%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO887^22 : 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 : n029.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 09:13:42 AM UTC 2026 % Result : Theorem 2.02s 2.24s % Output : Proof 2.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO887^22 : 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 % 0.17/0.34 % Computer : n029.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 01:08:47 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 2.02/2.24 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 2.02/2.24 % SZS status Theorem % 2.02/2.24 % SZS output start Proof % 2.02/2.24 ( % 2.02/2.24 (declare-sort $$unsorted 0) % 2.02/2.24 (declare-sort tptp.mworld 0) % 2.02/2.24 (declare-const tptp.mactual tptp.mworld) % 2.02/2.24 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 2.02/2.24 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 2.02/2.24 (declare-const tptp.f (-> $$unsorted tptp.mworld Bool)) % 2.02/2.24 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 2.02/2.24 (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)))))) % 2.02/2.24 (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))))))) % 2.02/2.24 (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))))))) % 2.02/2.24 (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))))))) % 2.02/2.24 (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))))))) % 2.02/2.24 (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)))))))) % 2.02/2.24 (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)))))))) % 2.02/2.24 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 2.02/2.24 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 2.02/2.24 (define @t1 () (@var "W" tptp.mworld)) % 2.02/2.24 (define @t2 () (_ tptp.mrel @t1)) % 2.02/2.24 (define @t3 () (_ @t2 @t1)) % 2.02/2.24 (define @t4 () (@list @t1)) % 2.02/2.24 (define @t5 () (forall @t4 @t3)) % 2.02/2.24 (define @t6 () (@var "U" tptp.mworld)) % 2.02/2.24 (define @t7 () (@var "V" tptp.mworld)) % 2.02/2.24 (define @t8 () (_ tptp.mrel @t7)) % 2.02/2.24 (define @t9 () (_ @t2 @t7)) % 2.02/2.24 (define @t10 () (@var "X" $$unsorted)) % 2.02/2.24 (define @t11 () (_ tptp.eiw_di @t10)) % 2.02/2.24 (define @t12 () (_ @t11 @t1)) % 2.02/2.24 (define @t13 () (@list @t10)) % 2.02/2.24 (define @t14 () (@var "__flatten_var_0" tptp.mworld)) % 2.02/2.24 (define @t15 () (_ tptp.f @t10)) % 2.02/2.24 (define @t16 () (@list @t10 @t14)) % 2.02/2.24 (define @t17 () (lambda @t16 (_ (_ tptp.mdia @t15) @t14))) % 2.02/2.24 (define @t18 () (lambda @t16 (_ @t15 @t14))) % 2.02/2.24 (define @t19 () (not (_ tptp.mlocal (_ (_ tptp.mimplies (_ tptp.mbox (_ tptp.mexists_di @t18))) (_ tptp.mexists_di @t17))))) % 2.02/2.24 (define @t20 () (@var "Phi" (-> tptp.mworld Bool))) % 2.02/2.24 (define @t21 () (lambda (@list @t20) (_ @t20 tptp.mactual))) % 2.02/2.24 (define @t22 () (@var "A" (-> tptp.mworld Bool))) % 2.02/2.24 (define @t23 () (_ @t22 @t1)) % 2.02/2.24 (define @t24 () (lambda (@list @t22 @t1) (not @t23))) % 2.02/2.24 (define @t25 () (@var "B" (-> tptp.mworld Bool))) % 2.02/2.24 (define @t26 () (_ @t25 @t1)) % 2.02/2.24 (define @t27 () (@list @t22 @t25 @t1)) % 2.02/2.24 (define @t28 () (lambda @t27 (and @t23 @t26))) % 2.02/2.24 (define @t29 () (lambda @t27 (or @t23 @t26))) % 2.02/2.24 (define @t30 () (lambda @t27 (=> @t23 @t26))) % 2.02/2.24 (define @t31 () (lambda @t27 (= @t23 @t26))) % 2.02/2.24 (define @t32 () (_ @t20 @t7)) % 2.02/2.24 (define @t33 () (@list @t7)) % 2.02/2.24 (define @t34 () (forall @t33 (=> @t9 @t32))) % 2.02/2.24 (define @t35 () (@list @t20 @t1)) % 2.02/2.24 (define @t36 () (lambda @t35 @t34)) % 2.02/2.24 (define @t37 () (and @t9 @t32)) % 2.02/2.24 (define @t38 () (exists @t33 @t37)) % 2.02/2.24 (define @t39 () (lambda @t35 @t38)) % 2.02/2.24 (define @t40 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 2.02/2.24 (define @t41 () (_ (_ @t40 @t10) @t1)) % 2.02/2.24 (define @t42 () (@list @t40 @t1)) % 2.02/2.24 (define @t43 () (lambda @t42 (forall @t13 (=> @t12 @t41)))) % 2.02/2.24 (define @t44 () (and @t12 @t41)) % 2.02/2.24 (define @t45 () (exists @t13 @t44)) % 2.02/2.24 (define @t46 () (lambda @t42 @t45)) % 2.02/2.24 (define @t47 () (tptp.mrel @t1 @t1)) % 2.02/2.24 (define @t48 () (@var "BOUND_VARIABLE_7731" tptp.mworld)) % 2.02/2.24 (define @t49 () (not (tptp.f @t10 @t48))) % 2.02/2.24 (define @t50 () (not (tptp.eiw_di @t10 tptp.mactual))) % 2.02/2.24 (define @t51 () (@list @t10 @t48)) % 2.02/2.24 (define @t52 () (tptp.f @t10 @t7)) % 2.02/2.24 (define @t53 () (not @t52)) % 2.02/2.24 (define @t54 () (not (forall @t13 (or (not (tptp.eiw_di @t10 @t7)) @t53)))) % 2.02/2.24 (define @t55 () (not (tptp.mrel @t1 @t48))) % 2.02/2.24 (define @t56 () (tptp.eiw_di @t10 @t1)) % 2.02/2.24 (define @t57 () (not @t56)) % 2.02/2.24 (define @t58 () (or @t57 @t55 @t49)) % 2.02/2.24 (define @t59 () (not (forall @t51 @t58))) % 2.02/2.24 (define @t60 () (tptp.mrel @t1 @t7)) % 2.02/2.24 (define @t61 () (not @t60)) % 2.02/2.24 (define @t62 () (forall @t33 (or @t61 @t54))) % 2.02/2.24 (define @t63 () (lambda @t4 (=> @t62 @t59))) % 2.02/2.24 (define @t64 () (_ @t63 tptp.mactual)) % 2.02/2.24 (define @t65 () (lambda @t4 @t59)) % 2.02/2.24 (define @t66 () (_ @t65 @t1)) % 2.02/2.24 (define @t67 () (=> @t62 @t66)) % 2.02/2.24 (define @t68 () (lambda @t4 @t67)) % 2.02/2.24 (define @t69 () (@list @t25 @t1)) % 2.02/2.24 (define @t70 () (or @t55 @t49)) % 2.02/2.24 (define @t71 () (or @t57 @t70)) % 2.02/2.24 (define @t72 () (forall @t51 @t71)) % 2.02/2.24 (define @t73 () (@list @t48)) % 2.02/2.24 (define @t74 () (forall @t73 @t71)) % 2.02/2.24 (define @t75 () (forall @t73 @t70)) % 2.02/2.24 (define @t76 () (or @t57 @t75)) % 2.02/2.24 (define @t77 () (forall @t33 (or @t61 @t53))) % 2.02/2.24 (define @t78 () (not @t77)) % 2.02/2.24 (define @t79 () (not (forall @t33 (or (not (tptp.mrel @t14 @t7)) @t53)))) % 2.02/2.24 (define @t80 () (lambda @t16 @t79)) % 2.02/2.24 (define @t81 () (_ @t80 @t10 @t1)) % 2.02/2.24 (define @t82 () (not @t81)) % 2.02/2.24 (define @t83 () (or @t57 @t82)) % 2.02/2.24 (define @t84 () (forall @t13 @t83)) % 2.02/2.24 (define @t85 () (not @t84)) % 2.02/2.24 (define @t86 () (lambda @t4 @t85)) % 2.02/2.24 (define @t87 () (_ @t40 @t10 @t1)) % 2.02/2.24 (define @t88 () (lambda @t42 (not (forall @t13 (or @t57 (not @t87)))))) % 2.02/2.24 (define @t89 () (_ @t15 @t7)) % 2.02/2.24 (define @t90 () (not @t89)) % 2.02/2.24 (define @t91 () (or @t61 @t90)) % 2.02/2.24 (define @t92 () (_ @t15 @t7)) % 2.02/2.24 (define @t93 () (not @t92)) % 2.02/2.24 (define @t94 () (or @t61 @t93)) % 2.02/2.24 (define @t95 () (forall @t33 @t94)) % 2.02/2.24 (define @t96 () (not @t95)) % 2.02/2.24 (define @t97 () (lambda @t4 @t96)) % 2.02/2.24 (define @t98 () (_ @t20 @t7)) % 2.02/2.24 (define @t99 () (_ (lambda @t35 (not (forall @t33 (or @t61 (not @t98))))) @t15)) % 2.02/2.24 (define @t100 () (lambda @t16 (_ @t99 @t14))) % 2.02/2.24 (define @t101 () (lambda @t4 @t62)) % 2.02/2.24 (define @t102 () (_ @t101 @t1)) % 2.02/2.24 (define @t103 () (=> @t102 @t26)) % 2.02/2.24 (define @t104 () (lambda @t69 @t103)) % 2.02/2.24 (define @t105 () (tptp.f @t10 @t1)) % 2.02/2.24 (define @t106 () (lambda @t4 (not (forall @t13 (or @t57 (not @t105)))))) % 2.02/2.24 (define @t107 () (_ @t106 @t7)) % 2.02/2.24 (define @t108 () (or @t61 @t107)) % 2.02/2.24 (define @t109 () (forall @t33 @t108)) % 2.02/2.24 (define @t110 () (lambda @t4 @t109)) % 2.02/2.24 (define @t111 () (lambda @t35 (forall @t33 (or @t61 @t98)))) % 2.02/2.24 (define @t112 () (_ @t15 @t1)) % 2.02/2.24 (define @t113 () (not @t112)) % 2.02/2.24 (define @t114 () (or @t57 @t113)) % 2.02/2.24 (define @t115 () (_ @t18 @t10 @t1)) % 2.02/2.24 (define @t116 () (not @t115)) % 2.02/2.24 (define @t117 () (or @t57 @t116)) % 2.02/2.24 (define @t118 () (forall @t13 @t117)) % 2.02/2.24 (define @t119 () (not @t118)) % 2.02/2.24 (define @t120 () (lambda @t4 @t119)) % 2.02/2.24 (define @t121 () (_ @t88 @t18)) % 2.02/2.24 (define @t122 () (not @t32)) % 2.02/2.24 (define @t123 () (not @t9)) % 2.02/2.24 (define @t124 () (or @t123 @t122)) % 2.02/2.24 (define @t125 () (forall @t33 (not @t37))) % 2.02/2.24 (define @t126 () (not @t125)) % 2.02/2.24 (define @t127 () (not @t41)) % 2.02/2.24 (define @t128 () (not @t12)) % 2.02/2.24 (define @t129 () (or @t128 @t127)) % 2.02/2.24 (define @t130 () (forall @t13 (not @t44))) % 2.02/2.24 (define @t131 () (not @t130)) % 2.02/2.24 (define @t132 () (or @t123 @t32)) % 2.02/2.24 (define @t133 () (@list tptp.mactual)) % 2.02/2.24 (define @t134 () (forall @t13 (or @t50 (not (tptp.f @t10 tptp.mactual))))) % 2.02/2.24 (define @t135 () (not @t134)) % 2.02/2.24 (define @t136 () (tptp.mrel tptp.mactual tptp.mactual)) % 2.02/2.24 (define @t137 () (not @t136)) % 2.02/2.24 (define @t138 () (or @t137 @t135)) % 2.02/2.24 (define @t139 () (@quantifiers_skolemize @t134 0)) % 2.02/2.24 (define @t140 () (tptp.f @t139 tptp.mactual)) % 2.02/2.24 (define @t141 () (not @t140)) % 2.02/2.24 (define @t142 () (tptp.eiw_di @t139 tptp.mactual)) % 2.02/2.24 (define @t143 () (not @t142)) % 2.02/2.24 (define @t144 () (or @t143 @t141)) % 2.02/2.24 (define @t145 () (not @t144)) % 2.02/2.24 (define @t146 () (or @t143 @t137 @t141)) % 2.02/2.24 (define @t147 () (forall @t4 @t47)) % 2.02/2.24 (assume @p1 @t5) % 2.02/2.24 (assume @p2 (forall (@list @t1 @t7 @t6) (=> (and @t9 (_ @t8 @t6)) (_ @t2 @t6)))) % 2.02/2.24 (assume @p3 (forall @t4 (exists @t13 @t12))) % 2.02/2.24 (assume @p4 (forall (@list @t1 @t7 @t10) (=> (and @t12 (_ @t8 @t1)) (_ @t11 @t7)))) % 2.02/2.24 (assume @p5 @t19) % 2.02/2.24 (assume @p6 true) % 2.02/2.24 (step @p7 (= tptp.mlocal @t21) :rule refl :args (@t21)) % 2.02/2.24 (step @p8 (= tptp.mnot @t24) :rule refl :args (@t24)) % 2.02/2.24 (step @p9 (= tptp.mand @t28) :rule refl :args (@t28)) % 2.02/2.24 (step @p10 (= tptp.mor @t29) :rule refl :args (@t29)) % 2.02/2.24 (step @p11 (= tptp.mimplies @t30) :rule refl :args (@t30)) % 2.02/2.24 (step @p12 (= tptp.mequiv @t31) :rule refl :args (@t31)) % 2.02/2.24 (step @p13 (= tptp.mbox @t36) :rule refl :args (@t36)) % 2.02/2.24 (step @p14 (= tptp.mdia @t39) :rule refl :args (@t39)) % 2.02/2.24 (step @p15 (= tptp.mforall_di @t43) :rule refl :args (@t43)) % 2.02/2.24 (step @p16 (= tptp.mexists_di @t46) :rule refl :args (@t46)) % 2.02/2.24 (step @p17 :rule refl :args (@t47)) % 2.02/2.24 (step @p18 :rule refl :args (@t3)) % 2.02/2.24 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t3 @t47))) % 2.02/2.24 (step @p20 :rule symm :premises (@p19)) % 2.02/2.24 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 2.02/2.24 (step @p22 :rule cong :premises (@p21) :args (@t5)) % 2.02/2.24 (step @p23 :rule eq_resolve :premises (@p1 @p22)) % 2.02/2.24 (step @p24 :rule beta-reduce :args ((= @t64 (=> (forall @t33 (or (not (tptp.mrel tptp.mactual @t7)) @t54)) (not (forall @t51 (or @t50 (not (tptp.mrel tptp.mactual @t48)) @t49))))))) % 2.02/2.24 (step @p25 :rule beta-reduce :args ((= (_ @t21 @t63) @t64))) % 2.02/2.24 (step @p26 :rule trans :premises (@p25 @p24)) % 2.02/2.24 (step @p27 :rule beta-reduce :args ((= @t66 @t59))) % 2.02/2.24 (step @p28 :rule refl :args (@t62)) % 2.02/2.24 (step @p29 :rule cong :premises (@p28 @p27) :args (@t67)) % 2.02/2.24 (step @p30 :rule cong :premises (@p29) :args (@t68)) % 2.02/2.24 (step @p31 :rule beta-reduce :args ((= (_ (lambda @t69 (=> @t62 @t26)) @t65) @t68))) % 2.02/2.24 (step @p32 :rule trans :premises (@p31 @p30)) % 2.02/2.24 (step @p33 :rule aci_norm :args ((= @t71 @t58))) % 2.02/2.24 (step @p34 :rule cong :premises (@p33) :args (@t72)) % 2.02/2.24 (step @p35 :rule quant-merge-prenex :args ((= (forall @t13 @t74) @t72))) % 2.02/2.24 (step @p36 :rule alpha_equiv :args (@t75 (@list @t48) (@list @t7))) % 2.02/2.24 (step @p37 :rule refl :args (@t57)) % 2.02/2.24 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t76)) % 2.02/2.24 (step @p39 :rule quant-miniscope-or :args ((= @t74 @t76))) % 2.02/2.24 (step @p40 :rule trans :premises (@p39 @p38)) % 2.02/2.24 (step @p41 :rule symm :premises (@p40)) % 2.02/2.24 (step @p42 :rule cong :premises (@p41) :args ((forall @t13 (or @t57 @t77)))) % 2.02/2.24 (step @p43 :rule trans :premises (@p42 @p35)) % 2.02/2.24 (step @p44 :rule trans :premises (@p43 @p34)) % 2.02/2.24 (step @p45 :rule bool-double-not-elim :args (@t77)) % 2.02/2.24 (step @p46 :rule beta-reduce :args ((= @t81 @t78))) % 2.02/2.24 (step @p47 :rule cong :premises (@p46) :args (@t82)) % 2.02/2.24 (step @p48 :rule trans :premises (@p47 @p45)) % 2.02/2.24 (step @p49 :rule refl :args (@t57)) % 2.02/2.24 (step @p50 :rule nary_cong :premises (@p49 @p48) :args (@t83)) % 2.02/2.24 (step @p51 :rule cong :premises (@p50) :args (@t84)) % 2.02/2.24 (step @p52 :rule trans :premises (@p51 @p44)) % 2.02/2.24 (step @p53 :rule cong :premises (@p52) :args (@t85)) % 2.02/2.24 (step @p54 :rule cong :premises (@p53) :args (@t86)) % 2.02/2.24 (step @p55 :rule beta-reduce :args ((= (_ @t88 @t80) @t86))) % 2.02/2.24 (step @p56 :rule trans :premises (@p55 @p54)) % 2.02/2.24 (step @p57 :rule beta-reduce :args ((= (_ (lambda @t4 @t78) @t14) @t79))) % 2.02/2.24 (step @p58 :rule refl :args (@t14)) % 2.02/2.24 (step @p59 :rule refl :args (@t52)) % 2.02/2.24 (step @p60 :rule refl :args (@t89)) % 2.02/2.24 (step @p61 :rule cong :premises (@p60 @p59) :args ((= @t89 @t52))) % 2.02/2.24 (step @p62 :rule symm :premises (@p61)) % 2.02/2.24 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 2.02/2.24 (step @p64 :rule cong :premises (@p63) :args (@t90)) % 2.02/2.24 (step @p65 :rule refl :args (@t61)) % 2.02/2.24 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t91)) % 2.02/2.24 (step @p67 :rule cong :premises (@p66) :args ((forall @t33 @t91))) % 2.02/2.24 (step @p68 :rule refl :args (@t92)) % 2.02/2.24 (step @p69 :rule cong :premises (@p68) :args (@t93)) % 2.02/2.24 (step @p70 :rule refl :args (@t61)) % 2.02/2.24 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t94)) % 2.02/2.24 (step @p72 :rule cong :premises (@p71) :args (@t95)) % 2.02/2.24 (step @p73 :rule trans :premises (@p72 @p67)) % 2.02/2.24 (step @p74 :rule cong :premises (@p73) :args (@t96)) % 2.02/2.24 (step @p75 :rule cong :premises (@p74) :args (@t97)) % 2.02/2.24 (step @p76 :rule beta-reduce :args ((= @t99 @t97))) % 2.02/2.24 (step @p77 :rule trans :premises (@p76 @p75)) % 2.02/2.24 (step @p78 :rule ho_cong :premises (@p77 @p58)) % 2.02/2.24 (step @p79 :rule trans :premises (@p78 @p57)) % 2.02/2.24 (step @p80 :rule cong :premises (@p79) :args (@t100)) % 2.02/2.24 (step @p81 :rule refl :args (@t88)) % 2.02/2.24 (step @p82 :rule ho_cong :premises (@p81 @p80)) % 2.02/2.24 (step @p83 :rule trans :premises (@p82 @p56)) % 2.02/2.24 (step @p84 :rule refl :args (@t26)) % 2.02/2.24 (step @p85 :rule beta-reduce :args ((= @t102 @t62))) % 2.02/2.24 (step @p86 :rule cong :premises (@p85 @p84) :args (@t103)) % 2.02/2.24 (step @p87 :rule cong :premises (@p86) :args (@t104)) % 2.02/2.24 (step @p88 :rule beta-reduce :args ((= (_ @t30 @t101) @t104))) % 2.02/2.24 (step @p89 :rule trans :premises (@p88 @p87)) % 2.02/2.24 (step @p90 :rule beta-reduce :args ((= @t107 @t54))) % 2.02/2.24 (step @p91 :rule nary_cong :premises (@p70 @p90) :args (@t108)) % 2.02/2.24 (step @p92 :rule cong :premises (@p91) :args (@t109)) % 2.02/2.24 (step @p93 :rule cong :premises (@p92) :args (@t110)) % 2.02/2.24 (step @p94 :rule beta-reduce :args ((= (_ @t111 @t106) @t110))) % 2.02/2.24 (step @p95 :rule trans :premises (@p94 @p93)) % 2.02/2.24 (step @p96 :rule refl :args (@t105)) % 2.02/2.24 (step @p97 :rule refl :args (@t112)) % 2.02/2.24 (step @p98 :rule cong :premises (@p97 @p96) :args ((= @t112 @t105))) % 2.02/2.24 (step @p99 :rule symm :premises (@p98)) % 2.02/2.24 (step @p100 :rule eq_resolve :premises (@p97 @p99)) % 2.02/2.24 (step @p101 :rule cong :premises (@p100) :args (@t113)) % 2.02/2.24 (step @p102 :rule nary_cong :premises (@p37 @p101) :args (@t114)) % 2.02/2.24 (step @p103 :rule cong :premises (@p102) :args ((forall @t13 @t114))) % 2.02/2.24 (step @p104 :rule beta-reduce :args ((= @t115 @t112))) % 2.02/2.24 (step @p105 :rule cong :premises (@p104) :args (@t116)) % 2.02/2.24 (step @p106 :rule nary_cong :premises (@p49 @p105) :args (@t117)) % 2.02/2.24 (step @p107 :rule cong :premises (@p106) :args (@t118)) % 2.02/2.24 (step @p108 :rule trans :premises (@p107 @p103)) % 2.02/2.24 (step @p109 :rule cong :premises (@p108) :args (@t119)) % 2.02/2.24 (step @p110 :rule cong :premises (@p109) :args (@t120)) % 2.02/2.24 (step @p111 :rule beta-reduce :args ((= @t121 @t120))) % 2.02/2.24 (step @p112 :rule trans :premises (@p111 @p110)) % 2.02/2.24 (step @p113 :rule refl :args (@t111)) % 2.02/2.24 (step @p114 :rule ho_cong :premises (@p113 @p112)) % 2.02/2.24 (step @p115 :rule trans :premises (@p114 @p95)) % 2.02/2.24 (step @p116 :rule refl :args (@t30)) % 2.02/2.24 (step @p117 :rule ho_cong :premises (@p116 @p115)) % 2.02/2.24 (step @p118 :rule trans :premises (@p117 @p89)) % 2.02/2.24 (step @p119 :rule ho_cong :premises (@p118 @p83)) % 2.02/2.24 (step @p120 :rule trans :premises (@p119 @p32)) % 2.02/2.24 (step @p121 :rule refl :args (@t21)) % 2.02/2.24 (step @p122 :rule ho_cong :premises (@p121 @p120)) % 2.02/2.24 (step @p123 :rule trans :premises (@p122 @p26)) % 2.02/2.24 (step @p124 :rule cong :premises (@p123) :args ((not (_ @t21 (_ (_ @t30 (_ @t111 @t121)) (_ @t88 @t100)))))) % 2.02/2.24 (step @p125 :rule refl :args (@t15)) % 2.02/2.24 (step @p126 :rule refl :args (@t98)) % 2.02/2.24 (step @p127 :rule refl :args (@t32)) % 2.02/2.24 (step @p128 :rule cong :premises (@p127 @p126) :args ((= @t32 @t98))) % 2.02/2.24 (step @p129 :rule symm :premises (@p128)) % 2.02/2.24 (step @p130 :rule eq_resolve :premises (@p127 @p129)) % 2.02/2.24 (step @p131 :rule cong :premises (@p130) :args (@t122)) % 2.02/2.24 (step @p132 :rule refl :args (@t60)) % 2.02/2.24 (step @p133 :rule refl :args (@t9)) % 2.02/2.24 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t9 @t60))) % 2.02/2.24 (step @p135 :rule symm :premises (@p134)) % 2.02/2.24 (step @p136 :rule eq_resolve :premises (@p133 @p135)) % 2.02/2.24 (step @p137 :rule cong :premises (@p136) :args (@t123)) % 2.02/2.24 (step @p138 :rule nary_cong :premises (@p137 @p131) :args (@t124)) % 2.02/2.24 (step @p139 :rule cong :premises (@p138) :args ((forall @t33 @t124))) % 2.02/2.24 (step @p140 :rule bool-and-de-morgan :args (@t9 @t32 true)) % 2.02/2.24 (step @p141 :rule cong :premises (@p140) :args (@t125)) % 2.02/2.24 (step @p142 :rule trans :premises (@p141 @p139)) % 2.02/2.24 (step @p143 :rule cong :premises (@p142) :args (@t126)) % 2.02/2.24 (step @p144 :rule exists-elim :args ((= @t38 @t126))) % 2.02/2.24 (step @p145 :rule trans :premises (@p144 @p143)) % 2.02/2.24 (step @p146 :rule cong :premises (@p145) :args (@t39)) % 2.02/2.24 (step @p147 :rule trans :premises (@p14 @p146)) % 2.02/2.24 (step @p148 :rule ho_cong :premises (@p147 @p125)) % 2.02/2.24 (step @p149 :rule ho_cong :premises (@p148 @p58)) % 2.02/2.24 (step @p150 :rule cong :premises (@p149) :args (@t17)) % 2.02/2.24 (step @p151 :rule refl :args (@t87)) % 2.02/2.24 (step @p152 :rule refl :args (@t41)) % 2.02/2.24 (step @p153 :rule cong :premises (@p152 @p151) :args ((= @t41 @t87))) % 2.02/2.24 (step @p154 :rule symm :premises (@p153)) % 2.02/2.24 (step @p155 :rule eq_resolve :premises (@p152 @p154)) % 2.02/2.24 (step @p156 :rule cong :premises (@p155) :args (@t127)) % 2.02/2.24 (step @p157 :rule refl :args (@t56)) % 2.02/2.24 (step @p158 :rule refl :args (@t12)) % 2.02/2.24 (step @p159 :rule cong :premises (@p158 @p157) :args ((= @t12 @t56))) % 2.02/2.24 (step @p160 :rule symm :premises (@p159)) % 2.02/2.24 (step @p161 :rule eq_resolve :premises (@p158 @p160)) % 2.02/2.24 (step @p162 :rule cong :premises (@p161) :args (@t128)) % 2.02/2.24 (step @p163 :rule nary_cong :premises (@p162 @p156) :args (@t129)) % 2.02/2.24 (step @p164 :rule cong :premises (@p163) :args ((forall @t13 @t129))) % 2.02/2.24 (step @p165 :rule bool-and-de-morgan :args (@t12 @t41 true)) % 2.02/2.24 (step @p166 :rule cong :premises (@p165) :args (@t130)) % 2.02/2.24 (step @p167 :rule trans :premises (@p166 @p164)) % 2.02/2.24 (step @p168 :rule cong :premises (@p167) :args (@t131)) % 2.02/2.24 (step @p169 :rule exists-elim :args ((= @t45 @t131))) % 2.02/2.24 (step @p170 :rule trans :premises (@p169 @p168)) % 2.02/2.24 (step @p171 :rule cong :premises (@p170) :args (@t46)) % 2.02/2.24 (step @p172 :rule trans :premises (@p16 @p171)) % 2.02/2.24 (step @p173 :rule ho_cong :premises (@p172 @p150)) % 2.02/2.24 (step @p174 :rule refl :args (@t18)) % 2.02/2.24 (step @p175 :rule ho_cong :premises (@p172 @p174)) % 2.02/2.24 (step @p176 :rule nary_cong :premises (@p137 @p130) :args (@t132)) % 2.02/2.24 (step @p177 :rule cong :premises (@p176) :args ((forall @t33 @t132))) % 2.02/2.24 (step @p178 :rule bool-impl-elim :args (@t9 @t32)) % 2.02/2.24 (step @p179 :rule cong :premises (@p178) :args (@t34)) % 2.02/2.24 (step @p180 :rule trans :premises (@p179 @p177)) % 2.02/2.24 (step @p181 :rule cong :premises (@p180) :args (@t36)) % 2.02/2.24 (step @p182 :rule trans :premises (@p13 @p181)) % 2.02/2.24 (step @p183 :rule ho_cong :premises (@p182 @p175)) % 2.02/2.24 (step @p184 :rule ho_cong :premises (@p11 @p183)) % 2.02/2.24 (step @p185 :rule ho_cong :premises (@p184 @p173)) % 2.02/2.24 (step @p186 :rule ho_cong :premises (@p7 @p185)) % 2.02/2.24 (step @p187 :rule cong :premises (@p186) :args (@t19)) % 2.02/2.24 (step @p188 :rule trans :premises (@p187 @p124)) % 2.02/2.24 (step @p189 :rule eq_resolve :premises (@p5 @p188)) % 2.02/2.24 (step @p190 :rule not_implies_elim1 :premises (@p189)) % 2.02/2.24 (step @p191 :rule instantiate :premises (@p190) :args (@t133)) % 2.02/2.24 (step @p192 :rule cnf_or_pos :args (@t138)) % 2.02/2.24 (step @p193 :rule reordering :premises (@p192) :args ((or @t137 @t135 (not @t138)))) % 2.02/2.24 (step @p194 :rule refl :args (@t145)) % 2.02/2.24 (step @p195 :rule bool-double-not-elim :args (@t134)) % 2.02/2.24 (step @p196 :rule nary_cong :premises (@p195 @p194) :args ((or (not @t135) @t145))) % 2.02/2.24 (assume-push @p226 @t135) % 2.02/2.24 (step @p198 :rule skolemize :premises (@p226)) % 2.02/2.24 (step-pop @p227 :rule scope :premises (@p198)) % 2.02/2.24 (step @p199 :rule process_scope :premises (@p227) :args (@t145)) % 2.02/2.24 (step @p201 :rule implies_elim :premises (@p199)) % 2.02/2.24 (step @p202 :rule eq_resolve :premises (@p201 @p196)) % 2.02/2.24 (step @p203 :rule bool-double-not-elim :args (@t142)) % 2.02/2.24 (step @p204 :rule refl :args (@t144)) % 2.02/2.24 (step @p205 :rule nary_cong :premises (@p204 @p203) :args ((or @t144 (not @t143)))) % 2.02/2.24 (step @p206 :rule cnf_or_neg :args (@t144 0)) % 2.02/2.24 (step @p207 :rule eq_resolve :premises (@p206 @p205)) % 2.02/2.24 (step @p208 :rule reordering :premises (@p207) :args ((or @t142 @t144))) % 2.02/2.24 (step @p209 :rule bool-double-not-elim :args (@t140)) % 2.02/2.24 (step @p210 :rule nary_cong :premises (@p204 @p209) :args ((or @t144 (not @t141)))) % 2.02/2.24 (step @p211 :rule cnf_or_neg :args (@t144 1)) % 2.02/2.24 (step @p212 :rule eq_resolve :premises (@p211 @p210)) % 2.02/2.24 (step @p213 :rule reordering :premises (@p212) :args ((or @t140 @t144))) % 2.02/2.24 (step @p214 :rule not_implies_elim2 :premises (@p189)) % 2.02/2.24 (step @p215 :rule not_not_elim :premises (@p214)) % 2.02/2.24 (step @p216 :rule instantiate :premises (@p215) :args ((@list @t139 tptp.mactual))) % 2.02/2.24 (step @p217 :rule cnf_or_pos :args (@t146)) % 2.02/2.24 (step @p218 :rule reordering :premises (@p217) :args ((or @t137 @t143 @t141 (not @t146)))) % 2.02/2.24 (step @p219 :rule chain_m_resolution :premises (@p218 @p216 @p213 @p208 @p202 @p193 @p191) :args (@t137 (@list false false false true true false) (@list @t146 @t140 @t142 @t144 @t134 @t138))) % 2.02/2.24 (assume-push @p228 @t147) % 2.02/2.24 (step @p221 :rule instantiate :premises (@p23) :args (@t133)) % 2.02/2.24 (step-pop @p229 :rule scope :premises (@p221)) % 2.02/2.24 (step @p222 :rule process_scope :premises (@p229) :args (@t136)) % 2.02/2.24 (step @p224 :rule implies_elim :premises (@p222)) % 2.02/2.24 (step @p225 false :rule chain_m_resolution :premises (@p224 @p219 @p23) :args (false (@list true false) (@list @t136 @t147))) % 2.02/2.24 ) % 2.02/2.24 % SZS output end Proof % 2.02/2.24 % cvc5 exiting %------------------------------------------------------------------------------