%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET747^4 : 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 : n002.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 08:48:33 AM UTC 2026 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET747^4 : 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 : n002.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 16:10:48 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.38/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort $$unsorted 0) % 0.38/0.57 (define tptp.fun_image () (let ((_let_1 (@var "X" $$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)))))))))) % 0.38/0.57 (define tptp.fun_composition () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "G" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_3 _let_1) (_ _let_3 (_ _let_2 _let_1))))))) % 0.38/0.57 (define tptp.fun_inv_image () (let ((_let_1 (@var "X" $$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)))))))))) % 0.38/0.57 (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)))))))) % 0.38/0.57 (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))))))))) % 0.38/0.57 (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))))) % 0.38/0.57 (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)))))))))) % 0.38/0.57 (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)))))))))) % 0.38/0.57 (define @t1 () (@var "LESS" (-> $$unsorted $$unsorted Bool))) % 0.38/0.57 (define @t2 () (@var "G" (-> $$unsorted $$unsorted))) % 0.38/0.57 (define @t3 () (@var "F" (-> $$unsorted $$unsorted))) % 0.38/0.57 (define @t4 () (and (_ (_ tptp.fun_increasing @t3) @t1) (_ (_ tptp.fun_decreasing @t2) @t1))) % 0.38/0.57 (define @t5 () (=> @t4 (_ (_ tptp.fun_decreasing (_ (_ tptp.fun_composition @t3) @t2)) @t1))) % 0.38/0.57 (define @t6 () (@list @t3 @t2 @t1)) % 0.38/0.57 (define @t7 () (forall @t6 @t5)) % 0.38/0.57 (define @t8 () (not @t7)) % 0.38/0.57 (define @t9 () (@var "X" $$unsorted)) % 0.38/0.57 (define @t10 () (_ @t3 @t9)) % 0.38/0.57 (define @t11 () (@var "Y" $$unsorted)) % 0.38/0.57 (define @t12 () (= @t11 @t10)) % 0.38/0.57 (define @t13 () (@var "A" (-> $$unsorted Bool))) % 0.38/0.57 (define @t14 () (@list @t9)) % 0.38/0.57 (define @t15 () (lambda (@list @t3 @t13 @t11) (exists @t14 (and (_ @t13 @t9) @t12)))) % 0.38/0.57 (define @t16 () (_ @t2 @t10)) % 0.38/0.57 (define @t17 () (lambda (@list @t3 @t2 @t9) @t16)) % 0.38/0.57 (define @t18 () (@var "B" (-> $$unsorted Bool))) % 0.38/0.57 (define @t19 () (@list @t11)) % 0.38/0.57 (define @t20 () (lambda (@list @t3 @t18 @t9) (exists @t19 (and (_ @t18 @t11) @t12)))) % 0.38/0.57 (define @t21 () (_ @t3 @t11)) % 0.38/0.57 (define @t22 () (@list @t9 @t11)) % 0.38/0.57 (define @t23 () (@list @t3)) % 0.38/0.57 (define @t24 () (lambda @t23 (forall @t22 (=> (= @t10 @t21) (= @t9 @t11))))) % 0.38/0.57 (define @t25 () (lambda @t23 (forall @t19 (exists @t14 @t12)))) % 0.38/0.57 (define @t26 () (lambda @t23 (and (_ tptp.fun_injective @t3) (_ tptp.fun_surjective @t3)))) % 0.38/0.57 (define @t27 () (@var "SMALLER" (-> $$unsorted $$unsorted Bool))) % 0.38/0.57 (define @t28 () (_ (_ @t27 @t21) @t10)) % 0.38/0.57 (define @t29 () (_ (_ @t27 @t9) @t11)) % 0.38/0.57 (define @t30 () (forall @t22 (=> @t29 @t28))) % 0.38/0.57 (define @t31 () (@list @t3 @t27)) % 0.38/0.57 (define @t32 () (lambda @t31 @t30)) % 0.38/0.57 (define @t33 () (_ (_ @t27 @t10) @t21)) % 0.38/0.57 (define @t34 () (forall @t22 (=> @t29 @t33))) % 0.38/0.57 (define @t35 () (lambda @t31 @t34)) % 0.38/0.57 (define @t36 () (@var "BOUND_VARIABLE_7712" $$unsorted)) % 0.38/0.57 (define @t37 () (@var "BOUND_VARIABLE_7714" $$unsorted)) % 0.38/0.57 (define @t38 () (_ @t1 (_ @t2 (_ @t3 @t37)) (_ @t2 (_ @t3 @t36)))) % 0.38/0.57 (define @t39 () (not (_ @t1 @t36 @t37))) % 0.38/0.57 (define @t40 () (_ @t2 @t9)) % 0.38/0.57 (define @t41 () (_ @t2 @t11)) % 0.38/0.57 (define @t42 () (not (_ @t1 @t9 @t11))) % 0.38/0.57 (define @t43 () (forall @t22 (or @t42 (_ @t1 @t41 @t40)))) % 0.38/0.57 (define @t44 () (not @t43)) % 0.38/0.57 (define @t45 () (_ @t3 @t11)) % 0.38/0.57 (define @t46 () (_ @t3 @t9)) % 0.38/0.57 (define @t47 () (forall @t22 (or @t42 (_ @t1 @t46 @t45)))) % 0.38/0.57 (define @t48 () (not @t47)) % 0.38/0.57 (define @t49 () (or @t48 @t44 @t39 @t38)) % 0.38/0.57 (define @t50 () (or @t39 @t38)) % 0.38/0.57 (define @t51 () (or @t48 @t44 @t50)) % 0.38/0.57 (define @t52 () (@list @t3 @t2 @t1 @t36 @t37)) % 0.38/0.57 (define @t53 () (forall @t52 @t51)) % 0.38/0.57 (define @t54 () (@list @t36 @t37)) % 0.38/0.57 (define @t55 () (forall @t54 @t51)) % 0.38/0.57 (define @t56 () (forall @t54 @t50)) % 0.38/0.57 (define @t57 () (or @t48 @t44 @t56)) % 0.38/0.57 (define @t58 () (_ @t2 @t46)) % 0.38/0.57 (define @t59 () (_ @t2 @t45)) % 0.38/0.57 (define @t60 () (forall @t22 (or @t42 (_ @t1 @t59 @t58)))) % 0.38/0.57 (define @t61 () (or @t48 @t44 @t60)) % 0.38/0.57 (define @t62 () (and @t47 @t43)) % 0.38/0.57 (define @t63 () (_ @t27 @t9 @t11)) % 0.38/0.57 (define @t64 () (not @t63)) % 0.38/0.57 (define @t65 () (@list @t27)) % 0.38/0.57 (define @t66 () (_ @t2 @t21)) % 0.38/0.57 (define @t67 () (_ @t27 @t66 @t16)) % 0.38/0.57 (define @t68 () (or @t64 @t67)) % 0.38/0.57 (define @t69 () (lambda @t14 @t16)) % 0.38/0.57 (define @t70 () (_ @t69 @t9)) % 0.38/0.57 (define @t71 () (_ @t69 @t11)) % 0.38/0.57 (define @t72 () (_ @t27 @t71 @t70)) % 0.38/0.57 (define @t73 () (or @t64 @t72)) % 0.38/0.57 (define @t74 () (forall @t22 @t73)) % 0.38/0.57 (define @t75 () (lambda @t65 @t74)) % 0.38/0.57 (define @t76 () (_ @t27 @t45 @t46)) % 0.38/0.57 (define @t77 () (lambda @t31 (forall @t22 (or @t64 @t76)))) % 0.38/0.57 (define @t78 () (lambda (@list @t2 @t9) @t16)) % 0.38/0.57 (define @t79 () (_ @t17 @t3)) % 0.38/0.57 (define @t80 () (lambda @t65 (forall @t22 (or @t64 (_ @t27 @t41 @t40))))) % 0.38/0.57 (define @t81 () (_ @t77 @t2)) % 0.38/0.57 (define @t82 () (_ @t27 @t46 @t45)) % 0.38/0.57 (define @t83 () (forall @t22 (or @t64 @t82))) % 0.38/0.57 (define @t84 () (lambda @t65 @t83)) % 0.38/0.57 (define @t85 () (_ (lambda @t31 @t83) @t3)) % 0.38/0.57 (define @t86 () (and (_ @t85 @t1) (_ @t81 @t1))) % 0.38/0.57 (define @t87 () (=> @t86 (_ (_ @t77 (_ @t79 @t2)) @t1))) % 0.38/0.57 (define @t88 () (forall @t6 @t87)) % 0.38/0.57 (define @t89 () (not @t29)) % 0.38/0.57 (define @t90 () (or @t89 @t28)) % 0.38/0.57 (define @t91 () (or @t89 @t33)) % 0.38/0.57 (define @t92 () (forall @t52 @t49)) % 0.38/0.57 (define @t93 () (@quantifiers_skolemize @t92 0)) % 0.38/0.57 (define @t94 () (@quantifiers_skolemize @t92 2)) % 0.38/0.57 (define @t95 () (not (_ @t94 @t9 @t11))) % 0.38/0.57 (define @t96 () (forall @t22 (or @t95 (_ @t94 (_ @t93 @t9) (_ @t93 @t11))))) % 0.38/0.57 (define @t97 () (@quantifiers_skolemize @t92 3)) % 0.38/0.57 (define @t98 () (_ @t93 @t97)) % 0.38/0.57 (define @t99 () (@quantifiers_skolemize @t92 1)) % 0.38/0.57 (define @t100 () (@quantifiers_skolemize @t92 4)) % 0.38/0.57 (define @t101 () (_ @t93 @t100)) % 0.38/0.57 (define @t102 () (_ @t94 (_ @t99 @t101) (_ @t99 @t98))) % 0.38/0.57 (define @t103 () (_ @t94 @t97 @t100)) % 0.38/0.57 (define @t104 () (not @t103)) % 0.38/0.57 (define @t105 () (forall @t22 (or @t95 (_ @t94 (_ @t99 @t11) (_ @t99 @t9))))) % 0.38/0.57 (define @t106 () (not @t105)) % 0.38/0.57 (define @t107 () (not @t96)) % 0.38/0.57 (define @t108 () (or @t107 @t106 @t104 @t102)) % 0.38/0.57 (define @t109 () (@list true)) % 0.38/0.57 (define @t110 () (@list @t108)) % 0.38/0.57 (define @t111 () (_ @t94 @t98 @t101)) % 0.38/0.57 (define @t112 () (not @t111)) % 0.38/0.57 (define @t113 () (or @t112 @t102)) % 0.38/0.57 (define @t114 () (@list true false)) % 0.38/0.57 (define @t115 () (or @t104 @t111)) % 0.38/0.57 (define @t116 () (not @t115)) % 0.38/0.57 (assume @p1 @t8) % 0.38/0.57 (assume @p2 true) % 0.38/0.57 (step @p3 (= tptp.fun_image @t15) :rule refl :args (@t15)) % 0.38/0.57 (step @p4 (= tptp.fun_composition @t17) :rule refl :args (@t17)) % 0.38/0.57 (step @p5 (= tptp.fun_inv_image @t20) :rule refl :args (@t20)) % 0.38/0.57 (step @p6 (= tptp.fun_injective @t24) :rule refl :args (@t24)) % 0.38/0.57 (step @p7 (= tptp.fun_surjective @t25) :rule refl :args (@t25)) % 0.38/0.57 (step @p8 (= tptp.fun_bijective @t26) :rule refl :args (@t26)) % 0.38/0.57 (step @p9 (= tptp.fun_decreasing @t32) :rule refl :args (@t32)) % 0.38/0.57 (step @p10 (= tptp.fun_increasing @t35) :rule refl :args (@t35)) % 0.38/0.57 (step @p11 :rule aci_norm :args ((= @t51 @t49))) % 0.38/0.57 (step @p12 :rule cong :premises (@p11) :args (@t53)) % 0.38/0.57 (step @p13 :rule quant-merge-prenex :args ((= (forall @t6 @t55) @t53))) % 0.38/0.57 (step @p14 :rule alpha_equiv :args (@t56 (@list @t36 @t37) (@list @t9 @t11))) % 0.38/0.57 (step @p15 :rule refl :args (@t44)) % 0.38/0.57 (step @p16 :rule refl :args (@t48)) % 0.38/0.57 (step @p17 :rule nary_cong :premises (@p16 @p15 @p14) :args (@t57)) % 0.38/0.57 (step @p18 :rule quant-miniscope-or :args ((= @t55 @t57))) % 0.38/0.57 (step @p19 :rule trans :premises (@p18 @p17)) % 0.38/0.57 (step @p20 :rule symm :premises (@p19)) % 0.38/0.57 (step @p21 :rule cong :premises (@p20) :args ((forall @t6 @t61))) % 0.38/0.57 (step @p22 :rule trans :premises (@p21 @p13)) % 0.38/0.57 (step @p23 :rule trans :premises (@p22 @p12)) % 0.38/0.57 (step @p24 :rule aci_norm :args ((= (or (or @t48 @t44) @t60) @t61))) % 0.38/0.57 (step @p25 :rule refl :args (@t60)) % 0.38/0.57 (step @p26 :rule bool-and-de-morgan :args (@t47 @t43 true)) % 0.38/0.57 (step @p27 :rule nary_cong :premises (@p26 @p25) :args ((or (not @t62) @t60))) % 0.38/0.57 (step @p28 :rule trans :premises (@p27 @p24)) % 0.38/0.57 (step @p29 :rule bool-impl-elim :args (@t62 @t60)) % 0.38/0.57 (step @p30 :rule trans :premises (@p29 @p28)) % 0.38/0.57 (step @p31 :rule cong :premises (@p30) :args ((forall @t6 (=> @t62 @t60)))) % 0.38/0.57 (step @p32 :rule trans :premises (@p31 @p23)) % 0.38/0.57 (step @p33 :rule beta-reduce :args ((= (_ (lambda @t65 (forall @t22 (or @t64 (_ @t27 @t59 @t58)))) @t1) @t60))) % 0.38/0.57 (step @p34 :rule refl :args (@t1)) % 0.38/0.57 (step @p35 :rule refl :args ((_ @t2 @t10))) % 0.38/0.57 (step @p36 :rule refl :args (@t46)) % 0.38/0.57 (step @p37 :rule cong :premises (@p36) :args (@t58)) % 0.38/0.57 (step @p38 :rule trans :premises (@p37 @p35)) % 0.38/0.57 (step @p39 :rule refl :args (@t2)) % 0.38/0.57 (step @p40 :rule ho_cong :premises (@p39 @p36)) % 0.38/0.57 (step @p41 :rule cong :premises (@p40 @p38) :args ((= (_ @t2 @t46) @t58))) % 0.38/0.57 (step @p42 :rule symm :premises (@p41)) % 0.38/0.57 (step @p43 :rule refl :args (@t16)) % 0.38/0.57 (step @p44 :rule eq_resolve :premises (@p43 @p42)) % 0.38/0.57 (step @p45 :rule refl :args (@t10)) % 0.38/0.57 (step @p46 :rule cong :premises (@p45 @p36) :args ((= @t10 @t46))) % 0.38/0.57 (step @p47 :rule symm :premises (@p46)) % 0.38/0.57 (step @p48 :rule eq_resolve :premises (@p45 @p47)) % 0.38/0.57 (step @p49 :rule ho_cong :premises (@p39 @p48)) % 0.38/0.57 (step @p50 :rule trans :premises (@p49 @p44)) % 0.38/0.57 (step @p51 :rule refl :args ((_ @t2 @t21))) % 0.38/0.57 (step @p52 :rule refl :args (@t45)) % 0.38/0.57 (step @p53 :rule cong :premises (@p52) :args (@t59)) % 0.38/0.57 (step @p54 :rule trans :premises (@p53 @p51)) % 0.38/0.57 (step @p55 :rule ho_cong :premises (@p39 @p52)) % 0.38/0.57 (step @p56 :rule cong :premises (@p55 @p54) :args ((= (_ @t2 @t45) @t59))) % 0.38/0.57 (step @p57 :rule symm :premises (@p56)) % 0.38/0.57 (step @p58 :rule refl :args (@t66)) % 0.38/0.57 (step @p59 :rule eq_resolve :premises (@p58 @p57)) % 0.38/0.57 (step @p60 :rule refl :args (@t21)) % 0.38/0.57 (step @p61 :rule cong :premises (@p60 @p52) :args ((= @t21 @t45))) % 0.38/0.57 (step @p62 :rule symm :premises (@p61)) % 0.38/0.57 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 0.38/0.57 (step @p64 :rule ho_cong :premises (@p39 @p63)) % 0.38/0.57 (step @p65 :rule trans :premises (@p64 @p59)) % 0.38/0.57 (step @p66 :rule cong :premises (@p65 @p50) :args (@t67)) % 0.38/0.57 (step @p67 :rule refl :args (@t64)) % 0.38/0.57 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t68)) % 0.38/0.57 (step @p69 :rule cong :premises (@p68) :args ((forall @t22 @t68))) % 0.38/0.57 (step @p70 :rule beta-reduce :args ((= @t70 @t16))) % 0.38/0.57 (step @p71 :rule beta-reduce :args ((= @t71 @t66))) % 0.38/0.57 (step @p72 :rule cong :premises (@p71 @p70) :args (@t72)) % 0.38/0.57 (step @p73 :rule refl :args (@t64)) % 0.38/0.57 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t73)) % 0.38/0.57 (step @p75 :rule cong :premises (@p74) :args (@t74)) % 0.38/0.57 (step @p76 :rule trans :premises (@p75 @p69)) % 0.38/0.57 (step @p77 :rule cong :premises (@p76) :args (@t75)) % 0.38/0.57 (step @p78 :rule beta-reduce :args ((= (_ @t77 @t69) @t75))) % 0.38/0.57 (step @p79 :rule trans :premises (@p78 @p77)) % 0.38/0.57 (step @p80 :rule beta-reduce :args ((= (_ @t78 @t2) @t69))) % 0.38/0.57 (step @p81 :rule refl :args (@t2)) % 0.38/0.57 (step @p82 :rule beta-reduce :args ((= @t79 @t78))) % 0.38/0.57 (step @p83 :rule ho_cong :premises (@p82 @p81)) % 0.38/0.57 (step @p84 :rule trans :premises (@p83 @p80)) % 0.38/0.57 (step @p85 :rule refl :args (@t77)) % 0.38/0.57 (step @p86 :rule ho_cong :premises (@p85 @p84)) % 0.38/0.57 (step @p87 :rule trans :premises (@p86 @p79)) % 0.38/0.57 (step @p88 :rule ho_cong :premises (@p87 @p34)) % 0.38/0.57 (step @p89 :rule trans :premises (@p88 @p33)) % 0.38/0.57 (step @p90 :rule beta-reduce :args ((= (_ @t80 @t1) @t43))) % 0.38/0.57 (step @p91 :rule beta-reduce :args ((= @t81 @t80))) % 0.38/0.57 (step @p92 :rule ho_cong :premises (@p91 @p34)) % 0.38/0.57 (step @p93 :rule trans :premises (@p92 @p90)) % 0.38/0.57 (step @p94 :rule beta-reduce :args ((= (_ @t84 @t1) @t47))) % 0.38/0.57 (step @p95 :rule beta-reduce :args ((= @t85 @t84))) % 0.38/0.57 (step @p96 :rule ho_cong :premises (@p95 @p34)) % 0.38/0.57 (step @p97 :rule trans :premises (@p96 @p94)) % 0.38/0.57 (step @p98 :rule nary_cong :premises (@p97 @p93) :args (@t86)) % 0.38/0.57 (step @p99 :rule cong :premises (@p98 @p89) :args (@t87)) % 0.38/0.57 (step @p100 :rule cong :premises (@p99) :args (@t88)) % 0.38/0.57 (step @p101 :rule trans :premises (@p100 @p32)) % 0.38/0.57 (step @p102 :rule cong :premises (@p101) :args ((not @t88))) % 0.38/0.57 (step @p103 :rule refl :args (@t3)) % 0.38/0.57 (step @p104 :rule ho_cong :premises (@p4 @p103)) % 0.38/0.57 (step @p105 :rule ho_cong :premises (@p104 @p81)) % 0.38/0.57 (step @p106 :rule refl :args ((_ @t27 @t21 @t10))) % 0.38/0.57 (step @p107 :rule cong :premises (@p52 @p36) :args (@t76)) % 0.38/0.57 (step @p108 :rule trans :premises (@p107 @p106)) % 0.38/0.57 (step @p109 :rule refl :args (@t27)) % 0.38/0.57 (step @p110 :rule ho_cong :premises (@p109 @p52)) % 0.38/0.57 (step @p111 :rule ho_cong :premises (@p110 @p36)) % 0.38/0.57 (step @p112 :rule cong :premises (@p111 @p108) :args ((= (_ (_ @t27 @t45) @t46) @t76))) % 0.38/0.57 (step @p113 :rule symm :premises (@p112)) % 0.38/0.57 (step @p114 :rule refl :args (@t28)) % 0.38/0.57 (step @p115 :rule eq_resolve :premises (@p114 @p113)) % 0.38/0.57 (step @p116 :rule ho_cong :premises (@p109 @p63)) % 0.38/0.57 (step @p117 :rule ho_cong :premises (@p116 @p48)) % 0.38/0.57 (step @p118 :rule trans :premises (@p117 @p115)) % 0.38/0.57 (step @p119 :rule refl :args (@t63)) % 0.38/0.57 (step @p120 :rule refl :args (@t29)) % 0.38/0.57 (step @p121 :rule cong :premises (@p120 @p119) :args ((= @t29 @t63))) % 0.38/0.57 (step @p122 :rule symm :premises (@p121)) % 0.38/0.57 (step @p123 :rule eq_resolve :premises (@p120 @p122)) % 0.38/0.57 (step @p124 :rule cong :premises (@p123) :args (@t89)) % 0.38/0.57 (step @p125 :rule nary_cong :premises (@p124 @p118) :args (@t90)) % 0.38/0.57 (step @p126 :rule cong :premises (@p125) :args ((forall @t22 @t90))) % 0.38/0.57 (step @p127 :rule bool-impl-elim :args (@t29 @t28)) % 0.38/0.57 (step @p128 :rule cong :premises (@p127) :args (@t30)) % 0.38/0.57 (step @p129 :rule trans :premises (@p128 @p126)) % 0.38/0.57 (step @p130 :rule cong :premises (@p129) :args (@t32)) % 0.38/0.57 (step @p131 :rule trans :premises (@p9 @p130)) % 0.38/0.57 (step @p132 :rule ho_cong :premises (@p131 @p105)) % 0.38/0.57 (step @p133 :rule ho_cong :premises (@p132 @p34)) % 0.38/0.57 (step @p134 :rule ho_cong :premises (@p131 @p81)) % 0.38/0.57 (step @p135 :rule ho_cong :premises (@p134 @p34)) % 0.38/0.57 (step @p136 :rule refl :args ((_ @t27 @t10 @t21))) % 0.38/0.57 (step @p137 :rule cong :premises (@p36 @p52) :args (@t82)) % 0.38/0.57 (step @p138 :rule trans :premises (@p137 @p136)) % 0.38/0.57 (step @p139 :rule ho_cong :premises (@p109 @p36)) % 0.38/0.57 (step @p140 :rule ho_cong :premises (@p139 @p52)) % 0.38/0.57 (step @p141 :rule cong :premises (@p140 @p138) :args ((= (_ (_ @t27 @t46) @t45) @t82))) % 0.38/0.57 (step @p142 :rule symm :premises (@p141)) % 0.38/0.57 (step @p143 :rule refl :args (@t33)) % 0.38/0.57 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 0.38/0.57 (step @p145 :rule ho_cong :premises (@p109 @p48)) % 0.38/0.57 (step @p146 :rule ho_cong :premises (@p145 @p63)) % 0.38/0.57 (step @p147 :rule trans :premises (@p146 @p144)) % 0.38/0.57 (step @p148 :rule nary_cong :premises (@p124 @p147) :args (@t91)) % 0.38/0.57 (step @p149 :rule cong :premises (@p148) :args ((forall @t22 @t91))) % 0.38/0.57 (step @p150 :rule bool-impl-elim :args (@t29 @t33)) % 0.38/0.57 (step @p151 :rule cong :premises (@p150) :args (@t34)) % 0.38/0.57 (step @p152 :rule trans :premises (@p151 @p149)) % 0.38/0.57 (step @p153 :rule cong :premises (@p152) :args (@t35)) % 0.38/0.57 (step @p154 :rule trans :premises (@p10 @p153)) % 0.38/0.57 (step @p155 :rule ho_cong :premises (@p154 @p103)) % 0.38/0.57 (step @p156 :rule ho_cong :premises (@p155 @p34)) % 0.38/0.57 (step @p157 :rule nary_cong :premises (@p156 @p135) :args (@t4)) % 0.38/0.57 (step @p158 :rule cong :premises (@p157 @p133) :args (@t5)) % 0.38/0.57 (step @p159 :rule cong :premises (@p158) :args (@t7)) % 0.38/0.57 (step @p160 :rule cong :premises (@p159) :args (@t8)) % 0.38/0.57 (step @p161 :rule trans :premises (@p160 @p102)) % 0.38/0.57 (step @p162 :rule eq_resolve :premises (@p1 @p161)) % 0.38/0.57 (step @p163 :rule skolemize :premises (@p162)) % 0.38/0.57 (step @p164 :rule bool-double-not-elim :args (@t96)) % 0.38/0.57 (step @p165 :rule refl :args (@t108)) % 0.38/0.57 (step @p166 :rule nary_cong :premises (@p165 @p164) :args ((or @t108 (not @t107)))) % 0.38/0.57 (step @p167 :rule cnf_or_neg :args (@t108 0)) % 0.38/0.57 (step @p168 :rule eq_resolve :premises (@p167 @p166)) % 0.38/0.57 (step @p169 :rule reordering :premises (@p168) :args ((or @t96 @t108))) % 0.38/0.57 (step @p170 :rule chain_m_resolution :premises (@p169 @p163) :args (@t96 @t109 @t110)) % 0.38/0.57 (step @p171 :rule bool-double-not-elim :args (@t105)) % 0.38/0.57 (step @p172 :rule nary_cong :premises (@p165 @p171) :args ((or @t108 (not @t106)))) % 0.38/0.57 (step @p173 :rule cnf_or_neg :args (@t108 1)) % 0.38/0.57 (step @p174 :rule eq_resolve :premises (@p173 @p172)) % 0.38/0.57 (step @p175 :rule reordering :premises (@p174) :args ((or @t105 @t108))) % 0.38/0.57 (step @p176 :rule chain_m_resolution :premises (@p175 @p163) :args (@t105 @t109 @t110)) % 0.38/0.57 (step @p177 :rule instantiate :premises (@p176) :args ((@list @t98 @t101))) % 0.38/0.57 (step @p178 :rule cnf_or_neg :args (@t108 3)) % 0.38/0.57 (step @p179 :rule chain_m_resolution :premises (@p178 @p163) :args ((not @t102) @t109 @t110)) % 0.38/0.57 (step @p180 :rule cnf_or_pos :args (@t113)) % 0.38/0.57 (step @p181 :rule reordering :premises (@p180) :args ((or @t102 @t112 (not @t113)))) % 0.38/0.57 (step @p182 :rule chain_m_resolution :premises (@p181 @p179 @p177) :args (@t112 @t114 (@list @t102 @t113))) % 0.38/0.57 (step @p183 :rule bool-double-not-elim :args (@t103)) % 0.38/0.57 (step @p184 :rule nary_cong :premises (@p165 @p183) :args ((or @t108 (not @t104)))) % 0.38/0.57 (step @p185 :rule cnf_or_neg :args (@t108 2)) % 0.38/0.57 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.38/0.57 (step @p187 :rule reordering :premises (@p186) :args ((or @t103 @t108))) % 0.38/0.57 (step @p188 :rule chain_m_resolution :premises (@p187 @p163) :args (@t103 @t109 @t110)) % 0.38/0.57 (step @p189 :rule cnf_or_pos :args (@t115)) % 0.38/0.57 (step @p190 :rule reordering :premises (@p189) :args ((or @t104 @t111 @t116))) % 0.38/0.57 (step @p191 :rule chain_m_resolution :premises (@p190 @p188 @p182) :args (@t116 (@list false true) (@list @t103 @t111))) % 0.38/0.57 (assume-push @p198 @t96) % 0.38/0.57 (step @p193 :rule instantiate :premises (@p170) :args ((@list @t97 @t100))) % 0.38/0.57 (step-pop @p199 :rule scope :premises (@p193)) % 0.38/0.57 (step @p194 :rule process_scope :premises (@p199) :args (@t115)) % 0.38/0.57 (step @p196 :rule implies_elim :premises (@p194)) % 0.38/0.57 (step @p197 false :rule chain_m_resolution :premises (@p196 @p191 @p170) :args (false @t114 (@list @t115 @t96))) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------