%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET716^4 : TPTP v9.2.1. 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 : n013.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 08:48:30 AM UTC 2026 % Result : Theorem 0.38s 0.58s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET716^4 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n013.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 % 0.17/0.34 % DateTime : Tue Jun 2 16:10:30 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.50 %----Proving TH0 % 0.38/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.58 % SZS status Theorem % 0.38/0.58 % SZS output start Proof % 0.38/0.58 ( % 0.38/0.58 (declare-sort $$unsorted 0) % 0.38/0.58 (define tptp.fun_image () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_4 _let_3) (exists (@list _let_1) (and (_ _let_4 _let_1) (= _let_3 (_ _let_2 _let_1)))))))))) % 0.38/0.58 (define tptp.fun_composition () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "G" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_3 _let_1) (_ _let_3 (_ _let_2 _let_1))))))) % 0.38/0.58 (define tptp.fun_inv_image () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "B" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_4 _let_1) (exists (@list _let_3) (and (_ _let_4 _let_3) (= _let_3 (_ _let_2 _let_1)))))))))) % 0.38/0.58 (define tptp.fun_injective () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "F" (-> $$unsorted $$unsorted)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (= (_ _let_3 _let_2) (_ _let_3 _let_1)) (= _let_2 _let_1)))))))) % 0.38/0.58 (define tptp.fun_surjective () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (lambda (@list _let_2) (forall (@list _let_3) (exists (@list _let_1) (= _let_3 (_ _let_2 _let_1))))))))) % 0.38/0.58 (define tptp.fun_bijective () (let ((_let_1 (@var "F" (-> $$unsorted $$unsorted)))) (lambda (@list _let_1) (and (_ tptp.fun_injective _let_1) (_ tptp.fun_surjective _let_1))))) % 0.38/0.58 (define tptp.fun_decreasing () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "SMALLER" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_4) (forall (@list _let_1 _let_3) (=> (_ (_ _let_4 _let_1) _let_3) (_ (_ _let_4 (_ _let_2 _let_3)) (_ _let_2 _let_1)))))))))) % 0.38/0.58 (define tptp.fun_increasing () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "SMALLER" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_4) (forall (@list _let_3 _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ (_ _let_4 (_ _let_2 _let_3)) (_ _let_2 _let_1)))))))))) % 0.38/0.58 (define @t1 () (@var "G" (-> $$unsorted $$unsorted))) % 0.38/0.58 (define @t2 () (@var "F" (-> $$unsorted $$unsorted))) % 0.38/0.58 (define @t3 () (_ tptp.fun_injective @t2)) % 0.38/0.58 (define @t4 () (and @t3 (_ tptp.fun_injective @t1))) % 0.38/0.58 (define @t5 () (=> @t4 (_ tptp.fun_injective (_ (_ tptp.fun_composition @t2) @t1)))) % 0.38/0.58 (define @t6 () (@list @t2 @t1)) % 0.38/0.58 (define @t7 () (forall @t6 @t5)) % 0.38/0.58 (define @t8 () (not @t7)) % 0.38/0.58 (define @t9 () (@var "X" $$unsorted)) % 0.38/0.58 (define @t10 () (_ @t2 @t9)) % 0.38/0.58 (define @t11 () (@var "Y" $$unsorted)) % 0.38/0.58 (define @t12 () (= @t11 @t10)) % 0.38/0.58 (define @t13 () (@var "A" (-> $$unsorted Bool))) % 0.38/0.58 (define @t14 () (@list @t9)) % 0.38/0.58 (define @t15 () (lambda (@list @t2 @t13 @t11) (exists @t14 (and (_ @t13 @t9) @t12)))) % 0.38/0.58 (define @t16 () (_ @t1 @t10)) % 0.38/0.58 (define @t17 () (lambda (@list @t2 @t1 @t9) @t16)) % 0.38/0.58 (define @t18 () (@var "B" (-> $$unsorted Bool))) % 0.38/0.58 (define @t19 () (@list @t11)) % 0.38/0.58 (define @t20 () (lambda (@list @t2 @t18 @t9) (exists @t19 (and (_ @t18 @t11) @t12)))) % 0.38/0.58 (define @t21 () (_ @t2 @t11)) % 0.38/0.58 (define @t22 () (= @t10 @t21)) % 0.38/0.58 (define @t23 () (=> @t22 (= @t9 @t11))) % 0.38/0.58 (define @t24 () (@list @t9 @t11)) % 0.38/0.58 (define @t25 () (forall @t24 @t23)) % 0.38/0.58 (define @t26 () (@list @t2)) % 0.38/0.58 (define @t27 () (lambda @t26 @t25)) % 0.38/0.58 (define @t28 () (lambda @t26 (forall @t19 (exists @t14 @t12)))) % 0.38/0.58 (define @t29 () (lambda @t26 (and @t3 (_ tptp.fun_surjective @t2)))) % 0.38/0.58 (define @t30 () (@var "SMALLER" (-> $$unsorted $$unsorted Bool))) % 0.38/0.58 (define @t31 () (_ (_ @t30 @t9) @t11)) % 0.38/0.58 (define @t32 () (@list @t2 @t30)) % 0.38/0.58 (define @t33 () (lambda @t32 (forall @t24 (=> @t31 (_ (_ @t30 @t21) @t10))))) % 0.38/0.58 (define @t34 () (lambda @t32 (forall @t24 (=> @t31 (_ (_ @t30 @t10) @t21))))) % 0.38/0.58 (define @t35 () (@var "BOUND_VARIABLE_7691" $$unsorted)) % 0.38/0.58 (define @t36 () (@var "BOUND_VARIABLE_7689" $$unsorted)) % 0.38/0.58 (define @t37 () (not (= (_ @t1 (_ @t2 @t36)) (_ @t1 (_ @t2 @t35))))) % 0.38/0.58 (define @t38 () (= @t11 @t9)) % 0.38/0.58 (define @t39 () (forall @t24 (or (not (= (_ @t1 @t9) (_ @t1 @t11))) @t38))) % 0.38/0.58 (define @t40 () (not @t39)) % 0.38/0.58 (define @t41 () (_ @t2 @t11)) % 0.38/0.58 (define @t42 () (_ @t2 @t9)) % 0.38/0.58 (define @t43 () (forall @t24 (or (not (= @t42 @t41)) @t38))) % 0.38/0.58 (define @t44 () (not @t43)) % 0.38/0.58 (define @t45 () (= @t35 @t36)) % 0.38/0.58 (define @t46 () (or @t44 @t40 @t37 @t45)) % 0.38/0.58 (define @t47 () (or @t37 @t45)) % 0.38/0.58 (define @t48 () (or @t44 @t40 @t47)) % 0.38/0.58 (define @t49 () (@list @t2 @t1 @t36 @t35)) % 0.38/0.58 (define @t50 () (forall @t49 @t48)) % 0.38/0.58 (define @t51 () (@list @t36 @t35)) % 0.38/0.58 (define @t52 () (forall @t51 @t48)) % 0.38/0.58 (define @t53 () (forall @t51 @t47)) % 0.38/0.58 (define @t54 () (or @t44 @t40 @t53)) % 0.38/0.58 (define @t55 () (_ @t1 @t41)) % 0.38/0.58 (define @t56 () (_ @t1 @t42)) % 0.38/0.58 (define @t57 () (forall @t24 (or (not (= @t56 @t55)) @t38))) % 0.38/0.58 (define @t58 () (or @t44 @t40 @t57)) % 0.38/0.58 (define @t59 () (and @t43 @t39)) % 0.38/0.58 (define @t60 () (_ @t1 @t21)) % 0.38/0.58 (define @t61 () (= @t16 @t60)) % 0.38/0.58 (define @t62 () (not @t61)) % 0.38/0.58 (define @t63 () (or @t62 @t38)) % 0.38/0.58 (define @t64 () (lambda @t14 @t16)) % 0.38/0.58 (define @t65 () (_ @t64 @t11)) % 0.38/0.58 (define @t66 () (_ @t64 @t9)) % 0.38/0.58 (define @t67 () (= @t66 @t65)) % 0.38/0.58 (define @t68 () (not @t67)) % 0.38/0.58 (define @t69 () (or @t68 @t38)) % 0.38/0.58 (define @t70 () (forall @t24 @t69)) % 0.38/0.58 (define @t71 () (lambda @t26 @t43)) % 0.38/0.58 (define @t72 () (lambda (@list @t1 @t9) @t16)) % 0.38/0.58 (define @t73 () (_ @t17 @t2)) % 0.38/0.58 (define @t74 () (_ @t71 @t1)) % 0.38/0.58 (define @t75 () (_ @t71 @t2)) % 0.38/0.58 (define @t76 () (and @t75 @t74)) % 0.38/0.58 (define @t77 () (=> @t76 (_ @t71 (_ @t73 @t1)))) % 0.38/0.58 (define @t78 () (forall @t6 @t77)) % 0.38/0.58 (define @t79 () (not @t22)) % 0.38/0.58 (define @t80 () (or @t79 @t38)) % 0.38/0.58 (define @t81 () (forall @t49 (or @t44 @t40 @t37 (= @t36 @t35)))) % 0.38/0.58 (define @t82 () (@quantifiers_skolemize @t81 0)) % 0.38/0.58 (define @t83 () (forall @t24 (or (not (= (_ @t82 @t9) (_ @t82 @t11))) @t38))) % 0.38/0.58 (define @t84 () (@quantifiers_skolemize @t81 3)) % 0.38/0.58 (define @t85 () (@quantifiers_skolemize @t81 2)) % 0.38/0.58 (define @t86 () (= @t85 @t84)) % 0.38/0.58 (define @t87 () (_ @t82 @t84)) % 0.38/0.58 (define @t88 () (@quantifiers_skolemize @t81 1)) % 0.38/0.58 (define @t89 () (_ @t82 @t85)) % 0.38/0.58 (define @t90 () (= (_ @t88 @t89) (_ @t88 @t87))) % 0.38/0.58 (define @t91 () (not @t90)) % 0.38/0.58 (define @t92 () (forall @t24 (or (not (= (_ @t88 @t9) (_ @t88 @t11))) @t38))) % 0.38/0.58 (define @t93 () (not @t92)) % 0.38/0.58 (define @t94 () (not @t83)) % 0.38/0.58 (define @t95 () (or @t94 @t93 @t91 @t86)) % 0.38/0.58 (define @t96 () (@list true)) % 0.38/0.58 (define @t97 () (@list @t95)) % 0.38/0.58 (define @t98 () (or @t91 (= @t87 @t89))) % 0.38/0.58 (define @t99 () (= @t89 @t87)) % 0.38/0.58 (define @t100 () (or @t91 @t99)) % 0.38/0.58 (define @t101 () (not @t99)) % 0.38/0.58 (define @t102 () (or @t101 @t86)) % 0.38/0.58 (define @t103 () (not @t102)) % 0.38/0.58 (define @t104 () (@list true false)) % 0.38/0.58 (define @t105 () (or @t101 (= @t84 @t85))) % 0.38/0.58 (assume @p1 @t8) % 0.38/0.58 (assume @p2 true) % 0.38/0.58 (step @p3 (= tptp.fun_image @t15) :rule refl :args (@t15)) % 0.38/0.58 (step @p4 (= tptp.fun_composition @t17) :rule refl :args (@t17)) % 0.38/0.58 (step @p5 (= tptp.fun_inv_image @t20) :rule refl :args (@t20)) % 0.38/0.58 (step @p6 (= tptp.fun_injective @t27) :rule refl :args (@t27)) % 0.38/0.58 (step @p7 (= tptp.fun_surjective @t28) :rule refl :args (@t28)) % 0.38/0.58 (step @p8 (= tptp.fun_bijective @t29) :rule refl :args (@t29)) % 0.38/0.58 (step @p9 (= tptp.fun_decreasing @t33) :rule refl :args (@t33)) % 0.38/0.58 (step @p10 (= tptp.fun_increasing @t34) :rule refl :args (@t34)) % 0.38/0.58 (step @p11 :rule eq-symm :args (@t35 @t36)) % 0.38/0.58 (step @p12 :rule refl :args (@t37)) % 0.38/0.58 (step @p13 :rule refl :args (@t40)) % 0.38/0.58 (step @p14 :rule refl :args (@t44)) % 0.38/0.58 (step @p15 :rule nary_cong :premises (@p14 @p13 @p12 @p11) :args (@t46)) % 0.38/0.58 (step @p16 :rule aci_norm :args ((= @t48 @t46))) % 0.38/0.58 (step @p17 :rule trans :premises (@p16 @p15)) % 0.38/0.58 (step @p18 :rule cong :premises (@p17) :args (@t50)) % 0.38/0.58 (step @p19 :rule quant-merge-prenex :args ((= (forall @t6 @t52) @t50))) % 0.38/0.58 (step @p20 :rule alpha_equiv :args (@t53 (@list @t36 @t35) (@list @t9 @t11))) % 0.38/0.58 (step @p21 :rule refl :args (@t40)) % 0.38/0.58 (step @p22 :rule refl :args (@t44)) % 0.38/0.58 (step @p23 :rule nary_cong :premises (@p22 @p21 @p20) :args (@t54)) % 0.38/0.58 (step @p24 :rule quant-miniscope-or :args ((= @t52 @t54))) % 0.38/0.58 (step @p25 :rule trans :premises (@p24 @p23)) % 0.38/0.58 (step @p26 :rule symm :premises (@p25)) % 0.38/0.58 (step @p27 :rule cong :premises (@p26) :args ((forall @t6 @t58))) % 0.38/0.58 (step @p28 :rule trans :premises (@p27 @p19)) % 0.38/0.58 (step @p29 :rule trans :premises (@p28 @p18)) % 0.38/0.58 (step @p30 :rule aci_norm :args ((= (or (or @t44 @t40) @t57) @t58))) % 0.38/0.58 (step @p31 :rule refl :args (@t57)) % 0.38/0.58 (step @p32 :rule bool-and-de-morgan :args (@t43 @t39 true)) % 0.38/0.58 (step @p33 :rule nary_cong :premises (@p32 @p31) :args ((or (not @t59) @t57))) % 0.38/0.58 (step @p34 :rule trans :premises (@p33 @p30)) % 0.38/0.58 (step @p35 :rule bool-impl-elim :args (@t59 @t57)) % 0.38/0.58 (step @p36 :rule trans :premises (@p35 @p34)) % 0.38/0.58 (step @p37 :rule cong :premises (@p36) :args ((forall @t6 (=> @t59 @t57)))) % 0.38/0.58 (step @p38 :rule trans :premises (@p37 @p29)) % 0.38/0.58 (step @p39 :rule refl :args (@t38)) % 0.38/0.58 (step @p40 :rule refl :args ((_ @t1 @t21))) % 0.38/0.58 (step @p41 :rule refl :args (@t41)) % 0.38/0.58 (step @p42 :rule cong :premises (@p41) :args (@t55)) % 0.38/0.58 (step @p43 :rule trans :premises (@p42 @p40)) % 0.38/0.58 (step @p44 :rule refl :args (@t1)) % 0.38/0.58 (step @p45 :rule ho_cong :premises (@p44 @p41)) % 0.38/0.58 (step @p46 :rule cong :premises (@p45 @p43) :args ((= (_ @t1 @t41) @t55))) % 0.38/0.58 (step @p47 :rule symm :premises (@p46)) % 0.38/0.58 (step @p48 :rule refl :args (@t60)) % 0.38/0.58 (step @p49 :rule eq_resolve :premises (@p48 @p47)) % 0.38/0.58 (step @p50 :rule refl :args (@t21)) % 0.38/0.58 (step @p51 :rule cong :premises (@p50 @p41) :args ((= @t21 @t41))) % 0.38/0.58 (step @p52 :rule symm :premises (@p51)) % 0.38/0.58 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.38/0.58 (step @p54 :rule ho_cong :premises (@p44 @p53)) % 0.38/0.58 (step @p55 :rule trans :premises (@p54 @p49)) % 0.38/0.58 (step @p56 :rule refl :args ((_ @t1 @t10))) % 0.38/0.58 (step @p57 :rule refl :args (@t42)) % 0.38/0.58 (step @p58 :rule cong :premises (@p57) :args (@t56)) % 0.38/0.58 (step @p59 :rule trans :premises (@p58 @p56)) % 0.38/0.58 (step @p60 :rule ho_cong :premises (@p44 @p57)) % 0.38/0.58 (step @p61 :rule cong :premises (@p60 @p59) :args ((= (_ @t1 @t42) @t56))) % 0.38/0.58 (step @p62 :rule symm :premises (@p61)) % 0.38/0.58 (step @p63 :rule refl :args (@t16)) % 0.38/0.58 (step @p64 :rule eq_resolve :premises (@p63 @p62)) % 0.38/0.58 (step @p65 :rule refl :args (@t10)) % 0.38/0.58 (step @p66 :rule cong :premises (@p65 @p57) :args ((= @t10 @t42))) % 0.38/0.58 (step @p67 :rule symm :premises (@p66)) % 0.38/0.58 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 0.38/0.58 (step @p69 :rule ho_cong :premises (@p44 @p68)) % 0.38/0.58 (step @p70 :rule trans :premises (@p69 @p64)) % 0.38/0.58 (step @p71 :rule cong :premises (@p70 @p55) :args (@t61)) % 0.38/0.58 (step @p72 :rule cong :premises (@p71) :args (@t62)) % 0.38/0.58 (step @p73 :rule nary_cong :premises (@p72 @p39) :args (@t63)) % 0.38/0.58 (step @p74 :rule cong :premises (@p73) :args ((forall @t24 @t63))) % 0.38/0.58 (step @p75 :rule refl :args (@t38)) % 0.38/0.58 (step @p76 :rule beta-reduce :args ((= @t65 @t60))) % 0.38/0.58 (step @p77 :rule beta-reduce :args ((= @t66 @t16))) % 0.38/0.58 (step @p78 :rule cong :premises (@p77 @p76) :args (@t67)) % 0.38/0.58 (step @p79 :rule cong :premises (@p78) :args (@t68)) % 0.38/0.58 (step @p80 :rule nary_cong :premises (@p79 @p75) :args (@t69)) % 0.38/0.58 (step @p81 :rule cong :premises (@p80) :args (@t70)) % 0.38/0.58 (step @p82 :rule trans :premises (@p81 @p74)) % 0.38/0.58 (step @p83 :rule beta-reduce :args ((= (_ @t71 @t64) @t70))) % 0.38/0.58 (step @p84 :rule trans :premises (@p83 @p82)) % 0.38/0.58 (step @p85 :rule beta-reduce :args ((= (_ @t72 @t1) @t64))) % 0.38/0.58 (step @p86 :rule refl :args (@t1)) % 0.38/0.58 (step @p87 :rule beta-reduce :args ((= @t73 @t72))) % 0.38/0.58 (step @p88 :rule ho_cong :premises (@p87 @p86)) % 0.38/0.58 (step @p89 :rule trans :premises (@p88 @p85)) % 0.38/0.58 (step @p90 :rule refl :args (@t71)) % 0.38/0.58 (step @p91 :rule ho_cong :premises (@p90 @p89)) % 0.38/0.58 (step @p92 :rule trans :premises (@p91 @p84)) % 0.38/0.58 (step @p93 :rule beta-reduce :args ((= @t74 @t39))) % 0.38/0.58 (step @p94 :rule beta-reduce :args ((= @t75 @t43))) % 0.38/0.58 (step @p95 :rule nary_cong :premises (@p94 @p93) :args (@t76)) % 0.38/0.58 (step @p96 :rule cong :premises (@p95 @p92) :args (@t77)) % 0.38/0.58 (step @p97 :rule cong :premises (@p96) :args (@t78)) % 0.38/0.58 (step @p98 :rule trans :premises (@p97 @p38)) % 0.38/0.58 (step @p99 :rule cong :premises (@p98) :args ((not @t78))) % 0.38/0.58 (step @p100 :rule refl :args (@t2)) % 0.38/0.58 (step @p101 :rule ho_cong :premises (@p4 @p100)) % 0.38/0.58 (step @p102 :rule ho_cong :premises (@p101 @p86)) % 0.38/0.58 (step @p103 :rule cong :premises (@p68 @p53) :args (@t22)) % 0.38/0.58 (step @p104 :rule cong :premises (@p103) :args (@t79)) % 0.38/0.58 (step @p105 :rule nary_cong :premises (@p104 @p39) :args (@t80)) % 0.38/0.58 (step @p106 :rule cong :premises (@p105) :args ((forall @t24 @t80))) % 0.38/0.58 (step @p107 :rule bool-impl-elim :args (@t22 @t38)) % 0.38/0.58 (step @p108 :rule cong :premises (@p107) :args ((forall @t24 (=> @t22 @t38)))) % 0.38/0.58 (step @p109 :rule trans :premises (@p108 @p106)) % 0.38/0.58 (step @p110 :rule eq-symm :args (@t9 @t11)) % 0.38/0.58 (step @p111 :rule refl :args (@t22)) % 0.38/0.58 (step @p112 :rule cong :premises (@p111 @p110) :args (@t23)) % 0.38/0.58 (step @p113 :rule cong :premises (@p112) :args (@t25)) % 0.38/0.58 (step @p114 :rule trans :premises (@p113 @p109)) % 0.38/0.58 (step @p115 :rule cong :premises (@p114) :args (@t27)) % 0.38/0.58 (step @p116 :rule trans :premises (@p6 @p115)) % 0.38/0.58 (step @p117 :rule ho_cong :premises (@p116 @p102)) % 0.38/0.58 (step @p118 :rule ho_cong :premises (@p116 @p86)) % 0.38/0.58 (step @p119 :rule ho_cong :premises (@p116 @p100)) % 0.38/0.58 (step @p120 :rule nary_cong :premises (@p119 @p118) :args (@t4)) % 0.38/0.58 (step @p121 :rule cong :premises (@p120 @p117) :args (@t5)) % 0.38/0.58 (step @p122 :rule cong :premises (@p121) :args (@t7)) % 0.38/0.58 (step @p123 :rule cong :premises (@p122) :args (@t8)) % 0.38/0.58 (step @p124 :rule trans :premises (@p123 @p99)) % 0.38/0.58 (step @p125 :rule eq_resolve :premises (@p1 @p124)) % 0.38/0.58 (step @p126 :rule skolemize :premises (@p125)) % 0.38/0.58 (step @p127 :rule bool-double-not-elim :args (@t83)) % 0.38/0.58 (step @p128 :rule refl :args (@t95)) % 0.38/0.58 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((or @t95 (not @t94)))) % 0.38/0.58 (step @p130 :rule cnf_or_neg :args (@t95 0)) % 0.38/0.58 (step @p131 :rule eq_resolve :premises (@p130 @p129)) % 0.38/0.58 (step @p132 :rule reordering :premises (@p131) :args ((or @t83 @t95))) % 0.38/0.58 (step @p133 :rule chain_m_resolution :premises (@p132 @p126) :args (@t83 @t96 @t97)) % 0.38/0.58 (step @p134 :rule bool-double-not-elim :args (@t92)) % 0.38/0.58 (step @p135 :rule nary_cong :premises (@p128 @p134) :args ((or @t95 (not @t93)))) % 0.38/0.58 (step @p136 :rule cnf_or_neg :args (@t95 1)) % 0.38/0.58 (step @p137 :rule eq_resolve :premises (@p136 @p135)) % 0.38/0.58 (step @p138 :rule reordering :premises (@p137) :args ((or @t92 @t95))) % 0.38/0.58 (step @p139 :rule chain_m_resolution :premises (@p138 @p126) :args (@t92 @t96 @t97)) % 0.38/0.58 (step @p140 :rule eq-symm :args (@t87 @t89)) % 0.38/0.58 (step @p141 :rule refl :args (@t91)) % 0.38/0.58 (step @p142 :rule nary_cong :premises (@p141 @p140) :args (@t98)) % 0.38/0.58 (step @p143 :rule refl :args (@t92)) % 0.38/0.58 (step @p144 :rule cong :premises (@p143 @p142) :args ((=> @t92 @t98))) % 0.38/0.58 (assume-push @p178 @t92) % 0.38/0.58 (step @p146 :rule instantiate :premises (@p139) :args ((@list @t89 @t87))) % 0.38/0.58 (step-pop @p179 :rule scope :premises (@p146)) % 0.38/0.58 (step @p147 :rule process_scope :premises (@p179) :args (@t98)) % 0.38/0.58 (step @p149 :rule eq_resolve :premises (@p147 @p144)) % 0.38/0.58 (step @p150 :rule implies_elim :premises (@p149)) % 0.38/0.58 (step @p151 :rule chain_m_resolution :premises (@p150 @p139) :args (@t100 (@list false) (@list @t92))) % 0.38/0.58 (step @p152 :rule bool-double-not-elim :args (@t90)) % 0.38/0.58 (step @p153 :rule nary_cong :premises (@p128 @p152) :args ((or @t95 (not @t91)))) % 0.38/0.58 (step @p154 :rule cnf_or_neg :args (@t95 2)) % 0.38/0.58 (step @p155 :rule eq_resolve :premises (@p154 @p153)) % 0.38/0.58 (step @p156 :rule reordering :premises (@p155) :args ((or @t90 @t95))) % 0.38/0.58 (step @p157 :rule chain_m_resolution :premises (@p156 @p126) :args (@t90 @t96 @t97)) % 0.38/0.58 (step @p158 :rule cnf_or_pos :args (@t100)) % 0.38/0.58 (step @p159 :rule reordering :premises (@p158) :args ((or @t91 @t99 (not @t100)))) % 0.38/0.58 (step @p160 :rule chain_m_resolution :premises (@p159 @p157 @p151) :args (@t99 (@list false false) (@list @t90 @t100))) % 0.38/0.58 (step @p161 :rule cnf_or_neg :args (@t95 3)) % 0.38/0.58 (step @p162 :rule chain_m_resolution :premises (@p161 @p126) :args ((not @t86) @t96 @t97)) % 0.38/0.58 (step @p163 :rule cnf_or_pos :args (@t102)) % 0.38/0.58 (step @p164 :rule reordering :premises (@p163) :args ((or @t86 @t101 @t103))) % 0.38/0.58 (step @p165 :rule chain_m_resolution :premises (@p164 @p162 @p160) :args (@t103 @t104 (@list @t86 @t99))) % 0.38/0.58 (step @p166 :rule eq-symm :args (@t84 @t85)) % 0.38/0.58 (step @p167 :rule refl :args (@t101)) % 0.38/0.58 (step @p168 :rule nary_cong :premises (@p167 @p166) :args (@t105)) % 0.38/0.58 (step @p169 :rule refl :args (@t83)) % 0.38/0.58 (step @p170 :rule cong :premises (@p169 @p168) :args ((=> @t83 @t105))) % 0.38/0.58 (assume-push @p180 @t83) % 0.38/0.58 (step @p172 :rule instantiate :premises (@p133) :args ((@list @t85 @t84))) % 0.38/0.58 (step-pop @p181 :rule scope :premises (@p172)) % 0.38/0.58 (step @p173 :rule process_scope :premises (@p181) :args (@t105)) % 0.38/0.58 (step @p175 :rule eq_resolve :premises (@p173 @p170)) % 0.38/0.58 (step @p176 :rule implies_elim :premises (@p175)) % 0.38/0.58 (step @p177 false :rule chain_m_resolution :premises (@p176 @p165 @p133) :args (false @t104 (@list @t102 @t83))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------