%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL590^1 : 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 : n009.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 11:23:07 AM UTC 2026 % Result : Theorem 0.20s 0.48s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL590^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.10/0.36 % Computer : n009.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Sep 5 20:56:52 UTC 2026 % 0.10/0.37 % CPUTime : % 0.14/0.43 %----Proving TH0 % 0.20/0.48 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.20/0.48 % SZS status Theorem % 0.20/0.48 % SZS output start Proof % 0.20/0.48 ( % 0.20/0.48 (declare-sort $$unsorted 0) % 0.20/0.48 (declare-sort tptp.individuals 0) % 0.20/0.48 (declare-const tptp.a (-> $$unsorted Bool)) % 0.20/0.48 (declare-const tptp.r (-> $$unsorted $$unsorted Bool)) % 0.20/0.48 (declare-const tptp.b (-> $$unsorted Bool)) % 0.20/0.48 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.20/0.48 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.20/0.48 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.20/0.48 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.20/0.48 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.20/0.48 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.20/0.48 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.20/0.48 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.20/0.48 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.20/0.48 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.20/0.48 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.20/0.48 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.20/0.48 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.20/0.48 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.20/0.48 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.20/0.48 (define @t1 () (_ tptp.mdia tptp.r)) % 0.20/0.48 (define @t2 () (_ tptp.mimpl (_ @t1 tptp.a))) % 0.20/0.48 (define @t3 () (not (_ tptp.mvalid (_ (_ tptp.mimpl (_ @t2 (_ (_ tptp.mbox tptp.r) tptp.b))) (_ @t2 (_ @t1 tptp.b)))))) % 0.20/0.48 (define @t4 () (@var "X" $$unsorted)) % 0.20/0.48 (define @t5 () (@list @t4)) % 0.20/0.48 (define @t6 () (lambda @t5 false)) % 0.20/0.48 (define @t7 () (lambda @t5 true)) % 0.20/0.48 (define @t8 () (@var "U" $$unsorted)) % 0.20/0.48 (define @t9 () (@var "X" (-> $$unsorted Bool))) % 0.20/0.48 (define @t10 () (_ @t9 @t8)) % 0.20/0.48 (define @t11 () (lambda (@list @t9 @t8) (not @t10))) % 0.20/0.48 (define @t12 () (@var "Y" (-> $$unsorted Bool))) % 0.20/0.48 (define @t13 () (_ @t12 @t8)) % 0.20/0.48 (define @t14 () (@list @t9 @t12 @t8)) % 0.20/0.48 (define @t15 () (lambda @t14 (or @t10 @t13))) % 0.20/0.48 (define @t16 () (lambda @t14 (and @t10 @t13))) % 0.20/0.48 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.20/0.48 (define @t18 () (@var "V" (-> $$unsorted Bool))) % 0.20/0.48 (define @t19 () (@var "U" (-> $$unsorted Bool))) % 0.20/0.48 (define @t20 () (@list @t19 @t18 @t17)) % 0.20/0.48 (define @t21 () (lambda @t20 (_ (_ (_ tptp.mor (_ tptp.mnot @t19)) @t18) @t17))) % 0.20/0.48 (define @t22 () (lambda @t20 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t19) @t18)) (_ (_ tptp.mimpl @t18) @t19)) @t17))) % 0.20/0.48 (define @t23 () (@var "Y" $$unsorted)) % 0.20/0.48 (define @t24 () (@var "P" (-> $$unsorted Bool))) % 0.20/0.48 (define @t25 () (_ @t24 @t23)) % 0.20/0.48 (define @t26 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.20/0.48 (define @t27 () (_ (_ @t26 @t4) @t23)) % 0.20/0.48 (define @t28 () (@list @t23)) % 0.20/0.48 (define @t29 () (forall @t28 (=> @t27 @t25))) % 0.20/0.48 (define @t30 () (@list @t26 @t24 @t4)) % 0.20/0.48 (define @t31 () (lambda @t30 @t29)) % 0.20/0.48 (define @t32 () (and @t27 @t25)) % 0.20/0.48 (define @t33 () (exists @t28 @t32)) % 0.20/0.48 (define @t34 () (lambda @t30 @t33)) % 0.20/0.48 (define @t35 () (@var "W" $$unsorted)) % 0.20/0.48 (define @t36 () (@var "X" tptp.individuals)) % 0.20/0.48 (define @t37 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.20/0.48 (define @t38 () (_ (_ @t37 @t36) @t35)) % 0.20/0.48 (define @t39 () (@list @t36)) % 0.20/0.48 (define @t40 () (@list @t37 @t35)) % 0.20/0.48 (define @t41 () (lambda @t40 (forall @t39 @t38))) % 0.20/0.48 (define @t42 () (lambda @t40 (exists @t39 @t38))) % 0.20/0.48 (define @t43 () (_ @t24 @t35)) % 0.20/0.48 (define @t44 () (@list @t35)) % 0.20/0.48 (define @t45 () (forall @t44 @t43)) % 0.20/0.48 (define @t46 () (@list @t24)) % 0.20/0.48 (define @t47 () (lambda @t46 @t45)) % 0.20/0.48 (define @t48 () (lambda @t46 (exists @t44 @t43))) % 0.20/0.48 (define @t49 () (not @t43)) % 0.20/0.48 (define @t50 () (lambda @t46 (exists @t44 @t49))) % 0.20/0.48 (define @t51 () (lambda @t46 (forall @t44 @t49))) % 0.20/0.48 (define @t52 () (@var "BOUND_VARIABLE_7877" $$unsorted)) % 0.20/0.48 (define @t53 () (not (tptp.a @t52))) % 0.20/0.48 (define @t54 () (not (tptp.r @t35 @t52))) % 0.20/0.48 (define @t55 () (tptp.b @t23)) % 0.20/0.48 (define @t56 () (not @t55)) % 0.20/0.48 (define @t57 () (not (tptp.r @t35 @t23))) % 0.20/0.48 (define @t58 () (not (forall @t28 (or @t57 @t56)))) % 0.20/0.48 (define @t59 () (forall @t28 (or @t57 @t55))) % 0.20/0.48 (define @t60 () (not (tptp.a @t23))) % 0.20/0.48 (define @t61 () (forall @t28 (or @t57 @t60))) % 0.20/0.48 (define @t62 () (and (not @t61) (not @t59))) % 0.20/0.48 (define @t63 () (or @t62 @t58 @t54 @t53)) % 0.20/0.48 (define @t64 () (or @t54 @t53)) % 0.20/0.48 (define @t65 () (or @t62 @t64 @t58)) % 0.20/0.48 (define @t66 () (@list @t35 @t52)) % 0.20/0.48 (define @t67 () (forall @t66 @t65)) % 0.20/0.48 (define @t68 () (@list @t52)) % 0.20/0.48 (define @t69 () (forall @t68 @t65)) % 0.20/0.48 (define @t70 () (forall @t68 @t64)) % 0.20/0.48 (define @t71 () (or @t62 @t70 @t58)) % 0.20/0.48 (define @t72 () (or (not (or @t61 @t59)) @t61 @t58)) % 0.20/0.48 (define @t73 () (not (tptp.r @t17 @t23))) % 0.20/0.48 (define @t74 () (not (forall @t28 (or @t73 @t56)))) % 0.20/0.48 (define @t75 () (forall @t28 (or @t73 @t60))) % 0.20/0.48 (define @t76 () (forall @t28 (or @t73 @t55))) % 0.20/0.48 (define @t77 () (or @t75 @t76)) % 0.20/0.48 (define @t78 () (not @t77)) % 0.20/0.48 (define @t79 () (or @t78 @t75 @t74)) % 0.20/0.48 (define @t80 () (@list @t17)) % 0.20/0.48 (define @t81 () (lambda @t80 @t79)) % 0.20/0.48 (define @t82 () (_ @t81 @t35)) % 0.20/0.48 (define @t83 () (forall @t44 @t82)) % 0.20/0.48 (define @t84 () (_ @t24 @t35)) % 0.20/0.48 (define @t85 () (lambda @t46 (forall @t44 @t84))) % 0.20/0.48 (define @t86 () (or @t75 @t74)) % 0.20/0.48 (define @t87 () (lambda @t80 @t86)) % 0.20/0.48 (define @t88 () (_ @t87 @t17)) % 0.20/0.48 (define @t89 () (or @t78 @t88)) % 0.20/0.48 (define @t90 () (lambda @t80 @t89)) % 0.20/0.48 (define @t91 () (_ @t18 @t17)) % 0.20/0.48 (define @t92 () (@list @t18 @t17)) % 0.20/0.48 (define @t93 () (not (tptp.r @t4 @t23))) % 0.20/0.48 (define @t94 () (lambda @t5 (not (forall @t28 (or @t93 @t56))))) % 0.20/0.48 (define @t95 () (_ @t94 @t17)) % 0.20/0.48 (define @t96 () (or @t75 @t95)) % 0.20/0.48 (define @t97 () (lambda @t80 @t96)) % 0.20/0.48 (define @t98 () (lambda @t92 (or @t75 @t91))) % 0.20/0.48 (define @t99 () (_ @t24 @t23)) % 0.20/0.48 (define @t100 () (not @t99)) % 0.20/0.48 (define @t101 () (@list @t24 @t4)) % 0.20/0.48 (define @t102 () (lambda @t101 (not (forall @t28 (or @t93 @t100))))) % 0.20/0.48 (define @t103 () (_ @t26 @t4 @t23)) % 0.20/0.48 (define @t104 () (not @t103)) % 0.20/0.48 (define @t105 () (_ (lambda @t30 (not (forall @t28 (or @t104 @t100)))) tptp.r)) % 0.20/0.48 (define @t106 () (lambda @t5 (not (forall @t28 (or @t93 @t60))))) % 0.20/0.48 (define @t107 () (_ @t106 @t17)) % 0.20/0.48 (define @t108 () (not @t107)) % 0.20/0.48 (define @t109 () (or @t108 @t91)) % 0.20/0.48 (define @t110 () (lambda @t92 @t109)) % 0.20/0.48 (define @t111 () (or (not (_ @t19 @t17)) @t91)) % 0.20/0.48 (define @t112 () (lambda @t20 @t111)) % 0.20/0.48 (define @t113 () (lambda @t80 @t77)) % 0.20/0.48 (define @t114 () (_ @t113 @t17)) % 0.20/0.48 (define @t115 () (not @t114)) % 0.20/0.48 (define @t116 () (or @t115 @t91)) % 0.20/0.48 (define @t117 () (lambda @t92 @t116)) % 0.20/0.48 (define @t118 () (lambda @t5 (forall @t28 (or @t93 @t55)))) % 0.20/0.48 (define @t119 () (_ @t118 @t17)) % 0.20/0.48 (define @t120 () (or @t75 @t119)) % 0.20/0.48 (define @t121 () (lambda @t80 @t120)) % 0.20/0.48 (define @t122 () (lambda @t101 (forall @t28 (or @t93 @t99)))) % 0.20/0.48 (define @t123 () (_ (lambda @t30 (forall @t28 (or @t104 @t99))) tptp.r)) % 0.20/0.48 (define @t124 () (_ @t112 (_ @t105 tptp.a))) % 0.20/0.48 (define @t125 () (not @t25)) % 0.20/0.48 (define @t126 () (not @t27)) % 0.20/0.48 (define @t127 () (or @t126 @t125)) % 0.20/0.48 (define @t128 () (forall @t28 (not @t32))) % 0.20/0.48 (define @t129 () (not @t128)) % 0.20/0.48 (define @t130 () (not (_ @t19 @t8))) % 0.20/0.48 (define @t131 () (@list @t8)) % 0.20/0.48 (define @t132 () (lambda @t131 (or @t130 (_ @t18 @t8)))) % 0.20/0.48 (define @t133 () (@list @t12 @t8)) % 0.20/0.48 (define @t134 () (lambda @t131 @t130)) % 0.20/0.49 (define @t135 () (_ @t134 @t8)) % 0.20/0.49 (define @t136 () (or @t135 @t13)) % 0.20/0.49 (define @t137 () (lambda @t133 @t136)) % 0.20/0.49 (define @t138 () (or @t126 @t25)) % 0.20/0.49 (define @t139 () (forall @t66 @t63)) % 0.20/0.49 (define @t140 () (@quantifiers_skolemize @t139 1)) % 0.20/0.49 (define @t141 () (@quantifiers_skolemize @t139 0)) % 0.20/0.49 (define @t142 () (tptp.r @t141 @t140)) % 0.20/0.49 (define @t143 () (tptp.a @t140)) % 0.20/0.49 (define @t144 () (not @t143)) % 0.20/0.49 (define @t145 () (not @t142)) % 0.20/0.49 (define @t146 () (not (tptp.r @t141 @t23))) % 0.20/0.49 (define @t147 () (forall @t28 (or @t146 @t56))) % 0.20/0.49 (define @t148 () (not @t147)) % 0.20/0.49 (define @t149 () (forall @t28 (or @t146 @t55))) % 0.20/0.49 (define @t150 () (not @t149)) % 0.20/0.49 (define @t151 () (forall @t28 (or @t146 @t60))) % 0.20/0.49 (define @t152 () (not @t151)) % 0.20/0.49 (define @t153 () (and @t152 @t150)) % 0.20/0.49 (define @t154 () (or @t153 @t148 @t145 @t144)) % 0.20/0.49 (define @t155 () (@list true)) % 0.20/0.49 (define @t156 () (@list @t154)) % 0.20/0.49 (define @t157 () (or @t145 @t144)) % 0.20/0.49 (define @t158 () (not @t157)) % 0.20/0.49 (define @t159 () (@list false false)) % 0.20/0.49 (define @t160 () (@list @t140)) % 0.20/0.49 (define @t161 () (tptp.b @t140)) % 0.20/0.49 (define @t162 () (or @t145 @t161)) % 0.20/0.49 (define @t163 () (not @t161)) % 0.20/0.49 (define @t164 () (or @t145 @t163)) % 0.20/0.49 (assume @p1 @t3) % 0.20/0.49 (assume @p2 true) % 0.20/0.49 (step @p3 (= tptp.mfalse @t6) :rule refl :args (@t6)) % 0.20/0.49 (step @p4 (= tptp.mtrue @t7) :rule refl :args (@t7)) % 0.20/0.49 (step @p5 (= tptp.mnot @t11) :rule refl :args (@t11)) % 0.20/0.49 (step @p6 (= tptp.mor @t15) :rule refl :args (@t15)) % 0.20/0.49 (step @p7 (= tptp.mand @t16) :rule refl :args (@t16)) % 0.20/0.49 (step @p8 (= tptp.mimpl @t21) :rule refl :args (@t21)) % 0.20/0.49 (step @p9 (= tptp.miff @t22) :rule refl :args (@t22)) % 0.20/0.49 (step @p10 (= tptp.mbox @t31) :rule refl :args (@t31)) % 0.20/0.49 (step @p11 (= tptp.mdia @t34) :rule refl :args (@t34)) % 0.20/0.49 (step @p12 (= tptp.mall @t41) :rule refl :args (@t41)) % 0.20/0.49 (step @p13 (= tptp.mexists @t42) :rule refl :args (@t42)) % 0.20/0.49 (step @p14 (= tptp.mvalid @t47) :rule refl :args (@t47)) % 0.20/0.49 (step @p15 (= tptp.msatisfiable @t48) :rule refl :args (@t48)) % 0.20/0.49 (step @p16 (= tptp.mcountersatisfiable @t50) :rule refl :args (@t50)) % 0.20/0.49 (step @p17 (= tptp.minvalid @t51) :rule refl :args (@t51)) % 0.20/0.49 (step @p18 :rule aci_norm :args ((= @t65 @t63))) % 0.20/0.49 (step @p19 :rule cong :premises (@p18) :args (@t67)) % 0.20/0.49 (step @p20 :rule quant-merge-prenex :args ((= (forall @t44 @t69) @t67))) % 0.20/0.49 (step @p21 :rule refl :args (@t58)) % 0.20/0.49 (step @p22 :rule alpha_equiv :args (@t70 (@list @t52) (@list @t23))) % 0.20/0.49 (step @p23 :rule refl :args (@t62)) % 0.20/0.49 (step @p24 :rule nary_cong :premises (@p23 @p22 @p21) :args (@t71)) % 0.20/0.49 (step @p25 :rule quant-miniscope-or :args ((= @t69 @t71))) % 0.20/0.49 (step @p26 :rule trans :premises (@p25 @p24)) % 0.20/0.49 (step @p27 :rule symm :premises (@p26)) % 0.20/0.49 (step @p28 :rule cong :premises (@p27) :args ((forall @t44 (or @t62 @t61 @t58)))) % 0.20/0.49 (step @p29 :rule trans :premises (@p28 @p20)) % 0.20/0.49 (step @p30 :rule trans :premises (@p29 @p19)) % 0.20/0.49 (step @p31 :rule refl :args (@t61)) % 0.20/0.49 (step @p32 :rule bool-or-de-morgan :args (@t61 @t59 false)) % 0.20/0.49 (step @p33 :rule nary_cong :premises (@p32 @p31 @p21) :args (@t72)) % 0.20/0.49 (step @p34 :rule cong :premises (@p33) :args ((forall @t44 @t72))) % 0.20/0.49 (step @p35 :rule trans :premises (@p34 @p30)) % 0.20/0.49 (step @p36 :rule beta-reduce :args ((= @t82 @t72))) % 0.20/0.49 (step @p37 :rule cong :premises (@p36) :args (@t83)) % 0.20/0.49 (step @p38 :rule trans :premises (@p37 @p35)) % 0.20/0.49 (step @p39 :rule beta-reduce :args ((= (_ @t85 @t81) @t83))) % 0.20/0.49 (step @p40 :rule trans :premises (@p39 @p38)) % 0.20/0.49 (step @p41 :rule aci_norm :args ((= (or @t78 @t86) @t79))) % 0.20/0.49 (step @p42 :rule beta-reduce :args ((= @t88 @t86))) % 0.20/0.49 (step @p43 :rule refl :args (@t78)) % 0.20/0.49 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t89)) % 0.20/0.49 (step @p45 :rule trans :premises (@p44 @p41)) % 0.20/0.49 (step @p46 :rule cong :premises (@p45) :args (@t90)) % 0.20/0.49 (step @p47 :rule beta-reduce :args ((= (_ (lambda @t92 (or @t78 @t91)) @t87) @t90))) % 0.20/0.49 (step @p48 :rule trans :premises (@p47 @p46)) % 0.20/0.49 (step @p49 :rule beta-reduce :args ((= @t95 @t74))) % 0.20/0.49 (step @p50 :rule refl :args (@t75)) % 0.20/0.49 (step @p51 :rule nary_cong :premises (@p50 @p49) :args (@t96)) % 0.20/0.49 (step @p52 :rule cong :premises (@p51) :args (@t97)) % 0.20/0.49 (step @p53 :rule beta-reduce :args ((= (_ @t98 @t94) @t97))) % 0.20/0.49 (step @p54 :rule trans :premises (@p53 @p52)) % 0.20/0.49 (step @p55 :rule beta-reduce :args ((= (_ @t102 tptp.b) @t94))) % 0.20/0.49 (step @p56 :rule refl :args (tptp.b)) % 0.20/0.49 (step @p57 :rule beta-reduce :args ((= @t105 @t102))) % 0.20/0.49 (step @p58 :rule ho_cong :premises (@p57 @p56)) % 0.20/0.49 (step @p59 :rule trans :premises (@p58 @p55)) % 0.20/0.49 (step @p60 :rule refl :args (@t91)) % 0.20/0.49 (step @p61 :rule bool-double-not-elim :args (@t75)) % 0.20/0.49 (step @p62 :rule beta-reduce :args ((= @t107 (not @t75)))) % 0.20/0.49 (step @p63 :rule cong :premises (@p62) :args (@t108)) % 0.20/0.49 (step @p64 :rule trans :premises (@p63 @p61)) % 0.20/0.49 (step @p65 :rule nary_cong :premises (@p64 @p60) :args (@t109)) % 0.20/0.49 (step @p66 :rule cong :premises (@p65) :args (@t110)) % 0.20/0.49 (step @p67 :rule beta-reduce :args ((= (_ @t112 @t106) @t110))) % 0.20/0.49 (step @p68 :rule trans :premises (@p67 @p66)) % 0.20/0.49 (step @p69 :rule beta-reduce :args ((= (_ @t102 tptp.a) @t106))) % 0.20/0.49 (step @p70 :rule refl :args (tptp.a)) % 0.20/0.49 (step @p71 :rule ho_cong :premises (@p57 @p70)) % 0.20/0.49 (step @p72 :rule trans :premises (@p71 @p69)) % 0.20/0.49 (step @p73 :rule refl :args (@t112)) % 0.20/0.49 (step @p74 :rule ho_cong :premises (@p73 @p72)) % 0.20/0.49 (step @p75 :rule trans :premises (@p74 @p68)) % 0.20/0.49 (step @p76 :rule ho_cong :premises (@p75 @p59)) % 0.20/0.49 (step @p77 :rule trans :premises (@p76 @p54)) % 0.20/0.49 (step @p78 :rule beta-reduce :args ((= @t114 @t77))) % 0.20/0.49 (step @p79 :rule cong :premises (@p78) :args (@t115)) % 0.20/0.49 (step @p80 :rule nary_cong :premises (@p79 @p60) :args (@t116)) % 0.20/0.49 (step @p81 :rule cong :premises (@p80) :args (@t117)) % 0.20/0.49 (step @p82 :rule beta-reduce :args ((= (_ @t112 @t113) @t117))) % 0.20/0.49 (step @p83 :rule trans :premises (@p82 @p81)) % 0.20/0.49 (step @p84 :rule beta-reduce :args ((= @t119 @t76))) % 0.20/0.49 (step @p85 :rule nary_cong :premises (@p50 @p84) :args (@t120)) % 0.20/0.49 (step @p86 :rule cong :premises (@p85) :args (@t121)) % 0.20/0.49 (step @p87 :rule beta-reduce :args ((= (_ @t98 @t118) @t121))) % 0.20/0.49 (step @p88 :rule trans :premises (@p87 @p86)) % 0.20/0.49 (step @p89 :rule beta-reduce :args ((= (_ @t122 tptp.b) @t118))) % 0.20/0.49 (step @p90 :rule beta-reduce :args ((= @t123 @t122))) % 0.20/0.49 (step @p91 :rule ho_cong :premises (@p90 @p56)) % 0.20/0.49 (step @p92 :rule trans :premises (@p91 @p89)) % 0.20/0.49 (step @p93 :rule ho_cong :premises (@p75 @p92)) % 0.20/0.49 (step @p94 :rule trans :premises (@p93 @p88)) % 0.20/0.49 (step @p95 :rule ho_cong :premises (@p73 @p94)) % 0.20/0.49 (step @p96 :rule trans :premises (@p95 @p83)) % 0.20/0.49 (step @p97 :rule ho_cong :premises (@p96 @p77)) % 0.20/0.49 (step @p98 :rule trans :premises (@p97 @p48)) % 0.20/0.49 (step @p99 :rule refl :args (@t85)) % 0.20/0.49 (step @p100 :rule ho_cong :premises (@p99 @p98)) % 0.20/0.49 (step @p101 :rule trans :premises (@p100 @p40)) % 0.20/0.49 (step @p102 :rule cong :premises (@p101) :args ((not (_ @t85 (_ (_ @t112 (_ @t124 (_ @t123 tptp.b))) (_ @t124 (_ @t105 tptp.b))))))) % 0.20/0.49 (step @p103 :rule refl :args (tptp.r)) % 0.20/0.49 (step @p104 :rule refl :args (@t99)) % 0.20/0.49 (step @p105 :rule refl :args (@t25)) % 0.20/0.49 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t25 @t99))) % 0.20/0.49 (step @p107 :rule symm :premises (@p106)) % 0.20/0.49 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.20/0.49 (step @p109 :rule cong :premises (@p108) :args (@t125)) % 0.20/0.49 (step @p110 :rule refl :args (@t103)) % 0.20/0.49 (step @p111 :rule refl :args (@t27)) % 0.20/0.49 (step @p112 :rule cong :premises (@p111 @p110) :args ((= @t27 @t103))) % 0.20/0.49 (step @p113 :rule symm :premises (@p112)) % 0.20/0.49 (step @p114 :rule eq_resolve :premises (@p111 @p113)) % 0.20/0.49 (step @p115 :rule cong :premises (@p114) :args (@t126)) % 0.20/0.49 (step @p116 :rule nary_cong :premises (@p115 @p109) :args (@t127)) % 0.20/0.49 (step @p117 :rule cong :premises (@p116) :args ((forall @t28 @t127))) % 0.20/0.49 (step @p118 :rule bool-and-de-morgan :args (@t27 @t25 true)) % 0.20/0.49 (step @p119 :rule cong :premises (@p118) :args (@t128)) % 0.20/0.49 (step @p120 :rule trans :premises (@p119 @p117)) % 0.20/0.49 (step @p121 :rule cong :premises (@p120) :args (@t129)) % 0.20/0.49 (step @p122 :rule exists-elim :args ((= @t33 @t129))) % 0.20/0.49 (step @p123 :rule trans :premises (@p122 @p121)) % 0.20/0.49 (step @p124 :rule cong :premises (@p123) :args (@t34)) % 0.20/0.49 (step @p125 :rule trans :premises (@p11 @p124)) % 0.20/0.49 (step @p126 :rule ho_cong :premises (@p125 @p103)) % 0.20/0.49 (step @p127 :rule ho_cong :premises (@p126 @p56)) % 0.20/0.49 (step @p128 :rule ho_cong :premises (@p126 @p70)) % 0.20/0.49 (step @p129 :rule beta-reduce :args ((= (_ @t132 @t17) @t111))) % 0.20/0.49 (step @p130 :rule refl :args (@t17)) % 0.20/0.49 (step @p131 :rule beta-reduce :args ((= (_ (lambda @t133 (or @t130 @t13)) @t18) @t132))) % 0.20/0.49 (step @p132 :rule refl :args (@t18)) % 0.20/0.49 (step @p133 :rule refl :args (@t13)) % 0.20/0.49 (step @p134 :rule beta-reduce :args ((= @t135 @t130))) % 0.20/0.49 (step @p135 :rule nary_cong :premises (@p134 @p133) :args (@t136)) % 0.20/0.49 (step @p136 :rule cong :premises (@p135) :args (@t137)) % 0.20/0.49 (step @p137 :rule beta-reduce :args ((= (_ @t15 @t134) @t137))) % 0.20/0.49 (step @p138 :rule trans :premises (@p137 @p136)) % 0.20/0.49 (step @p139 :rule beta-reduce :args ((= (_ @t11 @t19) @t134))) % 0.20/0.49 (step @p140 :rule refl :args (@t15)) % 0.20/0.49 (step @p141 :rule ho_cong :premises (@p140 @p139)) % 0.20/0.49 (step @p142 :rule trans :premises (@p141 @p138)) % 0.20/0.49 (step @p143 :rule ho_cong :premises (@p142 @p132)) % 0.20/0.49 (step @p144 :rule trans :premises (@p143 @p131)) % 0.20/0.49 (step @p145 :rule ho_cong :premises (@p144 @p130)) % 0.20/0.49 (step @p146 :rule trans :premises (@p145 @p129)) % 0.20/0.49 (step @p147 :rule refl :args (@t19)) % 0.20/0.49 (step @p148 :rule ho_cong :premises (@p5 @p147)) % 0.20/0.49 (step @p149 :rule ho_cong :premises (@p6 @p148)) % 0.20/0.49 (step @p150 :rule ho_cong :premises (@p149 @p132)) % 0.20/0.49 (step @p151 :rule ho_cong :premises (@p150 @p130)) % 0.20/0.49 (step @p152 :rule trans :premises (@p151 @p146)) % 0.20/0.49 (step @p153 :rule cong :premises (@p152) :args (@t21)) % 0.20/0.49 (step @p154 :rule trans :premises (@p8 @p153)) % 0.20/0.49 (step @p155 :rule ho_cong :premises (@p154 @p128)) % 0.20/0.49 (step @p156 :rule ho_cong :premises (@p155 @p127)) % 0.20/0.49 (step @p157 :rule nary_cong :premises (@p115 @p108) :args (@t138)) % 0.20/0.49 (step @p158 :rule cong :premises (@p157) :args ((forall @t28 @t138))) % 0.20/0.49 (step @p159 :rule bool-impl-elim :args (@t27 @t25)) % 0.20/0.49 (step @p160 :rule cong :premises (@p159) :args (@t29)) % 0.20/0.49 (step @p161 :rule trans :premises (@p160 @p158)) % 0.20/0.49 (step @p162 :rule cong :premises (@p161) :args (@t31)) % 0.20/0.49 (step @p163 :rule trans :premises (@p10 @p162)) % 0.20/0.49 (step @p164 :rule ho_cong :premises (@p163 @p103)) % 0.20/0.49 (step @p165 :rule ho_cong :premises (@p164 @p56)) % 0.20/0.49 (step @p166 :rule ho_cong :premises (@p155 @p165)) % 0.20/0.49 (step @p167 :rule ho_cong :premises (@p154 @p166)) % 0.20/0.49 (step @p168 :rule ho_cong :premises (@p167 @p156)) % 0.20/0.49 (step @p169 :rule refl :args (@t84)) % 0.20/0.49 (step @p170 :rule refl :args (@t43)) % 0.20/0.49 (step @p171 :rule cong :premises (@p170 @p169) :args ((= @t43 @t84))) % 0.20/0.49 (step @p172 :rule symm :premises (@p171)) % 0.20/0.49 (step @p173 :rule eq_resolve :premises (@p170 @p172)) % 0.20/0.49 (step @p174 :rule cong :premises (@p173) :args (@t45)) % 0.20/0.49 (step @p175 :rule cong :premises (@p174) :args (@t47)) % 0.20/0.49 (step @p176 :rule trans :premises (@p14 @p175)) % 0.20/0.49 (step @p177 :rule ho_cong :premises (@p176 @p168)) % 0.20/0.49 (step @p178 :rule cong :premises (@p177) :args (@t3)) % 0.20/0.49 (step @p179 :rule trans :premises (@p178 @p102)) % 0.20/0.49 (step @p180 :rule eq_resolve :premises (@p1 @p179)) % 0.20/0.49 (step @p181 :rule skolemize :premises (@p180)) % 0.20/0.49 (step @p182 :rule bool-double-not-elim :args (@t142)) % 0.20/0.49 (step @p183 :rule refl :args (@t154)) % 0.20/0.49 (step @p184 :rule nary_cong :premises (@p183 @p182) :args ((or @t154 (not @t145)))) % 0.20/0.49 (step @p185 :rule cnf_or_neg :args (@t154 2)) % 0.20/0.49 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.20/0.49 (step @p187 :rule reordering :premises (@p186) :args ((or @t142 @t154))) % 0.20/0.49 (step @p188 :rule chain_m_resolution :premises (@p187 @p181) :args (@t142 @t155 @t156)) % 0.20/0.49 (step @p189 :rule cnf_or_neg :args (@t154 0)) % 0.20/0.49 (step @p190 :rule chain_m_resolution :premises (@p189 @p181) :args ((not @t153) @t155 @t156)) % 0.20/0.49 (step @p191 :rule bool-double-not-elim :args (@t143)) % 0.20/0.49 (step @p192 :rule nary_cong :premises (@p183 @p191) :args ((or @t154 (not @t144)))) % 0.20/0.49 (step @p193 :rule cnf_or_neg :args (@t154 3)) % 0.20/0.49 (step @p194 :rule eq_resolve :premises (@p193 @p192)) % 0.20/0.49 (step @p195 :rule reordering :premises (@p194) :args ((or @t143 @t154))) % 0.20/0.49 (step @p196 :rule chain_m_resolution :premises (@p195 @p181) :args (@t143 @t155 @t156)) % 0.20/0.49 (step @p197 :rule cnf_or_pos :args (@t157)) % 0.20/0.49 (step @p198 :rule reordering :premises (@p197) :args ((or @t145 @t144 @t158))) % 0.20/0.49 (step @p199 :rule chain_m_resolution :premises (@p198 @p188 @p196) :args (@t158 @t159 (@list @t142 @t143))) % 0.20/0.49 (assume-push @p233 @t151) % 0.20/0.49 (step @p201 :rule instantiate :premises (@p233) :args (@t160)) % 0.20/0.49 (step-pop @p234 :rule scope :premises (@p201)) % 0.20/0.49 (step @p202 :rule process_scope :premises (@p234) :args (@t157)) % 0.20/0.49 (step @p204 :rule implies_elim :premises (@p202)) % 0.20/0.49 (step @p205 :rule chain_m_resolution :premises (@p204 @p199) :args (@t152 @t155 (@list @t157))) % 0.20/0.49 (step @p206 :rule bool-double-not-elim :args (@t149)) % 0.20/0.49 (step @p207 :rule bool-double-not-elim :args (@t151)) % 0.20/0.49 (step @p208 :rule refl :args (@t153)) % 0.20/0.49 (step @p209 :rule nary_cong :premises (@p208 @p207 @p206) :args ((or @t153 (not @t152) (not @t150)))) % 0.20/0.49 (step @p210 :rule cnf_and_neg :args (@t153)) % 0.20/0.49 (step @p211 :rule eq_resolve :premises (@p210 @p209)) % 0.20/0.49 (step @p212 :rule reordering :premises (@p211) :args ((or @t151 @t149 @t153))) % 0.20/0.49 (step @p213 :rule chain_m_resolution :premises (@p212 @p205 @p190) :args (@t149 (@list true true) (@list @t151 @t153))) % 0.20/0.49 (assume-push @p235 @t149) % 0.20/0.49 (step @p215 :rule instantiate :premises (@p235) :args (@t160)) % 0.20/0.49 (step-pop @p236 :rule scope :premises (@p215)) % 0.20/0.49 (step @p216 :rule process_scope :premises (@p236) :args (@t162)) % 0.20/0.49 (step @p218 :rule implies_elim :premises (@p216)) % 0.20/0.49 (step @p219 :rule chain_m_resolution :premises (@p218 @p213) :args (@t162 (@list false) (@list @t149))) % 0.20/0.49 (step @p220 :rule bool-double-not-elim :args (@t147)) % 0.20/0.49 (step @p221 :rule nary_cong :premises (@p183 @p220) :args ((or @t154 (not @t148)))) % 0.20/0.49 (step @p222 :rule cnf_or_neg :args (@t154 1)) % 0.20/0.49 (step @p223 :rule eq_resolve :premises (@p222 @p221)) % 0.20/0.49 (step @p224 :rule reordering :premises (@p223) :args ((or @t147 @t154))) % 0.20/0.49 (step @p225 :rule chain_m_resolution :premises (@p224 @p181) :args (@t147 @t155 @t156)) % 0.20/0.49 (step @p226 :rule instantiate :premises (@p225) :args (@t160)) % 0.20/0.49 (step @p227 :rule cnf_or_pos :args (@t164)) % 0.20/0.49 (step @p228 :rule reordering :premises (@p227) :args ((or @t145 @t163 (not @t164)))) % 0.20/0.49 (step @p229 :rule chain_m_resolution :premises (@p228 @p188 @p226) :args (@t163 @t159 (@list @t142 @t164))) % 0.20/0.49 (step @p230 :rule cnf_or_pos :args (@t162)) % 0.20/0.49 (step @p231 :rule reordering :premises (@p230) :args ((or @t145 @t161 (not @t162)))) % 0.20/0.49 (step @p232 false :rule chain_m_resolution :premises (@p231 @p229 @p219 @p188) :args (false (@list true false false) (@list @t161 @t162 @t142))) % 0.20/0.49 ) % 0.20/0.49 % SZS output end Proof % 0.20/0.49 % cvc5 exiting %------------------------------------------------------------------------------