%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU778^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n028.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 08:53:09 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 : SEU778^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n028.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 17:51:35 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----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 $$unsorted 0) % 0.38/0.58 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.58 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.58 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.58 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.38/0.58 (declare-const tptp.dpsetconstr (-> $$unsorted $$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted)) % 0.38/0.58 (declare-const tptp.setOfPairsIsBReln1 Bool) % 0.38/0.58 (define tptp.breln () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (let ((_let_3 (@var "C" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (_ (_ tptp.subset _let_3) (_ (_ tptp.cartprod _let_2) _let_1))))))) % 0.38/0.58 (define tptp.breln1 () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2 _let_1) (_ (_ (_ tptp.breln _let_2) _let_2) _let_1))))) % 0.38/0.58 (define tptp.breln1compset () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "Xy" $$unsorted))) (let ((_let_3 (@var "Xz" $$unsorted))) (let ((_let_4 (@var "R" $$unsorted))) (let ((_let_5 (@var "Xx" $$unsorted))) (let ((_let_6 (@var "A" $$unsorted))) (lambda (@list _let_6 _let_4 _let_1) (_ (_ (_ tptp.dpsetconstr _let_6) _let_6) (lambda (@list _let_5 _let_2) (exists (@list _let_3) (and (_ (_ tptp.in _let_3) _let_6) (_ (_ tptp.in (_ (_ tptp.kpair _let_5) _let_3)) _let_4) (_ (_ tptp.in (_ (_ tptp.kpair _let_3) _let_2)) _let_1))))))))))))) % 0.38/0.58 (define @t1 () (@var "Xy" $$unsorted)) % 0.38/0.58 (define @t2 () (@var "Xx" $$unsorted)) % 0.38/0.58 (define @t3 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.38/0.58 (define @t4 () (_ (_ @t3 @t2) @t1)) % 0.38/0.58 (define @t5 () (@list @t2 @t1)) % 0.38/0.58 (define @t6 () (lambda @t5 @t4)) % 0.38/0.58 (define @t7 () (@var "A" $$unsorted)) % 0.38/0.58 (define @t8 () (_ (_ tptp.dpsetconstr @t7) @t7)) % 0.38/0.58 (define @t9 () (_ @t8 @t6)) % 0.38/0.58 (define @t10 () (_ tptp.breln1 @t7)) % 0.38/0.58 (define @t11 () (@list @t7 @t3)) % 0.38/0.58 (define @t12 () (forall @t11 (_ @t10 @t9))) % 0.38/0.58 (define @t13 () (= tptp.setOfPairsIsBReln1 @t12)) % 0.38/0.58 (define @t14 () (@var "S" $$unsorted)) % 0.38/0.58 (define @t15 () (@var "R" $$unsorted)) % 0.38/0.58 (define @t16 () (=> (_ @t10 @t14) (_ @t10 (_ (_ (_ tptp.breln1compset @t7) @t15) @t14)))) % 0.38/0.58 (define @t17 () (@list @t14)) % 0.38/0.58 (define @t18 () (forall @t17 @t16)) % 0.38/0.58 (define @t19 () (=> (_ @t10 @t15) @t18)) % 0.38/0.58 (define @t20 () (@list @t7 @t15)) % 0.38/0.58 (define @t21 () (forall @t20 @t19)) % 0.38/0.58 (define @t22 () (=> tptp.setOfPairsIsBReln1 @t21)) % 0.38/0.58 (define @t23 () (not @t22)) % 0.38/0.58 (define @t24 () (@var "B" $$unsorted)) % 0.38/0.58 (define @t25 () (_ tptp.cartprod @t7)) % 0.38/0.58 (define @t26 () (@var "C" $$unsorted)) % 0.38/0.58 (define @t27 () (_ tptp.subset @t26)) % 0.38/0.58 (define @t28 () (_ @t27 (_ @t25 @t24))) % 0.38/0.58 (define @t29 () (lambda (@list @t7 @t24 @t26) @t28)) % 0.38/0.58 (define @t30 () (lambda @t20 (_ (_ (_ tptp.breln @t7) @t7) @t15))) % 0.38/0.58 (define @t31 () (@var "Xz" $$unsorted)) % 0.38/0.58 (define @t32 () (_ (_ tptp.kpair @t31) @t1)) % 0.38/0.58 (define @t33 () (_ (_ tptp.in @t32) @t14)) % 0.38/0.58 (define @t34 () (_ (_ tptp.kpair @t2) @t31)) % 0.38/0.58 (define @t35 () (_ (_ tptp.in @t34) @t15)) % 0.38/0.58 (define @t36 () (_ (_ tptp.in @t31) @t7)) % 0.38/0.58 (define @t37 () (and @t36 @t35 @t33)) % 0.38/0.58 (define @t38 () (@list @t31)) % 0.38/0.58 (define @t39 () (exists @t38 @t37)) % 0.38/0.58 (define @t40 () (lambda @t5 @t39)) % 0.38/0.58 (define @t41 () (@list @t7 @t15 @t14)) % 0.38/0.58 (define @t42 () (lambda @t41 (_ @t8 @t40))) % 0.38/0.58 (define @t43 () (tptp.cartprod @t7 @t7)) % 0.38/0.58 (define @t44 () (@var "BOUND_VARIABLE_7628" $$unsorted)) % 0.38/0.58 (define @t45 () (tptp.kpair @t31 @t1)) % 0.38/0.58 (define @t46 () (tptp.kpair @t2 @t31)) % 0.38/0.58 (define @t47 () (tptp.in @t46 @t15)) % 0.38/0.58 (define @t48 () (not @t47)) % 0.38/0.58 (define @t49 () (tptp.in @t31 @t7)) % 0.38/0.58 (define @t50 () (not @t49)) % 0.38/0.58 (define @t51 () (tptp.subset (tptp.dpsetconstr @t7 @t7 (lambda @t5 (not (forall @t38 (or @t50 @t48 (not (tptp.in @t45 @t44))))))) @t43)) % 0.38/0.58 (define @t52 () (not (tptp.subset @t44 @t43))) % 0.38/0.58 (define @t53 () (tptp.subset @t15 @t43)) % 0.38/0.58 (define @t54 () (not @t53)) % 0.38/0.58 (define @t55 () (or @t54 @t52 @t51)) % 0.38/0.58 (define @t56 () (@list @t7 @t15 @t44)) % 0.38/0.58 (define @t57 () (forall @t56 @t55)) % 0.38/0.58 (define @t58 () (_ @t3 @t2 @t1)) % 0.38/0.58 (define @t59 () (lambda @t5 @t58)) % 0.38/0.58 (define @t60 () (tptp.dpsetconstr @t7 @t7 @t59)) % 0.38/0.58 (define @t61 () (tptp.subset @t60 @t43)) % 0.38/0.58 (define @t62 () (_ @t25 @t7)) % 0.38/0.58 (define @t63 () (_ (_ tptp.subset @t9) @t62)) % 0.38/0.58 (define @t64 () (_ tptp.subset @t15)) % 0.38/0.58 (define @t65 () (_ @t64 @t62)) % 0.38/0.58 (define @t66 () (lambda (@list @t15) @t65)) % 0.38/0.58 (define @t67 () (_ (lambda @t20 @t65) @t7)) % 0.38/0.58 (define @t68 () (forall @t11 (_ @t67 @t9))) % 0.38/0.58 (define @t69 () (lambda (@list @t26) (_ @t27 @t62))) % 0.38/0.58 (define @t70 () (lambda (@list @t24 @t26) @t28)) % 0.38/0.58 (define @t71 () (=> tptp.setOfPairsIsBReln1 @t57)) % 0.38/0.58 (define @t72 () (or @t52 @t51)) % 0.38/0.58 (define @t73 () (or @t54 @t72)) % 0.38/0.58 (define @t74 () (forall @t56 @t73)) % 0.38/0.58 (define @t75 () (@list @t44)) % 0.38/0.58 (define @t76 () (forall @t75 @t73)) % 0.38/0.58 (define @t77 () (forall @t75 @t72)) % 0.38/0.58 (define @t78 () (or @t54 @t77)) % 0.38/0.58 (define @t79 () (tptp.in @t45 @t14)) % 0.38/0.58 (define @t80 () (not @t79)) % 0.38/0.58 (define @t81 () (or @t50 @t48 @t80)) % 0.38/0.58 (define @t82 () (forall @t38 @t81)) % 0.38/0.58 (define @t83 () (not @t82)) % 0.38/0.58 (define @t84 () (lambda @t5 @t83)) % 0.38/0.58 (define @t85 () (tptp.dpsetconstr @t7 @t7 @t84)) % 0.38/0.58 (define @t86 () (tptp.subset @t85 @t43)) % 0.38/0.58 (define @t87 () (tptp.subset @t14 @t43)) % 0.38/0.58 (define @t88 () (forall @t17 (or (not @t87) @t86))) % 0.38/0.58 (define @t89 () (not @t65)) % 0.38/0.58 (define @t90 () (or @t89 @t88)) % 0.38/0.58 (define @t91 () (not @t33)) % 0.38/0.58 (define @t92 () (not @t35)) % 0.38/0.58 (define @t93 () (not @t36)) % 0.38/0.58 (define @t94 () (or @t93 @t92 @t91)) % 0.38/0.58 (define @t95 () (forall @t38 @t94)) % 0.38/0.58 (define @t96 () (lambda @t5 (not @t95))) % 0.38/0.58 (define @t97 () (_ @t8 @t96)) % 0.38/0.58 (define @t98 () (_ @t8 @t84)) % 0.38/0.58 (define @t99 () (_ tptp.subset @t14)) % 0.38/0.58 (define @t100 () (_ @t99 @t62)) % 0.38/0.58 (define @t101 () (not @t100)) % 0.38/0.58 (define @t102 () (_ (_ tptp.subset @t98) @t62)) % 0.38/0.58 (define @t103 () (or @t101 @t102)) % 0.38/0.58 (define @t104 () (lambda @t17 @t98)) % 0.38/0.58 (define @t105 () (lambda (@list @t15 @t14) @t98)) % 0.38/0.58 (define @t106 () (_ (lambda @t41 @t98) @t7)) % 0.38/0.58 (define @t107 () (=> (_ @t67 @t14) (_ @t67 (_ (_ @t106 @t15) @t14)))) % 0.38/0.58 (define @t108 () (forall @t17 @t107)) % 0.38/0.58 (define @t109 () (=> (_ @t67 @t15) @t108)) % 0.38/0.58 (define @t110 () (forall @t20 @t109)) % 0.38/0.58 (define @t111 () (=> tptp.setOfPairsIsBReln1 @t110)) % 0.38/0.58 (define @t112 () (forall @t38 (not @t37))) % 0.38/0.58 (define @t113 () (not @t112)) % 0.38/0.58 (define @t114 () (@quantifiers_skolemize @t57 0)) % 0.38/0.58 (define @t115 () (tptp.cartprod @t114 @t114)) % 0.38/0.58 (define @t116 () (@quantifiers_skolemize @t57 2)) % 0.38/0.58 (define @t117 () (@quantifiers_skolemize @t57 1)) % 0.38/0.58 (define @t118 () (lambda @t5 (not (forall @t38 (or (not (tptp.in @t31 @t114)) (not (tptp.in @t46 @t117)) (not (tptp.in @t45 @t116))))))) % 0.38/0.58 (define @t119 () (@purify @t118)) % 0.38/0.58 (define @t120 () (tptp.subset (tptp.dpsetconstr @t114 @t114 @t119) @t115)) % 0.38/0.58 (define @t121 () (not (tptp.subset @t116 @t115))) % 0.38/0.58 (define @t122 () (not (tptp.subset @t117 @t115))) % 0.38/0.58 (define @t123 () (or @t122 @t121 @t120)) % 0.38/0.58 (define @t124 () (not @t123)) % 0.38/0.58 (define @t125 () (not @t57)) % 0.38/0.58 (define @t126 () (tptp.dpsetconstr @t114 @t114 @t118)) % 0.38/0.58 (define @t127 () (tptp.subset @t126 @t115)) % 0.38/0.58 (define @t128 () (or @t122 @t121 @t127)) % 0.38/0.58 (define @t129 () (not @t128)) % 0.38/0.58 (define @t130 () (@list true)) % 0.38/0.58 (define @t131 () (forall @t11 (tptp.subset (tptp.dpsetconstr @t7 @t7 @t3) @t43))) % 0.38/0.58 (assume @p1 @t13) % 0.38/0.58 (assume @p2 @t23) % 0.38/0.58 (assume @p3 true) % 0.38/0.58 (step @p4 (= tptp.breln @t29) :rule refl :args (@t29)) % 0.38/0.58 (step @p5 (= tptp.breln1 @t30) :rule refl :args (@t30)) % 0.38/0.58 (step @p6 (= tptp.breln1compset @t42) :rule refl :args (@t42)) % 0.38/0.58 (step @p7 :rule refl :args (@t57)) % 0.38/0.58 (step @p8 :rule refl :args (@t43)) % 0.38/0.58 (step @p9 :rule lambda-elim :args ((= @t59 @t3))) % 0.38/0.58 (step @p10 :rule refl :args (@t7)) % 0.38/0.58 (step @p11 :rule cong :premises (@p10 @p10 @p9) :args (@t60)) % 0.38/0.58 (step @p12 :rule cong :premises (@p11 @p8) :args (@t61)) % 0.38/0.58 (step @p13 :rule cong :premises (@p12) :args ((forall @t11 @t61))) % 0.38/0.58 (step @p14 :rule refl :args ((tptp.subset @t9 @t62))) % 0.38/0.58 (step @p15 :rule refl :args (@t43)) % 0.38/0.58 (step @p16 :rule refl :args ((tptp.dpsetconstr @t7 @t7 @t6))) % 0.38/0.58 (step @p17 :rule refl :args (@t58)) % 0.38/0.58 (step @p18 :rule cong :premises (@p17) :args (@t59)) % 0.38/0.58 (step @p19 :rule refl :args (@t7)) % 0.38/0.58 (step @p20 :rule cong :premises (@p19 @p19 @p18) :args (@t60)) % 0.38/0.58 (step @p21 :rule trans :premises (@p20 @p16)) % 0.38/0.58 (step @p22 :rule cong :premises (@p21 @p15) :args (@t61)) % 0.38/0.58 (step @p23 :rule trans :premises (@p22 @p14)) % 0.38/0.58 (step @p24 :rule refl :args (tptp.subset)) % 0.38/0.58 (step @p25 :rule ho_cong :premises (@p24 @p21)) % 0.38/0.58 (step @p26 :rule ho_cong :premises (@p25 @p15)) % 0.38/0.58 (step @p27 :rule cong :premises (@p26 @p23) :args ((= (_ (_ tptp.subset @t60) @t43) @t61))) % 0.38/0.58 (step @p28 :rule symm :premises (@p27)) % 0.38/0.58 (step @p29 :rule refl :args (@t63)) % 0.38/0.58 (step @p30 :rule eq_resolve :premises (@p29 @p28)) % 0.38/0.58 (step @p31 :rule refl :args (@t62)) % 0.38/0.58 (step @p32 :rule cong :premises (@p31 @p15) :args ((= @t62 @t43))) % 0.38/0.58 (step @p33 :rule symm :premises (@p32)) % 0.38/0.58 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 0.38/0.58 (step @p35 :rule refl :args (@t8)) % 0.38/0.58 (step @p36 :rule ho_cong :premises (@p35 @p18)) % 0.38/0.58 (step @p37 :rule cong :premises (@p36 @p21) :args ((= (_ @t8 @t59) @t60))) % 0.38/0.58 (step @p38 :rule symm :premises (@p37)) % 0.38/0.58 (step @p39 :rule refl :args (@t9)) % 0.38/0.58 (step @p40 :rule eq_resolve :premises (@p39 @p38)) % 0.38/0.58 (step @p41 :rule refl :args (@t4)) % 0.38/0.58 (step @p42 :rule cong :premises (@p41 @p17) :args ((= @t4 @t58))) % 0.38/0.58 (step @p43 :rule symm :premises (@p42)) % 0.38/0.58 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.38/0.58 (step @p45 :rule cong :premises (@p44) :args (@t6)) % 0.38/0.58 (step @p46 :rule ho_cong :premises (@p35 @p45)) % 0.38/0.58 (step @p47 :rule trans :premises (@p46 @p40)) % 0.38/0.58 (step @p48 :rule ho_cong :premises (@p24 @p47)) % 0.38/0.58 (step @p49 :rule ho_cong :premises (@p48 @p34)) % 0.38/0.58 (step @p50 :rule trans :premises (@p49 @p30)) % 0.38/0.58 (step @p51 :rule cong :premises (@p50) :args ((forall @t11 @t63))) % 0.38/0.58 (step @p52 :rule trans :premises (@p51 @p13)) % 0.38/0.58 (step @p53 :rule beta-reduce :args ((= (_ @t66 @t9) @t63))) % 0.38/0.58 (step @p54 :rule refl :args (@t9)) % 0.38/0.58 (step @p55 :rule beta-reduce :args ((= @t67 @t66))) % 0.38/0.58 (step @p56 :rule ho_cong :premises (@p55 @p54)) % 0.38/0.58 (step @p57 :rule trans :premises (@p56 @p53)) % 0.38/0.58 (step @p58 :rule cong :premises (@p57) :args (@t68)) % 0.38/0.58 (step @p59 :rule trans :premises (@p58 @p52)) % 0.38/0.58 (step @p60 :rule refl :args (tptp.setOfPairsIsBReln1)) % 0.38/0.58 (step @p61 :rule cong :premises (@p60 @p59) :args ((= tptp.setOfPairsIsBReln1 @t68))) % 0.38/0.58 (step @p62 :rule beta-reduce :args ((= (_ @t69 @t15) @t65))) % 0.38/0.58 (step @p63 :rule refl :args (@t15)) % 0.38/0.58 (step @p64 :rule beta-reduce :args ((= (_ @t70 @t7) @t69))) % 0.38/0.58 (step @p65 :rule beta-reduce :args ((= (_ @t29 @t7) @t70))) % 0.38/0.58 (step @p66 :rule ho_cong :premises (@p65 @p10)) % 0.38/0.58 (step @p67 :rule trans :premises (@p66 @p64)) % 0.38/0.58 (step @p68 :rule ho_cong :premises (@p67 @p63)) % 0.38/0.58 (step @p69 :rule trans :premises (@p68 @p62)) % 0.38/0.58 (step @p70 :rule ho_cong :premises (@p4 @p10)) % 0.38/0.58 (step @p71 :rule ho_cong :premises (@p70 @p10)) % 0.38/0.58 (step @p72 :rule ho_cong :premises (@p71 @p63)) % 0.38/0.58 (step @p73 :rule trans :premises (@p72 @p69)) % 0.38/0.58 (step @p74 :rule cong :premises (@p73) :args (@t30)) % 0.38/0.58 (step @p75 :rule trans :premises (@p5 @p74)) % 0.38/0.58 (step @p76 :rule ho_cong :premises (@p75 @p10)) % 0.38/0.58 (step @p77 :rule ho_cong :premises (@p76 @p54)) % 0.38/0.58 (step @p78 :rule cong :premises (@p77) :args (@t12)) % 0.38/0.58 (step @p79 :rule cong :premises (@p60 @p78) :args (@t13)) % 0.38/0.58 (step @p80 :rule trans :premises (@p79 @p61)) % 0.38/0.58 (step @p81 :rule eq_resolve :premises (@p1 @p80)) % 0.38/0.58 (step @p82 :rule cong :premises (@p81 @p7) :args (@t71)) % 0.38/0.58 (step @p83 :rule cong :premises (@p82) :args ((not @t71))) % 0.38/0.58 (step @p84 :rule aci_norm :args ((= @t73 @t55))) % 0.38/0.58 (step @p85 :rule cong :premises (@p84) :args (@t74)) % 0.38/0.58 (step @p86 :rule quant-merge-prenex :args ((= (forall @t20 @t76) @t74))) % 0.38/0.58 (step @p87 :rule alpha_equiv :args (@t77 (@list @t44) (@list @t14))) % 0.38/0.58 (step @p88 :rule refl :args (@t54)) % 0.38/0.58 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t78)) % 0.38/0.58 (step @p90 :rule quant-miniscope-or :args ((= @t76 @t78))) % 0.38/0.58 (step @p91 :rule trans :premises (@p90 @p89)) % 0.38/0.58 (step @p92 :rule symm :premises (@p91)) % 0.38/0.58 (step @p93 :rule cong :premises (@p92) :args ((forall @t20 (or @t54 @t88)))) % 0.38/0.58 (step @p94 :rule trans :premises (@p93 @p86)) % 0.38/0.58 (step @p95 :rule trans :premises (@p94 @p85)) % 0.38/0.58 (step @p96 :rule refl :args (@t88)) % 0.38/0.58 (step @p97 :rule refl :args ((tptp.subset @t15 @t62))) % 0.38/0.58 (step @p98 :rule refl :args (@t15)) % 0.38/0.58 (step @p99 :rule cong :premises (@p98 @p15) :args (@t53)) % 0.38/0.58 (step @p100 :rule trans :premises (@p99 @p97)) % 0.38/0.58 (step @p101 :rule refl :args (@t64)) % 0.38/0.58 (step @p102 :rule ho_cong :premises (@p101 @p15)) % 0.38/0.58 (step @p103 :rule cong :premises (@p102 @p100) :args ((= (_ @t64 @t43) @t53))) % 0.38/0.58 (step @p104 :rule symm :premises (@p103)) % 0.38/0.58 (step @p105 :rule refl :args (@t65)) % 0.38/0.58 (step @p106 :rule eq_resolve :premises (@p105 @p104)) % 0.38/0.58 (step @p107 :rule ho_cong :premises (@p101 @p34)) % 0.38/0.58 (step @p108 :rule trans :premises (@p107 @p106)) % 0.38/0.58 (step @p109 :rule cong :premises (@p108) :args (@t89)) % 0.38/0.58 (step @p110 :rule nary_cong :premises (@p109 @p96) :args (@t90)) % 0.38/0.58 (step @p111 :rule cong :premises (@p110) :args ((forall @t20 @t90))) % 0.38/0.58 (step @p112 :rule trans :premises (@p111 @p95)) % 0.38/0.58 (step @p113 :rule bool-impl-elim :args (@t65 @t88)) % 0.38/0.58 (step @p114 :rule cong :premises (@p113) :args ((forall @t20 (=> @t65 @t88)))) % 0.38/0.58 (step @p115 :rule trans :premises (@p114 @p112)) % 0.38/0.58 (step @p116 :rule refl :args ((tptp.subset @t97 @t62))) % 0.38/0.58 (step @p117 :rule refl :args ((tptp.dpsetconstr @t7 @t7 @t96))) % 0.38/0.58 (step @p118 :rule refl :args ((tptp.in @t32 @t14))) % 0.38/0.58 (step @p119 :rule refl :args (@t14)) % 0.38/0.58 (step @p120 :rule refl :args (@t45)) % 0.38/0.58 (step @p121 :rule cong :premises (@p120 @p119) :args (@t79)) % 0.38/0.58 (step @p122 :rule trans :premises (@p121 @p118)) % 0.38/0.58 (step @p123 :rule cong :premises (@p122) :args (@t80)) % 0.38/0.58 (step @p124 :rule refl :args ((tptp.in @t34 @t15))) % 0.38/0.58 (step @p125 :rule refl :args (@t46)) % 0.38/0.58 (step @p126 :rule cong :premises (@p125 @p98) :args (@t47)) % 0.38/0.58 (step @p127 :rule trans :premises (@p126 @p124)) % 0.38/0.58 (step @p128 :rule cong :premises (@p127) :args (@t48)) % 0.38/0.58 (step @p129 :rule refl :args (@t49)) % 0.38/0.58 (step @p130 :rule cong :premises (@p129) :args (@t50)) % 0.38/0.58 (step @p131 :rule nary_cong :premises (@p130 @p128 @p123) :args (@t81)) % 0.38/0.58 (step @p132 :rule cong :premises (@p131) :args (@t82)) % 0.38/0.58 (step @p133 :rule cong :premises (@p132) :args (@t83)) % 0.38/0.58 (step @p134 :rule cong :premises (@p133) :args (@t84)) % 0.38/0.58 (step @p135 :rule cong :premises (@p19 @p19 @p134) :args (@t85)) % 0.38/0.58 (step @p136 :rule trans :premises (@p135 @p117)) % 0.38/0.58 (step @p137 :rule cong :premises (@p136 @p15) :args (@t86)) % 0.38/0.58 (step @p138 :rule trans :premises (@p137 @p116)) % 0.38/0.58 (step @p139 :rule ho_cong :premises (@p24 @p136)) % 0.38/0.58 (step @p140 :rule ho_cong :premises (@p139 @p15)) % 0.38/0.58 (step @p141 :rule cong :premises (@p140 @p138) :args ((= (_ (_ tptp.subset @t85) @t43) @t86))) % 0.38/0.58 (step @p142 :rule symm :premises (@p141)) % 0.38/0.58 (step @p143 :rule refl :args ((_ (_ tptp.subset @t97) @t62))) % 0.38/0.58 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 0.38/0.58 (step @p145 :rule ho_cong :premises (@p35 @p134)) % 0.38/0.58 (step @p146 :rule cong :premises (@p145 @p136) :args ((= @t98 @t85))) % 0.38/0.58 (step @p147 :rule symm :premises (@p146)) % 0.38/0.58 (step @p148 :rule refl :args (@t97)) % 0.38/0.58 (step @p149 :rule eq_resolve :premises (@p148 @p147)) % 0.38/0.58 (step @p150 :rule ho_cong :premises (@p24 @p149)) % 0.38/0.58 (step @p151 :rule ho_cong :premises (@p150 @p34)) % 0.38/0.58 (step @p152 :rule trans :premises (@p151 @p144)) % 0.38/0.58 (step 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:rule cong :premises (@p167) :args ((forall @t17 (=> @t100 @t102)))) % 0.38/0.58 (step @p169 :rule trans :premises (@p168 @p166)) % 0.38/0.58 (step @p170 :rule beta-reduce :args ((= (_ @t66 @t98) @t102))) % 0.38/0.58 (step @p171 :rule beta-reduce :args ((= (_ @t104 @t14) @t98))) % 0.38/0.58 (step @p172 :rule refl :args (@t14)) % 0.38/0.58 (step @p173 :rule beta-reduce :args ((= (_ @t105 @t15) @t104))) % 0.38/0.58 (step @p174 :rule beta-reduce :args ((= @t106 @t105))) % 0.38/0.58 (step @p175 :rule ho_cong :premises (@p174 @p63)) % 0.38/0.58 (step @p176 :rule trans :premises (@p175 @p173)) % 0.38/0.58 (step @p177 :rule ho_cong :premises (@p176 @p172)) % 0.38/0.58 (step @p178 :rule trans :premises (@p177 @p171)) % 0.38/0.58 (step @p179 :rule ho_cong :premises (@p55 @p178)) % 0.38/0.58 (step @p180 :rule trans :premises (@p179 @p170)) % 0.38/0.58 (step @p181 :rule beta-reduce :args ((= (_ @t66 @t14) @t100))) % 0.38/0.58 (step @p182 :rule ho_cong :premises (@p55 @p172)) % 0.38/0.58 (step 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:rule symm :premises (@p212)) % 0.38/0.58 (step @p214 :rule refl :args (@t35)) % 0.38/0.58 (step @p215 :rule eq_resolve :premises (@p214 @p213)) % 0.38/0.58 (step @p216 :rule refl :args (@t34)) % 0.38/0.58 (step @p217 :rule cong :premises (@p216 @p125) :args ((= @t34 @t46))) % 0.38/0.58 (step @p218 :rule symm :premises (@p217)) % 0.38/0.58 (step @p219 :rule eq_resolve :premises (@p216 @p218)) % 0.38/0.58 (step @p220 :rule ho_cong :premises (@p195 @p219)) % 0.38/0.58 (step @p221 :rule ho_cong :premises (@p220 @p98)) % 0.38/0.58 (step @p222 :rule trans :premises (@p221 @p215)) % 0.38/0.58 (step @p223 :rule cong :premises (@p222) :args (@t92)) % 0.38/0.58 (step @p224 :rule refl :args (@t36)) % 0.38/0.58 (step @p225 :rule cong :premises (@p224 @p129) :args ((= @t36 @t49))) % 0.38/0.58 (step @p226 :rule symm :premises (@p225)) % 0.38/0.58 (step @p227 :rule eq_resolve :premises (@p224 @p226)) % 0.38/0.58 (step @p228 :rule cong :premises (@p227) :args (@t93)) % 0.38/0.58 (step @p229 :rule nary_cong :premises (@p228 @p223 @p209) :args (@t94)) % 0.38/0.58 (step @p230 :rule cong :premises (@p229) :args (@t95)) % 0.38/0.58 (step @p231 :rule aci_norm :args ((= (or @t93 (or @t92 @t91)) @t94))) % 0.38/0.58 (step @p232 :rule bool-and-de-morgan :args (@t35 @t33 true)) % 0.38/0.58 (step @p233 :rule refl :args (@t93)) % 0.38/0.58 (step @p234 :rule nary_cong :premises (@p233 @p232) :args ((or @t93 (not (and @t35 @t33))))) % 0.38/0.58 (step @p235 :rule bool-and-de-morgan :args (@t36 @t35 (and @t33))) % 0.38/0.58 (step @p236 :rule trans :premises (@p235 @p234)) % 0.38/0.58 (step @p237 :rule trans :premises (@p236 @p231)) % 0.38/0.58 (step @p238 :rule cong :premises (@p237) :args (@t112)) % 0.38/0.58 (step @p239 :rule trans :premises (@p238 @p230)) % 0.38/0.58 (step @p240 :rule cong :premises (@p239) :args (@t113)) % 0.38/0.58 (step @p241 :rule exists-elim :args ((= @t39 @t113))) % 0.38/0.58 (step @p242 :rule trans :premises (@p241 @p240)) % 0.38/0.58 (step @p243 :rule cong :premises (@p242) :args (@t40)) % 0.38/0.58 (step @p244 :rule refl :args (@t8)) % 0.38/0.58 (step @p245 :rule ho_cong :premises (@p244 @p243)) % 0.38/0.58 (step @p246 :rule cong :premises (@p245) :args (@t42)) % 0.38/0.58 (step @p247 :rule trans :premises (@p6 @p246)) % 0.38/0.58 (step @p248 :rule ho_cong :premises (@p247 @p10)) % 0.38/0.58 (step @p249 :rule ho_cong :premises (@p248 @p63)) % 0.38/0.58 (step @p250 :rule ho_cong :premises (@p249 @p172)) % 0.38/0.58 (step @p251 :rule ho_cong :premises (@p76 @p250)) % 0.38/0.58 (step @p252 :rule ho_cong :premises (@p76 @p172)) % 0.38/0.58 (step @p253 :rule cong :premises (@p252 @p251) :args (@t16)) % 0.38/0.58 (step @p254 :rule cong :premises (@p253) :args (@t18)) % 0.38/0.58 (step @p255 :rule ho_cong :premises (@p76 @p63)) % 0.38/0.58 (step @p256 :rule cong :premises (@p255 @p254) :args (@t19)) % 0.38/0.58 (step @p257 :rule cong :premises (@p256) :args (@t21)) % 0.38/0.58 (step @p258 :rule cong :premises (@p60 @p257) :args (@t22)) % 0.38/0.58 (step @p259 :rule cong :premises (@p258) :args (@t23)) % 0.38/0.58 (step @p260 :rule trans :premises (@p259 @p194)) % 0.38/0.58 (step @p261 :rule trans :premises (@p260 @p83)) % 0.38/0.58 (step @p262 :rule eq_resolve :premises (@p2 @p261)) % 0.38/0.58 (step @p263 :rule not_implies_elim1 :premises (@p262)) % 0.38/0.58 (step @p264 :rule not_implies_elim2 :premises (@p262)) % 0.38/0.58 (step @p265 :rule refl :args (@t124)) % 0.38/0.58 (step @p266 :rule bool-double-not-elim :args (@t57)) % 0.38/0.58 (step @p267 :rule nary_cong :premises (@p266 @p265) :args ((or (not @t125) @t124))) % 0.38/0.58 (step @p268 :rule refl :args (@t115)) % 0.38/0.58 (step @p269 :rule eq-refl :args (@t118)) % 0.38/0.58 (step @p270 :rule skolem_intro :args (@t119)) % 0.38/0.58 (step @p271 :rule refl :args (@t118)) % 0.38/0.58 (step @p272 :rule cong :premises (@p271 @p270) :args ((= @t118 @t119))) % 0.38/0.58 (step @p273 :rule trans :premises (@p272 @p269)) % 0.38/0.58 (step @p274 :rule true_elim :premises (@p273)) % 0.38/0.58 (step @p275 :rule refl :args (@t114)) % 0.38/0.58 (step @p276 :rule cong :premises (@p275 @p275 @p274) :args (@t126)) % 0.38/0.58 (step @p277 :rule cong :premises (@p276 @p268) :args (@t127)) % 0.38/0.58 (step @p278 :rule refl :args (@t121)) % 0.38/0.58 (step @p279 :rule refl :args (@t122)) % 0.38/0.58 (step @p280 :rule nary_cong :premises (@p279 @p278 @p277) :args (@t128)) % 0.38/0.58 (step @p281 :rule cong :premises (@p280) :args (@t129)) % 0.38/0.58 (step @p282 :rule refl :args (@t125)) % 0.38/0.58 (step @p283 :rule cong :premises (@p282 @p281) :args ((=> @t125 @t129))) % 0.38/0.58 (assume-push @p300 @t125) % 0.38/0.58 (step @p285 :rule skolemize :premises (@p264)) % 0.38/0.58 (step-pop @p301 :rule scope :premises (@p285)) % 0.38/0.58 (step @p286 :rule process_scope :premises (@p301) :args (@t129)) % 0.38/0.58 (step @p288 :rule eq_resolve :premises (@p286 @p283)) % 0.38/0.58 (step @p289 :rule implies_elim :premises (@p288)) % 0.38/0.58 (step @p290 :rule eq_resolve :premises (@p289 @p267)) % 0.38/0.58 (step @p291 :rule chain_m_resolution :premises (@p290 @p264) :args (@t124 @t130 (@list @t57))) % 0.38/0.58 (step @p292 :rule cnf_or_neg :args (@t123 2)) % 0.38/0.58 (step @p293 :rule chain_m_resolution :premises (@p292 @p291) :args ((not @t120) @t130 (@list @t123))) % 0.38/0.58 (assume-push @p302 @t131) % 0.38/0.58 (step @p295 :rule instantiate :premises (@p263) :args ((@list @t114 @t119))) % 0.38/0.58 (step-pop @p303 :rule scope :premises (@p295)) % 0.38/0.58 (step @p296 :rule process_scope :premises (@p303) :args (@t120)) % 0.38/0.58 (step @p298 :rule implies_elim :premises (@p296)) % 0.38/0.58 (step @p299 false :rule chain_m_resolution :premises (@p298 @p293 @p263) :args (false (@list true false) (@list @t120 @t131))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------