%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO061^4 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n015.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 0.29s 0.55s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SYO061^4 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.32 % Computer : n015.cluster.edu % 0.15/0.32 % Model : x86_64 x86_64 % 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.32 % Memory : 8042.1875MB % 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.32 % CPULimit : 300 % 0.15/0.32 % WCLimit : 300 % 0.15/0.32 % DateTime : Tue Jun 2 23:53:19 EDT 2026 % 0.15/0.32 % CPUTime : % 0.29/0.47 %----Proving TH0 % 0.29/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.29/0.55 % SZS status Theorem % 0.29/0.55 % SZS output start Proof % 0.29/0.55 ( % 0.29/0.55 (declare-sort $$unsorted 0) % 0.29/0.55 (declare-const tptp.irel (-> $$unsorted $$unsorted Bool)) % 0.29/0.55 (declare-const tptp.a (-> $$unsorted Bool)) % 0.29/0.55 (declare-const tptp.b (-> $$unsorted Bool)) % 0.29/0.55 (declare-const tptp.ifalse (-> $$unsorted Bool)) % 0.29/0.55 (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)))))) % 0.29/0.55 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.29/0.55 (define tptp.mand () (let ((_let_1 (@var "U" $$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))))))) % 0.29/0.55 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.29/0.55 (define tptp.mbox_s4 () (let ((_let_1 (@var "Y" $$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)))))))) % 0.29/0.55 (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))))) % 0.29/0.55 (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))))) % 0.29/0.55 (define tptp.itrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.29/0.55 (define tptp.iand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.29/0.55 (define tptp.ior () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mbox_s4 _let_3)) (_ tptp.mbox_s4 _let_2)) _let_1)))))) % 0.29/0.55 (define tptp.iimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.29/0.55 (define tptp.iimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Q" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.iimplies _let_3) _let_2) _let_1)))))) % 0.29/0.55 (define tptp.iequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.29/0.55 (define tptp.ixor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.inot (_ (_ tptp.iequiv _let_3) _let_2)) _let_1)))))) % 0.29/0.55 (define tptp.ivalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.29/0.55 (define tptp.isatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.29/0.55 (define tptp.icountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.29/0.55 (define tptp.iinvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.29/0.55 (define @t1 () (@var "X" $$unsorted)) % 0.29/0.55 (define @t2 () (_ tptp.irel @t1)) % 0.29/0.55 (define @t3 () (@list @t1)) % 0.29/0.55 (define @t4 () (@var "Z" $$unsorted)) % 0.29/0.55 (define @t5 () (@var "Y" $$unsorted)) % 0.29/0.55 (define @t6 () (_ @t2 @t5)) % 0.29/0.55 (define @t7 () (_ tptp.ivalid (_ (_ tptp.iimplies (_ tptp.iatom tptp.a)) (_ tptp.iatom tptp.b)))) % 0.29/0.55 (define @t8 () (not @t7)) % 0.29/0.55 (define @t9 () (@var "U" $$unsorted)) % 0.29/0.55 (define @t10 () (@var "X" (-> $$unsorted Bool))) % 0.29/0.55 (define @t11 () (_ @t10 @t9)) % 0.29/0.55 (define @t12 () (lambda (@list @t10 @t9) (not @t11))) % 0.29/0.55 (define @t13 () (@var "Y" (-> $$unsorted Bool))) % 0.29/0.55 (define @t14 () (_ @t13 @t9)) % 0.29/0.55 (define @t15 () (@list @t10 @t13 @t9)) % 0.29/0.55 (define @t16 () (lambda @t15 (or @t11 @t14))) % 0.29/0.55 (define @t17 () (lambda @t15 (and @t11 @t14))) % 0.29/0.55 (define @t18 () (@var "__flatten_var_0" $$unsorted)) % 0.29/0.55 (define @t19 () (@var "V" (-> $$unsorted Bool))) % 0.29/0.55 (define @t20 () (@var "U" (-> $$unsorted Bool))) % 0.29/0.55 (define @t21 () (@list @t20 @t19 @t18)) % 0.29/0.55 (define @t22 () (lambda @t21 (_ (_ (_ tptp.mor (_ tptp.mnot @t20)) @t19) @t18))) % 0.29/0.55 (define @t23 () (@var "P" (-> $$unsorted Bool))) % 0.29/0.55 (define @t24 () (_ @t23 @t5)) % 0.29/0.55 (define @t25 () (@list @t5)) % 0.29/0.55 (define @t26 () (forall @t25 (=> @t6 @t24))) % 0.29/0.55 (define @t27 () (@list @t23 @t1)) % 0.29/0.55 (define @t28 () (lambda @t27 @t26)) % 0.29/0.55 (define @t29 () (@list @t23 @t18)) % 0.29/0.55 (define @t30 () (lambda @t29 (_ @t23 @t18))) % 0.29/0.55 (define @t31 () (_ tptp.mbox_s4 @t23)) % 0.29/0.55 (define @t32 () (lambda @t29 (_ (_ tptp.mnot @t31) @t18))) % 0.29/0.55 (define @t33 () (@var "W" $$unsorted)) % 0.29/0.55 (define @t34 () (@list @t33)) % 0.29/0.55 (define @t35 () (lambda @t34 true)) % 0.29/0.55 (define @t36 () (@var "Q" (-> $$unsorted Bool))) % 0.29/0.55 (define @t37 () (@list @t23 @t36 @t18)) % 0.29/0.55 (define @t38 () (lambda @t37 (_ (_ (_ tptp.mand @t23) @t36) @t18))) % 0.29/0.55 (define @t39 () (_ tptp.mbox_s4 @t36)) % 0.29/0.55 (define @t40 () (lambda @t37 (_ (_ (_ tptp.mor @t31) @t39) @t18))) % 0.29/0.55 (define @t41 () (lambda @t37 (_ (_ (_ tptp.mimplies @t31) @t39) @t18))) % 0.29/0.55 (define @t42 () (_ (_ tptp.iimplies @t36) @t23)) % 0.29/0.55 (define @t43 () (lambda @t37 (_ @t42 @t18))) % 0.29/0.55 (define @t44 () (lambda @t37 (_ (_ (_ tptp.iand (_ (_ tptp.iimplies @t23) @t36)) @t42) @t18))) % 0.29/0.55 (define @t45 () (lambda @t37 (_ (_ tptp.inot (_ (_ tptp.iequiv @t23) @t36)) @t18))) % 0.29/0.55 (define @t46 () (@var "Phi" (-> $$unsorted Bool))) % 0.29/0.55 (define @t47 () (_ @t46 @t33)) % 0.29/0.55 (define @t48 () (forall @t34 @t47)) % 0.29/0.55 (define @t49 () (@list @t46)) % 0.29/0.55 (define @t50 () (lambda @t49 @t48)) % 0.29/0.55 (define @t51 () (lambda @t49 (exists @t34 @t47))) % 0.29/0.55 (define @t52 () (not @t47)) % 0.29/0.55 (define @t53 () (lambda @t49 (exists @t34 @t52))) % 0.29/0.55 (define @t54 () (lambda @t49 (forall @t34 @t52))) % 0.29/0.55 (define @t55 () (@var "BOUND_VARIABLE_8061" $$unsorted)) % 0.29/0.55 (define @t56 () (tptp.b @t55)) % 0.29/0.55 (define @t57 () (not (tptp.irel @t33 @t55))) % 0.29/0.55 (define @t58 () (tptp.a @t5)) % 0.29/0.55 (define @t59 () (not (tptp.irel @t33 @t5))) % 0.29/0.55 (define @t60 () (not (forall @t25 (or @t59 @t58)))) % 0.29/0.55 (define @t61 () (or @t57 @t56)) % 0.29/0.55 (define @t62 () (or @t60 @t61)) % 0.29/0.55 (define @t63 () (forall (@list @t33 @t55) @t62)) % 0.29/0.55 (define @t64 () (@list @t55)) % 0.29/0.55 (define @t65 () (forall @t64 @t62)) % 0.29/0.55 (define @t66 () (forall @t64 @t61)) % 0.29/0.55 (define @t67 () (or @t60 @t66)) % 0.29/0.55 (define @t68 () (tptp.b @t5)) % 0.29/0.55 (define @t69 () (or @t60 (forall @t25 (or @t59 @t68)))) % 0.29/0.55 (define @t70 () (not (tptp.irel @t18 @t5))) % 0.29/0.55 (define @t71 () (not (forall @t25 (or @t70 @t58)))) % 0.29/0.55 (define @t72 () (@list @t18)) % 0.29/0.55 (define @t73 () (lambda @t72 (or @t71 (forall @t25 (or @t70 @t68))))) % 0.29/0.55 (define @t74 () (_ @t73 @t33)) % 0.29/0.55 (define @t75 () (forall @t34 @t74)) % 0.29/0.55 (define @t76 () (_ @t46 @t33)) % 0.29/0.55 (define @t77 () (lambda @t49 (forall @t34 @t76))) % 0.29/0.55 (define @t78 () (_ tptp.b @t5)) % 0.29/0.55 (define @t79 () (or @t70 @t78)) % 0.29/0.55 (define @t80 () (lambda @t72 (_ tptp.b @t18))) % 0.29/0.55 (define @t81 () (_ @t80 @t5)) % 0.29/0.55 (define @t82 () (or @t70 @t81)) % 0.29/0.55 (define @t83 () (forall @t25 @t82)) % 0.29/0.55 (define @t84 () (or @t71 @t83)) % 0.29/0.55 (define @t85 () (lambda @t72 @t84)) % 0.29/0.55 (define @t86 () (_ @t36 @t5)) % 0.29/0.55 (define @t87 () (forall @t25 (or @t70 @t86))) % 0.29/0.55 (define @t88 () (@list @t36 @t18)) % 0.29/0.55 (define @t89 () (_ @t30 tptp.b)) % 0.29/0.55 (define @t90 () (_ tptp.a @t5)) % 0.29/0.55 (define @t91 () (or @t70 @t90)) % 0.29/0.55 (define @t92 () (lambda @t72 (_ tptp.a @t18))) % 0.29/0.55 (define @t93 () (_ @t92 @t5)) % 0.29/0.55 (define @t94 () (or @t70 @t93)) % 0.29/0.55 (define @t95 () (forall @t25 @t94)) % 0.29/0.55 (define @t96 () (not @t95)) % 0.29/0.55 (define @t97 () (or @t96 @t87)) % 0.29/0.55 (define @t98 () (lambda @t88 @t97)) % 0.29/0.55 (define @t99 () (_ @t23 @t5)) % 0.29/0.55 (define @t100 () (forall @t25 (or @t70 @t99))) % 0.29/0.55 (define @t101 () (not @t100)) % 0.29/0.55 (define @t102 () (or @t101 @t87)) % 0.29/0.55 (define @t103 () (lambda @t37 @t102)) % 0.29/0.55 (define @t104 () (_ @t30 tptp.a)) % 0.29/0.55 (define @t105 () (tptp.irel @t1 @t5)) % 0.29/0.55 (define @t106 () (not @t105)) % 0.29/0.55 (define @t107 () (lambda @t3 (forall @t25 (or @t106 @t86)))) % 0.29/0.55 (define @t108 () (_ @t107 @t18)) % 0.29/0.55 (define @t109 () (or @t101 @t108)) % 0.29/0.55 (define @t110 () (lambda @t72 @t109)) % 0.29/0.55 (define @t111 () (_ @t19 @t18)) % 0.29/0.55 (define @t112 () (@list @t19 @t18)) % 0.29/0.55 (define @t113 () (forall @t25 (or @t106 @t99))) % 0.29/0.55 (define @t114 () (lambda @t27 @t113)) % 0.29/0.55 (define @t115 () (lambda @t3 @t113)) % 0.29/0.55 (define @t116 () (_ @t115 @t18)) % 0.29/0.55 (define @t117 () (not @t116)) % 0.29/0.55 (define @t118 () (or @t117 @t111)) % 0.29/0.55 (define @t119 () (lambda @t112 @t118)) % 0.29/0.55 (define @t120 () (or (not (_ @t20 @t18)) @t111)) % 0.29/0.55 (define @t121 () (lambda @t21 @t120)) % 0.29/0.55 (define @t122 () (not @t6)) % 0.29/0.55 (define @t123 () (or @t122 @t24)) % 0.29/0.55 (define @t124 () (not (_ @t20 @t9))) % 0.29/0.55 (define @t125 () (@list @t9)) % 0.29/0.55 (define @t126 () (lambda @t125 (or @t124 (_ @t19 @t9)))) % 0.29/0.55 (define @t127 () (@list @t13 @t9)) % 0.29/0.55 (define @t128 () (lambda @t125 @t124)) % 0.29/0.55 (define @t129 () (_ @t128 @t9)) % 0.29/0.55 (define @t130 () (or @t129 @t14)) % 0.29/0.55 (define @t131 () (lambda @t127 @t130)) % 0.29/0.55 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.29/0.55 (assume @p2 (forall (@list @t1 @t5 @t4) (=> (and @t6 (_ (_ tptp.irel @t5) @t4)) (_ @t2 @t4)))) % 0.29/0.55 (assume @p3 (= tptp.ifalse (_ tptp.inot tptp.itrue))) % 0.29/0.55 (assume @p4 @t7) % 0.29/0.55 (assume @p5 @t8) % 0.29/0.55 (assume @p6 true) % 0.29/0.55 (step @p7 (= tptp.mnot @t12) :rule refl :args (@t12)) % 0.29/0.55 (step @p8 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.29/0.55 (step @p9 (= tptp.mand @t17) :rule refl :args (@t17)) % 0.29/0.55 (step @p10 (= tptp.mimplies @t22) :rule refl :args (@t22)) % 0.29/0.55 (step @p11 (= tptp.mbox_s4 @t28) :rule refl :args (@t28)) % 0.29/0.55 (step @p12 (= tptp.iatom @t30) :rule refl :args (@t30)) % 0.29/0.55 (step @p13 (= tptp.inot @t32) :rule refl :args (@t32)) % 0.29/0.55 (step @p14 (= tptp.itrue @t35) :rule refl :args (@t35)) % 0.29/0.55 (step @p15 (= tptp.iand @t38) :rule refl :args (@t38)) % 0.29/0.55 (step @p16 (= tptp.ior @t40) :rule refl :args (@t40)) % 0.29/0.55 (step @p17 (= tptp.iimplies @t41) :rule refl :args (@t41)) % 0.29/0.55 (step @p18 (= tptp.iimplied @t43) :rule refl :args (@t43)) % 0.29/0.55 (step @p19 (= tptp.iequiv @t44) :rule refl :args (@t44)) % 0.29/0.55 (step @p20 (= tptp.ixor @t45) :rule refl :args (@t45)) % 0.29/0.55 (step @p21 (= tptp.ivalid @t50) :rule refl :args (@t50)) % 0.29/0.55 (step @p22 (= tptp.isatisfiable @t51) :rule refl :args (@t51)) % 0.29/0.55 (step @p23 (= tptp.icountersatisfiable @t53) :rule refl :args (@t53)) % 0.29/0.55 (step @p24 (= tptp.iinvalid @t54) :rule refl :args (@t54)) % 0.29/0.55 (step @p25 :rule aci_norm :args ((= @t62 (or @t60 @t57 @t56)))) % 0.29/0.55 (step @p26 :rule cong :premises (@p25) :args (@t63)) % 0.29/0.55 (step @p27 :rule quant-merge-prenex :args ((= (forall @t34 @t65) @t63))) % 0.29/0.55 (step @p28 :rule alpha_equiv :args (@t66 (@list @t55) (@list @t5))) % 0.29/0.55 (step @p29 :rule refl :args (@t60)) % 0.29/0.55 (step @p30 :rule nary_cong :premises (@p29 @p28) :args (@t67)) % 0.29/0.55 (step @p31 :rule quant-miniscope-or :args ((= @t65 @t67))) % 0.29/0.55 (step @p32 :rule trans :premises (@p31 @p30)) % 0.29/0.55 (step @p33 :rule symm :premises (@p32)) % 0.29/0.55 (step @p34 :rule cong :premises (@p33) :args ((forall @t34 @t69))) % 0.29/0.55 (step @p35 :rule trans :premises (@p34 @p27)) % 0.29/0.55 (step @p36 :rule trans :premises (@p35 @p26)) % 0.29/0.55 (step @p37 :rule beta-reduce :args ((= @t74 @t69))) % 0.29/0.55 (step @p38 :rule cong :premises (@p37) :args (@t75)) % 0.29/0.55 (step @p39 :rule trans :premises (@p38 @p36)) % 0.29/0.55 (step @p40 :rule beta-reduce :args ((= (_ @t77 @t73) @t75))) % 0.29/0.55 (step @p41 :rule trans :premises (@p40 @p39)) % 0.29/0.55 (step @p42 :rule refl :args (@t68)) % 0.29/0.55 (step @p43 :rule refl :args (@t78)) % 0.29/0.55 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t78 @t68))) % 0.29/0.55 (step @p45 :rule symm :premises (@p44)) % 0.29/0.55 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.29/0.55 (step @p47 :rule refl :args (@t70)) % 0.29/0.55 (step @p48 :rule nary_cong :premises (@p47 @p46) :args (@t79)) % 0.29/0.55 (step @p49 :rule cong :premises (@p48) :args ((forall @t25 @t79))) % 0.29/0.55 (step @p50 :rule beta-reduce :args ((= @t81 @t78))) % 0.29/0.55 (step @p51 :rule refl :args (@t70)) % 0.29/0.55 (step @p52 :rule nary_cong :premises (@p51 @p50) :args (@t82)) % 0.29/0.55 (step @p53 :rule cong :premises (@p52) :args (@t83)) % 0.29/0.55 (step @p54 :rule trans :premises (@p53 @p49)) % 0.29/0.55 (step @p55 :rule refl :args (@t71)) % 0.29/0.55 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t84)) % 0.29/0.55 (step @p57 :rule cong :premises (@p56) :args (@t85)) % 0.29/0.55 (step @p58 :rule beta-reduce :args ((= (_ (lambda @t88 (or @t71 @t87)) @t80) @t85))) % 0.29/0.55 (step @p59 :rule trans :premises (@p58 @p57)) % 0.29/0.55 (step @p60 :rule beta-reduce :args ((= @t89 @t80))) % 0.29/0.55 (step @p61 :rule refl :args (@t87)) % 0.29/0.55 (step @p62 :rule refl :args (@t58)) % 0.29/0.55 (step @p63 :rule refl :args (@t90)) % 0.29/0.55 (step @p64 :rule cong :premises (@p63 @p62) :args ((= @t90 @t58))) % 0.29/0.55 (step @p65 :rule symm :premises (@p64)) % 0.29/0.55 (step @p66 :rule eq_resolve :premises (@p63 @p65)) % 0.29/0.55 (step @p67 :rule nary_cong :premises (@p47 @p66) :args (@t91)) % 0.29/0.55 (step @p68 :rule cong :premises (@p67) :args ((forall @t25 @t91))) % 0.29/0.55 (step @p69 :rule beta-reduce :args ((= @t93 @t90))) % 0.29/0.55 (step @p70 :rule nary_cong :premises (@p51 @p69) :args (@t94)) % 0.29/0.55 (step @p71 :rule cong :premises (@p70) :args (@t95)) % 0.29/0.55 (step @p72 :rule trans :premises (@p71 @p68)) % 0.29/0.55 (step @p73 :rule cong :premises (@p72) :args (@t96)) % 0.29/0.55 (step @p74 :rule nary_cong :premises (@p73 @p61) :args (@t97)) % 0.29/0.55 (step @p75 :rule cong :premises (@p74) :args (@t98)) % 0.29/0.55 (step @p76 :rule beta-reduce :args ((= (_ @t103 @t92) @t98))) % 0.29/0.55 (step @p77 :rule trans :premises (@p76 @p75)) % 0.29/0.55 (step @p78 :rule beta-reduce :args ((= @t104 @t92))) % 0.29/0.55 (step @p79 :rule refl :args (@t103)) % 0.29/0.55 (step @p80 :rule ho_cong :premises (@p79 @p78)) % 0.29/0.55 (step @p81 :rule trans :premises (@p80 @p77)) % 0.29/0.55 (step @p82 :rule ho_cong :premises (@p81 @p60)) % 0.29/0.55 (step @p83 :rule trans :premises (@p82 @p59)) % 0.29/0.55 (step @p84 :rule refl :args (@t77)) % 0.29/0.55 (step @p85 :rule ho_cong :premises (@p84 @p83)) % 0.29/0.55 (step @p86 :rule trans :premises (@p85 @p41)) % 0.29/0.55 (step @p87 :rule cong :premises (@p86) :args ((not (_ @t77 (_ (_ @t103 @t104) @t89))))) % 0.29/0.55 (step @p88 :rule refl :args (tptp.b)) % 0.29/0.55 (step @p89 :rule ho_cong :premises (@p12 @p88)) % 0.29/0.55 (step @p90 :rule refl :args (tptp.a)) % 0.29/0.55 (step @p91 :rule ho_cong :premises (@p12 @p90)) % 0.29/0.55 (step @p92 :rule beta-reduce :args ((= (_ (lambda @t72 @t102) @t18) @t102))) % 0.29/0.55 (step @p93 :rule refl :args (@t18)) % 0.29/0.55 (step @p94 :rule beta-reduce :args ((= @t108 @t87))) % 0.29/0.55 (step @p95 :rule refl :args (@t101)) % 0.29/0.55 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t109)) % 0.29/0.55 (step @p97 :rule cong :premises (@p96) :args (@t110)) % 0.29/0.55 (step @p98 :rule beta-reduce :args ((= (_ (lambda @t112 (or @t101 @t111)) @t107) @t110))) % 0.29/0.55 (step @p99 :rule trans :premises (@p98 @p97)) % 0.29/0.55 (step @p100 :rule beta-reduce :args ((= (_ @t114 @t36) @t107))) % 0.29/0.55 (step @p101 :rule refl :args (@t111)) % 0.29/0.55 (step @p102 :rule beta-reduce :args ((= @t116 @t100))) % 0.29/0.55 (step @p103 :rule cong :premises (@p102) :args (@t117)) % 0.29/0.55 (step @p104 :rule nary_cong :premises (@p103 @p101) :args (@t118)) % 0.29/0.55 (step @p105 :rule cong :premises (@p104) :args (@t119)) % 0.29/0.55 (step @p106 :rule beta-reduce :args ((= (_ @t121 @t115) @t119))) % 0.29/0.55 (step @p107 :rule trans :premises (@p106 @p105)) % 0.29/0.55 (step @p108 :rule beta-reduce :args ((= (_ @t114 @t23) @t115))) % 0.29/0.55 (step @p109 :rule refl :args (@t121)) % 0.29/0.55 (step @p110 :rule ho_cong :premises (@p109 @p108)) % 0.29/0.55 (step @p111 :rule trans :premises (@p110 @p107)) % 0.29/0.55 (step @p112 :rule ho_cong :premises (@p111 @p100)) % 0.29/0.55 (step @p113 :rule trans :premises (@p112 @p99)) % 0.29/0.55 (step @p114 :rule ho_cong :premises (@p113 @p93)) % 0.29/0.55 (step @p115 :rule trans :premises (@p114 @p92)) % 0.29/0.55 (step @p116 :rule refl :args (@t36)) % 0.29/0.55 (step @p117 :rule refl :args (@t99)) % 0.29/0.55 (step @p118 :rule refl :args (@t24)) % 0.29/0.55 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t24 @t99))) % 0.29/0.55 (step @p120 :rule symm :premises (@p119)) % 0.29/0.55 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 0.29/0.55 (step @p122 :rule refl :args (@t105)) % 0.29/0.55 (step @p123 :rule refl :args (@t6)) % 0.29/0.55 (step @p124 :rule cong :premises (@p123 @p122) :args ((= @t6 @t105))) % 0.29/0.55 (step @p125 :rule symm :premises (@p124)) % 0.29/0.55 (step @p126 :rule eq_resolve :premises (@p123 @p125)) % 0.29/0.55 (step @p127 :rule cong :premises (@p126) :args (@t122)) % 0.37/0.56 (step @p128 :rule nary_cong :premises (@p127 @p121) :args (@t123)) % 0.37/0.56 (step @p129 :rule cong :premises (@p128) :args ((forall @t25 @t123))) % 0.37/0.56 (step @p130 :rule bool-impl-elim :args (@t6 @t24)) % 0.37/0.56 (step @p131 :rule cong :premises (@p130) :args (@t26)) % 0.37/0.56 (step @p132 :rule trans :premises (@p131 @p129)) % 0.37/0.56 (step @p133 :rule cong :premises (@p132) :args (@t28)) % 0.37/0.56 (step @p134 :rule trans :premises (@p11 @p133)) % 0.37/0.56 (step @p135 :rule ho_cong :premises (@p134 @p116)) % 0.37/0.56 (step @p136 :rule refl :args (@t23)) % 0.37/0.56 (step @p137 :rule ho_cong :premises (@p134 @p136)) % 0.37/0.56 (step @p138 :rule beta-reduce :args ((= (_ @t126 @t18) @t120))) % 0.37/0.56 (step @p139 :rule beta-reduce :args ((= (_ (lambda @t127 (or @t124 @t14)) @t19) @t126))) % 0.37/0.56 (step @p140 :rule refl :args (@t19)) % 0.37/0.56 (step @p141 :rule refl :args (@t14)) % 0.37/0.56 (step @p142 :rule beta-reduce :args ((= @t129 @t124))) % 0.37/0.56 (step @p143 :rule nary_cong :premises (@p142 @p141) :args (@t130)) % 0.37/0.56 (step @p144 :rule cong :premises (@p143) :args (@t131)) % 0.37/0.56 (step @p145 :rule beta-reduce :args ((= (_ @t16 @t128) @t131))) % 0.37/0.56 (step @p146 :rule trans :premises (@p145 @p144)) % 0.37/0.56 (step @p147 :rule beta-reduce :args ((= (_ @t12 @t20) @t128))) % 0.37/0.56 (step @p148 :rule refl :args (@t16)) % 0.37/0.56 (step @p149 :rule ho_cong :premises (@p148 @p147)) % 0.37/0.56 (step @p150 :rule trans :premises (@p149 @p146)) % 0.37/0.56 (step @p151 :rule ho_cong :premises (@p150 @p140)) % 0.37/0.56 (step @p152 :rule trans :premises (@p151 @p139)) % 0.37/0.56 (step @p153 :rule ho_cong :premises (@p152 @p93)) % 0.37/0.56 (step @p154 :rule trans :premises (@p153 @p138)) % 0.37/0.56 (step @p155 :rule refl :args (@t20)) % 0.37/0.56 (step @p156 :rule ho_cong :premises (@p7 @p155)) % 0.37/0.56 (step @p157 :rule ho_cong :premises (@p8 @p156)) % 0.37/0.56 (step @p158 :rule ho_cong :premises (@p157 @p140)) % 0.37/0.56 (step @p159 :rule ho_cong :premises (@p158 @p93)) % 0.37/0.56 (step @p160 :rule trans :premises (@p159 @p154)) % 0.37/0.56 (step @p161 :rule cong :premises (@p160) :args (@t22)) % 0.37/0.56 (step @p162 :rule trans :premises (@p10 @p161)) % 0.37/0.56 (step @p163 :rule ho_cong :premises (@p162 @p137)) % 0.37/0.56 (step @p164 :rule ho_cong :premises (@p163 @p135)) % 0.37/0.56 (step @p165 :rule ho_cong :premises (@p164 @p93)) % 0.37/0.56 (step @p166 :rule trans :premises (@p165 @p115)) % 0.37/0.56 (step @p167 :rule cong :premises (@p166) :args (@t41)) % 0.37/0.56 (step @p168 :rule trans :premises (@p17 @p167)) % 0.37/0.56 (step @p169 :rule ho_cong :premises (@p168 @p91)) % 0.37/0.56 (step @p170 :rule ho_cong :premises (@p169 @p89)) % 0.37/0.56 (step @p171 :rule refl :args (@t76)) % 0.37/0.56 (step @p172 :rule refl :args (@t47)) % 0.37/0.56 (step @p173 :rule cong :premises (@p172 @p171) :args ((= @t47 @t76))) % 0.37/0.56 (step @p174 :rule symm :premises (@p173)) % 0.37/0.56 (step @p175 :rule eq_resolve :premises (@p172 @p174)) % 0.37/0.56 (step @p176 :rule cong :premises (@p175) :args (@t48)) % 0.37/0.56 (step @p177 :rule cong :premises (@p176) :args (@t50)) % 0.37/0.56 (step @p178 :rule trans :premises (@p21 @p177)) % 0.37/0.56 (step @p179 :rule ho_cong :premises (@p178 @p170)) % 0.37/0.56 (step @p180 :rule cong :premises (@p179) :args (@t8)) % 0.37/0.56 (step @p181 :rule trans :premises (@p180 @p87)) % 0.37/0.56 (step @p182 :rule eq_resolve :premises (@p5 @p181)) % 0.37/0.56 (step @p183 :rule trans :premises (@p179 @p86)) % 0.37/0.56 (step @p184 :rule eq_resolve :premises (@p4 @p183)) % 0.37/0.56 (step @p185 false :rule contra :premises (@p184 @p182)) % 0.37/0.56 ) % 0.37/0.56 % SZS output end Proof % 0.37/0.56 % cvc5 exiting %------------------------------------------------------------------------------