%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL613^1 : 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 11:23:10 AM UTC 2026 % Result : Theorem 0.20s 0.53s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL613^1 : 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 % 0.10/0.37 % Computer : n009.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Sat Sep 5 06:37:06 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.45 %----Proving TH0 % 0.20/0.53 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.20/0.53 % SZS status Theorem % 0.20/0.53 % SZS output start Proof % 0.20/0.53 ( % 0.20/0.53 (declare-sort $$unsorted 0) % 0.20/0.53 (declare-sort tptp.individuals 0) % 0.20/0.53 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.20/0.53 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.20/0.53 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.20/0.53 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.20/0.53 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.20/0.53 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.20/0.53 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.20/0.53 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.20/0.53 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.20/0.53 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.20/0.53 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.20/0.53 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.20/0.53 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.20/0.53 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.20/0.53 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.20/0.53 (define @t1 () (@var "X" (-> $$unsorted Bool))) % 0.20/0.53 (define @t2 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.20/0.53 (define @t3 () (_ tptp.mbox @t2)) % 0.20/0.53 (define @t4 () (@var "Y" (-> $$unsorted Bool))) % 0.20/0.53 (define @t5 () (@list @t2 @t1 @t4)) % 0.20/0.53 (define @t6 () (forall @t5 (_ tptp.mvalid (_ (_ tptp.mimpl (_ @t3 (_ (_ tptp.mand @t1) @t4))) (_ @t3 @t1))))) % 0.20/0.53 (define @t7 () (not @t6)) % 0.20/0.53 (define @t8 () (@var "X" $$unsorted)) % 0.20/0.53 (define @t9 () (@list @t8)) % 0.20/0.53 (define @t10 () (lambda @t9 false)) % 0.20/0.53 (define @t11 () (lambda @t9 true)) % 0.20/0.53 (define @t12 () (@var "U" $$unsorted)) % 0.20/0.53 (define @t13 () (_ @t1 @t12)) % 0.20/0.53 (define @t14 () (lambda (@list @t1 @t12) (not @t13))) % 0.20/0.53 (define @t15 () (_ @t4 @t12)) % 0.20/0.53 (define @t16 () (@list @t1 @t4 @t12)) % 0.20/0.53 (define @t17 () (lambda @t16 (or @t13 @t15))) % 0.20/0.53 (define @t18 () (and @t13 @t15)) % 0.20/0.53 (define @t19 () (lambda @t16 @t18)) % 0.20/0.53 (define @t20 () (@var "__flatten_var_0" $$unsorted)) % 0.20/0.53 (define @t21 () (@var "V" (-> $$unsorted Bool))) % 0.20/0.53 (define @t22 () (@var "U" (-> $$unsorted Bool))) % 0.20/0.53 (define @t23 () (@list @t22 @t21 @t20)) % 0.20/0.53 (define @t24 () (lambda @t23 (_ (_ (_ tptp.mor (_ tptp.mnot @t22)) @t21) @t20))) % 0.20/0.53 (define @t25 () (lambda @t23 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t22) @t21)) (_ (_ tptp.mimpl @t21) @t22)) @t20))) % 0.20/0.53 (define @t26 () (@var "Y" $$unsorted)) % 0.20/0.53 (define @t27 () (@var "P" (-> $$unsorted Bool))) % 0.20/0.53 (define @t28 () (_ @t27 @t26)) % 0.20/0.53 (define @t29 () (_ (_ @t2 @t8) @t26)) % 0.20/0.53 (define @t30 () (@list @t26)) % 0.20/0.53 (define @t31 () (forall @t30 (=> @t29 @t28))) % 0.20/0.53 (define @t32 () (@list @t2 @t27 @t8)) % 0.20/0.53 (define @t33 () (lambda @t32 @t31)) % 0.20/0.53 (define @t34 () (lambda @t32 (exists @t30 (and @t29 @t28)))) % 0.20/0.53 (define @t35 () (@var "W" $$unsorted)) % 0.20/0.53 (define @t36 () (@var "X" tptp.individuals)) % 0.20/0.53 (define @t37 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.20/0.53 (define @t38 () (_ (_ @t37 @t36) @t35)) % 0.20/0.53 (define @t39 () (@list @t36)) % 0.20/0.53 (define @t40 () (@list @t37 @t35)) % 0.20/0.53 (define @t41 () (lambda @t40 (forall @t39 @t38))) % 0.20/0.53 (define @t42 () (lambda @t40 (exists @t39 @t38))) % 0.20/0.53 (define @t43 () (_ @t27 @t35)) % 0.20/0.53 (define @t44 () (@list @t35)) % 0.20/0.53 (define @t45 () (forall @t44 @t43)) % 0.20/0.53 (define @t46 () (@list @t27)) % 0.20/0.53 (define @t47 () (lambda @t46 @t45)) % 0.20/0.53 (define @t48 () (lambda @t46 (exists @t44 @t43))) % 0.20/0.53 (define @t49 () (not @t43)) % 0.20/0.53 (define @t50 () (lambda @t46 (exists @t44 @t49))) % 0.20/0.53 (define @t51 () (lambda @t46 (forall @t44 @t49))) % 0.20/0.53 (define @t52 () (@var "BOUND_VARIABLE_7828" $$unsorted)) % 0.20/0.53 (define @t53 () (_ @t1 @t52)) % 0.20/0.53 (define @t54 () (not (_ @t2 @t35 @t52))) % 0.20/0.53 (define @t55 () (_ @t4 @t26)) % 0.20/0.53 (define @t56 () (_ @t1 @t26)) % 0.20/0.53 (define @t57 () (and @t56 @t55)) % 0.20/0.53 (define @t58 () (not (_ @t2 @t35 @t26))) % 0.20/0.53 (define @t59 () (not (forall @t30 (or @t58 @t57)))) % 0.20/0.53 (define @t60 () (or @t59 @t54 @t53)) % 0.20/0.53 (define @t61 () (forall (@list @t2 @t1 @t4 @t35 @t52) @t60)) % 0.20/0.53 (define @t62 () (@list @t35 @t52)) % 0.20/0.53 (define @t63 () (or @t54 @t53)) % 0.20/0.53 (define @t64 () (or @t59 @t63)) % 0.20/0.53 (define @t65 () (forall @t62 @t64)) % 0.20/0.53 (define @t66 () (@list @t52)) % 0.20/0.53 (define @t67 () (forall @t66 @t64)) % 0.20/0.53 (define @t68 () (forall @t66 @t63)) % 0.20/0.53 (define @t69 () (or @t59 @t68)) % 0.20/0.53 (define @t70 () (or @t59 (forall @t30 (or @t58 @t56)))) % 0.20/0.53 (define @t71 () (not (_ @t2 @t20 @t26))) % 0.20/0.53 (define @t72 () (forall @t30 (or @t71 @t56))) % 0.20/0.53 (define @t73 () (forall @t30 (or @t71 @t57))) % 0.20/0.53 (define @t74 () (not @t73)) % 0.20/0.53 (define @t75 () (@list @t20)) % 0.20/0.53 (define @t76 () (lambda @t75 (or @t74 @t72))) % 0.20/0.53 (define @t77 () (_ @t76 @t35)) % 0.20/0.53 (define @t78 () (forall @t44 @t77)) % 0.20/0.53 (define @t79 () (_ @t27 @t35)) % 0.20/0.53 (define @t80 () (lambda @t46 (forall @t44 @t79))) % 0.20/0.53 (define @t81 () (_ @t2 @t8 @t26)) % 0.20/0.53 (define @t82 () (not @t81)) % 0.20/0.53 (define @t83 () (lambda @t9 (forall @t30 (or @t82 @t56)))) % 0.20/0.53 (define @t84 () (_ @t83 @t20)) % 0.20/0.53 (define @t85 () (or @t74 @t84)) % 0.20/0.53 (define @t86 () (lambda @t75 @t85)) % 0.20/0.53 (define @t87 () (_ @t21 @t20)) % 0.20/0.53 (define @t88 () (@list @t21 @t20)) % 0.20/0.53 (define @t89 () (_ @t27 @t26)) % 0.20/0.53 (define @t90 () (forall @t30 (or @t82 @t89))) % 0.20/0.53 (define @t91 () (lambda (@list @t27 @t8) @t90)) % 0.20/0.53 (define @t92 () (_ (lambda @t32 @t90) @t2)) % 0.20/0.53 (define @t93 () (lambda @t9 (forall @t30 (or @t82 @t57)))) % 0.20/0.53 (define @t94 () (_ @t93 @t20)) % 0.20/0.53 (define @t95 () (not @t94)) % 0.20/0.53 (define @t96 () (or @t95 @t87)) % 0.20/0.53 (define @t97 () (lambda @t88 @t96)) % 0.20/0.53 (define @t98 () (or (not (_ @t22 @t20)) @t87)) % 0.20/0.53 (define @t99 () (lambda @t23 @t98)) % 0.20/0.53 (define @t100 () (_ @t4 @t26)) % 0.20/0.53 (define @t101 () (_ @t1 @t26)) % 0.20/0.53 (define @t102 () (and @t101 @t100)) % 0.20/0.53 (define @t103 () (or @t82 @t102)) % 0.20/0.53 (define @t104 () (@list @t12)) % 0.20/0.53 (define @t105 () (lambda @t104 @t18)) % 0.20/0.53 (define @t106 () (_ @t105 @t26)) % 0.20/0.53 (define @t107 () (or @t82 @t106)) % 0.20/0.53 (define @t108 () (forall @t30 @t107)) % 0.20/0.53 (define @t109 () (lambda @t9 @t108)) % 0.20/0.53 (define @t110 () (@list @t4 @t12)) % 0.20/0.53 (define @t111 () (lambda @t110 @t18)) % 0.20/0.53 (define @t112 () (_ @t19 @t1)) % 0.20/0.53 (define @t113 () (forall @t5 (_ @t80 (_ (_ @t99 (_ @t92 (_ @t112 @t4))) (_ @t92 @t1))))) % 0.20/0.53 (define @t114 () (not @t29)) % 0.20/0.53 (define @t115 () (or @t114 @t28)) % 0.20/0.53 (define @t116 () (not (_ @t22 @t12))) % 0.20/0.53 (define @t117 () (lambda @t104 (or @t116 (_ @t21 @t12)))) % 0.20/0.53 (define @t118 () (lambda @t104 @t116)) % 0.20/0.53 (define @t119 () (_ @t118 @t12)) % 0.20/0.53 (define @t120 () (or @t119 @t15)) % 0.20/0.53 (define @t121 () (lambda @t110 @t120)) % 0.20/0.53 (define @t122 () (@quantifiers_skolemize @t61 4)) % 0.20/0.53 (define @t123 () (@quantifiers_skolemize @t61 3)) % 0.20/0.53 (define @t124 () (@quantifiers_skolemize @t61 0)) % 0.20/0.53 (define @t125 () (_ @t124 @t123 @t122)) % 0.20/0.53 (define @t126 () (@quantifiers_skolemize @t61 1)) % 0.20/0.53 (define @t127 () (_ @t126 @t122)) % 0.20/0.53 (define @t128 () (not @t125)) % 0.20/0.53 (define @t129 () (@quantifiers_skolemize @t61 2)) % 0.20/0.53 (define @t130 () (forall @t30 (or (not (_ @t124 @t123 @t26)) (and (_ @t126 @t26) (_ @t129 @t26))))) % 0.20/0.53 (define @t131 () (not @t130)) % 0.20/0.53 (define @t132 () (or @t131 @t128 @t127)) % 0.20/0.53 (define @t133 () (@list true)) % 0.20/0.53 (define @t134 () (@list @t132)) % 0.20/0.53 (define @t135 () (and @t127 (_ @t129 @t122))) % 0.20/0.53 (define @t136 () (not @t135)) % 0.20/0.53 (define @t137 () (or @t128 @t135)) % 0.20/0.53 (assume @p1 @t7) % 0.20/0.53 (assume @p2 true) % 0.20/0.53 (step @p3 (= tptp.mfalse @t10) :rule refl :args (@t10)) % 0.20/0.53 (step @p4 (= tptp.mtrue @t11) :rule refl :args (@t11)) % 0.20/0.53 (step @p5 (= tptp.mnot @t14) :rule refl :args (@t14)) % 0.20/0.53 (step @p6 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.20/0.53 (step @p7 (= tptp.mand @t19) :rule refl :args (@t19)) % 0.20/0.53 (step @p8 (= tptp.mimpl @t24) :rule refl :args (@t24)) % 0.20/0.53 (step @p9 (= tptp.miff @t25) :rule refl :args (@t25)) % 0.20/0.53 (step @p10 (= tptp.mbox @t33) :rule refl :args (@t33)) % 0.20/0.53 (step @p11 (= tptp.mdia @t34) :rule refl :args (@t34)) % 0.20/0.53 (step @p12 (= tptp.mall @t41) :rule refl :args (@t41)) % 0.20/0.53 (step @p13 (= tptp.mexists @t42) :rule refl :args (@t42)) % 0.20/0.53 (step @p14 (= tptp.mvalid @t47) :rule refl :args (@t47)) % 0.20/0.53 (step @p15 (= tptp.msatisfiable @t48) :rule refl :args (@t48)) % 0.20/0.53 (step @p16 (= tptp.mcountersatisfiable @t50) :rule refl :args (@t50)) % 0.20/0.53 (step @p17 (= tptp.minvalid @t51) :rule refl :args (@t51)) % 0.20/0.53 (step @p18 :rule quant-merge-prenex :args ((= (forall @t5 (forall @t62 @t60)) @t61))) % 0.20/0.53 (step @p19 :rule aci_norm :args ((= @t64 @t60))) % 0.20/0.53 (step @p20 :rule cong :premises (@p19) :args (@t65)) % 0.20/0.53 (step @p21 :rule quant-merge-prenex :args ((= (forall @t44 @t67) @t65))) % 0.20/0.53 (step @p22 :rule alpha_equiv :args (@t68 (@list @t52) (@list @t26))) % 0.20/0.53 (step @p23 :rule refl :args (@t59)) % 0.20/0.53 (step @p24 :rule nary_cong :premises (@p23 @p22) :args (@t69)) % 0.20/0.53 (step @p25 :rule quant-miniscope-or :args ((= @t67 @t69))) % 0.20/0.53 (step @p26 :rule trans :premises (@p25 @p24)) % 0.20/0.53 (step @p27 :rule symm :premises (@p26)) % 0.20/0.53 (step @p28 :rule cong :premises (@p27) :args ((forall @t44 @t70))) % 0.20/0.53 (step @p29 :rule trans :premises (@p28 @p21)) % 0.20/0.53 (step @p30 :rule trans :premises (@p29 @p20)) % 0.20/0.53 (step @p31 :rule beta-reduce :args ((= @t77 @t70))) % 0.20/0.53 (step @p32 :rule cong :premises (@p31) :args (@t78)) % 0.20/0.53 (step @p33 :rule trans :premises (@p32 @p30)) % 0.20/0.53 (step @p34 :rule beta-reduce :args ((= (_ @t80 @t76) @t78))) % 0.20/0.53 (step @p35 :rule trans :premises (@p34 @p33)) % 0.20/0.53 (step @p36 :rule beta-reduce :args ((= @t84 @t72))) % 0.20/0.53 (step @p37 :rule refl :args (@t74)) % 0.20/0.53 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t85)) % 0.20/0.53 (step @p39 :rule cong :premises (@p38) :args (@t86)) % 0.20/0.53 (step @p40 :rule beta-reduce :args ((= (_ (lambda @t88 (or @t74 @t87)) @t83) @t86))) % 0.20/0.53 (step @p41 :rule trans :premises (@p40 @p39)) % 0.20/0.53 (step @p42 :rule beta-reduce :args ((= (_ @t91 @t1) @t83))) % 0.20/0.53 (step @p43 :rule refl :args (@t1)) % 0.20/0.53 (step @p44 :rule beta-reduce :args ((= @t92 @t91))) % 0.20/0.53 (step @p45 :rule ho_cong :premises (@p44 @p43)) % 0.20/0.53 (step @p46 :rule trans :premises (@p45 @p42)) % 0.20/0.53 (step @p47 :rule refl :args (@t87)) % 0.20/0.53 (step @p48 :rule beta-reduce :args ((= @t94 @t73))) % 0.20/0.53 (step @p49 :rule cong :premises (@p48) :args (@t95)) % 0.20/0.53 (step @p50 :rule nary_cong :premises (@p49 @p47) :args (@t96)) % 0.20/0.53 (step @p51 :rule cong :premises (@p50) :args (@t97)) % 0.20/0.53 (step @p52 :rule beta-reduce :args ((= (_ @t99 @t93) @t97))) % 0.20/0.53 (step @p53 :rule trans :premises (@p52 @p51)) % 0.20/0.53 (step @p54 :rule refl :args (@t55)) % 0.20/0.53 (step @p55 :rule refl :args (@t100)) % 0.20/0.53 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t100 @t55))) % 0.20/0.53 (step @p57 :rule symm :premises (@p56)) % 0.20/0.53 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.20/0.53 (step @p59 :rule refl :args (@t56)) % 0.20/0.53 (step @p60 :rule refl :args (@t101)) % 0.20/0.53 (step @p61 :rule cong :premises (@p60 @p59) :args ((= @t101 @t56))) % 0.20/0.53 (step @p62 :rule symm :premises (@p61)) % 0.20/0.53 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 0.20/0.53 (step @p64 :rule nary_cong :premises (@p63 @p58) :args (@t102)) % 0.20/0.53 (step @p65 :rule refl :args (@t82)) % 0.20/0.53 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t103)) % 0.20/0.53 (step @p67 :rule cong :premises (@p66) :args ((forall @t30 @t103))) % 0.20/0.53 (step @p68 :rule beta-reduce :args ((= @t106 @t102))) % 0.20/0.53 (step @p69 :rule refl :args (@t82)) % 0.20/0.53 (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t107)) % 0.20/0.53 (step @p71 :rule cong :premises (@p70) :args (@t108)) % 0.20/0.53 (step @p72 :rule trans :premises (@p71 @p67)) % 0.20/0.53 (step @p73 :rule cong :premises (@p72) :args (@t109)) % 0.20/0.53 (step @p74 :rule beta-reduce :args ((= (_ @t91 @t105) @t109))) % 0.20/0.53 (step @p75 :rule trans :premises (@p74 @p73)) % 0.20/0.53 (step @p76 :rule beta-reduce :args ((= (_ @t111 @t4) @t105))) % 0.20/0.53 (step @p77 :rule refl :args (@t4)) % 0.20/0.53 (step @p78 :rule beta-reduce :args ((= @t112 @t111))) % 0.20/0.53 (step @p79 :rule ho_cong :premises (@p78 @p77)) % 0.20/0.53 (step @p80 :rule trans :premises (@p79 @p76)) % 0.20/0.53 (step @p81 :rule ho_cong :premises (@p44 @p80)) % 0.20/0.53 (step @p82 :rule trans :premises (@p81 @p75)) % 0.20/0.53 (step @p83 :rule refl :args (@t99)) % 0.20/0.53 (step @p84 :rule ho_cong :premises (@p83 @p82)) % 0.20/0.53 (step @p85 :rule trans :premises (@p84 @p53)) % 0.20/0.53 (step @p86 :rule ho_cong :premises (@p85 @p46)) % 0.20/0.53 (step @p87 :rule trans :premises (@p86 @p41)) % 0.20/0.53 (step @p88 :rule refl :args (@t80)) % 0.20/0.53 (step @p89 :rule ho_cong :premises (@p88 @p87)) % 0.20/0.53 (step @p90 :rule trans :premises (@p89 @p35)) % 0.20/0.53 (step @p91 :rule cong :premises (@p90) :args (@t113)) % 0.20/0.53 (step @p92 :rule trans :premises (@p91 @p18)) % 0.20/0.53 (step @p93 :rule cong :premises (@p92) :args ((not @t113))) % 0.20/0.53 (step @p94 :rule refl :args (@t2)) % 0.20/0.53 (step @p95 :rule refl :args (@t89)) % 0.20/0.53 (step @p96 :rule refl :args (@t28)) % 0.20/0.53 (step @p97 :rule cong :premises (@p96 @p95) :args ((= @t28 @t89))) % 0.20/0.53 (step @p98 :rule symm :premises (@p97)) % 0.20/0.53 (step @p99 :rule eq_resolve :premises (@p96 @p98)) % 0.20/0.53 (step @p100 :rule refl :args (@t81)) % 0.20/0.53 (step @p101 :rule refl :args (@t29)) % 0.20/0.53 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t29 @t81))) % 0.20/0.53 (step @p103 :rule symm :premises (@p102)) % 0.20/0.53 (step @p104 :rule eq_resolve :premises (@p101 @p103)) % 0.20/0.53 (step @p105 :rule cong :premises (@p104) :args (@t114)) % 0.20/0.53 (step @p106 :rule nary_cong :premises (@p105 @p99) :args (@t115)) % 0.20/0.53 (step @p107 :rule cong :premises (@p106) :args ((forall @t30 @t115))) % 0.20/0.53 (step @p108 :rule bool-impl-elim :args (@t29 @t28)) % 0.20/0.53 (step @p109 :rule cong :premises (@p108) :args (@t31)) % 0.20/0.53 (step @p110 :rule trans :premises (@p109 @p107)) % 0.20/0.53 (step @p111 :rule cong :premises (@p110) :args (@t33)) % 0.20/0.53 (step @p112 :rule trans :premises (@p10 @p111)) % 0.20/0.53 (step @p113 :rule ho_cong :premises (@p112 @p94)) % 0.20/0.53 (step @p114 :rule ho_cong :premises (@p113 @p43)) % 0.20/0.53 (step @p115 :rule ho_cong :premises (@p7 @p43)) % 0.20/0.53 (step @p116 :rule ho_cong :premises (@p115 @p77)) % 0.20/0.53 (step @p117 :rule ho_cong :premises (@p113 @p116)) % 0.20/0.53 (step @p118 :rule beta-reduce :args ((= (_ @t117 @t20) @t98))) % 0.20/0.53 (step @p119 :rule refl :args (@t20)) % 0.20/0.53 (step @p120 :rule beta-reduce :args ((= (_ (lambda @t110 (or @t116 @t15)) @t21) @t117))) % 0.20/0.53 (step @p121 :rule refl :args (@t21)) % 0.20/0.53 (step @p122 :rule refl :args (@t15)) % 0.20/0.53 (step @p123 :rule beta-reduce :args ((= @t119 @t116))) % 0.20/0.53 (step @p124 :rule nary_cong :premises (@p123 @p122) :args (@t120)) % 0.20/0.53 (step @p125 :rule cong :premises (@p124) :args (@t121)) % 0.20/0.53 (step @p126 :rule beta-reduce :args ((= (_ @t17 @t118) @t121))) % 0.20/0.53 (step @p127 :rule trans :premises (@p126 @p125)) % 0.20/0.53 (step @p128 :rule beta-reduce :args ((= (_ @t14 @t22) @t118))) % 0.20/0.53 (step @p129 :rule refl :args (@t17)) % 0.20/0.53 (step @p130 :rule ho_cong :premises (@p129 @p128)) % 0.20/0.53 (step @p131 :rule trans :premises (@p130 @p127)) % 0.20/0.53 (step @p132 :rule ho_cong :premises (@p131 @p121)) % 0.20/0.53 (step @p133 :rule trans :premises (@p132 @p120)) % 0.20/0.53 (step @p134 :rule ho_cong :premises (@p133 @p119)) % 0.20/0.53 (step @p135 :rule trans :premises (@p134 @p118)) % 0.20/0.53 (step @p136 :rule refl :args (@t22)) % 0.20/0.53 (step @p137 :rule ho_cong :premises (@p5 @p136)) % 0.20/0.53 (step @p138 :rule ho_cong :premises (@p6 @p137)) % 0.20/0.53 (step @p139 :rule ho_cong :premises (@p138 @p121)) % 0.20/0.53 (step @p140 :rule ho_cong :premises (@p139 @p119)) % 0.20/0.53 (step @p141 :rule trans :premises (@p140 @p135)) % 0.20/0.53 (step @p142 :rule cong :premises (@p141) :args (@t24)) % 0.20/0.53 (step @p143 :rule trans :premises (@p8 @p142)) % 0.20/0.53 (step @p144 :rule ho_cong :premises (@p143 @p117)) % 0.20/0.53 (step @p145 :rule ho_cong :premises (@p144 @p114)) % 0.20/0.53 (step @p146 :rule refl :args (@t79)) % 0.20/0.53 (step @p147 :rule refl :args (@t43)) % 0.20/0.53 (step @p148 :rule cong :premises (@p147 @p146) :args ((= @t43 @t79))) % 0.20/0.53 (step @p149 :rule symm :premises (@p148)) % 0.20/0.53 (step @p150 :rule eq_resolve :premises (@p147 @p149)) % 0.20/0.53 (step @p151 :rule cong :premises (@p150) :args (@t45)) % 0.20/0.53 (step @p152 :rule cong :premises (@p151) :args (@t47)) % 0.20/0.53 (step @p153 :rule trans :premises (@p14 @p152)) % 0.20/0.53 (step @p154 :rule ho_cong :premises (@p153 @p145)) % 0.20/0.53 (step @p155 :rule cong :premises (@p154) :args (@t6)) % 0.20/0.53 (step @p156 :rule cong :premises (@p155) :args (@t7)) % 0.20/0.53 (step @p157 :rule trans :premises (@p156 @p93)) % 0.20/0.53 (step @p158 :rule eq_resolve :premises (@p1 @p157)) % 0.20/0.53 (step @p159 :rule skolemize :premises (@p158)) % 0.20/0.53 (step @p160 :rule bool-double-not-elim :args (@t125)) % 0.20/0.53 (step @p161 :rule refl :args (@t132)) % 0.20/0.53 (step @p162 :rule nary_cong :premises (@p161 @p160) :args ((or @t132 (not @t128)))) % 0.20/0.53 (step @p163 :rule cnf_or_neg :args (@t132 1)) % 0.20/0.53 (step @p164 :rule eq_resolve :premises (@p163 @p162)) % 0.20/0.53 (step @p165 :rule reordering :premises (@p164) :args ((or @t125 @t132))) % 0.20/0.53 (step @p166 :rule chain_m_resolution :premises (@p165 @p159) :args (@t125 @t133 @t134)) % 0.20/0.53 (step @p167 :rule cnf_or_neg :args (@t132 2)) % 0.20/0.53 (step @p168 :rule chain_m_resolution :premises (@p167 @p159) :args ((not @t127) @t133 @t134)) % 0.20/0.53 (step @p169 :rule cnf_and_pos :args (@t135 0)) % 0.20/0.53 (step @p170 :rule reordering :premises (@p169) :args ((or @t127 @t136))) % 0.20/0.53 (step @p171 :rule chain_m_resolution :premises (@p170 @p168) :args (@t136 @t133 (@list @t127))) % 0.20/0.53 (step @p172 :rule bool-double-not-elim :args (@t130)) % 0.20/0.53 (step @p173 :rule nary_cong :premises (@p161 @p172) :args ((or @t132 (not @t131)))) % 0.20/0.53 (step @p174 :rule cnf_or_neg :args (@t132 0)) % 0.20/0.53 (step @p175 :rule eq_resolve :premises (@p174 @p173)) % 0.20/0.53 (step @p176 :rule reordering :premises (@p175) :args ((or @t130 @t132))) % 0.20/0.53 (step @p177 :rule chain_m_resolution :premises (@p176 @p159) :args (@t130 @t133 @t134)) % 0.20/0.53 (step @p178 :rule instantiate :premises (@p177) :args ((@list @t122))) % 0.20/0.53 (step @p179 :rule cnf_or_pos :args (@t137)) % 0.20/0.53 (step @p180 :rule reordering :premises (@p179) :args ((or @t128 @t135 (not @t137)))) % 0.20/0.53 (step @p181 false :rule chain_m_resolution :premises (@p180 @p178 @p171 @p166) :args (false (@list false true false) (@list @t137 @t135 @t125))) % 0.20/0.53 ) % 0.20/0.53 % SZS output end Proof % 0.20/0.53 % cvc5 exiting %------------------------------------------------------------------------------