%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO059^4 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/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 09:11:54 AM UTC 2026 % Result : Theorem 0.73s 0.95s % Output : Proof 0.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO059^4 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n020.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 23:53:10 EDT 2026 % 0.17/0.34 % CPUTime : % 0.26/0.49 %----Proving TH0 % 0.73/0.95 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.73/0.95 % SZS status Theorem % 0.73/0.95 % SZS output start Proof % 0.73/0.95 ( % 0.73/0.95 (declare-sort $$unsorted 0) % 0.73/0.95 (declare-const tptp.irel (-> $$unsorted $$unsorted Bool)) % 0.73/0.95 (declare-const tptp.a (-> $$unsorted Bool)) % 0.73/0.95 (declare-const tptp.ifalse (-> $$unsorted Bool)) % 0.73/0.95 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.73/0.95 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.73/0.95 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.73/0.95 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.73/0.95 (define tptp.mbox_s4 () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.irel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.73/0.95 (define tptp.iatom () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 0.73/0.95 (define tptp.inot () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 _let_2)) _let_1))))) % 0.73/0.95 (define tptp.itrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.73/0.95 (define tptp.iand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mand _let_3) _let_2) _let_1)))))) % 0.73/0.95 (define tptp.ior () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mbox_s4 _let_3)) (_ tptp.mbox_s4 _let_2)) _let_1)))))) % 0.73/0.95 (define tptp.iimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mimplies (_ tptp.mbox_s4 _let_3)) (_ tptp.mbox_s4 _let_2)) _let_1)))))) % 0.73/0.95 (define tptp.iimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Q" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.iimplies _let_3) _let_2) _let_1)))))) % 0.73/0.95 (define tptp.iequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Q" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.iand (_ (_ tptp.iimplies _let_2) _let_3)) (_ (_ tptp.iimplies _let_3) _let_2)) _let_1)))))) % 0.73/0.95 (define tptp.ixor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.inot (_ (_ tptp.iequiv _let_3) _let_2)) _let_1)))))) % 0.73/0.95 (define tptp.ivalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.73/0.95 (define tptp.isatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.73/0.95 (define tptp.icountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.73/0.95 (define tptp.iinvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.73/0.95 (define @t1 () (@var "X" $$unsorted)) % 0.73/0.95 (define @t2 () (_ tptp.irel @t1)) % 0.73/0.95 (define @t3 () (_ @t2 @t1)) % 0.73/0.95 (define @t4 () (@list @t1)) % 0.73/0.95 (define @t5 () (forall @t4 @t3)) % 0.73/0.95 (define @t6 () (@var "Z" $$unsorted)) % 0.73/0.95 (define @t7 () (@var "Y" $$unsorted)) % 0.73/0.95 (define @t8 () (_ @t2 @t7)) % 0.73/0.95 (define @t9 () (_ tptp.iatom tptp.a)) % 0.73/0.95 (define @t10 () (not (_ tptp.ivalid (_ tptp.inot (_ tptp.inot @t9))))) % 0.73/0.95 (define @t11 () (@var "U" $$unsorted)) % 0.73/0.95 (define @t12 () (@var "X" (-> $$unsorted Bool))) % 0.73/0.95 (define @t13 () (_ @t12 @t11)) % 0.73/0.95 (define @t14 () (lambda (@list @t12 @t11) (not @t13))) % 0.73/0.95 (define @t15 () (@var "Y" (-> $$unsorted Bool))) % 0.73/0.95 (define @t16 () (_ @t15 @t11)) % 0.73/0.95 (define @t17 () (@list @t12 @t15 @t11)) % 0.73/0.95 (define @t18 () (lambda @t17 (or @t13 @t16))) % 0.73/0.95 (define @t19 () (lambda @t17 (and @t13 @t16))) % 0.73/0.95 (define @t20 () (@var "__flatten_var_0" $$unsorted)) % 0.73/0.95 (define @t21 () (@var "V" (-> $$unsorted Bool))) % 0.73/0.95 (define @t22 () (@var "U" (-> $$unsorted Bool))) % 0.73/0.95 (define @t23 () (lambda (@list @t22 @t21 @t20) (_ (_ (_ tptp.mor (_ tptp.mnot @t22)) @t21) @t20))) % 0.73/0.95 (define @t24 () (@var "P" (-> $$unsorted Bool))) % 0.73/0.95 (define @t25 () (_ @t24 @t7)) % 0.73/0.95 (define @t26 () (@list @t7)) % 0.73/0.95 (define @t27 () (forall @t26 (=> @t8 @t25))) % 0.73/0.95 (define @t28 () (@list @t24 @t1)) % 0.73/0.95 (define @t29 () (lambda @t28 @t27)) % 0.73/0.95 (define @t30 () (@list @t24 @t20)) % 0.73/0.95 (define @t31 () (lambda @t30 (_ @t24 @t20))) % 0.73/0.95 (define @t32 () (_ tptp.mbox_s4 @t24)) % 0.73/0.95 (define @t33 () (lambda @t30 (_ (_ tptp.mnot @t32) @t20))) % 0.73/0.95 (define @t34 () (@var "W" $$unsorted)) % 0.73/0.95 (define @t35 () (@list @t34)) % 0.73/0.95 (define @t36 () (lambda @t35 true)) % 0.73/0.95 (define @t37 () (@var "Q" (-> $$unsorted Bool))) % 0.73/0.95 (define @t38 () (@list @t24 @t37 @t20)) % 0.73/0.95 (define @t39 () (lambda @t38 (_ (_ (_ tptp.mand @t24) @t37) @t20))) % 0.73/0.95 (define @t40 () (_ tptp.mbox_s4 @t37)) % 0.73/0.95 (define @t41 () (lambda @t38 (_ (_ (_ tptp.mor @t32) @t40) @t20))) % 0.73/0.95 (define @t42 () (lambda @t38 (_ (_ (_ tptp.mimplies @t32) @t40) @t20))) % 0.73/0.95 (define @t43 () (_ (_ tptp.iimplies @t37) @t24)) % 0.73/0.95 (define @t44 () (lambda @t38 (_ @t43 @t20))) % 0.73/0.95 (define @t45 () (lambda @t38 (_ (_ (_ tptp.iand (_ (_ tptp.iimplies @t24) @t37)) @t43) @t20))) % 0.73/0.95 (define @t46 () (lambda @t38 (_ (_ tptp.inot (_ (_ tptp.iequiv @t24) @t37)) @t20))) % 0.73/0.95 (define @t47 () (@var "Phi" (-> $$unsorted Bool))) % 0.73/0.95 (define @t48 () (_ @t47 @t34)) % 0.73/0.95 (define @t49 () (forall @t35 @t48)) % 0.73/0.95 (define @t50 () (@list @t47)) % 0.73/0.95 (define @t51 () (lambda @t50 @t49)) % 0.73/0.95 (define @t52 () (lambda @t50 (exists @t35 @t48))) % 0.73/0.95 (define @t53 () (not @t48)) % 0.73/0.95 (define @t54 () (lambda @t50 (exists @t35 @t53))) % 0.73/0.95 (define @t55 () (lambda @t50 (forall @t35 @t53))) % 0.73/0.95 (define @t56 () (tptp.a @t34)) % 0.73/0.95 (define @t57 () (_ tptp.a @t34)) % 0.73/0.95 (define @t58 () (@list @t20)) % 0.73/0.95 (define @t59 () (lambda @t58 (_ tptp.a @t20))) % 0.73/0.95 (define @t60 () (_ @t59 @t34)) % 0.73/0.95 (define @t61 () (forall @t35 @t60)) % 0.73/0.95 (define @t62 () (_ @t47 @t34)) % 0.73/0.95 (define @t63 () (lambda @t50 (forall @t35 @t62))) % 0.73/0.95 (define @t64 () (_ @t31 tptp.a)) % 0.73/0.95 (define @t65 () (@var "BOUND_VARIABLE_8044" $$unsorted)) % 0.73/0.95 (define @t66 () (tptp.a @t65)) % 0.73/0.95 (define @t67 () (@list @t65)) % 0.73/0.95 (define @t68 () (not (forall @t67 (or (not (tptp.irel @t7 @t65)) @t66)))) % 0.73/0.95 (define @t69 () (not (forall @t26 (or (not (tptp.irel @t34 @t7)) @t68)))) % 0.73/0.95 (define @t70 () (not (tptp.irel @t20 @t7))) % 0.73/0.95 (define @t71 () (lambda @t58 (not (forall @t26 (or @t70 @t68))))) % 0.73/0.95 (define @t72 () (_ @t71 @t34)) % 0.73/0.95 (define @t73 () (forall @t35 @t72)) % 0.73/0.95 (define @t74 () (tptp.a @t7)) % 0.73/0.95 (define @t75 () (forall @t26 (or @t70 @t74))) % 0.73/0.95 (define @t76 () (not @t75)) % 0.73/0.95 (define @t77 () (lambda @t58 @t76)) % 0.73/0.95 (define @t78 () (or @t70 (_ @t77 @t7))) % 0.73/0.95 (define @t79 () (forall @t26 @t78)) % 0.73/0.95 (define @t80 () (not @t79)) % 0.73/0.95 (define @t81 () (lambda @t58 @t80)) % 0.73/0.95 (define @t82 () (_ @t24 @t7)) % 0.73/0.95 (define @t83 () (not (forall @t26 (or @t70 @t82)))) % 0.73/0.95 (define @t84 () (lambda @t30 @t83)) % 0.73/0.95 (define @t85 () (_ tptp.a @t7)) % 0.73/0.95 (define @t86 () (or @t70 @t85)) % 0.73/0.95 (define @t87 () (_ @t59 @t7)) % 0.73/0.95 (define @t88 () (or @t70 @t87)) % 0.73/0.95 (define @t89 () (forall @t26 @t88)) % 0.73/0.95 (define @t90 () (not @t89)) % 0.73/0.95 (define @t91 () (lambda @t58 @t90)) % 0.73/0.95 (define @t92 () (forall @t26 (or (not (tptp.irel @t11 @t7)) @t82))) % 0.73/0.95 (define @t93 () (@list @t11)) % 0.73/0.95 (define @t94 () (tptp.irel @t1 @t7)) % 0.73/0.95 (define @t95 () (forall @t26 (or (not @t94) @t82))) % 0.73/0.95 (define @t96 () (lambda @t4 @t95)) % 0.73/0.95 (define @t97 () (_ @t96 @t11)) % 0.73/0.95 (define @t98 () (not @t97)) % 0.73/0.95 (define @t99 () (lambda @t93 @t98)) % 0.73/0.95 (define @t100 () (not @t8)) % 0.73/0.95 (define @t101 () (or @t100 @t25)) % 0.73/0.95 (define @t102 () (forall @t35 @t69)) % 0.73/0.95 (define @t103 () (@quantifiers_skolemize @t102 0)) % 0.73/0.95 (define @t104 () (forall @t26 (or (not (tptp.irel @t103 @t7)) @t68))) % 0.73/0.95 (define @t105 () (not @t102)) % 0.73/0.95 (define @t106 () (not (not @t104))) % 0.73/0.95 (define @t107 () (@list true)) % 0.73/0.95 (define @t108 () (@list @t103)) % 0.73/0.95 (define @t109 () (tptp.irel @t1 @t1)) % 0.73/0.95 (define @t110 () (forall @t67 (or (not (tptp.irel @t103 @t65)) @t66))) % 0.73/0.95 (define @t111 () (not @t110)) % 0.73/0.95 (define @t112 () (tptp.irel @t103 @t103)) % 0.73/0.95 (define @t113 () (not @t112)) % 0.73/0.95 (define @t114 () (or @t113 @t111)) % 0.73/0.95 (define @t115 () (@quantifiers_skolemize @t110 0)) % 0.73/0.95 (define @t116 () (tptp.a @t115)) % 0.73/0.95 (define @t117 () (or (not (tptp.irel @t103 @t115)) @t116)) % 0.73/0.95 (define @t118 () (forall @t35 @t56)) % 0.73/0.95 (assume @p1 @t5) % 0.73/0.95 (assume @p2 (forall (@list @t1 @t7 @t6) (=> (and @t8 (_ (_ tptp.irel @t7) @t6)) (_ @t2 @t6)))) % 0.73/0.95 (assume @p3 (= tptp.ifalse (_ tptp.inot tptp.itrue))) % 0.73/0.95 (assume @p4 (_ tptp.ivalid @t9)) % 0.73/0.95 (assume @p5 @t10) % 0.73/0.95 (assume @p6 true) % 0.73/0.95 (step @p7 (= tptp.mnot @t14) :rule refl :args (@t14)) % 0.73/0.95 (step @p8 (= tptp.mor @t18) :rule refl :args (@t18)) % 0.73/0.95 (step @p9 (= tptp.mand @t19) :rule refl :args (@t19)) % 0.73/0.95 (step @p10 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.73/0.95 (step @p11 (= tptp.mbox_s4 @t29) :rule refl :args (@t29)) % 0.73/0.95 (step @p12 (= tptp.iatom @t31) :rule refl :args (@t31)) % 0.73/0.95 (step @p13 (= tptp.inot @t33) :rule refl :args (@t33)) % 0.73/0.95 (step @p14 (= tptp.itrue @t36) :rule refl :args (@t36)) % 0.73/0.95 (step @p15 (= tptp.iand @t39) :rule refl :args (@t39)) % 0.73/0.95 (step @p16 (= tptp.ior @t41) :rule refl :args (@t41)) % 0.73/0.95 (step @p17 (= tptp.iimplies @t42) :rule refl :args (@t42)) % 0.73/0.95 (step @p18 (= tptp.iimplied @t44) :rule refl :args (@t44)) % 0.73/0.95 (step @p19 (= tptp.iequiv @t45) :rule refl :args (@t45)) % 0.73/0.95 (step @p20 (= tptp.ixor @t46) :rule refl :args (@t46)) % 0.73/0.95 (step @p21 (= tptp.ivalid @t51) :rule refl :args (@t51)) % 0.73/0.95 (step @p22 (= tptp.isatisfiable @t52) :rule refl :args (@t52)) % 0.73/0.95 (step @p23 (= tptp.icountersatisfiable @t54) :rule refl :args (@t54)) % 0.73/0.95 (step @p24 (= tptp.iinvalid @t55) :rule refl :args (@t55)) % 0.73/0.95 (step @p25 :rule refl :args (@t56)) % 0.73/0.95 (step @p26 :rule refl :args (@t57)) % 0.73/0.95 (step @p27 :rule cong :premises (@p26 @p25) :args ((= @t57 @t56))) % 0.73/0.95 (step @p28 :rule symm :premises (@p27)) % 0.73/0.95 (step @p29 :rule eq_resolve :premises (@p26 @p28)) % 0.73/0.95 (step @p30 :rule cong :premises (@p29) :args ((forall @t35 @t57))) % 0.73/0.95 (step @p31 :rule beta-reduce :args ((= @t60 @t57))) % 0.73/0.95 (step @p32 :rule cong :premises (@p31) :args (@t61)) % 0.73/0.95 (step @p33 :rule trans :premises (@p32 @p30)) % 0.73/0.95 (step @p34 :rule beta-reduce :args ((= (_ @t63 @t59) @t61))) % 0.73/0.95 (step @p35 :rule trans :premises (@p34 @p33)) % 0.73/0.95 (step @p36 :rule beta-reduce :args ((= @t64 @t59))) % 0.73/0.95 (step @p37 :rule refl :args (@t63)) % 0.73/0.95 (step @p38 :rule ho_cong :premises (@p37 @p36)) % 0.73/0.95 (step @p39 :rule trans :premises (@p38 @p35)) % 0.73/0.95 (step @p40 :rule refl :args (tptp.a)) % 0.73/0.95 (step @p41 :rule ho_cong :premises (@p12 @p40)) % 0.73/0.95 (step @p42 :rule refl :args (@t62)) % 0.73/0.95 (step @p43 :rule refl :args (@t48)) % 0.73/0.95 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t48 @t62))) % 0.73/0.95 (step @p45 :rule symm :premises (@p44)) % 0.73/0.95 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.73/0.95 (step @p47 :rule cong :premises (@p46) :args (@t49)) % 0.73/0.95 (step @p48 :rule cong :premises (@p47) :args (@t51)) % 0.73/0.95 (step @p49 :rule trans :premises (@p21 @p48)) % 0.73/0.95 (step @p50 :rule ho_cong :premises (@p49 @p41)) % 0.73/0.95 (step @p51 :rule trans :premises (@p50 @p39)) % 0.73/0.95 (step @p52 :rule eq_resolve :premises (@p4 @p51)) % 0.73/0.95 (step @p53 :rule beta-reduce :args ((= @t72 @t69))) % 0.73/0.95 (step @p54 :rule cong :premises (@p53) :args (@t73)) % 0.73/0.95 (step @p55 :rule beta-reduce :args ((= (_ @t63 @t71) @t73))) % 0.73/0.95 (step @p56 :rule trans :premises (@p55 @p54)) % 0.73/0.95 (step @p57 :rule beta-reduce :args ((= (_ (lambda @t58 (not (forall @t67 (or (not (tptp.irel @t20 @t65)) @t66)))) @t7) @t68))) % 0.73/0.95 (step @p58 :rule refl :args (@t7)) % 0.73/0.95 (step @p59 :rule alpha_equiv :args (@t75 (@list @t7) (@list @t65))) % 0.73/0.95 (step @p60 :rule cong :premises (@p59) :args (@t76)) % 0.73/0.95 (step @p61 :rule cong :premises (@p60) :args (@t77)) % 0.73/0.95 (step @p62 :rule ho_cong :premises (@p61 @p58)) % 0.73/0.95 (step @p63 :rule trans :premises (@p62 @p57)) % 0.73/0.95 (step @p64 :rule refl :args (@t70)) % 0.73/0.95 (step @p65 :rule nary_cong :premises (@p64 @p63) :args (@t78)) % 0.73/0.95 (step @p66 :rule cong :premises (@p65) :args (@t79)) % 0.73/0.95 (step @p67 :rule cong :premises (@p66) :args (@t80)) % 0.73/0.95 (step @p68 :rule cong :premises (@p67) :args (@t81)) % 0.73/0.95 (step @p69 :rule beta-reduce :args ((= (_ @t84 @t77) @t81))) % 0.73/0.95 (step @p70 :rule trans :premises (@p69 @p68)) % 0.73/0.95 (step @p71 :rule refl :args (@t74)) % 0.73/0.95 (step @p72 :rule refl :args (@t85)) % 0.73/0.95 (step @p73 :rule cong :premises (@p72 @p71) :args ((= @t85 @t74))) % 0.73/0.95 (step @p74 :rule symm :premises (@p73)) % 0.73/0.95 (step @p75 :rule eq_resolve :premises (@p72 @p74)) % 0.73/0.95 (step @p76 :rule refl :args (@t70)) % 0.73/0.95 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t86)) % 0.73/0.95 (step @p78 :rule cong :premises (@p77) :args ((forall @t26 @t86))) % 0.73/0.95 (step @p79 :rule beta-reduce :args ((= @t87 @t85))) % 0.73/0.95 (step @p80 :rule nary_cong :premises (@p64 @p79) :args (@t88)) % 0.73/0.95 (step @p81 :rule cong :premises (@p80) :args (@t89)) % 0.73/0.95 (step @p82 :rule trans :premises (@p81 @p78)) % 0.73/0.95 (step @p83 :rule cong :premises (@p82) :args (@t90)) % 0.73/0.95 (step @p84 :rule cong :premises (@p83) :args (@t91)) % 0.73/0.95 (step @p85 :rule beta-reduce :args ((= (_ @t84 @t59) @t91))) % 0.73/0.95 (step @p86 :rule trans :premises (@p85 @p84)) % 0.73/0.95 (step @p87 :rule refl :args (@t84)) % 0.73/0.95 (step @p88 :rule ho_cong :premises (@p87 @p36)) % 0.73/0.95 (step @p89 :rule trans :premises (@p88 @p86)) % 0.73/0.95 (step @p90 :rule ho_cong :premises (@p87 @p89)) % 0.73/0.95 (step @p91 :rule trans :premises (@p90 @p70)) % 0.73/0.95 (step @p92 :rule ho_cong :premises (@p37 @p91)) % 0.73/0.95 (step @p93 :rule trans :premises (@p92 @p56)) % 0.73/0.95 (step @p94 :rule cong :premises (@p93) :args ((not (_ @t63 (_ @t84 (_ @t84 @t64)))))) % 0.73/0.95 (step @p95 :rule beta-reduce :args ((= (_ (lambda @t93 (not @t92)) @t20) @t83))) % 0.73/0.95 (step @p96 :rule refl :args (@t20)) % 0.73/0.95 (step @p97 :rule beta-reduce :args ((= @t97 @t92))) % 0.73/0.95 (step @p98 :rule cong :premises (@p97) :args (@t98)) % 0.73/0.95 (step @p99 :rule cong :premises (@p98) :args (@t99)) % 0.73/0.95 (step @p100 :rule beta-reduce :args ((= (_ @t14 @t96) @t99))) % 0.73/0.95 (step @p101 :rule trans :premises (@p100 @p99)) % 0.73/0.95 (step @p102 :rule beta-reduce :args ((= (_ (lambda @t28 @t95) @t24) @t96))) % 0.73/0.95 (step @p103 :rule refl :args (@t14)) % 0.73/0.95 (step @p104 :rule ho_cong :premises (@p103 @p102)) % 0.73/0.95 (step @p105 :rule trans :premises (@p104 @p101)) % 0.73/0.95 (step @p106 :rule ho_cong :premises (@p105 @p96)) % 0.73/0.95 (step @p107 :rule trans :premises (@p106 @p95)) % 0.73/0.95 (step @p108 :rule refl :args (@t24)) % 0.73/0.95 (step @p109 :rule refl :args (@t82)) % 0.73/0.95 (step @p110 :rule refl :args (@t25)) % 0.73/0.95 (step @p111 :rule cong :premises (@p110 @p109) :args ((= @t25 @t82))) % 0.73/0.95 (step @p112 :rule symm :premises (@p111)) % 0.73/0.95 (step @p113 :rule eq_resolve :premises (@p110 @p112)) % 0.73/0.95 (step @p114 :rule refl :args (@t94)) % 0.73/0.95 (step @p115 :rule refl :args (@t8)) % 0.73/0.95 (step @p116 :rule cong :premises (@p115 @p114) :args ((= @t8 @t94))) % 0.73/0.95 (step @p117 :rule symm :premises (@p116)) % 0.73/0.95 (step @p118 :rule eq_resolve :premises (@p115 @p117)) % 0.73/0.95 (step @p119 :rule cong :premises (@p118) :args (@t100)) % 0.73/0.95 (step @p120 :rule nary_cong :premises (@p119 @p113) :args (@t101)) % 0.73/0.95 (step @p121 :rule cong :premises (@p120) :args ((forall @t26 @t101))) % 0.73/0.95 (step @p122 :rule bool-impl-elim :args (@t8 @t25)) % 0.73/0.95 (step @p123 :rule cong :premises (@p122) :args (@t27)) % 0.73/0.95 (step @p124 :rule trans :premises (@p123 @p121)) % 0.73/0.95 (step @p125 :rule cong :premises (@p124) :args (@t29)) % 0.73/0.95 (step @p126 :rule trans :premises (@p11 @p125)) % 0.73/0.95 (step @p127 :rule ho_cong :premises (@p126 @p108)) % 0.73/0.95 (step @p128 :rule ho_cong :premises (@p7 @p127)) % 0.73/0.95 (step @p129 :rule ho_cong :premises (@p128 @p96)) % 0.73/0.95 (step @p130 :rule trans :premises (@p129 @p107)) % 0.73/0.95 (step @p131 :rule cong :premises (@p130) :args (@t33)) % 0.73/0.95 (step @p132 :rule trans :premises (@p13 @p131)) % 0.73/0.95 (step @p133 :rule ho_cong :premises (@p132 @p41)) % 0.73/0.95 (step @p134 :rule ho_cong :premises (@p132 @p133)) % 0.73/0.95 (step @p135 :rule ho_cong :premises (@p49 @p134)) % 0.73/0.95 (step @p136 :rule cong :premises (@p135) :args (@t10)) % 0.73/0.95 (step @p137 :rule trans :premises (@p136 @p94)) % 0.73/0.95 (step @p138 :rule eq_resolve :premises (@p5 @p137)) % 0.73/0.95 (step @p139 :rule refl :args (@t104)) % 0.73/0.95 (step @p140 :rule bool-double-not-elim :args (@t102)) % 0.73/0.95 (step @p141 :rule nary_cong :premises (@p140 @p139) :args ((or (not @t105) @t104))) % 0.73/0.95 (step @p142 :rule bool-double-not-elim :args (@t104)) % 0.73/0.95 (step @p143 :rule refl :args (@t105)) % 0.73/0.95 (step @p144 :rule cong :premises (@p143 @p142) :args ((=> @t105 @t106))) % 0.73/0.95 (assume-push @p174 @t105) % 0.73/0.95 (step @p146 :rule skolemize :premises (@p138)) % 0.73/0.95 (step-pop @p175 :rule scope :premises (@p146)) % 0.73/0.95 (step @p147 :rule process_scope :premises (@p175) :args (@t106)) % 0.73/0.95 (step @p149 :rule eq_resolve :premises (@p147 @p144)) % 0.73/0.95 (step @p150 :rule implies_elim :premises (@p149)) % 0.73/0.95 (step @p151 :rule eq_resolve :premises (@p150 @p141)) % 0.73/0.95 (step @p152 :rule chain_m_resolution :premises (@p151 @p138) :args (@t104 @t107 (@list @t102))) % 0.73/0.95 (step @p153 :rule instantiate :premises (@p152) :args (@t108)) % 0.73/0.95 (step @p154 :rule refl :args (@t109)) % 0.73/0.95 (step @p155 :rule refl :args (@t3)) % 0.73/0.95 (step @p156 :rule cong :premises (@p155 @p154) :args ((= @t3 @t109))) % 0.73/0.95 (step @p157 :rule symm :premises (@p156)) % 0.73/0.95 (step @p158 :rule eq_resolve :premises (@p155 @p157)) % 0.73/0.95 (step @p159 :rule cong :premises (@p158) :args (@t5)) % 0.73/0.95 (step @p160 :rule eq_resolve :premises (@p1 @p159)) % 0.73/0.95 (step @p161 :rule instantiate :premises (@p160) :args (@t108)) % 0.73/0.95 (step @p162 :rule cnf_or_pos :args (@t114)) % 0.73/0.95 (step @p163 :rule reordering :premises (@p162) :args ((or @t113 @t111 (not @t114)))) % 0.73/0.95 (step @p164 :rule chain_m_resolution :premises (@p163 @p161 @p153) :args (@t111 (@list false false) (@list @t112 @t114))) % 0.73/0.95 (step @p165 :rule skolemize :premises (@p164)) % 0.73/0.95 (step @p166 :rule cnf_or_neg :args (@t117 1)) % 0.73/0.95 (step @p167 :rule chain_m_resolution :premises (@p166 @p165) :args ((not @t116) @t107 (@list @t117))) % 0.73/0.95 (assume-push @p176 @t118) % 0.73/0.95 (step @p169 :rule instantiate :premises (@p52) :args ((@list @t115))) % 0.73/0.95 (step-pop @p177 :rule scope :premises (@p169)) % 0.73/0.95 (step @p170 :rule process_scope :premises (@p177) :args (@t116)) % 0.73/0.95 (step @p172 :rule implies_elim :premises (@p170)) % 0.73/0.95 (step @p173 false :rule chain_m_resolution :premises (@p172 @p167 @p52) :args (false (@list true false) (@list @t116 @t118))) % 0.73/0.95 ) % 0.73/0.95 % SZS output end Proof % 0.73/0.95 % cvc5 exiting %------------------------------------------------------------------------------