%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL587^1 : TPTP v9.3.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n002.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 0.21s 0.51s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL587^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.10/0.36 % Computer : n002.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 15:40:20 UTC 2026 % 0.10/0.36 % CPUTime : % 0.10/0.44 %----Proving TH0 % 0.21/0.51 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.21/0.51 % SZS status Theorem % 0.21/0.51 % SZS output start Proof % 0.21/0.51 ( % 0.21/0.51 (declare-sort $$unsorted 0) % 0.21/0.51 (declare-sort tptp.individuals 0) % 0.21/0.51 (declare-const tptp.r (-> $$unsorted $$unsorted Bool)) % 0.21/0.51 (declare-const tptp.a (-> $$unsorted Bool)) % 0.21/0.51 (declare-const tptp.b (-> $$unsorted Bool)) % 0.21/0.51 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.21/0.51 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.21/0.51 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.21/0.51 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.21/0.51 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.21/0.51 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.21/0.51 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.21/0.51 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.21/0.51 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.21/0.51 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.21/0.51 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.21/0.51 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.21/0.51 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.21/0.51 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.21/0.51 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.21/0.51 (define @t1 () (_ tptp.mbox tptp.r)) % 0.21/0.51 (define @t2 () (not (_ tptp.mvalid (_ (_ tptp.mimpl (_ @t1 tptp.b)) (_ @t1 (_ (_ tptp.mimpl tptp.a) tptp.b)))))) % 0.21/0.51 (define @t3 () (@var "X" $$unsorted)) % 0.21/0.51 (define @t4 () (@list @t3)) % 0.21/0.51 (define @t5 () (lambda @t4 false)) % 0.21/0.51 (define @t6 () (lambda @t4 true)) % 0.21/0.51 (define @t7 () (@var "U" $$unsorted)) % 0.21/0.51 (define @t8 () (@var "X" (-> $$unsorted Bool))) % 0.21/0.51 (define @t9 () (_ @t8 @t7)) % 0.21/0.51 (define @t10 () (lambda (@list @t8 @t7) (not @t9))) % 0.21/0.51 (define @t11 () (@var "Y" (-> $$unsorted Bool))) % 0.21/0.51 (define @t12 () (_ @t11 @t7)) % 0.21/0.51 (define @t13 () (@list @t8 @t11 @t7)) % 0.21/0.51 (define @t14 () (lambda @t13 (or @t9 @t12))) % 0.21/0.51 (define @t15 () (lambda @t13 (and @t9 @t12))) % 0.21/0.51 (define @t16 () (@var "__flatten_var_0" $$unsorted)) % 0.21/0.51 (define @t17 () (@var "V" (-> $$unsorted Bool))) % 0.21/0.51 (define @t18 () (@var "U" (-> $$unsorted Bool))) % 0.21/0.51 (define @t19 () (@list @t18 @t17 @t16)) % 0.21/0.51 (define @t20 () (lambda @t19 (_ (_ (_ tptp.mor (_ tptp.mnot @t18)) @t17) @t16))) % 0.21/0.51 (define @t21 () (lambda @t19 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t18) @t17)) (_ (_ tptp.mimpl @t17) @t18)) @t16))) % 0.21/0.51 (define @t22 () (@var "Y" $$unsorted)) % 0.21/0.51 (define @t23 () (@var "P" (-> $$unsorted Bool))) % 0.21/0.51 (define @t24 () (_ @t23 @t22)) % 0.21/0.51 (define @t25 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.21/0.51 (define @t26 () (_ (_ @t25 @t3) @t22)) % 0.21/0.51 (define @t27 () (@list @t22)) % 0.21/0.51 (define @t28 () (forall @t27 (=> @t26 @t24))) % 0.21/0.51 (define @t29 () (@list @t25 @t23 @t3)) % 0.21/0.51 (define @t30 () (lambda @t29 @t28)) % 0.21/0.51 (define @t31 () (lambda @t29 (exists @t27 (and @t26 @t24)))) % 0.21/0.51 (define @t32 () (@var "W" $$unsorted)) % 0.21/0.51 (define @t33 () (@var "X" tptp.individuals)) % 0.21/0.51 (define @t34 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.21/0.51 (define @t35 () (_ (_ @t34 @t33) @t32)) % 0.21/0.51 (define @t36 () (@list @t33)) % 0.21/0.51 (define @t37 () (@list @t34 @t32)) % 0.21/0.51 (define @t38 () (lambda @t37 (forall @t36 @t35))) % 0.21/0.51 (define @t39 () (lambda @t37 (exists @t36 @t35))) % 0.21/0.51 (define @t40 () (_ @t23 @t32)) % 0.21/0.51 (define @t41 () (@list @t32)) % 0.21/0.51 (define @t42 () (forall @t41 @t40)) % 0.21/0.51 (define @t43 () (@list @t23)) % 0.21/0.51 (define @t44 () (lambda @t43 @t42)) % 0.21/0.51 (define @t45 () (lambda @t43 (exists @t41 @t40))) % 0.21/0.51 (define @t46 () (not @t40)) % 0.21/0.51 (define @t47 () (lambda @t43 (exists @t41 @t46))) % 0.21/0.51 (define @t48 () (lambda @t43 (forall @t41 @t46))) % 0.21/0.51 (define @t49 () (@var "BOUND_VARIABLE_7843" $$unsorted)) % 0.21/0.51 (define @t50 () (tptp.b @t49)) % 0.21/0.51 (define @t51 () (not (tptp.a @t49))) % 0.21/0.51 (define @t52 () (not (tptp.r @t32 @t49))) % 0.21/0.51 (define @t53 () (tptp.b @t22)) % 0.21/0.51 (define @t54 () (not (tptp.r @t32 @t22))) % 0.21/0.51 (define @t55 () (not (forall @t27 (or @t54 @t53)))) % 0.21/0.51 (define @t56 () (or @t55 @t52 @t51 @t50)) % 0.21/0.51 (define @t57 () (or @t52 @t51 @t50)) % 0.21/0.51 (define @t58 () (or @t55 @t57)) % 0.21/0.51 (define @t59 () (@list @t32 @t49)) % 0.21/0.51 (define @t60 () (forall @t59 @t58)) % 0.21/0.51 (define @t61 () (@list @t49)) % 0.21/0.51 (define @t62 () (forall @t61 @t58)) % 0.21/0.51 (define @t63 () (forall @t61 @t57)) % 0.21/0.51 (define @t64 () (or @t55 @t63)) % 0.21/0.51 (define @t65 () (tptp.a @t22)) % 0.21/0.51 (define @t66 () (not @t65)) % 0.21/0.51 (define @t67 () (or @t55 (forall @t27 (or @t54 @t66 @t53)))) % 0.21/0.51 (define @t68 () (not (tptp.r @t16 @t22))) % 0.21/0.51 (define @t69 () (forall @t27 (or @t68 @t66 @t53))) % 0.21/0.51 (define @t70 () (forall @t27 (or @t68 @t53))) % 0.21/0.51 (define @t71 () (not @t70)) % 0.21/0.51 (define @t72 () (@list @t16)) % 0.21/0.51 (define @t73 () (lambda @t72 (or @t71 @t69))) % 0.21/0.51 (define @t74 () (_ @t73 @t32)) % 0.21/0.51 (define @t75 () (forall @t41 @t74)) % 0.21/0.51 (define @t76 () (_ @t23 @t32)) % 0.21/0.51 (define @t77 () (lambda @t43 (forall @t41 @t76))) % 0.21/0.51 (define @t78 () (not (tptp.r @t3 @t22))) % 0.21/0.51 (define @t79 () (lambda @t4 (forall @t27 (or @t78 @t66 @t53)))) % 0.21/0.51 (define @t80 () (_ @t79 @t16)) % 0.21/0.51 (define @t81 () (or @t71 @t80)) % 0.21/0.51 (define @t82 () (lambda @t72 @t81)) % 0.21/0.51 (define @t83 () (_ @t17 @t16)) % 0.21/0.51 (define @t84 () (@list @t17 @t16)) % 0.21/0.51 (define @t85 () (_ tptp.b @t22)) % 0.21/0.51 (define @t86 () (_ tptp.a @t22)) % 0.21/0.51 (define @t87 () (not @t86)) % 0.21/0.51 (define @t88 () (or @t78 @t87 @t85)) % 0.21/0.51 (define @t89 () (or @t87 @t85)) % 0.21/0.51 (define @t90 () (not (_ tptp.a @t16))) % 0.21/0.51 (define @t91 () (lambda @t72 (or @t90 (_ tptp.b @t16)))) % 0.21/0.51 (define @t92 () (_ @t91 @t22)) % 0.21/0.51 (define @t93 () (or @t78 @t92)) % 0.21/0.51 (define @t94 () (forall @t27 @t93)) % 0.21/0.51 (define @t95 () (lambda @t4 @t94)) % 0.21/0.51 (define @t96 () (_ @t23 @t22)) % 0.21/0.51 (define @t97 () (lambda (@list @t23 @t3) (forall @t27 (or @t78 @t96)))) % 0.21/0.51 (define @t98 () (lambda @t84 (or @t90 @t83))) % 0.21/0.51 (define @t99 () (or (not (_ @t18 @t16)) @t83)) % 0.21/0.51 (define @t100 () (lambda @t19 @t99)) % 0.21/0.51 (define @t101 () (_ @t100 tptp.a)) % 0.21/0.51 (define @t102 () (_ @t25 @t3 @t22)) % 0.21/0.51 (define @t103 () (_ (lambda @t29 (forall @t27 (or (not @t102) @t96))) tptp.r)) % 0.21/0.51 (define @t104 () (lambda @t4 (forall @t27 (or @t78 @t53)))) % 0.21/0.51 (define @t105 () (_ @t104 @t16)) % 0.21/0.51 (define @t106 () (not @t105)) % 0.21/0.51 (define @t107 () (or @t106 @t83)) % 0.21/0.51 (define @t108 () (lambda @t84 @t107)) % 0.21/0.51 (define @t109 () (not (_ @t18 @t7))) % 0.21/0.51 (define @t110 () (@list @t7)) % 0.21/0.51 (define @t111 () (lambda @t110 (or @t109 (_ @t17 @t7)))) % 0.21/0.51 (define @t112 () (@list @t11 @t7)) % 0.21/0.51 (define @t113 () (lambda @t110 @t109)) % 0.21/0.51 (define @t114 () (_ @t113 @t7)) % 0.21/0.51 (define @t115 () (or @t114 @t12)) % 0.21/0.51 (define @t116 () (lambda @t112 @t115)) % 0.21/0.51 (define @t117 () (not @t26)) % 0.21/0.51 (define @t118 () (or @t117 @t24)) % 0.21/0.51 (define @t119 () (forall @t59 @t56)) % 0.21/0.51 (define @t120 () (@quantifiers_skolemize @t119 0)) % 0.21/0.51 (define @t121 () (forall @t27 (or (not (tptp.r @t120 @t22)) @t53))) % 0.21/0.51 (define @t122 () (@quantifiers_skolemize @t119 1)) % 0.21/0.51 (define @t123 () (tptp.b @t122)) % 0.21/0.51 (define @t124 () (tptp.r @t120 @t122)) % 0.21/0.51 (define @t125 () (not @t124)) % 0.21/0.51 (define @t126 () (not @t121)) % 0.21/0.51 (define @t127 () (or @t126 @t125 (not (tptp.a @t122)) @t123)) % 0.21/0.51 (define @t128 () (@list true)) % 0.21/0.51 (define @t129 () (@list @t127)) % 0.21/0.51 (define @t130 () (or @t125 @t123)) % 0.21/0.51 (define @t131 () (not @t130)) % 0.21/0.51 (assume @p1 @t2) % 0.21/0.51 (assume @p2 true) % 0.21/0.51 (step @p3 (= tptp.mfalse @t5) :rule refl :args (@t5)) % 0.21/0.51 (step @p4 (= tptp.mtrue @t6) :rule refl :args (@t6)) % 0.21/0.51 (step @p5 (= tptp.mnot @t10) :rule refl :args (@t10)) % 0.21/0.51 (step @p6 (= tptp.mor @t14) :rule refl :args (@t14)) % 0.21/0.51 (step @p7 (= tptp.mand @t15) :rule refl :args (@t15)) % 0.21/0.51 (step @p8 (= tptp.mimpl @t20) :rule refl :args (@t20)) % 0.21/0.51 (step @p9 (= tptp.miff @t21) :rule refl :args (@t21)) % 0.21/0.51 (step @p10 (= tptp.mbox @t30) :rule refl :args (@t30)) % 0.21/0.51 (step @p11 (= tptp.mdia @t31) :rule refl :args (@t31)) % 0.21/0.51 (step @p12 (= tptp.mall @t38) :rule refl :args (@t38)) % 0.21/0.51 (step @p13 (= tptp.mexists @t39) :rule refl :args (@t39)) % 0.21/0.51 (step @p14 (= tptp.mvalid @t44) :rule refl :args (@t44)) % 0.21/0.51 (step @p15 (= tptp.msatisfiable @t45) :rule refl :args (@t45)) % 0.21/0.51 (step @p16 (= tptp.mcountersatisfiable @t47) :rule refl :args (@t47)) % 0.21/0.51 (step @p17 (= tptp.minvalid @t48) :rule refl :args (@t48)) % 0.21/0.51 (step @p18 :rule aci_norm :args ((= @t58 @t56))) % 0.21/0.51 (step @p19 :rule cong :premises (@p18) :args (@t60)) % 0.21/0.51 (step @p20 :rule quant-merge-prenex :args ((= (forall @t41 @t62) @t60))) % 0.21/0.51 (step @p21 :rule alpha_equiv :args (@t63 (@list @t49) (@list @t22))) % 0.21/0.51 (step @p22 :rule refl :args (@t55)) % 0.21/0.52 (step @p23 :rule nary_cong :premises (@p22 @p21) :args (@t64)) % 0.21/0.52 (step @p24 :rule quant-miniscope-or :args ((= @t62 @t64))) % 0.21/0.52 (step @p25 :rule trans :premises (@p24 @p23)) % 0.21/0.52 (step @p26 :rule symm :premises (@p25)) % 0.21/0.52 (step @p27 :rule cong :premises (@p26) :args ((forall @t41 @t67))) % 0.21/0.52 (step @p28 :rule trans :premises (@p27 @p20)) % 0.21/0.52 (step @p29 :rule trans :premises (@p28 @p19)) % 0.21/0.52 (step @p30 :rule beta-reduce :args ((= @t74 @t67))) % 0.21/0.52 (step @p31 :rule cong :premises (@p30) :args (@t75)) % 0.21/0.52 (step @p32 :rule trans :premises (@p31 @p29)) % 0.21/0.52 (step @p33 :rule beta-reduce :args ((= (_ @t77 @t73) @t75))) % 0.21/0.52 (step @p34 :rule trans :premises (@p33 @p32)) % 0.21/0.52 (step @p35 :rule beta-reduce :args ((= @t80 @t69))) % 0.21/0.52 (step @p36 :rule refl :args (@t71)) % 0.21/0.52 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t81)) % 0.21/0.52 (step @p38 :rule cong :premises (@p37) :args (@t82)) % 0.21/0.52 (step @p39 :rule beta-reduce :args ((= (_ (lambda @t84 (or @t71 @t83)) @t79) @t82))) % 0.21/0.52 (step @p40 :rule trans :premises (@p39 @p38)) % 0.21/0.52 (step @p41 :rule refl :args (@t53)) % 0.21/0.52 (step @p42 :rule refl :args (@t85)) % 0.21/0.52 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t85 @t53))) % 0.21/0.52 (step @p44 :rule symm :premises (@p43)) % 0.21/0.52 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.21/0.52 (step @p46 :rule refl :args (@t65)) % 0.21/0.52 (step @p47 :rule refl :args (@t86)) % 0.21/0.52 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t86 @t65))) % 0.21/0.52 (step @p49 :rule symm :premises (@p48)) % 0.21/0.52 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.21/0.52 (step @p51 :rule cong :premises (@p50) :args (@t87)) % 0.21/0.52 (step @p52 :rule refl :args (@t78)) % 0.21/0.52 (step @p53 :rule nary_cong :premises (@p52 @p51 @p45) :args (@t88)) % 0.21/0.52 (step @p54 :rule cong :premises (@p53) :args ((forall @t27 @t88))) % 0.21/0.52 (step @p55 :rule aci_norm :args ((= (or @t78 @t89) @t88))) % 0.21/0.52 (step @p56 :rule beta-reduce :args ((= @t92 @t89))) % 0.21/0.52 (step @p57 :rule refl :args (@t78)) % 0.21/0.52 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t93)) % 0.21/0.52 (step @p59 :rule trans :premises (@p58 @p55)) % 0.21/0.52 (step @p60 :rule cong :premises (@p59) :args (@t94)) % 0.21/0.52 (step @p61 :rule trans :premises (@p60 @p54)) % 0.21/0.52 (step @p62 :rule cong :premises (@p61) :args (@t95)) % 0.21/0.52 (step @p63 :rule beta-reduce :args ((= (_ @t97 @t91) @t95))) % 0.21/0.52 (step @p64 :rule trans :premises (@p63 @p62)) % 0.21/0.52 (step @p65 :rule beta-reduce :args ((= (_ @t98 tptp.b) @t91))) % 0.21/0.52 (step @p66 :rule refl :args (tptp.b)) % 0.21/0.52 (step @p67 :rule beta-reduce :args ((= @t101 @t98))) % 0.21/0.52 (step @p68 :rule ho_cong :premises (@p67 @p66)) % 0.21/0.52 (step @p69 :rule trans :premises (@p68 @p65)) % 0.21/0.52 (step @p70 :rule beta-reduce :args ((= @t103 @t97))) % 0.21/0.52 (step @p71 :rule ho_cong :premises (@p70 @p69)) % 0.21/0.52 (step @p72 :rule trans :premises (@p71 @p64)) % 0.21/0.52 (step @p73 :rule refl :args (@t83)) % 0.21/0.52 (step @p74 :rule beta-reduce :args ((= @t105 @t70))) % 0.21/0.52 (step @p75 :rule cong :premises (@p74) :args (@t106)) % 0.21/0.52 (step @p76 :rule nary_cong :premises (@p75 @p73) :args (@t107)) % 0.21/0.52 (step @p77 :rule cong :premises (@p76) :args (@t108)) % 0.21/0.52 (step @p78 :rule beta-reduce :args ((= (_ @t100 @t104) @t108))) % 0.21/0.52 (step @p79 :rule trans :premises (@p78 @p77)) % 0.21/0.52 (step @p80 :rule beta-reduce :args ((= (_ @t97 tptp.b) @t104))) % 0.21/0.52 (step @p81 :rule ho_cong :premises (@p70 @p66)) % 0.21/0.52 (step @p82 :rule trans :premises (@p81 @p80)) % 0.21/0.52 (step @p83 :rule refl :args (@t100)) % 0.21/0.52 (step @p84 :rule ho_cong :premises (@p83 @p82)) % 0.21/0.52 (step @p85 :rule trans :premises (@p84 @p79)) % 0.21/0.52 (step @p86 :rule ho_cong :premises (@p85 @p72)) % 0.21/0.52 (step @p87 :rule trans :premises (@p86 @p40)) % 0.21/0.52 (step @p88 :rule refl :args (@t77)) % 0.21/0.52 (step @p89 :rule ho_cong :premises (@p88 @p87)) % 0.21/0.52 (step @p90 :rule trans :premises (@p89 @p34)) % 0.21/0.52 (step @p91 :rule cong :premises (@p90) :args ((not (_ @t77 (_ (_ @t100 (_ @t103 tptp.b)) (_ @t103 (_ @t101 tptp.b))))))) % 0.21/0.52 (step @p92 :rule refl :args (tptp.a)) % 0.21/0.52 (step @p93 :rule beta-reduce :args ((= (_ @t111 @t16) @t99))) % 0.21/0.52 (step @p94 :rule refl :args (@t16)) % 0.21/0.52 (step @p95 :rule beta-reduce :args ((= (_ (lambda @t112 (or @t109 @t12)) @t17) @t111))) % 0.21/0.52 (step @p96 :rule refl :args (@t17)) % 0.21/0.52 (step @p97 :rule refl :args (@t12)) % 0.21/0.52 (step @p98 :rule beta-reduce :args ((= @t114 @t109))) % 0.21/0.52 (step @p99 :rule nary_cong :premises (@p98 @p97) :args (@t115)) % 0.21/0.52 (step @p100 :rule cong :premises (@p99) :args (@t116)) % 0.21/0.52 (step @p101 :rule beta-reduce :args ((= (_ @t14 @t113) @t116))) % 0.21/0.52 (step @p102 :rule trans :premises (@p101 @p100)) % 0.21/0.52 (step @p103 :rule beta-reduce :args ((= (_ @t10 @t18) @t113))) % 0.21/0.52 (step @p104 :rule refl :args (@t14)) % 0.21/0.52 (step @p105 :rule ho_cong :premises (@p104 @p103)) % 0.21/0.52 (step @p106 :rule trans :premises (@p105 @p102)) % 0.21/0.52 (step @p107 :rule ho_cong :premises (@p106 @p96)) % 0.21/0.52 (step @p108 :rule trans :premises (@p107 @p95)) % 0.21/0.52 (step @p109 :rule ho_cong :premises (@p108 @p94)) % 0.21/0.52 (step @p110 :rule trans :premises (@p109 @p93)) % 0.21/0.52 (step @p111 :rule refl :args (@t18)) % 0.21/0.52 (step @p112 :rule ho_cong :premises (@p5 @p111)) % 0.21/0.52 (step @p113 :rule ho_cong :premises (@p6 @p112)) % 0.21/0.52 (step @p114 :rule ho_cong :premises (@p113 @p96)) % 0.21/0.52 (step @p115 :rule ho_cong :premises (@p114 @p94)) % 0.21/0.52 (step @p116 :rule trans :premises (@p115 @p110)) % 0.21/0.52 (step @p117 :rule cong :premises (@p116) :args (@t20)) % 0.21/0.52 (step @p118 :rule trans :premises (@p8 @p117)) % 0.21/0.52 (step @p119 :rule ho_cong :premises (@p118 @p92)) % 0.21/0.52 (step @p120 :rule ho_cong :premises (@p119 @p66)) % 0.21/0.52 (step @p121 :rule refl :args (tptp.r)) % 0.21/0.52 (step @p122 :rule refl :args (@t96)) % 0.21/0.52 (step @p123 :rule refl :args (@t24)) % 0.21/0.52 (step @p124 :rule cong :premises (@p123 @p122) :args ((= @t24 @t96))) % 0.21/0.52 (step @p125 :rule symm :premises (@p124)) % 0.21/0.52 (step @p126 :rule eq_resolve :premises (@p123 @p125)) % 0.21/0.52 (step @p127 :rule refl :args (@t102)) % 0.21/0.52 (step @p128 :rule refl :args (@t26)) % 0.21/0.52 (step @p129 :rule cong :premises (@p128 @p127) :args ((= @t26 @t102))) % 0.21/0.52 (step @p130 :rule symm :premises (@p129)) % 0.21/0.52 (step @p131 :rule eq_resolve :premises (@p128 @p130)) % 0.21/0.52 (step @p132 :rule cong :premises (@p131) :args (@t117)) % 0.21/0.52 (step @p133 :rule nary_cong :premises (@p132 @p126) :args (@t118)) % 0.21/0.52 (step @p134 :rule cong :premises (@p133) :args ((forall @t27 @t118))) % 0.21/0.52 (step @p135 :rule bool-impl-elim :args (@t26 @t24)) % 0.21/0.52 (step @p136 :rule cong :premises (@p135) :args (@t28)) % 0.21/0.52 (step @p137 :rule trans :premises (@p136 @p134)) % 0.21/0.52 (step @p138 :rule cong :premises (@p137) :args (@t30)) % 0.21/0.52 (step @p139 :rule trans :premises (@p10 @p138)) % 0.21/0.52 (step @p140 :rule ho_cong :premises (@p139 @p121)) % 0.21/0.52 (step @p141 :rule ho_cong :premises (@p140 @p120)) % 0.21/0.52 (step @p142 :rule ho_cong :premises (@p140 @p66)) % 0.21/0.52 (step @p143 :rule ho_cong :premises (@p118 @p142)) % 0.21/0.52 (step @p144 :rule ho_cong :premises (@p143 @p141)) % 0.21/0.52 (step @p145 :rule refl :args (@t76)) % 0.21/0.52 (step @p146 :rule refl :args (@t40)) % 0.21/0.52 (step @p147 :rule cong :premises (@p146 @p145) :args ((= @t40 @t76))) % 0.21/0.52 (step @p148 :rule symm :premises (@p147)) % 0.21/0.52 (step @p149 :rule eq_resolve :premises (@p146 @p148)) % 0.21/0.52 (step @p150 :rule cong :premises (@p149) :args (@t42)) % 0.21/0.52 (step @p151 :rule cong :premises (@p150) :args (@t44)) % 0.21/0.52 (step @p152 :rule trans :premises (@p14 @p151)) % 0.21/0.52 (step @p153 :rule ho_cong :premises (@p152 @p144)) % 0.21/0.52 (step @p154 :rule cong :premises (@p153) :args (@t2)) % 0.21/0.52 (step @p155 :rule trans :premises (@p154 @p91)) % 0.21/0.52 (step @p156 :rule eq_resolve :premises (@p1 @p155)) % 0.21/0.52 (step @p157 :rule skolemize :premises (@p156)) % 0.21/0.52 (step @p158 :rule bool-double-not-elim :args (@t121)) % 0.21/0.52 (step @p159 :rule refl :args (@t127)) % 0.21/0.52 (step @p160 :rule nary_cong :premises (@p159 @p158) :args ((or @t127 (not @t126)))) % 0.21/0.52 (step @p161 :rule cnf_or_neg :args (@t127 0)) % 0.21/0.52 (step @p162 :rule eq_resolve :premises (@p161 @p160)) % 0.21/0.52 (step @p163 :rule reordering :premises (@p162) :args ((or @t121 @t127))) % 0.21/0.52 (step @p164 :rule chain_m_resolution :premises (@p163 @p157) :args (@t121 @t128 @t129)) % 0.21/0.52 (step @p165 :rule cnf_or_neg :args (@t127 3)) % 0.21/0.52 (step @p166 :rule chain_m_resolution :premises (@p165 @p157) :args ((not @t123) @t128 @t129)) % 0.21/0.52 (step @p167 :rule bool-double-not-elim :args (@t124)) % 0.21/0.52 (step @p168 :rule nary_cong :premises (@p159 @p167) :args ((or @t127 (not @t125)))) % 0.21/0.52 (step @p169 :rule cnf_or_neg :args (@t127 1)) % 0.21/0.52 (step @p170 :rule eq_resolve :premises (@p169 @p168)) % 0.21/0.52 (step @p171 :rule reordering :premises (@p170) :args ((or @t124 @t127))) % 0.21/0.52 (step @p172 :rule chain_m_resolution :premises (@p171 @p157) :args (@t124 @t128 @t129)) % 0.21/0.52 (step @p173 :rule cnf_or_pos :args (@t130)) % 0.21/0.52 (step @p174 :rule reordering :premises (@p173) :args ((or @t125 @t123 @t131))) % 0.21/0.52 (step @p175 :rule chain_m_resolution :premises (@p174 @p172 @p166) :args (@t131 (@list false true) (@list @t124 @t123))) % 0.21/0.52 (assume-push @p182 @t121) % 0.21/0.52 (step @p177 :rule instantiate :premises (@p164) :args ((@list @t122))) % 0.21/0.52 (step-pop @p183 :rule scope :premises (@p177)) % 0.21/0.52 (step @p178 :rule process_scope :premises (@p183) :args (@t130)) % 0.21/0.52 (step @p180 :rule implies_elim :premises (@p178)) % 0.21/0.52 (step @p181 false :rule chain_m_resolution :premises (@p180 @p175 @p164) :args (false (@list true false) (@list @t130 @t121))) % 0.21/0.52 ) % 0.21/0.52 % SZS output end Proof % 0.21/0.52 % cvc5 exiting %------------------------------------------------------------------------------