%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET047^1 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n013.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 08:47:08 AM UTC 2026 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET047^1 : TPTP v9.2.1. Released v8.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.33 % Computer : n013.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue Jun 2 14:47:45 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.48 %----Proving TH0 % 0.38/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort $$unsorted 0) % 0.38/0.57 (declare-sort tptp.mworld 0) % 0.38/0.57 (declare-const tptp.mactual tptp.mworld) % 0.38/0.57 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.38/0.57 (declare-const tptp.set_equal (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.38/0.57 (declare-const tptp.element (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.38/0.57 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.38/0.57 (define tptp.mnot () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.57 (define tptp.mand () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.57 (define tptp.mor () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.57 (define tptp.mimplies () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.57 (define tptp.mequiv () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.57 (define tptp.mbox () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.38/0.57 (define tptp.mdia () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (exists (@list _let_1) (and (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.38/0.57 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.57 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.57 (define @t1 () (@var "__flatten_var_0" tptp.mworld)) % 0.38/0.57 (define @t2 () (@var "Y" $$unsorted)) % 0.38/0.57 (define @t3 () (@var "Z" $$unsorted)) % 0.38/0.57 (define @t4 () (_ tptp.element @t3)) % 0.38/0.57 (define @t5 () (_ @t4 @t2)) % 0.38/0.57 (define @t6 () (@var "X" $$unsorted)) % 0.38/0.57 (define @t7 () (_ @t4 @t6)) % 0.38/0.57 (define @t8 () (@list @t3 @t1)) % 0.38/0.57 (define @t9 () (lambda @t8 (_ (_ (_ tptp.mequiv @t7) @t5) @t1))) % 0.38/0.57 (define @t10 () (_ tptp.set_equal @t6)) % 0.38/0.57 (define @t11 () (_ @t10 @t2)) % 0.38/0.57 (define @t12 () (_ tptp.mequiv @t11)) % 0.38/0.57 (define @t13 () (@list @t2 @t1)) % 0.38/0.57 (define @t14 () (lambda @t13 (_ (_ @t12 (_ tptp.mforall_di @t9)) @t1))) % 0.38/0.57 (define @t15 () (@list @t6 @t1)) % 0.38/0.57 (define @t16 () (lambda @t15 (_ (_ tptp.mforall_di @t14) @t1))) % 0.38/0.57 (define @t17 () (_ (_ tptp.set_equal @t2) @t6)) % 0.38/0.57 (define @t18 () (lambda @t13 (_ (_ @t12 @t17) @t1))) % 0.38/0.57 (define @t19 () (lambda @t15 (_ (_ tptp.mforall_di @t18) @t1))) % 0.38/0.57 (define @t20 () (not (_ tptp.mlocal (_ tptp.mforall_di @t19)))) % 0.38/0.57 (define @t21 () (@var "Phi" (-> tptp.mworld Bool))) % 0.38/0.57 (define @t22 () (lambda (@list @t21) (_ @t21 tptp.mactual))) % 0.38/0.57 (define @t23 () (@var "W" tptp.mworld)) % 0.38/0.57 (define @t24 () (@var "A" (-> tptp.mworld Bool))) % 0.38/0.57 (define @t25 () (_ @t24 @t23)) % 0.38/0.57 (define @t26 () (lambda (@list @t24 @t23) (not @t25))) % 0.38/0.57 (define @t27 () (@var "B" (-> tptp.mworld Bool))) % 0.38/0.57 (define @t28 () (_ @t27 @t23)) % 0.38/0.57 (define @t29 () (@list @t24 @t27 @t23)) % 0.38/0.57 (define @t30 () (lambda @t29 (and @t25 @t28))) % 0.38/0.57 (define @t31 () (lambda @t29 (or @t25 @t28))) % 0.38/0.57 (define @t32 () (lambda @t29 (=> @t25 @t28))) % 0.38/0.57 (define @t33 () (lambda @t29 (= @t25 @t28))) % 0.38/0.57 (define @t34 () (@var "V" tptp.mworld)) % 0.38/0.57 (define @t35 () (_ @t21 @t34)) % 0.38/0.57 (define @t36 () (_ (_ tptp.mrel @t23) @t34)) % 0.38/0.57 (define @t37 () (@list @t34)) % 0.38/0.57 (define @t38 () (@list @t21 @t23)) % 0.38/0.57 (define @t39 () (lambda @t38 (forall @t37 (=> @t36 @t35)))) % 0.38/0.57 (define @t40 () (lambda @t38 (exists @t37 (and @t36 @t35)))) % 0.38/0.57 (define @t41 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.38/0.57 (define @t42 () (_ (_ @t41 @t6) @t23)) % 0.38/0.57 (define @t43 () (@list @t6)) % 0.38/0.57 (define @t44 () (forall @t43 @t42)) % 0.38/0.57 (define @t45 () (@list @t41 @t23)) % 0.38/0.57 (define @t46 () (lambda @t45 @t44)) % 0.38/0.57 (define @t47 () (lambda @t45 (exists @t43 @t42))) % 0.38/0.57 (define @t48 () (@var "BOUND_VARIABLE_7688" $$unsorted)) % 0.38/0.57 (define @t49 () (@var "BOUND_VARIABLE_7648" $$unsorted)) % 0.38/0.57 (define @t50 () (@list @t49)) % 0.38/0.57 (define @t51 () (@list @t6 @t48)) % 0.38/0.57 (define @t52 () (forall @t51 (= (forall @t50 (= (tptp.element @t49 @t6 tptp.mactual) (tptp.element @t49 @t48 tptp.mactual))) (tptp.set_equal @t6 @t48 tptp.mactual)))) % 0.38/0.57 (define @t53 () (tptp.set_equal @t6 @t48 @t23)) % 0.38/0.57 (define @t54 () (tptp.element @t49 @t6 @t23)) % 0.38/0.57 (define @t55 () (forall @t50 (= @t54 (tptp.element @t49 @t48 @t23)))) % 0.38/0.57 (define @t56 () (= @t55 @t53)) % 0.38/0.57 (define @t57 () (forall @t51 @t56)) % 0.38/0.57 (define @t58 () (@list @t23)) % 0.38/0.57 (define @t59 () (lambda @t58 @t57)) % 0.38/0.57 (define @t60 () (_ @t59 tptp.mactual)) % 0.38/0.57 (define @t61 () (@list @t48)) % 0.38/0.57 (define @t62 () (forall @t61 @t56)) % 0.38/0.57 (define @t63 () (tptp.element @t49 @t6 @t1)) % 0.38/0.57 (define @t64 () (forall @t61 (= (forall @t50 (= @t63 (tptp.element @t49 @t48 @t1))) (tptp.set_equal @t6 @t48 @t1)))) % 0.38/0.57 (define @t65 () (lambda @t15 @t64)) % 0.38/0.57 (define @t66 () (_ @t65 @t6 @t23)) % 0.38/0.57 (define @t67 () (forall @t43 @t66)) % 0.38/0.57 (define @t68 () (lambda @t58 @t67)) % 0.38/0.57 (define @t69 () (_ @t41 @t6 @t23)) % 0.38/0.57 (define @t70 () (forall @t43 @t69)) % 0.38/0.57 (define @t71 () (lambda @t45 @t70)) % 0.38/0.57 (define @t72 () (_ (_ @t10 @t48) @t23)) % 0.38/0.57 (define @t73 () (= @t72 @t55)) % 0.38/0.57 (define @t74 () (_ @t11 @t1)) % 0.38/0.57 (define @t75 () (= @t74 (forall @t50 (= @t63 (tptp.element @t49 @t2 @t1))))) % 0.38/0.57 (define @t76 () (lambda @t13 @t75)) % 0.38/0.57 (define @t77 () (_ @t76 @t48 @t23)) % 0.38/0.57 (define @t78 () (forall @t61 @t77)) % 0.38/0.57 (define @t79 () (lambda @t58 @t78)) % 0.38/0.57 (define @t80 () (@list @t6)) % 0.38/0.57 (define @t81 () (tptp.element @t49 @t2 @t23)) % 0.38/0.57 (define @t82 () (forall @t50 (= @t54 @t81))) % 0.38/0.57 (define @t83 () (_ @t11 @t23)) % 0.38/0.57 (define @t84 () (lambda @t58 @t82)) % 0.38/0.57 (define @t85 () (_ @t84 @t23)) % 0.38/0.57 (define @t86 () (lambda @t58 (= @t85 @t83))) % 0.38/0.57 (define @t87 () (@list @t27 @t23)) % 0.38/0.57 (define @t88 () (lambda @t87 (= @t28 @t83))) % 0.38/0.57 (define @t89 () (_ tptp.element @t49)) % 0.38/0.57 (define @t90 () (_ (_ @t89 @t2) @t23)) % 0.38/0.57 (define @t91 () (_ (_ @t89 @t6) @t23)) % 0.38/0.57 (define @t92 () (= @t91 @t90)) % 0.38/0.57 (define @t93 () (= (_ @t7 @t1) (_ @t5 @t1))) % 0.38/0.57 (define @t94 () (lambda @t8 @t93)) % 0.38/0.57 (define @t95 () (_ @t94 @t49 @t23)) % 0.38/0.57 (define @t96 () (forall @t50 @t95)) % 0.38/0.57 (define @t97 () (lambda @t58 @t96)) % 0.38/0.57 (define @t98 () (_ @t5 @t23)) % 0.38/0.57 (define @t99 () (_ @t7 @t23)) % 0.38/0.57 (define @t100 () (lambda @t58 (= @t98 @t99))) % 0.38/0.57 (define @t101 () (lambda @t87 (= @t99 @t28))) % 0.38/0.57 (define @t102 () (_ @t33 @t7)) % 0.38/0.57 (define @t103 () (lambda @t8 (_ (_ @t102 @t5) @t1))) % 0.38/0.57 (define @t104 () (lambda @t87 (= @t83 @t28))) % 0.38/0.57 (define @t105 () (_ @t33 @t11)) % 0.38/0.57 (define @t106 () (lambda @t13 (_ (_ @t105 (_ @t71 @t103)) @t1))) % 0.38/0.57 (define @t107 () (@var "BOUND_VARIABLE_7760" $$unsorted)) % 0.38/0.57 (define @t108 () (@list @t6 @t107)) % 0.38/0.57 (define @t109 () (forall @t108 (= (tptp.set_equal @t6 @t107 tptp.mactual) (tptp.set_equal @t107 @t6 tptp.mactual)))) % 0.38/0.57 (define @t110 () (@quantifiers_skolemize @t109 1)) % 0.38/0.57 (define @t111 () (tptp.element @t49 @t110 tptp.mactual)) % 0.38/0.57 (define @t112 () (@quantifiers_skolemize @t109 0)) % 0.38/0.57 (define @t113 () (tptp.element @t49 @t112 tptp.mactual)) % 0.38/0.57 (define @t114 () (forall @t50 (= @t111 @t113))) % 0.38/0.57 (define @t115 () (tptp.set_equal @t110 @t112 tptp.mactual)) % 0.38/0.57 (define @t116 () (= @t114 @t115)) % 0.38/0.57 (define @t117 () (forall @t50 (= @t113 @t111))) % 0.38/0.57 (define @t118 () (= @t115 @t117)) % 0.38/0.57 (define @t119 () (@list false)) % 0.38/0.57 (define @t120 () (@list @t52)) % 0.38/0.57 (define @t121 () (tptp.set_equal @t107 @t6 @t23)) % 0.38/0.57 (define @t122 () (tptp.set_equal @t6 @t107 @t23)) % 0.38/0.57 (define @t123 () (= @t122 @t121)) % 0.38/0.57 (define @t124 () (forall @t108 @t123)) % 0.38/0.57 (define @t125 () (lambda @t58 @t124)) % 0.38/0.57 (define @t126 () (_ @t125 tptp.mactual)) % 0.38/0.57 (define @t127 () (@list @t107)) % 0.38/0.57 (define @t128 () (forall @t127 @t123)) % 0.38/0.57 (define @t129 () (forall @t127 (= (tptp.set_equal @t6 @t107 @t1) (tptp.set_equal @t107 @t6 @t1)))) % 0.38/0.57 (define @t130 () (lambda @t15 @t129)) % 0.38/0.57 (define @t131 () (_ @t130 @t6 @t23)) % 0.38/0.57 (define @t132 () (forall @t43 @t131)) % 0.38/0.57 (define @t133 () (lambda @t58 @t132)) % 0.38/0.57 (define @t134 () (_ (_ (_ tptp.set_equal @t107) @t6) @t23)) % 0.38/0.57 (define @t135 () (_ (_ @t10 @t107) @t23)) % 0.38/0.57 (define @t136 () (= @t135 @t134)) % 0.38/0.57 (define @t137 () (= @t74 (_ @t17 @t1))) % 0.38/0.57 (define @t138 () (lambda @t13 @t137)) % 0.38/0.57 (define @t139 () (_ @t138 @t107 @t23)) % 0.38/0.57 (define @t140 () (forall @t127 @t139)) % 0.38/0.57 (define @t141 () (lambda @t58 @t140)) % 0.38/0.57 (define @t142 () (_ @t17 @t23)) % 0.38/0.57 (define @t143 () (lambda @t58 (= @t142 @t83))) % 0.38/0.57 (define @t144 () (lambda @t13 (_ (_ @t105 @t17) @t1))) % 0.38/0.57 (define @t145 () (lambda @t15 (_ (_ @t71 @t144) @t1))) % 0.38/0.57 (define @t146 () (tptp.set_equal @t112 @t110 tptp.mactual)) % 0.38/0.57 (define @t147 () (= @t146 @t115)) % 0.38/0.57 (define @t148 () (= @t117 @t146)) % 0.38/0.57 (define @t149 () (= @t146 @t117)) % 0.38/0.57 (define @t150 () (not @t149)) % 0.38/0.57 (define @t151 () (not @t146)) % 0.38/0.57 (define @t152 () (not @t118)) % 0.38/0.57 (define @t153 () (not @t117)) % 0.38/0.57 (assume @p1 (_ tptp.mlocal (_ tptp.mforall_di @t16))) % 0.38/0.57 (assume @p2 @t20) % 0.38/0.57 (assume @p3 true) % 0.38/0.57 (step @p4 (= tptp.mlocal @t22) :rule refl :args (@t22)) % 0.38/0.57 (step @p5 (= tptp.mnot @t26) :rule refl :args (@t26)) % 0.38/0.57 (step @p6 (= tptp.mand @t30) :rule refl :args (@t30)) % 0.38/0.57 (step @p7 (= tptp.mor @t31) :rule refl :args (@t31)) % 0.38/0.57 (step @p8 (= tptp.mimplies @t32) :rule refl :args (@t32)) % 0.38/0.57 (step @p9 (= tptp.mequiv @t33) :rule refl :args (@t33)) % 0.38/0.57 (step @p10 (= tptp.mbox @t39) :rule refl :args (@t39)) % 0.38/0.57 (step @p11 (= tptp.mdia @t40) :rule refl :args (@t40)) % 0.38/0.57 (step @p12 (= tptp.mforall_di @t46) :rule refl :args (@t46)) % 0.38/0.57 (step @p13 (= tptp.mexists_di @t47) :rule refl :args (@t47)) % 0.38/0.57 (step @p14 :rule beta-reduce :args ((= @t60 @t52))) % 0.38/0.57 (step @p15 :rule beta-reduce :args ((= (_ @t22 @t59) @t60))) % 0.38/0.57 (step @p16 :rule trans :premises (@p15 @p14)) % 0.38/0.57 (step @p17 :rule quant-merge-prenex :args ((= (forall @t43 @t62) @t57))) % 0.38/0.57 (step @p18 :rule beta-reduce :args ((= @t66 @t62))) % 0.38/0.57 (step @p19 :rule cong :premises (@p18) :args (@t67)) % 0.38/0.57 (step @p20 :rule trans :premises (@p19 @p17)) % 0.38/0.57 (step @p21 :rule cong :premises (@p20) :args (@t68)) % 0.38/0.57 (step @p22 :rule beta-reduce :args ((= (_ @t71 @t65) @t68))) % 0.38/0.57 (step @p23 :rule trans :premises (@p22 @p21)) % 0.38/0.57 (step @p24 :rule beta-reduce :args ((= (_ (lambda @t58 @t62) @t1) @t64))) % 0.38/0.57 (step @p25 :rule refl :args (@t1)) % 0.38/0.57 (step @p26 :rule eq-symm :args (@t53 @t55)) % 0.38/0.57 (step @p27 :rule cong :premises (@p26) :args ((forall @t61 (= @t53 @t55)))) % 0.38/0.57 (step @p28 :rule refl :args (@t55)) % 0.38/0.57 (step @p29 :rule refl :args (@t53)) % 0.38/0.57 (step @p30 :rule refl :args (@t72)) % 0.38/0.57 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t72 @t53))) % 0.38/0.57 (step @p32 :rule symm :premises (@p31)) % 0.38/0.57 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 0.38/0.57 (step @p34 :rule cong :premises (@p33 @p28) :args (@t73)) % 0.38/0.57 (step @p35 :rule cong :premises (@p34) :args ((forall @t61 @t73))) % 0.38/0.57 (step @p36 :rule trans :premises (@p35 @p27)) % 0.38/0.57 (step @p37 :rule beta-reduce :args ((= @t77 @t73))) % 0.38/0.57 (step @p38 :rule cong :premises (@p37) :args (@t78)) % 0.38/0.57 (step @p39 :rule trans :premises (@p38 @p36)) % 0.38/0.57 (step @p40 :rule cong :premises (@p39) :args (@t79)) % 0.38/0.57 (step @p41 :rule beta-reduce :args ((= (_ (lambda @t45 (forall @t61 (_ @t41 @t48 @t23))) @t76) @t79))) % 0.38/0.57 (step @p42 :rule trans :premises (@p41 @p40)) % 0.38/0.57 (step @p43 :rule refl :args (@t76)) % 0.38/0.57 (step @p44 :rule alpha_equiv :args (@t70 @t80 (@list @t48))) % 0.38/0.57 (step @p45 :rule cong :premises (@p44) :args (@t71)) % 0.38/0.57 (step @p46 :rule ho_cong :premises (@p45 @p43)) % 0.38/0.57 (step @p47 :rule trans :premises (@p46 @p42)) % 0.38/0.57 (step @p48 :rule beta-reduce :args ((= (_ (lambda @t58 (= @t83 @t82)) @t1) @t75))) % 0.38/0.57 (step @p49 :rule beta-reduce :args ((= @t85 @t82))) % 0.38/0.57 (step @p50 :rule refl :args (@t83)) % 0.38/0.57 (step @p51 :rule cong :premises (@p50 @p49) :args ((= @t83 @t85))) % 0.38/0.57 (step @p52 :rule eq-symm :args (@t85 @t83)) % 0.38/0.57 (step @p53 :rule trans :premises (@p52 @p51)) % 0.38/0.57 (step @p54 :rule cong :premises (@p53) :args (@t86)) % 0.38/0.57 (step @p55 :rule beta-reduce :args ((= (_ @t88 @t84) @t86))) % 0.38/0.57 (step @p56 :rule trans :premises (@p55 @p54)) % 0.38/0.57 (step @p57 :rule refl :args (@t81)) % 0.38/0.57 (step @p58 :rule refl :args (@t90)) % 0.38/0.57 (step @p59 :rule cong :premises (@p58 @p57) :args ((= @t90 @t81))) % 0.38/0.57 (step @p60 :rule symm :premises (@p59)) % 0.38/0.57 (step 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0.38/0.57 (step @p170 :rule refl :args (@t134)) % 0.38/0.57 (step @p171 :rule cong :premises (@p170 @p169) :args ((= @t134 @t121))) % 0.38/0.57 (step @p172 :rule symm :premises (@p171)) % 0.38/0.57 (step @p173 :rule eq_resolve :premises (@p170 @p172)) % 0.38/0.57 (step @p174 :rule refl :args (@t122)) % 0.38/0.57 (step @p175 :rule refl :args (@t135)) % 0.38/0.57 (step @p176 :rule cong :premises (@p175 @p174) :args ((= @t135 @t122))) % 0.38/0.57 (step @p177 :rule symm :premises (@p176)) % 0.38/0.57 (step @p178 :rule eq_resolve :premises (@p175 @p177)) % 0.38/0.57 (step @p179 :rule cong :premises (@p178 @p173) :args (@t136)) % 0.38/0.57 (step @p180 :rule cong :premises (@p179) :args ((forall @t127 @t136))) % 0.38/0.57 (step @p181 :rule beta-reduce :args ((= @t139 @t136))) % 0.38/0.57 (step @p182 :rule cong :premises (@p181) :args (@t140)) % 0.38/0.57 (step @p183 :rule trans :premises (@p182 @p180)) % 0.38/0.57 (step @p184 :rule cong :premises (@p183) :args (@t141)) % 0.38/0.57 (step @p185 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@p196)) % 0.38/0.57 (step @p200 :rule ho_cong :premises (@p199 @p25)) % 0.38/0.57 (step @p201 :rule trans :premises (@p200 @p192)) % 0.38/0.57 (step @p202 :rule cong :premises (@p201) :args (@t144)) % 0.38/0.57 (step @p203 :rule ho_cong :premises (@p95 @p202)) % 0.38/0.57 (step @p204 :rule trans :premises (@p203 @p191)) % 0.38/0.57 (step @p205 :rule ho_cong :premises (@p204 @p25)) % 0.38/0.57 (step @p206 :rule trans :premises (@p205 @p168)) % 0.38/0.57 (step @p207 :rule cong :premises (@p206) :args (@t145)) % 0.38/0.57 (step @p208 :rule ho_cong :premises (@p95 @p207)) % 0.38/0.57 (step @p209 :rule trans :premises (@p208 @p167)) % 0.38/0.57 (step @p210 :rule ho_cong :premises (@p114 @p209)) % 0.38/0.57 (step @p211 :rule trans :premises (@p210 @p160)) % 0.38/0.57 (step @p212 :rule cong :premises (@p211) :args ((not (_ @t22 (_ @t71 @t145))))) % 0.38/0.57 (step @p213 :rule ho_cong :premises (@p132 @p197)) % 0.38/0.57 (step @p214 :rule ho_cong :premises (@p213 @p25)) % 0.38/0.57 (step @p215 :rule cong :premises (@p214) :args (@t18)) % 0.38/0.57 (step @p216 :rule ho_cong :premises (@p129 @p215)) % 0.38/0.57 (step @p217 :rule ho_cong :premises (@p216 @p25)) % 0.38/0.57 (step @p218 :rule cong :premises (@p217) :args (@t19)) % 0.38/0.57 (step @p219 :rule ho_cong :premises (@p129 @p218)) % 0.38/0.57 (step @p220 :rule ho_cong :premises (@p4 @p219)) % 0.38/0.57 (step @p221 :rule cong :premises (@p220) :args (@t20)) % 0.38/0.57 (step @p222 :rule trans :premises (@p221 @p212)) % 0.38/0.57 (step @p223 :rule eq_resolve :premises (@p2 @p222)) % 0.38/0.57 (step @p224 :rule skolemize :premises (@p223)) % 0.38/0.57 (step @p225 :rule cnf_equiv_neg2 :args (@t147)) % 0.38/0.57 (step @p226 :rule eq-symm :args (@t117 @t146)) % 0.38/0.57 (step @p227 :rule cong :premises (@p149 @p226) :args ((=> @t52 @t148))) % 0.38/0.57 (assume-push @p251 @t52) % 0.38/0.57 (step @p229 :rule instantiate :premises (@p142) :args ((@list @t112 @t110))) % 0.38/0.57 (step-pop @p252 :rule scope :premises (@p229)) % 0.38/0.57 (step @p230 :rule process_scope :premises (@p252) :args (@t148)) % 0.38/0.57 (step @p232 :rule eq_resolve :premises (@p230 @p227)) % 0.38/0.57 (step @p233 :rule implies_elim :premises (@p232)) % 0.38/0.57 (step @p234 :rule chain_m_resolution :premises (@p233 @p142) :args (@t149 @t119 @t120)) % 0.38/0.57 (step @p235 :rule cnf_equiv_pos1 :args (@t149)) % 0.38/0.57 (step @p236 :rule reordering :premises (@p235) :args ((or @t151 @t117 @t150))) % 0.38/0.57 (step @p237 :rule cnf_equiv_pos2 :args (@t118)) % 0.38/0.57 (step @p238 :rule reordering :premises (@p237) :args ((or @t115 @t153 @t152))) % 0.38/0.57 (step @p239 :rule chain_m_resolution :premises (@p238 @p157 @p236 @p234 @p225 @p224) :args (@t151 (@list false false false true true) (@list @t118 @t117 @t149 @t115 @t147))) % 0.38/0.57 (step @p240 :rule cnf_equiv_neg1 :args (@t147)) % 0.38/0.57 (step @p241 :rule reordering :premises (@p240) :args ((or @t146 @t115 @t147))) % 0.38/0.57 (step @p242 :rule chain_m_resolution :premises (@p241 @p239 @p224) :args (@t115 (@list true true) (@list @t146 @t147))) % 0.38/0.57 (step @p243 :rule cnf_equiv_pos2 :args (@t149)) % 0.38/0.57 (step @p244 :rule reordering :premises (@p243) :args ((or @t146 @t153 @t150))) % 0.38/0.57 (step @p245 :rule chain_m_resolution :premises (@p244 @p239 @p234) :args (@t153 (@list true false) (@list @t146 @t149))) % 0.38/0.57 (step @p246 :rule cnf_equiv_pos1 :args (@t118)) % 0.38/0.57 (step @p247 :rule reordering :premises (@p246) :args ((or (not @t115) @t117 @t152))) % 0.38/0.57 (step @p248 false :rule chain_m_resolution :premises (@p247 @p245 @p242 @p157) :args (false (@list true false false) (@list @t117 @t115 @t118))) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------