%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET924^1 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n022.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:48:59 AM UTC 2026 % Result : Theorem 0.37s 0.59s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET924^1 : TPTP v9.2.1. Released v8.1.0. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n022.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 16:17:38 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.37/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.59 % SZS status Theorem % 0.37/0.59 % SZS output start Proof % 0.37/0.59 ( % 0.37/0.59 (declare-sort $$unsorted 0) % 0.37/0.59 (declare-sort tptp.mworld 0) % 0.37/0.59 (declare-const tptp.mactual tptp.mworld) % 0.37/0.59 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.37/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.37/0.59 (declare-const tptp.empty (-> $$unsorted tptp.mworld Bool)) % 0.37/0.59 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.qmltpeq (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.37/0.59 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.37/0.59 (define tptp.mnot () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.59 (define tptp.mand () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.59 (define tptp.mor () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.59 (define tptp.mimplies () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.59 (define tptp.mequiv () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.59 (define tptp.mbox () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.37/0.59 (define tptp.mdia () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (exists (@list _let_1) (and (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.37/0.59 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.59 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.59 (define @t1 () (@var "__flatten_var_0" tptp.mworld)) % 0.37/0.59 (define @t2 () (@var "X" $$unsorted)) % 0.37/0.59 (define @t3 () (_ tptp.qmltpeq @t2)) % 0.37/0.59 (define @t4 () (@list @t2 @t1)) % 0.37/0.59 (define @t5 () (@var "Y" $$unsorted)) % 0.37/0.59 (define @t6 () (_ tptp.qmltpeq @t5)) % 0.37/0.59 (define @t7 () (_ @t3 @t5)) % 0.37/0.59 (define @t8 () (@list @t5 @t1)) % 0.37/0.59 (define @t9 () (@var "Z" $$unsorted)) % 0.37/0.59 (define @t10 () (@var "C" $$unsorted)) % 0.37/0.59 (define @t11 () (@var "B" $$unsorted)) % 0.37/0.59 (define @t12 () (@var "A" $$unsorted)) % 0.37/0.59 (define @t13 () (_ (_ tptp.qmltpeq @t12) @t11)) % 0.37/0.59 (define @t14 () (_ tptp.mimplies @t13)) % 0.37/0.59 (define @t15 () (@list @t10 @t1)) % 0.37/0.59 (define @t16 () (@list @t11 @t1)) % 0.37/0.59 (define @t17 () (@list @t12 @t1)) % 0.37/0.59 (define @t18 () (_ tptp.set_difference @t10)) % 0.37/0.59 (define @t19 () (_ tptp.singleton @t12)) % 0.37/0.59 (define @t20 () (_ tptp.empty @t12)) % 0.37/0.59 (define @t21 () (_ tptp.mand @t13)) % 0.37/0.59 (define @t22 () (_ tptp.in @t11)) % 0.37/0.59 (define @t23 () (_ tptp.in @t12)) % 0.37/0.59 (define @t24 () (_ tptp.in @t10)) % 0.37/0.59 (define @t25 () (_ @t23 @t11)) % 0.37/0.59 (define @t26 () (_ tptp.set_difference @t19)) % 0.37/0.59 (define @t27 () (_ (_ tptp.qmltpeq (_ @t26 @t11)) @t19)) % 0.37/0.59 (define @t28 () (lambda @t16 (_ (_ (_ tptp.mequiv @t27) (_ tptp.mnot @t25)) @t1))) % 0.37/0.59 (define @t29 () (lambda @t17 (_ (_ tptp.mforall_di @t28) @t1))) % 0.37/0.59 (define @t30 () (_ tptp.mlocal (_ tptp.mforall_di @t29))) % 0.37/0.59 (define @t31 () (not @t30)) % 0.37/0.59 (define @t32 () (@var "Phi" (-> tptp.mworld Bool))) % 0.37/0.59 (define @t33 () (lambda (@list @t32) (_ @t32 tptp.mactual))) % 0.37/0.59 (define @t34 () (@var "W" tptp.mworld)) % 0.37/0.59 (define @t35 () (@var "A" (-> tptp.mworld Bool))) % 0.37/0.59 (define @t36 () (_ @t35 @t34)) % 0.37/0.59 (define @t37 () (lambda (@list @t35 @t34) (not @t36))) % 0.37/0.59 (define @t38 () (@var "B" (-> tptp.mworld Bool))) % 0.37/0.59 (define @t39 () (_ @t38 @t34)) % 0.37/0.59 (define @t40 () (@list @t35 @t38 @t34)) % 0.37/0.59 (define @t41 () (lambda @t40 (and @t36 @t39))) % 0.37/0.59 (define @t42 () (lambda @t40 (or @t36 @t39))) % 0.37/0.59 (define @t43 () (lambda @t40 (=> @t36 @t39))) % 0.37/0.59 (define @t44 () (lambda @t40 (= @t36 @t39))) % 0.37/0.59 (define @t45 () (@var "V" tptp.mworld)) % 0.37/0.59 (define @t46 () (_ @t32 @t45)) % 0.37/0.59 (define @t47 () (_ (_ tptp.mrel @t34) @t45)) % 0.37/0.59 (define @t48 () (@list @t45)) % 0.37/0.59 (define @t49 () (@list @t32 @t34)) % 0.37/0.59 (define @t50 () (lambda @t49 (forall @t48 (=> @t47 @t46)))) % 0.37/0.59 (define @t51 () (lambda @t49 (exists @t48 (and @t47 @t46)))) % 0.37/0.59 (define @t52 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.37/0.59 (define @t53 () (_ (_ @t52 @t2) @t34)) % 0.37/0.59 (define @t54 () (@list @t2)) % 0.37/0.59 (define @t55 () (forall @t54 @t53)) % 0.37/0.59 (define @t56 () (@list @t52 @t34)) % 0.37/0.59 (define @t57 () (lambda @t56 @t55)) % 0.37/0.59 (define @t58 () (lambda @t56 (exists @t54 @t53))) % 0.37/0.59 (define @t59 () (tptp.singleton @t2)) % 0.37/0.59 (define @t60 () (@var "BOUND_VARIABLE_8914" $$unsorted)) % 0.37/0.59 (define @t61 () (tptp.set_difference @t59 @t60)) % 0.37/0.59 (define @t62 () (@list @t2 @t60)) % 0.37/0.59 (define @t63 () (= (not (tptp.in @t2 @t60 @t34)) (tptp.qmltpeq @t61 @t59 @t34))) % 0.37/0.59 (define @t64 () (forall @t62 @t63)) % 0.37/0.59 (define @t65 () (@list @t34)) % 0.37/0.59 (define @t66 () (lambda @t65 @t64)) % 0.37/0.59 (define @t67 () (_ @t66 tptp.mactual)) % 0.37/0.59 (define @t68 () (@list @t60)) % 0.37/0.59 (define @t69 () (forall @t68 @t63)) % 0.37/0.59 (define @t70 () (tptp.singleton @t12)) % 0.37/0.59 (define @t71 () (tptp.set_difference @t70 @t2)) % 0.37/0.59 (define @t72 () (forall @t54 (= (not (tptp.in @t12 @t2 @t1)) (tptp.qmltpeq @t71 @t70 @t1)))) % 0.37/0.59 (define @t73 () (lambda @t17 @t72)) % 0.37/0.59 (define @t74 () (forall @t54 (_ @t73 @t2 @t34))) % 0.37/0.59 (define @t75 () (lambda @t65 @t74)) % 0.37/0.59 (define @t76 () (_ @t52 @t2 @t34)) % 0.37/0.59 (define @t77 () (lambda @t56 (forall @t54 @t76))) % 0.37/0.59 (define @t78 () (tptp.qmltpeq @t71 @t70 @t34)) % 0.37/0.59 (define @t79 () (tptp.in @t12 @t2 @t34)) % 0.37/0.59 (define @t80 () (_ @t26 @t2)) % 0.37/0.59 (define @t81 () (_ (_ (_ tptp.qmltpeq @t80) @t19) @t34)) % 0.37/0.59 (define @t82 () (_ (_ @t23 @t2) @t34)) % 0.37/0.59 (define @t83 () (not @t82)) % 0.37/0.59 (define @t84 () (= @t83 @t81)) % 0.37/0.59 (define @t85 () (= (_ @t27 @t1) (not (_ @t25 @t1)))) % 0.37/0.59 (define @t86 () (lambda @t16 @t85)) % 0.37/0.59 (define @t87 () (_ @t86 @t2 @t34)) % 0.37/0.59 (define @t88 () (forall @t54 @t87)) % 0.37/0.59 (define @t89 () (lambda @t65 @t88)) % 0.37/0.59 (define @t90 () (not (_ @t25 @t34))) % 0.37/0.59 (define @t91 () (_ @t27 @t34)) % 0.37/0.59 (define @t92 () (lambda @t65 @t90)) % 0.37/0.59 (define @t93 () (_ @t92 @t34)) % 0.37/0.59 (define @t94 () (lambda @t65 (= @t93 @t91))) % 0.37/0.59 (define @t95 () (@list @t38 @t34)) % 0.37/0.59 (define @t96 () (_ @t37 @t25)) % 0.37/0.59 (define @t97 () (lambda @t95 (= @t91 @t39))) % 0.37/0.59 (define @t98 () (_ @t44 @t27)) % 0.37/0.59 (define @t99 () (lambda @t16 (_ (_ @t98 @t96) @t1))) % 0.37/0.59 (define @t100 () (lambda @t17 (_ (_ @t77 @t99) @t1))) % 0.37/0.59 (assume @p1 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t4 (_ (_ @t3 @t2) @t1))))) % 0.37/0.59 (assume @p2 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t4 (_ (_ tptp.mforall_di (lambda @t8 (_ (_ (_ tptp.mimplies @t7) (_ @t6 @t2)) @t1))) @t1))))) % 0.37/0.59 (assume @p3 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t4 (_ (_ tptp.mforall_di (lambda @t8 (_ (_ tptp.mforall_di (lambda (@list @t9 @t1) (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t7) (_ @t6 @t9))) (_ @t3 @t9)) @t1))) @t1))) @t1))))) % 0.37/0.59 (assume @p4 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t17 (_ (_ tptp.mforall_di (lambda @t16 (_ (_ tptp.mforall_di (lambda @t15 (_ (_ @t14 (_ (_ tptp.qmltpeq (_ (_ tptp.set_difference @t12) @t10)) (_ (_ tptp.set_difference @t11) @t10))) @t1))) @t1))) @t1))))) % 0.37/0.59 (assume @p5 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t17 (_ (_ tptp.mforall_di (lambda @t16 (_ (_ tptp.mforall_di (lambda @t15 (_ (_ @t14 (_ (_ tptp.qmltpeq (_ @t18 @t12)) (_ @t18 @t11))) @t1))) @t1))) @t1))))) % 0.37/0.59 (assume @p6 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t17 (_ (_ tptp.mforall_di (lambda @t16 (_ (_ @t14 (_ (_ tptp.qmltpeq @t19) (_ tptp.singleton @t11))) @t1))) @t1))))) % 0.37/0.59 (assume @p7 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t17 (_ (_ tptp.mforall_di (lambda @t16 (_ (_ (_ tptp.mimplies (_ @t21 @t20)) (_ tptp.empty @t11)) @t1))) @t1))))) % 0.37/0.59 (assume @p8 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t17 (_ (_ tptp.mforall_di (lambda @t16 (_ (_ tptp.mforall_di (lambda @t15 (_ (_ (_ tptp.mimplies (_ @t21 (_ @t23 @t10))) (_ @t22 @t10)) @t1))) @t1))) @t1))))) % 0.37/0.59 (assume @p9 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t17 (_ (_ tptp.mforall_di (lambda @t16 (_ (_ tptp.mforall_di (lambda @t15 (_ (_ (_ tptp.mimplies (_ @t21 (_ @t24 @t12))) (_ @t24 @t11)) @t1))) @t1))) @t1))))) % 0.37/0.59 (assume @p10 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t17 (_ (_ tptp.mforall_di (lambda @t16 (_ (_ (_ tptp.mimplies @t25) (_ tptp.mnot (_ @t22 @t12))) @t1))) @t1))))) % 0.37/0.59 (assume @p11 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t17 (_ @t20 @t1))))) % 0.37/0.59 (assume @p12 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t17 (_ (_ tptp.mnot @t20) @t1))))) % 0.37/0.59 (assume @p13 @t31) % 0.37/0.59 (assume @p14 @t30) % 0.37/0.59 (assume @p15 true) % 0.37/0.59 (step @p16 (= tptp.mlocal @t33) :rule refl :args (@t33)) % 0.37/0.59 (step @p17 (= tptp.mnot @t37) :rule refl :args (@t37)) % 0.37/0.59 (step @p18 (= tptp.mand @t41) :rule refl :args (@t41)) % 0.37/0.59 (step @p19 (= tptp.mor @t42) :rule refl :args (@t42)) % 0.37/0.59 (step @p20 (= tptp.mimplies @t43) :rule refl :args (@t43)) % 0.37/0.59 (step @p21 (= tptp.mequiv @t44) :rule refl :args (@t44)) % 0.37/0.59 (step @p22 (= tptp.mbox @t50) :rule refl :args (@t50)) % 0.37/0.59 (step @p23 (= tptp.mdia @t51) :rule refl :args (@t51)) % 0.37/0.59 (step @p24 (= tptp.mforall_di @t57) :rule refl :args (@t57)) % 0.37/0.59 (step @p25 (= tptp.mexists_di @t58) :rule refl :args (@t58)) % 0.37/0.59 (step @p26 :rule beta-reduce :args ((= @t67 (forall @t62 (= (not (tptp.in @t2 @t60 tptp.mactual)) (tptp.qmltpeq @t61 @t59 tptp.mactual)))))) % 0.37/0.59 (step @p27 :rule beta-reduce :args ((= (_ @t33 @t66) @t67))) % 0.37/0.59 (step @p28 :rule trans :premises (@p27 @p26)) % 0.37/0.59 (step @p29 :rule quant-merge-prenex :args ((= (forall @t54 @t69) @t64))) % 0.37/0.59 (step @p30 :rule beta-reduce :args ((= (_ (lambda @t17 (forall @t68 (= (not (tptp.in @t12 @t60 @t1)) (tptp.qmltpeq (tptp.set_difference @t70 @t60) @t70 @t1)))) @t2 @t34) @t69))) % 0.37/0.59 (step @p31 :rule refl :args (@t34)) % 0.37/0.59 (step @p32 :rule refl :args (@t2)) % 0.37/0.59 (step @p33 :rule alpha_equiv :args (@t72 (@list @t2) (@list @t60))) % 0.37/0.59 (step @p34 :rule cong :premises (@p33) :args (@t73)) % 0.37/0.59 (step @p35 :rule ho_cong :premises (@p34 @p32 @p31)) % 0.37/0.59 (step @p36 :rule trans :premises (@p35 @p30)) % 0.37/0.59 (step @p37 :rule cong :premises (@p36) :args (@t74)) % 0.37/0.59 (step @p38 :rule trans :premises (@p37 @p29)) % 0.37/0.59 (step @p39 :rule cong :premises (@p38) :args (@t75)) % 0.37/0.59 (step @p40 :rule beta-reduce :args ((= (_ @t77 @t73) @t75))) % 0.37/0.59 (step @p41 :rule trans :premises (@p40 @p39)) % 0.37/0.59 (step @p42 :rule beta-reduce :args ((= (_ (lambda @t65 (forall @t54 (= (not @t79) @t78))) @t1) @t72))) % 0.37/0.59 (step @p43 :rule refl :args (@t1)) % 0.37/0.59 (step @p44 :rule refl :args ((tptp.qmltpeq @t80 @t19 @t34))) % 0.37/0.59 (step @p45 :rule refl :args (@t70)) % 0.37/0.59 (step @p46 :rule refl :args ((tptp.set_difference @t19 @t2))) % 0.37/0.59 (step @p47 :rule cong :premises (@p45 @p32) :args (@t71)) % 0.37/0.59 (step @p48 :rule trans :premises (@p47 @p46)) % 0.37/0.59 (step @p49 :rule cong :premises (@p48 @p45 @p31) :args (@t78)) % 0.37/0.59 (step @p50 :rule trans :premises (@p49 @p44)) % 0.37/0.59 (step @p51 :rule refl :args (tptp.qmltpeq)) % 0.37/0.59 (step @p52 :rule ho_cong :premises (@p51 @p48)) % 0.37/0.59 (step @p53 :rule ho_cong :premises (@p52 @p45)) % 0.37/0.59 (step @p54 :rule ho_cong :premises (@p53 @p31)) % 0.37/0.59 (step @p55 :rule cong :premises (@p54 @p50) :args ((= (_ (_ (_ tptp.qmltpeq @t71) @t70) @t34) @t78))) % 0.37/0.59 (step @p56 :rule symm :premises (@p55)) % 0.37/0.59 (step @p57 :rule refl :args (@t81)) % 0.37/0.59 (step @p58 :rule eq_resolve :premises (@p57 @p56)) % 0.37/0.59 (step @p59 :rule refl :args (@t19)) % 0.37/0.59 (step @p60 :rule cong :premises (@p59 @p45) :args ((= @t19 @t70))) % 0.37/0.59 (step @p61 :rule symm :premises (@p60)) % 0.37/0.59 (step @p62 :rule eq_resolve :premises (@p59 @p61)) % 0.37/0.59 (step @p63 :rule refl :args (tptp.set_difference)) % 0.37/0.59 (step @p64 :rule ho_cong :premises (@p63 @p45)) % 0.37/0.59 (step @p65 :rule ho_cong :premises (@p64 @p32)) % 0.37/0.59 (step @p66 :rule cong :premises (@p65 @p48) :args ((= (_ (_ tptp.set_difference @t70) @t2) @t71))) % 0.37/0.59 (step @p67 :rule symm :premises (@p66)) % 0.37/0.59 (step @p68 :rule refl :args (@t80)) % 0.37/0.59 (step @p69 :rule eq_resolve :premises (@p68 @p67)) % 0.37/0.59 (step @p70 :rule ho_cong :premises (@p63 @p62)) % 0.37/0.59 (step @p71 :rule ho_cong :premises (@p70 @p32)) % 0.37/0.59 (step @p72 :rule trans :premises (@p71 @p69)) % 0.37/0.59 (step @p73 :rule ho_cong :premises (@p51 @p72)) % 0.37/0.59 (step @p74 :rule ho_cong :premises (@p73 @p62)) % 0.37/0.59 (step @p75 :rule ho_cong :premises (@p74 @p31)) % 0.37/0.59 (step @p76 :rule trans :premises (@p75 @p58)) % 0.37/0.59 (step @p77 :rule refl :args (@t79)) % 0.37/0.59 (step @p78 :rule refl :args (@t82)) % 0.37/0.59 (step @p79 :rule cong :premises (@p78 @p77) :args ((= @t82 @t79))) % 0.37/0.59 (step @p80 :rule symm :premises (@p79)) % 0.37/0.59 (step @p81 :rule eq_resolve :premises (@p78 @p80)) % 0.37/0.59 (step @p82 :rule cong :premises (@p81) :args (@t83)) % 0.37/0.59 (step @p83 :rule cong :premises (@p82 @p76) :args (@t84)) % 0.37/0.59 (step @p84 :rule cong :premises (@p83) :args ((forall @t54 @t84))) % 0.37/0.59 (step @p85 :rule eq-symm :args (@t81 @t83)) % 0.37/0.59 (step @p86 :rule beta-reduce :args ((= @t87 (= @t81 @t83)))) % 0.37/0.59 (step @p87 :rule trans :premises (@p86 @p85)) % 0.37/0.59 (step @p88 :rule cong :premises (@p87) :args (@t88)) % 0.37/0.59 (step @p89 :rule trans :premises (@p88 @p84)) % 0.37/0.59 (step @p90 :rule cong :premises (@p89) :args (@t89)) % 0.37/0.59 (step @p91 :rule beta-reduce :args ((= (_ @t77 @t86) @t89))) % 0.37/0.59 (step @p92 :rule trans :premises (@p91 @p90)) % 0.37/0.59 (step @p93 :rule beta-reduce :args ((= (_ (lambda @t65 (= @t91 @t90)) @t1) @t85))) % 0.37/0.59 (step @p94 :rule beta-reduce :args ((= @t93 @t90))) % 0.37/0.59 (step @p95 :rule refl :args (@t91)) % 0.37/0.59 (step @p96 :rule cong :premises (@p95 @p94) :args ((= @t91 @t93))) % 0.37/0.59 (step @p97 :rule eq-symm :args (@t93 @t91)) % 0.37/0.59 (step @p98 :rule trans :premises (@p97 @p96)) % 0.37/0.59 (step @p99 :rule cong :premises (@p98) :args (@t94)) % 0.37/0.59 (step @p100 :rule beta-reduce :args ((= (_ (lambda @t95 (= @t39 @t91)) @t92) @t94))) % 0.37/0.59 (step @p101 :rule trans :premises (@p100 @p99)) % 0.37/0.59 (step @p102 :rule beta-reduce :args ((= @t96 @t92))) % 0.37/0.59 (step @p103 :rule eq-symm :args (@t91 @t39)) % 0.37/0.59 (step @p104 :rule cong :premises (@p103) :args (@t97)) % 0.37/0.59 (step @p105 :rule beta-reduce :args ((= @t98 @t97))) % 0.37/0.59 (step @p106 :rule trans :premises (@p105 @p104)) % 0.37/0.59 (step @p107 :rule ho_cong :premises (@p106 @p102)) % 0.37/0.59 (step @p108 :rule trans :premises (@p107 @p101)) % 0.37/0.59 (step @p109 :rule ho_cong :premises (@p108 @p43)) % 0.37/0.59 (step @p110 :rule trans :premises (@p109 @p93)) % 0.37/0.59 (step @p111 :rule cong :premises (@p110) :args (@t99)) % 0.37/0.59 (step @p112 :rule refl :args (@t77)) % 0.37/0.59 (step @p113 :rule ho_cong :premises (@p112 @p111)) % 0.37/0.59 (step @p114 :rule trans :premises (@p113 @p92)) % 0.37/0.59 (step @p115 :rule ho_cong :premises (@p114 @p43)) % 0.37/0.59 (step @p116 :rule trans :premises (@p115 @p42)) % 0.37/0.59 (step @p117 :rule cong :premises (@p116) :args (@t100)) % 0.37/0.59 (step @p118 :rule ho_cong :premises (@p112 @p117)) % 0.37/0.59 (step @p119 :rule trans :premises (@p118 @p41)) % 0.37/0.59 (step @p120 :rule refl :args (@t33)) % 0.37/0.59 (step @p121 :rule ho_cong :premises (@p120 @p119)) % 0.37/0.59 (step @p122 :rule trans :premises (@p121 @p28)) % 0.37/0.59 (step @p123 :rule cong :premises (@p122) :args ((not (_ @t33 (_ @t77 @t100))))) % 0.37/0.59 (step @p124 :rule refl :args (@t25)) % 0.37/0.59 (step @p125 :rule ho_cong :premises (@p17 @p124)) % 0.37/0.59 (step @p126 :rule refl :args (@t27)) % 0.37/0.59 (step @p127 :rule ho_cong :premises (@p21 @p126)) % 0.37/0.59 (step @p128 :rule ho_cong :premises (@p127 @p125)) % 0.37/0.59 (step @p129 :rule ho_cong :premises (@p128 @p43)) % 0.37/0.59 (step @p130 :rule cong :premises (@p129) :args (@t28)) % 0.37/0.59 (step @p131 :rule refl :args (@t76)) % 0.37/0.59 (step @p132 :rule refl :args (@t53)) % 0.37/0.59 (step @p133 :rule cong :premises (@p132 @p131) :args ((= @t53 @t76))) % 0.37/0.59 (step @p134 :rule symm :premises (@p133)) % 0.37/0.59 (step @p135 :rule eq_resolve :premises (@p132 @p134)) % 0.37/0.59 (step @p136 :rule cong :premises (@p135) :args (@t55)) % 0.37/0.59 (step @p137 :rule cong :premises (@p136) :args (@t57)) % 0.37/0.59 (step @p138 :rule trans :premises (@p24 @p137)) % 0.37/0.59 (step @p139 :rule ho_cong :premises (@p138 @p130)) % 0.37/0.59 (step @p140 :rule ho_cong :premises (@p139 @p43)) % 0.37/0.59 (step @p141 :rule cong :premises (@p140) :args (@t29)) % 0.37/0.59 (step @p142 :rule ho_cong :premises (@p138 @p141)) % 0.37/0.59 (step @p143 :rule ho_cong :premises (@p16 @p142)) % 0.37/0.59 (step @p144 :rule cong :premises (@p143) :args (@t31)) % 0.37/0.59 (step @p145 :rule trans :premises (@p144 @p123)) % 0.37/0.59 (step @p146 :rule eq_resolve :premises (@p13 @p145)) % 0.37/0.59 (step @p147 :rule trans :premises (@p143 @p122)) % 0.37/0.59 (step @p148 :rule eq_resolve :premises (@p14 @p147)) % 0.37/0.59 (step @p149 false :rule contra :premises (@p148 @p146)) % 0.37/0.59 ) % 0.37/0.59 % SZS output end Proof % 0.37/0.59 % cvc5 exiting %------------------------------------------------------------------------------