%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL607^1 : TPTP v9.3.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n001.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:09 AM UTC 2026 % Result : Theorem 0.21s 0.50s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL607^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.12/0.37 % Computer : n001.cluster.edu % 0.12/0.37 % Model : x86_64 x86_64 % 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.37 % Memory : 8046.5625MB % 0.12/0.37 % OS : Linux 6.8.0-71-generic % 0.12/0.37 % CPULimit : 300 % 0.12/0.37 % WCLimit : 300 % 0.12/0.37 % DateTime : Fri Sep 4 23:30:15 UTC 2026 % 0.12/0.37 % CPUTime : % 0.12/0.45 %----Proving TH0 % 0.21/0.50 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.21/0.50 % SZS status Theorem % 0.21/0.50 % SZS output start Proof % 0.21/0.50 ( % 0.21/0.50 (declare-sort $$unsorted 0) % 0.21/0.50 (declare-sort tptp.individuals 0) % 0.21/0.50 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.21/0.50 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.21/0.50 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.21/0.50 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.21/0.50 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.21/0.50 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.21/0.50 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.21/0.50 (define tptp.mbox () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.21/0.50 (define tptp.mdia () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.21/0.50 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.21/0.50 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.21/0.50 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.21/0.50 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.21/0.50 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.21/0.50 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.21/0.50 (define @t1 () (@var "A" (-> $$unsorted Bool))) % 0.21/0.50 (define @t2 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.21/0.50 (define @t3 () (@list @t2 @t1)) % 0.21/0.50 (define @t4 () (forall @t3 (_ tptp.mvalid (_ (_ tptp.miff (_ (_ tptp.mdia @t2) @t1)) (_ tptp.mnot (_ (_ tptp.mbox @t2) (_ tptp.mnot @t1))))))) % 0.21/0.50 (define @t5 () (not @t4)) % 0.21/0.50 (define @t6 () (@var "X" $$unsorted)) % 0.21/0.50 (define @t7 () (@list @t6)) % 0.21/0.50 (define @t8 () (lambda @t7 false)) % 0.21/0.50 (define @t9 () (lambda @t7 true)) % 0.21/0.50 (define @t10 () (@var "U" $$unsorted)) % 0.21/0.50 (define @t11 () (@var "X" (-> $$unsorted Bool))) % 0.21/0.50 (define @t12 () (_ @t11 @t10)) % 0.21/0.50 (define @t13 () (lambda (@list @t11 @t10) (not @t12))) % 0.21/0.50 (define @t14 () (@var "Y" (-> $$unsorted Bool))) % 0.21/0.50 (define @t15 () (_ @t14 @t10)) % 0.21/0.50 (define @t16 () (@list @t11 @t14 @t10)) % 0.21/0.50 (define @t17 () (lambda @t16 (or @t12 @t15))) % 0.21/0.50 (define @t18 () (lambda @t16 (and @t12 @t15))) % 0.21/0.50 (define @t19 () (@var "__flatten_var_0" $$unsorted)) % 0.21/0.50 (define @t20 () (@var "V" (-> $$unsorted Bool))) % 0.21/0.50 (define @t21 () (@var "U" (-> $$unsorted Bool))) % 0.21/0.50 (define @t22 () (@list @t21 @t20 @t19)) % 0.21/0.50 (define @t23 () (lambda @t22 (_ (_ (_ tptp.mor (_ tptp.mnot @t21)) @t20) @t19))) % 0.21/0.50 (define @t24 () (lambda @t22 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t21) @t20)) (_ (_ tptp.mimpl @t20) @t21)) @t19))) % 0.21/0.50 (define @t25 () (@var "Y" $$unsorted)) % 0.21/0.50 (define @t26 () (@var "P" (-> $$unsorted Bool))) % 0.21/0.50 (define @t27 () (_ @t26 @t25)) % 0.21/0.50 (define @t28 () (_ (_ @t2 @t6) @t25)) % 0.21/0.50 (define @t29 () (@list @t25)) % 0.21/0.50 (define @t30 () (forall @t29 (=> @t28 @t27))) % 0.21/0.50 (define @t31 () (@list @t2 @t26 @t6)) % 0.21/0.50 (define @t32 () (lambda @t31 @t30)) % 0.21/0.50 (define @t33 () (and @t28 @t27)) % 0.21/0.50 (define @t34 () (exists @t29 @t33)) % 0.21/0.50 (define @t35 () (lambda @t31 @t34)) % 0.21/0.50 (define @t36 () (@var "W" $$unsorted)) % 0.21/0.50 (define @t37 () (@var "X" tptp.individuals)) % 0.21/0.50 (define @t38 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.21/0.50 (define @t39 () (_ (_ @t38 @t37) @t36)) % 0.21/0.50 (define @t40 () (@list @t37)) % 0.21/0.50 (define @t41 () (@list @t38 @t36)) % 0.21/0.50 (define @t42 () (lambda @t41 (forall @t40 @t39))) % 0.21/0.50 (define @t43 () (lambda @t41 (exists @t40 @t39))) % 0.21/0.50 (define @t44 () (_ @t26 @t36)) % 0.21/0.50 (define @t45 () (@list @t36)) % 0.21/0.50 (define @t46 () (forall @t45 @t44)) % 0.21/0.50 (define @t47 () (@list @t26)) % 0.21/0.50 (define @t48 () (lambda @t47 @t46)) % 0.21/0.50 (define @t49 () (lambda @t47 (exists @t45 @t44))) % 0.21/0.50 (define @t50 () (not @t44)) % 0.21/0.50 (define @t51 () (lambda @t47 (exists @t45 @t50))) % 0.21/0.50 (define @t52 () (lambda @t47 (forall @t45 @t50))) % 0.21/0.50 (define @t53 () (_ @t1 @t25)) % 0.21/0.50 (define @t54 () (not @t53)) % 0.21/0.50 (define @t55 () (forall @t29 (or (not (_ @t2 @t36 @t25)) @t54))) % 0.21/0.50 (define @t56 () (or @t55 (not @t55))) % 0.21/0.50 (define @t57 () (forall @t29 (or (not (_ @t2 @t19 @t25)) @t54))) % 0.21/0.50 (define @t58 () (not @t57)) % 0.21/0.50 (define @t59 () (or @t57 @t58)) % 0.21/0.50 (define @t60 () (@list @t19)) % 0.21/0.50 (define @t61 () (lambda @t60 @t59)) % 0.21/0.50 (define @t62 () (_ @t61 @t36)) % 0.21/0.50 (define @t63 () (forall @t45 @t62)) % 0.21/0.50 (define @t64 () (_ @t26 @t36)) % 0.21/0.50 (define @t65 () (lambda @t47 (forall @t45 @t64))) % 0.21/0.50 (define @t66 () (forall @t29 (or (not (_ @t2 @t10 @t25)) @t54))) % 0.21/0.50 (define @t67 () (@list @t10)) % 0.21/0.50 (define @t68 () (lambda @t67 (not @t66))) % 0.21/0.50 (define @t69 () (_ @t68 @t19)) % 0.21/0.50 (define @t70 () (not @t69)) % 0.21/0.50 (define @t71 () (or @t70 @t58)) % 0.21/0.50 (define @t72 () (or @t57 @t69)) % 0.21/0.50 (define @t73 () (and @t72 @t71)) % 0.21/0.50 (define @t74 () (lambda @t60 @t73)) % 0.21/0.50 (define @t75 () (_ @t20 @t19)) % 0.21/0.50 (define @t76 () (not @t75)) % 0.21/0.50 (define @t77 () (@list @t20 @t19)) % 0.21/0.50 (define @t78 () (_ @t2 @t6 @t25)) % 0.21/0.50 (define @t79 () (not @t78)) % 0.21/0.50 (define @t80 () (forall @t29 (or @t79 @t54))) % 0.21/0.50 (define @t81 () (lambda @t7 @t80)) % 0.21/0.50 (define @t82 () (_ @t81 @t10)) % 0.21/0.50 (define @t83 () (not @t82)) % 0.21/0.50 (define @t84 () (lambda @t67 @t83)) % 0.21/0.50 (define @t85 () (_ @t1 @t25)) % 0.21/0.50 (define @t86 () (not @t85)) % 0.21/0.50 (define @t87 () (or @t79 @t86)) % 0.21/0.50 (define @t88 () (lambda @t67 (not (_ @t1 @t10)))) % 0.21/0.50 (define @t89 () (_ @t88 @t25)) % 0.21/0.50 (define @t90 () (or @t79 @t89)) % 0.21/0.50 (define @t91 () (forall @t29 @t90)) % 0.21/0.50 (define @t92 () (lambda @t7 @t91)) % 0.21/0.50 (define @t93 () (_ @t26 @t25)) % 0.21/0.50 (define @t94 () (forall @t29 (or @t79 @t93))) % 0.21/0.50 (define @t95 () (@list @t26 @t6)) % 0.21/0.50 (define @t96 () (lambda @t95 @t94)) % 0.21/0.50 (define @t97 () (_ @t13 @t1)) % 0.21/0.50 (define @t98 () (_ (lambda @t31 @t94) @t2)) % 0.21/0.50 (define @t99 () (lambda @t7 (not @t80))) % 0.21/0.50 (define @t100 () (_ @t99 @t19)) % 0.21/0.50 (define @t101 () (or @t76 @t100)) % 0.21/0.50 (define @t102 () (not @t100)) % 0.21/0.50 (define @t103 () (or @t102 @t75)) % 0.21/0.50 (define @t104 () (and @t103 @t101)) % 0.21/0.50 (define @t105 () (lambda @t77 @t104)) % 0.21/0.50 (define @t106 () (_ @t21 @t19)) % 0.21/0.50 (define @t107 () (or @t76 @t106)) % 0.21/0.50 (define @t108 () (not @t106)) % 0.21/0.50 (define @t109 () (or @t108 @t75)) % 0.21/0.50 (define @t110 () (and @t109 @t107)) % 0.21/0.50 (define @t111 () (lambda @t22 @t110)) % 0.21/0.50 (define @t112 () (not (forall @t29 (or @t79 (not @t93))))) % 0.21/0.50 (define @t113 () (lambda @t95 @t112)) % 0.21/0.50 (define @t114 () (_ (lambda @t31 @t112) @t2)) % 0.21/0.50 (define @t115 () (forall @t3 (_ @t65 (_ (_ @t111 (_ @t114 @t1)) (_ @t13 (_ @t98 @t97)))))) % 0.21/0.50 (define @t116 () (not @t28)) % 0.21/0.50 (define @t117 () (or @t116 @t27)) % 0.21/0.50 (define @t118 () (not @t27)) % 0.21/0.50 (define @t119 () (or @t116 @t118)) % 0.21/0.50 (define @t120 () (forall @t29 (not @t33))) % 0.21/0.50 (define @t121 () (not @t120)) % 0.21/0.50 (define @t122 () (_ @t21 @t10)) % 0.21/0.50 (define @t123 () (_ @t20 @t10)) % 0.21/0.50 (define @t124 () (or (not @t123) @t122)) % 0.21/0.50 (define @t125 () (not @t122)) % 0.21/0.50 (define @t126 () (or @t125 @t123)) % 0.21/0.50 (define @t127 () (lambda @t60 @t107)) % 0.21/0.50 (define @t128 () (_ @t127 @t10)) % 0.21/0.50 (define @t129 () (and @t126 @t128)) % 0.21/0.50 (define @t130 () (lambda @t67 @t129)) % 0.21/0.50 (define @t131 () (@list @t14 @t10)) % 0.21/0.50 (define @t132 () (@var "BOUND_VARIABLE_7519" (-> $$unsorted Bool))) % 0.21/0.50 (define @t133 () (_ @t132 @t19)) % 0.21/0.50 (define @t134 () (lambda (@list @t132 @t19) (or @t76 @t133))) % 0.21/0.50 (define @t135 () (lambda @t22 @t109)) % 0.21/0.50 (define @t136 () (lambda @t60 @t109)) % 0.21/0.50 (define @t137 () (_ @t136 @t10)) % 0.21/0.50 (define @t138 () (and @t137 @t15)) % 0.21/0.50 (define @t139 () (lambda @t131 @t138)) % 0.21/0.50 (define @t140 () (lambda @t77 @t109)) % 0.21/0.50 (define @t141 () (lambda @t67 @t126)) % 0.21/0.50 (define @t142 () (lambda @t67 @t125)) % 0.21/0.50 (define @t143 () (_ @t142 @t10)) % 0.21/0.50 (define @t144 () (or @t143 @t15)) % 0.21/0.50 (define @t145 () (lambda @t131 @t144)) % 0.21/0.50 (assume @p1 @t5) % 0.21/0.50 (assume @p2 true) % 0.21/0.50 (step @p3 (= tptp.mfalse @t8) :rule refl :args (@t8)) % 0.21/0.50 (step @p4 (= tptp.mtrue @t9) :rule refl :args (@t9)) % 0.21/0.50 (step @p5 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.21/0.50 (step @p6 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.21/0.50 (step @p7 (= tptp.mand @t18) :rule refl :args (@t18)) % 0.21/0.50 (step @p8 (= tptp.mimpl @t23) :rule refl :args (@t23)) % 0.21/0.50 (step @p9 (= tptp.miff @t24) :rule refl :args (@t24)) % 0.21/0.50 (step @p10 (= tptp.mbox @t32) :rule refl :args (@t32)) % 0.21/0.50 (step @p11 (= tptp.mdia @t35) :rule refl :args (@t35)) % 0.21/0.50 (step @p12 (= tptp.mall @t42) :rule refl :args (@t42)) % 0.21/0.50 (step @p13 (= tptp.mexists @t43) :rule refl :args (@t43)) % 0.21/0.50 (step @p14 (= tptp.mvalid @t48) :rule refl :args (@t48)) % 0.21/0.50 (step @p15 (= tptp.msatisfiable @t49) :rule refl :args (@t49)) % 0.21/0.50 (step @p16 (= tptp.mcountersatisfiable @t51) :rule refl :args (@t51)) % 0.21/0.50 (step @p17 (= tptp.minvalid @t52) :rule refl :args (@t52)) % 0.21/0.50 (step @p18 :rule evaluate :args ((not true))) % 0.21/0.50 (step @p19 :rule quant-unused-vars :args ((= (forall @t3 true) true))) % 0.21/0.50 (step @p20 :rule quant-unused-vars :args ((= (forall @t45 true) true))) % 0.21/0.50 (step @p21 :rule bool-or-taut :args (false @t55 false false)) % 0.21/0.50 (step @p22 :rule cong :premises (@p21) :args ((forall @t45 @t56))) % 0.21/0.50 (step @p23 :rule trans :premises (@p22 @p20)) % 0.21/0.50 (step @p24 :rule beta-reduce :args ((= @t62 @t56))) % 0.21/0.50 (step @p25 :rule cong :premises (@p24) :args (@t63)) % 0.21/0.50 (step @p26 :rule trans :premises (@p25 @p23)) % 0.21/0.50 (step @p27 :rule beta-reduce :args ((= (_ @t65 @t61) @t63))) % 0.21/0.50 (step @p28 :rule trans :premises (@p27 @p26)) % 0.21/0.50 (step @p29 :rule aci_norm :args ((= (and @t59 @t59) @t59))) % 0.21/0.50 (step @p30 :rule refl :args (@t58)) % 0.21/0.50 (step @p31 :rule bool-double-not-elim :args (@t57)) % 0.21/0.50 (step @p32 :rule beta-reduce :args ((= @t69 @t58))) % 0.21/0.50 (step @p33 :rule cong :premises (@p32) :args (@t70)) % 0.21/0.50 (step @p34 :rule trans :premises (@p33 @p31)) % 0.21/0.50 (step @p35 :rule nary_cong :premises (@p34 @p30) :args (@t71)) % 0.21/0.50 (step @p36 :rule refl :args (@t57)) % 0.21/0.50 (step @p37 :rule nary_cong :premises (@p36 @p32) :args (@t72)) % 0.21/0.50 (step @p38 :rule nary_cong :premises (@p37 @p35) :args (@t73)) % 0.21/0.50 (step @p39 :rule trans :premises (@p38 @p29)) % 0.21/0.50 (step @p40 :rule cong :premises (@p39) :args (@t74)) % 0.21/0.50 (step @p41 :rule beta-reduce :args ((= (_ (lambda @t77 (and (or @t57 @t75) (or @t76 @t58))) @t68) @t74))) % 0.21/0.50 (step @p42 :rule trans :premises (@p41 @p40)) % 0.21/0.50 (step @p43 :rule beta-reduce :args ((= @t82 @t66))) % 0.21/0.50 (step @p44 :rule cong :premises (@p43) :args (@t83)) % 0.21/0.50 (step @p45 :rule cong :premises (@p44) :args (@t84)) % 0.21/0.50 (step @p46 :rule beta-reduce :args ((= (_ @t13 @t81) @t84))) % 0.21/0.50 (step @p47 :rule trans :premises (@p46 @p45)) % 0.21/0.50 (step @p48 :rule refl :args (@t53)) % 0.21/0.50 (step @p49 :rule refl :args (@t85)) % 0.21/0.50 (step @p50 :rule cong :premises (@p49 @p48) :args ((= @t85 @t53))) % 0.21/0.50 (step @p51 :rule symm :premises (@p50)) % 0.21/0.50 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 0.21/0.50 (step @p53 :rule cong :premises (@p52) :args (@t86)) % 0.21/0.50 (step @p54 :rule refl :args (@t79)) % 0.21/0.50 (step @p55 :rule nary_cong :premises (@p54 @p53) :args (@t87)) % 0.21/0.50 (step @p56 :rule cong :premises (@p55) :args ((forall @t29 @t87))) % 0.21/0.50 (step @p57 :rule beta-reduce :args ((= @t89 @t86))) % 0.21/0.50 (step @p58 :rule refl :args (@t79)) % 0.21/0.50 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t90)) % 0.21/0.50 (step @p60 :rule cong :premises (@p59) :args (@t91)) % 0.21/0.50 (step @p61 :rule trans :premises (@p60 @p56)) % 0.21/0.50 (step @p62 :rule cong :premises (@p61) :args (@t92)) % 0.21/0.50 (step @p63 :rule beta-reduce :args ((= (_ @t96 @t88) @t92))) % 0.21/0.50 (step @p64 :rule trans :premises (@p63 @p62)) % 0.21/0.50 (step @p65 :rule beta-reduce :args ((= @t97 @t88))) % 0.21/0.50 (step @p66 :rule beta-reduce :args ((= @t98 @t96))) % 0.21/0.50 (step @p67 :rule ho_cong :premises (@p66 @p65)) % 0.21/0.50 (step @p68 :rule trans :premises (@p67 @p64)) % 0.21/0.50 (step @p69 :rule refl :args (@t13)) % 0.21/0.50 (step @p70 :rule ho_cong :premises (@p69 @p68)) % 0.21/0.50 (step @p71 :rule trans :premises (@p70 @p47)) % 0.21/0.50 (step @p72 :rule beta-reduce :args ((= @t100 @t58))) % 0.21/0.50 (step @p73 :rule refl :args (@t76)) % 0.21/0.50 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t101)) % 0.21/0.50 (step @p75 :rule refl :args (@t75)) % 0.21/0.50 (step @p76 :rule cong :premises (@p72) :args (@t102)) % 0.21/0.50 (step @p77 :rule trans :premises (@p76 @p31)) % 0.21/0.50 (step @p78 :rule nary_cong :premises (@p77 @p75) :args (@t103)) % 0.21/0.50 (step @p79 :rule nary_cong :premises (@p78 @p74) :args (@t104)) % 0.21/0.50 (step @p80 :rule cong :premises (@p79) :args (@t105)) % 0.21/0.50 (step @p81 :rule beta-reduce :args ((= (_ @t111 @t99) @t105))) % 0.21/0.50 (step @p82 :rule trans :premises (@p81 @p80)) % 0.21/0.50 (step @p83 :rule beta-reduce :args ((= (_ @t113 @t1) @t99))) % 0.21/0.50 (step @p84 :rule refl :args (@t1)) % 0.21/0.50 (step @p85 :rule beta-reduce :args ((= @t114 @t113))) % 0.21/0.50 (step @p86 :rule ho_cong :premises (@p85 @p84)) % 0.21/0.50 (step @p87 :rule trans :premises (@p86 @p83)) % 0.21/0.50 (step @p88 :rule refl :args (@t111)) % 0.21/0.50 (step @p89 :rule ho_cong :premises (@p88 @p87)) % 0.21/0.50 (step @p90 :rule trans :premises (@p89 @p82)) % 0.21/0.50 (step @p91 :rule ho_cong :premises (@p90 @p71)) % 0.21/0.50 (step @p92 :rule trans :premises (@p91 @p42)) % 0.21/0.50 (step @p93 :rule refl :args (@t65)) % 0.21/0.50 (step @p94 :rule ho_cong :premises (@p93 @p92)) % 0.21/0.50 (step @p95 :rule trans :premises (@p94 @p28)) % 0.21/0.50 (step @p96 :rule cong :premises (@p95) :args (@t115)) % 0.21/0.50 (step @p97 :rule trans :premises (@p96 @p19)) % 0.21/0.50 (step @p98 :rule cong :premises (@p97) :args ((not @t115))) % 0.21/0.50 (step @p99 :rule trans :premises (@p98 @p18)) % 0.21/0.50 (step @p100 :rule ho_cong :premises (@p5 @p84)) % 0.21/0.50 (step @p101 :rule refl :args (@t2)) % 0.21/0.50 (step @p102 :rule refl :args (@t93)) % 0.21/0.50 (step @p103 :rule refl :args (@t27)) % 0.21/0.50 (step @p104 :rule cong :premises (@p103 @p102) :args ((= @t27 @t93))) % 0.21/0.50 (step @p105 :rule symm :premises (@p104)) % 0.21/0.50 (step @p106 :rule eq_resolve :premises (@p103 @p105)) % 0.21/0.50 (step @p107 :rule refl :args (@t78)) % 0.21/0.50 (step @p108 :rule refl :args (@t28)) % 0.21/0.50 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t28 @t78))) % 0.21/0.50 (step @p110 :rule symm :premises (@p109)) % 0.21/0.50 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 0.21/0.50 (step @p112 :rule cong :premises (@p111) :args (@t116)) % 0.21/0.50 (step @p113 :rule nary_cong :premises (@p112 @p106) :args (@t117)) % 0.21/0.50 (step @p114 :rule cong :premises (@p113) :args ((forall @t29 @t117))) % 0.21/0.50 (step @p115 :rule bool-impl-elim :args (@t28 @t27)) % 0.21/0.50 (step @p116 :rule cong :premises (@p115) :args (@t30)) % 0.21/0.50 (step @p117 :rule trans :premises (@p116 @p114)) % 0.21/0.50 (step @p118 :rule cong :premises (@p117) :args (@t32)) % 0.21/0.50 (step @p119 :rule trans :premises (@p10 @p118)) % 0.21/0.50 (step @p120 :rule ho_cong :premises (@p119 @p101)) % 0.21/0.50 (step @p121 :rule ho_cong :premises (@p120 @p100)) % 0.21/0.50 (step @p122 :rule ho_cong :premises (@p5 @p121)) % 0.21/0.50 (step @p123 :rule cong :premises (@p106) :args (@t118)) % 0.21/0.50 (step @p124 :rule nary_cong :premises (@p112 @p123) :args (@t119)) % 0.21/0.50 (step @p125 :rule cong :premises (@p124) :args ((forall @t29 @t119))) % 0.21/0.50 (step @p126 :rule bool-and-de-morgan :args (@t28 @t27 true)) % 0.21/0.50 (step @p127 :rule cong :premises (@p126) :args (@t120)) % 0.21/0.50 (step @p128 :rule trans :premises (@p127 @p125)) % 0.21/0.50 (step @p129 :rule cong :premises (@p128) :args (@t121)) % 0.21/0.50 (step @p130 :rule exists-elim :args ((= @t34 @t121))) % 0.21/0.50 (step @p131 :rule trans :premises (@p130 @p129)) % 0.21/0.50 (step @p132 :rule cong :premises (@p131) :args (@t35)) % 0.21/0.50 (step @p133 :rule trans :premises (@p11 @p132)) % 0.21/0.50 (step @p134 :rule ho_cong :premises (@p133 @p101)) % 0.21/0.50 (step @p135 :rule ho_cong :premises (@p134 @p84)) % 0.21/0.50 (step @p136 :rule beta-reduce :args ((= (_ (lambda @t67 (and @t126 @t124)) @t19) @t110))) % 0.21/0.50 (step @p137 :rule refl :args (@t19)) % 0.21/0.50 (step @p138 :rule beta-reduce :args ((= @t128 @t124))) % 0.21/0.50 (step @p139 :rule refl :args (@t126)) % 0.21/0.50 (step @p140 :rule nary_cong :premises (@p139 @p138) :args (@t129)) % 0.21/0.50 (step @p141 :rule cong :premises (@p140) :args (@t130)) % 0.21/0.50 (step @p142 :rule beta-reduce :args ((= (_ (lambda @t131 (and @t126 @t15)) @t127) @t130))) % 0.21/0.50 (step @p143 :rule trans :premises (@p142 @p141)) % 0.21/0.50 (step @p144 :rule beta-reduce :args ((= (_ @t134 @t21) @t127))) % 0.21/0.50 (step @p145 :rule refl :args (@t21)) % 0.21/0.50 (step @p146 :rule beta-reduce :args ((= (_ (lambda (@list @t21 @t132 @t19) (or @t108 @t133)) @t20) @t134))) % 0.21/0.50 (step @p147 :rule refl :args (@t20)) % 0.21/0.50 (step @p148 :rule alpha_equiv :args (@t135 (@list @t20) (@list @t132))) % 0.21/0.50 (step @p149 :rule ho_cong :premises (@p148 @p147)) % 0.21/0.50 (step @p150 :rule trans :premises (@p149 @p146)) % 0.21/0.50 (step @p151 :rule ho_cong :premises (@p150 @p145)) % 0.21/0.50 (step @p152 :rule trans :premises (@p151 @p144)) % 0.21/0.50 (step @p153 :rule refl :args (@t15)) % 0.21/0.50 (step @p154 :rule beta-reduce :args ((= @t137 @t126))) % 0.21/0.50 (step @p155 :rule nary_cong :premises (@p154 @p153) :args (@t138)) % 0.21/0.50 (step @p156 :rule cong :premises (@p155) :args (@t139)) % 0.21/0.50 (step @p157 :rule beta-reduce :args ((= (_ @t18 @t136) @t139))) % 0.21/0.50 (step @p158 :rule trans :premises (@p157 @p156)) % 0.21/0.50 (step @p159 :rule beta-reduce :args ((= (_ @t140 @t20) @t136))) % 0.21/0.50 (step @p160 :rule refl :args (@t20)) % 0.21/0.50 (step @p161 :rule beta-reduce :args ((= (_ @t135 @t21) @t140))) % 0.21/0.50 (step @p162 :rule ho_cong :premises (@p161 @p160)) % 0.21/0.50 (step @p163 :rule trans :premises (@p162 @p159)) % 0.21/0.50 (step @p164 :rule refl :args (@t18)) % 0.21/0.50 (step @p165 :rule ho_cong :premises (@p164 @p163)) % 0.21/0.50 (step @p166 :rule trans :premises (@p165 @p158)) % 0.21/0.50 (step @p167 :rule ho_cong :premises (@p166 @p152)) % 0.21/0.50 (step @p168 :rule trans :premises (@p167 @p143)) % 0.21/0.50 (step @p169 :rule ho_cong :premises (@p168 @p137)) % 0.21/0.50 (step @p170 :rule trans :premises (@p169 @p136)) % 0.21/0.50 (step @p171 :rule beta-reduce :args ((= (_ @t141 @t19) @t109))) % 0.21/0.50 (step @p172 :rule beta-reduce :args ((= (_ (lambda @t131 (or @t125 @t15)) @t20) @t141))) % 0.21/0.50 (step @p173 :rule beta-reduce :args ((= @t143 @t125))) % 0.21/0.50 (step @p174 :rule nary_cong :premises (@p173 @p153) :args (@t144)) % 0.21/0.50 (step @p175 :rule cong :premises (@p174) :args (@t145)) % 0.21/0.50 (step @p176 :rule beta-reduce :args ((= (_ @t17 @t142) @t145))) % 0.21/0.50 (step @p177 :rule trans :premises (@p176 @p175)) % 0.21/0.50 (step @p178 :rule beta-reduce :args ((= (_ @t13 @t21) @t142))) % 0.21/0.50 (step @p179 :rule refl :args (@t17)) % 0.21/0.50 (step @p180 :rule ho_cong :premises (@p179 @p178)) % 0.21/0.50 (step @p181 :rule trans :premises (@p180 @p177)) % 0.21/0.50 (step @p182 :rule ho_cong :premises (@p181 @p160)) % 0.21/0.50 (step @p183 :rule trans :premises (@p182 @p172)) % 0.21/0.50 (step @p184 :rule ho_cong :premises (@p183 @p137)) % 0.21/0.50 (step @p185 :rule trans :premises (@p184 @p171)) % 0.21/0.50 (step @p186 :rule ho_cong :premises (@p5 @p145)) % 0.21/0.50 (step @p187 :rule ho_cong :premises (@p6 @p186)) % 0.21/0.50 (step @p188 :rule ho_cong :premises (@p187 @p160)) % 0.21/0.50 (step @p189 :rule ho_cong :premises (@p188 @p137)) % 0.21/0.50 (step @p190 :rule trans :premises (@p189 @p185)) % 0.21/0.50 (step @p191 :rule cong :premises (@p190) :args (@t23)) % 0.21/0.50 (step @p192 :rule trans :premises (@p8 @p191)) % 0.21/0.50 (step @p193 :rule ho_cong :premises (@p192 @p160)) % 0.21/0.50 (step @p194 :rule ho_cong :premises (@p193 @p145)) % 0.21/0.50 (step @p195 :rule ho_cong :premises (@p192 @p145)) % 0.21/0.50 (step @p196 :rule ho_cong :premises (@p195 @p160)) % 0.21/0.50 (step @p197 :rule ho_cong :premises (@p7 @p196)) % 0.21/0.50 (step @p198 :rule ho_cong :premises (@p197 @p194)) % 0.21/0.50 (step @p199 :rule ho_cong :premises (@p198 @p137)) % 0.21/0.50 (step @p200 :rule trans :premises (@p199 @p170)) % 0.21/0.50 (step @p201 :rule cong :premises (@p200) :args (@t24)) % 0.21/0.50 (step @p202 :rule trans :premises (@p9 @p201)) % 0.21/0.50 (step @p203 :rule ho_cong :premises (@p202 @p135)) % 0.21/0.50 (step @p204 :rule ho_cong :premises (@p203 @p122)) % 0.21/0.50 (step @p205 :rule refl :args (@t64)) % 0.21/0.50 (step @p206 :rule refl :args (@t44)) % 0.21/0.50 (step @p207 :rule cong :premises (@p206 @p205) :args ((= @t44 @t64))) % 0.21/0.50 (step @p208 :rule symm :premises (@p207)) % 0.21/0.50 (step @p209 :rule eq_resolve :premises (@p206 @p208)) % 0.21/0.50 (step @p210 :rule cong :premises (@p209) :args (@t46)) % 0.21/0.50 (step @p211 :rule cong :premises (@p210) :args (@t48)) % 0.21/0.50 (step @p212 :rule trans :premises (@p14 @p211)) % 0.21/0.50 (step @p213 :rule ho_cong :premises (@p212 @p204)) % 0.21/0.51 (step @p214 :rule cong :premises (@p213) :args (@t4)) % 0.21/0.51 (step @p215 :rule cong :premises (@p214) :args (@t5)) % 0.21/0.51 (step @p216 :rule trans :premises (@p215 @p99)) % 0.21/0.51 (step @p217 false :rule eq_resolve :premises (@p1 @p216)) % 0.21/0.51 ) % 0.21/0.51 % SZS output end Proof % 0.21/0.51 % cvc5 exiting %------------------------------------------------------------------------------