @p464 :rule beta-reduce :args ((= (_ (lambda @t22 (and @t39 @t360)) @t2) @t344))) % 168.93/169.58 (step @p465 :rule beta-reduce :args ((= @t362 @t360))) % 168.93/169.58 (step @p466 :rule refl :args (@t39)) % 168.93/169.58 (step @p467 :rule nary_cong :premises (@p466 @p465) :args (@t363)) % 168.93/169.58 (step @p468 :rule cong :premises (@p467) :args (@t364)) % 168.93/169.58 (step @p469 :rule beta-reduce :args ((= (_ @t365 @t361) @t364))) % 168.93/169.58 (step @p470 :rule trans :premises (@p469 @p468)) % 168.93/169.58 (step @p471 :rule refl :args ((tptp.mbox @t366 @t20))) % 168.93/169.58 (step @p472 :rule refl :args (@t338)) % 168.93/169.58 (step @p473 :rule refl :args (@t339)) % 168.93/169.58 (step @p474 :rule cong :premises (@p473) :args (@t340)) % 168.93/169.58 (step @p475 :rule nary_cong :premises (@p474 @p472) :args (@t341)) % 168.93/169.58 (step @p476 :rule cong :premises (@p475) :args (@t342)) % 168.93/169.58 (step @p477 :rule cong :premises (@p476) :args (@t343)) % 168.93/169.58 (step @p478 :rule cong :premises (@p477 @p175) :args (@t359)) % 168.93/169.58 (step @p479 :rule trans :premises (@p478 @p471)) % 168.93/169.58 (step @p480 :rule refl :args (tptp.mbox)) % 168.93/169.58 (step @p481 :rule ho_cong :premises (@p480 @p477)) % 168.93/169.58 (step @p482 :rule ho_cong :premises (@p481 @p175)) % 168.93/169.58 (step @p483 :rule cong :premises (@p482 @p479) :args ((= @t367 @t359))) % 168.93/169.58 (step @p484 :rule symm :premises (@p483)) % 168.93/169.58 (step @p485 :rule refl :args ((_ (_ tptp.mbox @t366) @t20))) % 168.93/169.58 (step @p486 :rule eq_resolve :premises (@p485 @p484)) % 168.93/169.58 (step @p487 :rule cong :premises (@p433) :args (@t368)) % 168.93/169.58 (step @p488 :rule nary_cong :premises (@p487 @p486) :args (@t369)) % 168.93/169.58 (step @p489 :rule cong :premises (@p488) :args ((forall @t47 @t369))) % 168.93/169.58 (step @p490 :rule bool-impl-elim :args (@t350 @t367)) % 168.93/169.58 (step @p491 :rule cong :premises (@p490) :args ((forall @t47 @t370))) % 168.93/169.58 (step @p492 :rule trans :premises (@p491 @p489)) % 168.93/169.58 (step @p493 :rule beta-reduce :args ((= @t374 @t370))) % 168.93/169.58 (step @p494 :rule cong :premises (@p493) :args (@t375)) % 168.93/169.58 (step @p495 :rule trans :premises (@p494 @p492)) % 168.93/169.58 (step @p496 :rule cong :premises (@p495) :args (@t376)) % 168.93/169.58 (step @p497 :rule beta-reduce :args ((= (_ @t146 @t373) @t376))) % 168.93/169.58 (step @p498 :rule trans :premises (@p497 @p496)) % 168.93/169.58 (step @p499 :rule beta-reduce :args ((= (_ @t378 @t2) @t372))) % 168.93/169.58 ; trust TRUST_THEORY_REWRITE % 168.93/169.58 (step @p500 :rule trust :premises () :args ((= @t381 @t378))) % 168.93/169.58 (step @p501 :rule beta-reduce :args ((= (_ @t382 @t380) @t381))) % 168.93/169.58 (step @p502 :rule trans :premises (@p501 @p500)) % 168.93/169.58 (step @p503 :rule refl :args (@t379)) % 168.93/169.58 (step @p504 :rule refl :args (@t377)) % 168.93/169.58 (step @p505 :rule cong :premises (@p504 @p503) :args ((= @t377 @t379))) % 168.93/169.58 (step @p506 :rule symm :premises (@p505)) % 168.93/169.58 (step @p507 :rule eq_resolve :premises (@p504 @p506)) % 168.93/169.58 (step @p508 :rule refl :args (@t310)) % 168.93/169.58 (step @p509 :rule refl :args (@t39)) % 168.93/169.58 (step @p510 :rule cong :premises (@p509 @p508) :args ((= @t39 @t310))) % 168.93/169.58 (step @p511 :rule symm :premises (@p510)) % 168.93/169.58 (step @p512 :rule eq_resolve :premises (@p509 @p511)) % 168.93/169.58 (step @p513 :rule cong :premises (@p512) :args (@t196)) % 168.93/169.58 (step @p514 :rule nary_cong :premises (@p513 @p507) :args (@t383)) % 168.93/169.58 (step @p515 :rule cong :premises (@p514) :args ((forall @t40 @t383))) % 168.93/169.58 (step @p516 :rule bool-impl-elim :args (@t39 @t377)) % 168.93/169.58 (step @p517 :rule cong :premises (@p516) :args ((forall @t40 @t384))) % 168.93/169.58 (step @p518 :rule trans :premises (@p517 @p515)) % 168.93/169.58 (step @p519 :rule beta-reduce :args ((= @t387 @t384))) % 168.93/169.58 (step @p520 :rule cong :premises (@p519) :args (@t388)) % 168.93/169.58 (step @p521 :rule trans :premises (@p520 @p518)) % 168.93/169.58 (step @p522 :rule cong :premises (@p521) :args (@t389)) % 168.93/169.58 (step @p523 :rule beta-reduce :args ((= (_ @t311 @t386) @t389))) % 168.93/169.58 (step @p524 :rule trans :premises (@p523 @p522)) % 168.93/169.58 (step @p525 :rule beta-reduce :args ((= (_ @t391 @t2) @t385))) % 168.93/169.58 (step @p526 :rule beta-reduce :args ((= (_ @t392 @t77) @t391))) % 168.93/169.58 (step @p527 :rule refl :args (@t77)) % 168.93/169.58 (step @p528 :rule beta-reduce :args ((= @t393 @t392))) % 168.93/169.58 (step @p529 :rule ho_cong :premises (@p528 @p527)) % 168.93/169.58 (step @p530 :rule trans :premises (@p529 @p526)) % 168.93/169.58 (step @p531 :rule ho_cong :premises (@p530 @p123)) % 168.93/169.58 (step @p532 :rule trans :premises (@p531 @p525)) % 168.93/169.58 (step @p533 :rule cong :premises (@p532) :args (@t394)) % 168.93/169.58 (step @p534 :rule ho_cong :premises (@p422 @p533)) % 168.93/169.58 (step @p535 :rule trans :premises (@p534 @p524)) % 168.93/169.58 (step @p536 :rule ho_cong :premises (@p68 @p535)) % 168.93/169.58 (step @p537 :rule beta-reduce :args ((= @t395 @t382))) % 168.93/169.58 (step @p538 :rule ho_cong :premises (@p537 @p536)) % 168.93/169.58 (step @p539 :rule trans :premises (@p538 @p502)) % 168.93/169.58 (step @p540 :rule ho_cong :premises (@p539 @p123)) % 168.93/169.58 (step @p541 :rule trans :premises (@p540 @p499)) % 168.93/169.58 (step @p542 :rule cong :premises (@p541) :args ((lambda @t13 (_ (_ @t395 (_ tptp.mbox (_ @t311 @t394))) @t2)))) % 168.93/169.58 (step @p543 :rule ho_cong :premises (@p132 @p542)) % 168.93/169.58 (step @p544 :rule trans :premises (@p543 @p498)) % 168.93/169.58 (step @p545 :rule beta-reduce :args ((= (_ @t34 @t6) @t365))) % 168.93/169.58 (step @p546 :rule ho_cong :premises (@p545 @p544)) % 168.93/169.58 (step @p547 :rule trans :premises (@p546 @p470)) % 168.93/169.58 (step @p548 :rule ho_cong :premises (@p547 @p123)) % 168.93/169.58 (step @p549 :rule trans :premises (@p548 @p464)) % 168.93/169.58 (step @p550 :rule refl :args (@t78)) % 168.93/169.58 (step @p551 :rule ho_cong :premises (@p16 @p550)) % 168.93/169.58 (step @p552 :rule ho_cong :premises (@p551 @p527)) % 168.93/169.58 (step @p553 :rule ho_cong :premises (@p552 @p123)) % 168.93/169.58 (step @p554 :rule cong :premises (@p553) :args (@t80)) % 168.93/169.58 (step @p555 :rule cong :premises (@p512) :args (@t41)) % 168.93/169.58 (step @p556 :rule cong :premises (@p555) :args (@t43)) % 168.93/169.58 (step @p557 :rule trans :premises (@p20 @p556)) % 168.93/169.58 (step @p558 :rule ho_cong :premises (@p557 @p554)) % 168.93/169.58 (step @p559 :rule ho_cong :premises (@p68 @p558)) % 168.93/169.58 (step @p560 :rule refl :args (@t12)) % 168.93/169.58 (step @p561 :rule ho_cong :premises (@p16 @p560)) % 168.93/169.58 (step @p562 :rule ho_cong :premises (@p561 @p559)) % 168.93/169.58 (step @p563 :rule ho_cong :premises (@p562 @p123)) % 168.93/169.58 (step @p564 :rule cong :premises (@p563) :args (@t81)) % 168.93/169.58 (step @p565 :rule ho_cong :premises (@p150 @p564)) % 168.93/169.58 (step @p566 :rule ho_cong :premises (@p15 @p252)) % 168.93/169.58 (step @p567 :rule ho_cong :premises (@p566 @p565)) % 168.93/169.58 (step @p568 :rule ho_cong :premises (@p567 @p123)) % 168.93/169.58 (step @p569 :rule trans :premises (@p568 @p549)) % 168.93/169.58 (step @p570 :rule cong :premises (@p569) :args (@t83)) % 168.93/169.58 (step @p571 :rule trans :premises (@p31 @p570)) % 168.93/169.58 (step @p572 :rule ho_cong :premises (@p571 @p463)) % 168.93/169.58 (step @p573 :rule ho_cong :premises (@p572 @p372)) % 168.93/169.58 (step @p574 :rule ho_cong :premises (@p463 @p372)) % 168.93/169.58 (step @p575 :rule ho_cong :premises (@p16 @p574)) % 168.93/169.58 (step @p576 :rule ho_cong :premises (@p575 @p573)) % 168.93/169.58 (step @p577 :rule ho_cong :premises (@p576 @p123)) % 168.93/169.58 (step @p578 :rule cong :premises (@p577) :args (@t17)) % 168.93/169.58 (step @p579 :rule ho_cong :premises (@p557 @p578)) % 168.93/169.58 (step @p580 :rule ho_cong :premises (@p159 @p579)) % 168.93/169.58 (step @p581 :rule cong :premises (@p580) :args (@t18)) % 168.93/169.58 (step @p582 :rule trans :premises (@p581 @p427)) % 168.93/169.58 (step @p583 :rule trans :premises (@p582 @p332 @p276)) % 168.93/169.58 (step @p584 :rule eq_resolve :premises (@p8 @p583)) % 168.93/169.58 (step @p585 :rule skolemize :premises (@p584)) % 168.93/169.58 (step @p586 :rule bool-double-not-elim :args (@t397)) % 168.93/169.58 (step @p587 :rule refl :args (@t412)) % 168.93/169.58 (step @p588 :rule nary_cong :premises (@p587 @p586) :args ((or @t412 (not @t411)))) % 168.93/169.58 (step @p589 :rule cnf_or_neg :args (@t412 0)) % 168.93/169.58 (step @p590 :rule eq_resolve :premises (@p589 @p588)) % 168.93/169.58 (step @p591 :rule reordering :premises (@p590) :args ((or @t397 @t412))) % 168.93/169.58 (step @p592 :rule chain_m_resolution :premises (@p591 @p585) :args (@t397 @t413 @t414)) % 168.93/169.58 (step @p593 :rule instantiate :premises (@p592) :args ((@list @t212))) % 168.93/169.58 (step @p594 :rule eq-symm :args (@t418 @t419)) % 168.93/169.58 (step @p595 :rule cong :premises (@p594) :args (@t421)) % 168.93/169.58 ; trust TRUST PREPROCESS_HO_ELIM % 168.93/169.58 (step @p596 :rule trust :premises () :args ((= @t423 @t421))) % 168.93/169.58 (step @p597 :rule trans :premises (@p596 @p595)) % 168.93/169.58 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 168.93/169.58 (step @p598 :rule trust :premises () :args (@t423)) % 168.93/169.58 (step @p599 :rule eq_resolve :premises (@p598 @p597)) % 168.93/169.58 (step @p600 :rule eq-symm :args (@t424 @t406)) % 168.93/169.58 (step @p601 :rule refl :args (@t425)) % 168.93/169.58 (step @p602 :rule cong :premises (@p601 @p600) :args ((=> @t425 @t426))) % 168.93/169.58 (assume-push @p665 @t425) % 168.93/169.58 (step @p604 :rule instantiate :premises (@p599) :args ((@list @t211 @t396 @t210))) % 168.93/169.58 (step-pop @p666 :rule scope :premises (@p604)) % 168.93/169.58 (step @p605 :rule process_scope :premises (@p666) :args (@t426)) % 168.93/169.58 (step @p607 :rule eq_resolve :premises (@p605 @p602)) % 168.93/169.58 (step @p608 :rule implies_elim :premises (@p607)) % 168.93/169.58 (step @p609 :rule chain_m_resolution :premises (@p608 @p599) :args (@t427 @t220 (@list @t425))) % 168.93/169.58 (step @p610 :rule instantiate :premises (@p592) :args ((@list @t408))) % 168.93/169.58 (step @p611 :rule cnf_or_neg :args (@t412 1)) % 168.93/169.58 (step @p612 :rule chain_m_resolution :premises (@p611 @p585) :args ((not @t410) @t413 @t414)) % 168.93/169.58 (step @p613 :rule cnf_and_neg :args (@t410)) % 168.93/169.58 (step @p614 :rule chain_m_resolution :premises (@p613 @p612 @p610) :args ((not @t407) @t428 (@list @t410 @t409))) % 168.93/169.58 (step @p615 :rule bool-double-not-elim :args (@t405)) % 168.93/169.58 (step @p616 :rule refl :args (@t407)) % 168.93/169.58 (step @p617 :rule nary_cong :premises (@p616 @p615) :args ((or @t407 (not @t406)))) % 168.93/169.58 (step @p618 :rule cnf_or_neg :args (@t407 0)) % 168.93/169.58 (step @p619 :rule eq_resolve :premises (@p618 @p617)) % 168.93/169.58 (step @p620 :rule reordering :premises (@p619) :args ((or @t405 @t407))) % 168.93/169.58 (step @p621 :rule chain_m_resolution :premises (@p620 @p614) :args (@t405 @t413 @t429)) % 168.93/169.58 (step @p622 :rule cnf_equiv_pos2 :args (@t427)) % 168.93/169.58 (step @p623 :rule reordering :premises (@p622) :args ((or @t406 @t430 (not @t427)))) % 168.93/169.58 (step @p624 :rule chain_m_resolution :premises (@p623 @p621 @p609) :args (@t430 (@list false false) (@list @t405 @t427))) % 168.93/169.58 (step @p625 :rule cnf_or_pos :args (@t432)) % 168.93/169.58 (step @p626 :rule reordering :premises (@p625) :args ((or @t431 @t424 (not @t432)))) % 168.93/169.58 (step @p627 :rule chain_m_resolution :premises (@p626 @p624 @p593) :args (@t431 @t428 (@list @t424 @t432))) % 168.93/169.58 (step @p628 :rule refl :args (@t213)) % 168.93/169.58 (step @p629 :rule bool-double-not-elim :args (@t215)) % 168.93/169.58 (step @p630 :rule refl :args (@t433)) % 168.93/169.58 (step @p631 :rule nary_cong :premises (@p630 @p629 @p628) :args ((or @t433 (not @t216) @t213))) % 168.93/169.58 (step @p632 :rule cnf_equiv_pos1 :args (@t219)) % 168.93/169.58 (step @p633 :rule eq_resolve :premises (@p632 @p631)) % 168.93/169.58 (step @p634 :rule reordering :premises (@p633) :args ((or @t215 @t213 @t433))) % 168.93/169.58 (step @p635 :rule chain_m_resolution :premises (@p634 @p627 @p275) :args (@t215 @t428 (@list @t213 @t219))) % 168.93/169.58 (step @p636 :rule bool-double-not-elim :args (@t401)) % 168.93/169.58 (step @p637 :rule nary_cong :premises (@p616 @p636) :args ((or @t407 (not @t402)))) % 168.93/169.58 (step @p638 :rule cnf_or_neg :args (@t407 2)) % 168.93/169.58 (step @p639 :rule eq_resolve :premises (@p638 @p637)) % 168.93/169.58 (step @p640 :rule reordering :premises (@p639) :args ((or @t401 @t407))) % 168.93/169.58 (step @p641 :rule chain_m_resolution :premises (@p640 @p614) :args (@t401 @t413 @t429)) % 168.93/169.58 (step @p642 :rule instantiate :premises (@p641) :args ((@list @t211))) % 168.93/169.58 (step @p643 :rule cnf_or_neg :args (@t407 3)) % 168.93/169.58 (step @p644 :rule chain_m_resolution :premises (@p643 @p614) :args ((not @t400) @t413 @t429)) % 168.93/169.58 (step @p645 :rule cnf_or_pos :args (@t436)) % 168.93/169.58 (step @p646 :rule reordering :premises (@p645) :args ((or @t400 @t435 (not @t436)))) % 168.93/169.58 (step @p647 :rule chain_m_resolution :premises (@p646 @p644 @p642) :args (@t435 @t428 (@list @t400 @t436))) % 168.93/169.58 (step @p648 :rule bool-double-not-elim :args (@t403)) % 168.93/169.58 (step @p649 :rule nary_cong :premises (@p616 @p648) :args ((or @t407 (not @t404)))) % 168.93/169.58 (step @p650 :rule cnf_or_neg :args (@t407 1)) % 168.93/169.58 (step @p651 :rule eq_resolve :premises (@p650 @p649)) % 168.93/169.58 (step @p652 :rule reordering :premises (@p651) :args ((or @t403 @t407))) % 168.93/169.58 (step @p653 :rule chain_m_resolution :premises (@p652 @p614) :args (@t403 @t413 @t429)) % 168.93/169.58 (step @p654 :rule cnf_or_pos :args (@t437)) % 168.93/169.58 (step @p655 :rule reordering :premises (@p654) :args ((or @t404 @t434 @t216 @t438))) % 168.93/169.58 (step @p656 :rule chain_m_resolution :premises (@p655 @p653 @p647 @p635) :args (@t438 (@list false true false) (@list @t403 @t434 @t215))) % 168.93/169.58 (assume-push @p667 @t96) % 168.93/169.58 (step @p658 :rule instantiate :premises (@p163) :args ((@list @t210 @t211 @t398))) % 168.93/169.58 (step-pop @p668 :rule scope :premises (@p658)) % 168.93/169.58 (step @p659 :rule process_scope :premises (@p668) :args (@t437)) % 168.93/169.58 (step @p661 :rule implies_elim :premises (@p659)) % 168.93/169.58 (step @p662 false :rule chain_m_resolution :premises (@p661 @p656 @p163) :args (false @t428 (@list @t437 @t96))) % 168.93/169.58 ) % 168.93/169.58 % SZS output end Proof % 168.93/169.58 % cvc5 exiting %------------------------------------------------------------------------------