%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU730^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n011.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 08:52:56 AM UTC 2026 % Result : Theorem 0.39s 0.60s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU730^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n011.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 17:49:20 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.39/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.60 % SZS status Theorem % 0.39/0.60 % SZS output start Proof % 0.39/0.60 ( % 0.39/0.60 (declare-sort $$unsorted 0) % 0.39/0.60 (declare-const tptp.doubleComplementE1 Bool) % 0.39/0.60 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.complementT_lem Bool) % 0.39/0.60 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.setminus (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.60 (declare-const tptp.subsetTI Bool) % 0.39/0.60 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.39/0.60 (define @t1 () (@var "A" $$unsorted)) % 0.39/0.60 (define @t2 () (_ tptp.powerset @t1)) % 0.39/0.60 (define @t3 () (@var "X" $$unsorted)) % 0.39/0.60 (define @t4 () (_ tptp.setminus @t1)) % 0.39/0.60 (define @t5 () (_ @t4 @t3)) % 0.39/0.60 (define @t6 () (_ (_ tptp.in @t5) @t2)) % 0.39/0.60 (define @t7 () (_ tptp.in @t3)) % 0.39/0.60 (define @t8 () (_ @t7 @t2)) % 0.39/0.60 (define @t9 () (@list @t1 @t3)) % 0.39/0.60 (define @t10 () (forall @t9 (=> @t8 @t6))) % 0.39/0.60 (define @t11 () (= tptp.complementT_lem @t10)) % 0.39/0.60 (define @t12 () (@var "Y" $$unsorted)) % 0.39/0.60 (define @t13 () (_ (_ tptp.subset @t3) @t12)) % 0.39/0.60 (define @t14 () (@var "Xx" $$unsorted)) % 0.39/0.60 (define @t15 () (_ tptp.in @t14)) % 0.39/0.60 (define @t16 () (_ @t15 @t12)) % 0.39/0.60 (define @t17 () (_ @t15 @t3)) % 0.39/0.60 (define @t18 () (=> @t17 @t16)) % 0.39/0.60 (define @t19 () (_ @t15 @t1)) % 0.39/0.60 (define @t20 () (@list @t14)) % 0.39/0.60 (define @t21 () (forall @t20 (=> @t19 @t18))) % 0.39/0.60 (define @t22 () (=> @t21 @t13)) % 0.39/0.60 (define @t23 () (_ tptp.in @t12)) % 0.39/0.60 (define @t24 () (_ @t23 @t2)) % 0.39/0.60 (define @t25 () (=> @t24 @t22)) % 0.39/0.60 (define @t26 () (@list @t12)) % 0.39/0.60 (define @t27 () (forall @t26 @t25)) % 0.39/0.60 (define @t28 () (=> @t8 @t27)) % 0.39/0.60 (define @t29 () (forall @t9 @t28)) % 0.39/0.60 (define @t30 () (= tptp.subsetTI @t29)) % 0.39/0.60 (define @t31 () (_ @t4 @t5)) % 0.39/0.60 (define @t32 () (_ @t15 @t31)) % 0.39/0.60 (define @t33 () (=> @t32 @t17)) % 0.39/0.60 (define @t34 () (forall @t20 (=> @t19 @t33))) % 0.39/0.60 (define @t35 () (=> @t8 @t34)) % 0.39/0.60 (define @t36 () (forall @t9 @t35)) % 0.39/0.60 (define @t37 () (= tptp.doubleComplementE1 @t36)) % 0.39/0.60 (define @t38 () (_ (_ tptp.subset @t31) @t3)) % 0.39/0.60 (define @t39 () (forall @t9 (=> @t8 @t38))) % 0.39/0.60 (define @t40 () (=> tptp.doubleComplementE1 @t39)) % 0.39/0.60 (define @t41 () (=> tptp.subsetTI @t40)) % 0.39/0.60 (define @t42 () (=> tptp.complementT_lem @t41)) % 0.39/0.60 (define @t43 () (not @t42)) % 0.39/0.60 (define @t44 () (tptp.setminus @t1 @t3)) % 0.39/0.60 (define @t45 () (tptp.setminus @t1 @t44)) % 0.39/0.60 (define @t46 () (tptp.subset @t45 @t3)) % 0.39/0.60 (define @t47 () (tptp.powerset @t1)) % 0.39/0.60 (define @t48 () (tptp.in @t3 @t47)) % 0.39/0.60 (define @t49 () (not @t48)) % 0.39/0.60 (define @t50 () (forall @t9 (or @t49 @t46))) % 0.39/0.60 (define @t51 () (@var "BOUND_VARIABLE_7548" $$unsorted)) % 0.39/0.60 (define @t52 () (tptp.in @t51 @t3)) % 0.39/0.60 (define @t53 () (not (tptp.in @t51 @t45))) % 0.39/0.60 (define @t54 () (not (tptp.in @t51 @t1))) % 0.39/0.60 (define @t55 () (or @t49 @t54 @t53 @t52)) % 0.39/0.60 (define @t56 () (or @t54 @t53 @t52)) % 0.39/0.60 (define @t57 () (or @t49 @t56)) % 0.39/0.60 (define @t58 () (@list @t1 @t3 @t51)) % 0.39/0.60 (define @t59 () (forall @t58 @t57)) % 0.39/0.60 (define @t60 () (@list @t51)) % 0.39/0.60 (define @t61 () (forall @t60 @t57)) % 0.39/0.60 (define @t62 () (forall @t60 @t56)) % 0.39/0.60 (define @t63 () (or @t49 @t62)) % 0.39/0.60 (define @t64 () (tptp.in @t14 @t3)) % 0.39/0.60 (define @t65 () (tptp.in @t14 @t45)) % 0.39/0.60 (define @t66 () (tptp.in @t14 @t1)) % 0.39/0.60 (define @t67 () (not @t66)) % 0.39/0.60 (define @t68 () (forall @t20 (or @t67 (not @t65) @t64))) % 0.39/0.61 (define @t69 () (not @t8)) % 0.39/0.61 (define @t70 () (or @t69 @t68)) % 0.39/0.61 (define @t71 () (not @t32)) % 0.39/0.61 (define @t72 () (not @t19)) % 0.39/0.61 (define @t73 () (or @t72 @t71 @t17)) % 0.39/0.61 (define @t74 () (=> tptp.doubleComplementE1 @t50)) % 0.39/0.61 (define @t75 () (@var "BOUND_VARIABLE_7514" $$unsorted)) % 0.39/0.61 (define @t76 () (tptp.subset @t3 @t75)) % 0.39/0.61 (define @t77 () (not @t64)) % 0.39/0.61 (define @t78 () (not (forall @t20 (or @t67 @t77 (tptp.in @t14 @t75))))) % 0.39/0.61 (define @t79 () (not (tptp.in @t75 @t47))) % 0.39/0.61 (define @t80 () (or @t79 @t78 @t76)) % 0.39/0.61 (define @t81 () (or @t49 @t80)) % 0.39/0.61 (define @t82 () (forall (@list @t1 @t3 @t75) @t81)) % 0.39/0.61 (define @t83 () (@list @t75)) % 0.39/0.61 (define @t84 () (forall @t83 @t81)) % 0.39/0.61 (define @t85 () (forall @t83 @t80)) % 0.39/0.61 (define @t86 () (or @t49 @t85)) % 0.39/0.61 (define @t87 () (tptp.subset @t3 @t12)) % 0.39/0.61 (define @t88 () (tptp.in @t14 @t12)) % 0.39/0.61 (define @t89 () (forall @t20 (or @t67 @t77 @t88))) % 0.39/0.61 (define @t90 () (not @t89)) % 0.39/0.61 (define @t91 () (tptp.in @t12 @t47)) % 0.39/0.61 (define @t92 () (forall @t26 (or (not @t91) @t90 @t87))) % 0.39/0.61 (define @t93 () (or @t69 @t92)) % 0.39/0.61 (define @t94 () (not @t24)) % 0.39/0.61 (define @t95 () (or @t94 @t90 @t13)) % 0.39/0.61 (define @t96 () (=> @t89 @t13)) % 0.39/0.61 (define @t97 () (not @t17)) % 0.39/0.61 (define @t98 () (or @t72 @t97 @t16)) % 0.39/0.61 (define @t99 () (=> tptp.subsetTI @t74)) % 0.39/0.61 (define @t100 () (tptp.in @t44 @t47)) % 0.39/0.61 (define @t101 () (or @t69 @t6)) % 0.39/0.61 (define @t102 () (=> tptp.complementT_lem @t99)) % 0.39/0.61 (define @t103 () (or @t69 @t38)) % 0.39/0.61 (define @t104 () (@quantifiers_skolemize @t50 1)) % 0.39/0.61 (define @t105 () (@quantifiers_skolemize @t50 0)) % 0.39/0.61 (define @t106 () (tptp.setminus @t105 @t104)) % 0.39/0.61 (define @t107 () (tptp.setminus @t105 @t106)) % 0.39/0.61 (define @t108 () (tptp.powerset @t105)) % 0.39/0.61 (define @t109 () (tptp.in @t104 @t108)) % 0.39/0.61 (define @t110 () (tptp.subset @t107 @t104)) % 0.39/0.61 (define @t111 () (not @t109)) % 0.39/0.61 (define @t112 () (or @t111 @t110)) % 0.39/0.61 (define @t113 () (@list true)) % 0.39/0.61 (define @t114 () (@list @t112)) % 0.39/0.61 (define @t115 () (tptp.in @t106 @t108)) % 0.39/0.61 (define @t116 () (or @t111 @t115)) % 0.39/0.61 (define @t117 () (@list false false)) % 0.39/0.61 (define @t118 () (tptp.in @t107 @t108)) % 0.39/0.61 (define @t119 () (not @t115)) % 0.39/0.61 (define @t120 () (or @t119 @t118)) % 0.39/0.61 (define @t121 () (forall @t20 (or (not (tptp.in @t14 @t105)) (not (tptp.in @t14 @t107)) (tptp.in @t14 @t104)))) % 0.39/0.61 (define @t122 () (not @t121)) % 0.39/0.61 (define @t123 () (not @t118)) % 0.39/0.61 (define @t124 () (or @t123 @t111 @t122 @t110)) % 0.39/0.61 (define @t125 () (@quantifiers_skolemize @t121 0)) % 0.39/0.61 (define @t126 () (tptp.in @t125 @t104)) % 0.39/0.61 (define @t127 () (tptp.in @t125 @t107)) % 0.39/0.61 (define @t128 () (not @t127)) % 0.39/0.61 (define @t129 () (tptp.in @t125 @t105)) % 0.39/0.61 (define @t130 () (not @t129)) % 0.39/0.61 (define @t131 () (or @t130 @t128 @t126)) % 0.39/0.61 (define @t132 () (@list @t131)) % 0.39/0.61 (define @t133 () (or @t111 @t130 @t128 @t126)) % 0.39/0.61 (define @t134 () (not @t133)) % 0.39/0.61 (define @t135 () (forall @t58 @t55)) % 0.39/0.61 (assume @p1 @t11) % 0.39/0.61 (assume @p2 @t30) % 0.39/0.61 (assume @p3 @t37) % 0.39/0.61 (assume @p4 @t43) % 0.39/0.61 (assume @p5 true) % 0.39/0.61 (step @p6 :rule refl :args (@t50)) % 0.39/0.61 (step @p7 :rule aci_norm :args ((= @t57 @t55))) % 0.39/0.61 (step @p8 :rule cong :premises (@p7) :args (@t59)) % 0.39/0.61 (step @p9 :rule quant-merge-prenex :args ((= (forall @t9 @t61) @t59))) % 0.39/0.61 (step @p10 :rule alpha_equiv :args (@t62 (@list @t51) (@list @t14))) % 0.39/0.61 (step @p11 :rule refl :args (@t49)) % 0.39/0.61 (step @p12 :rule nary_cong :premises (@p11 @p10) :args (@t63)) % 0.39/0.61 (step @p13 :rule quant-miniscope-or :args ((= @t61 @t63))) % 0.39/0.61 (step @p14 :rule trans :premises (@p13 @p12)) % 0.39/0.61 (step @p15 :rule symm :premises (@p14)) % 0.39/0.61 (step @p16 :rule cong :premises (@p15) :args ((forall @t9 (or @t49 @t68)))) % 0.39/0.61 (step @p17 :rule trans :premises (@p16 @p9)) % 0.39/0.61 (step @p18 :rule trans :premises (@p17 @p8)) % 0.39/0.61 (step @p19 :rule refl :args (@t68)) % 0.39/0.61 (step @p20 :rule refl :args ((tptp.in @t3 @t2))) % 0.39/0.61 (step @p21 :rule refl :args (@t47)) % 0.39/0.61 (step @p22 :rule refl :args (@t3)) % 0.39/0.61 (step @p23 :rule cong :premises (@p22 @p21) :args (@t48)) % 0.39/0.61 (step @p24 :rule trans :premises (@p23 @p20)) % 0.39/0.61 (step @p25 :rule refl :args (@t7)) % 0.39/0.61 (step @p26 :rule ho_cong :premises (@p25 @p21)) % 0.39/0.61 (step @p27 :rule cong :premises (@p26 @p24) :args ((= (_ @t7 @t47) @t48))) % 0.39/0.61 (step @p28 :rule symm :premises (@p27)) % 0.39/0.61 (step @p29 :rule refl :args (@t8)) % 0.39/0.61 (step @p30 :rule eq_resolve :premises (@p29 @p28)) % 0.39/0.61 (step @p31 :rule refl :args (@t2)) % 0.39/0.61 (step @p32 :rule cong :premises (@p31 @p21) :args ((= @t2 @t47))) % 0.39/0.61 (step @p33 :rule symm :premises (@p32)) % 0.39/0.61 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 0.39/0.61 (step @p35 :rule ho_cong :premises (@p25 @p34)) % 0.39/0.61 (step @p36 :rule trans :premises (@p35 @p30)) % 0.39/0.61 (step @p37 :rule cong :premises (@p36) :args (@t69)) % 0.39/0.61 (step @p38 :rule nary_cong :premises (@p37 @p19) :args (@t70)) % 0.39/0.61 (step @p39 :rule cong :premises (@p38) :args ((forall @t9 @t70))) % 0.39/0.61 (step @p40 :rule trans :premises (@p39 @p18)) % 0.39/0.61 (step @p41 :rule bool-impl-elim :args (@t8 @t68)) % 0.39/0.61 (step @p42 :rule cong :premises (@p41) :args ((forall @t9 (=> @t8 @t68)))) % 0.39/0.61 (step @p43 :rule trans :premises (@p42 @p40)) % 0.39/0.61 (step @p44 :rule refl :args (@t64)) % 0.39/0.61 (step @p45 :rule refl :args (@t17)) % 0.39/0.61 (step @p46 :rule cong :premises (@p45 @p44) :args ((= @t17 @t64))) % 0.39/0.61 (step @p47 :rule symm :premises (@p46)) % 0.39/0.61 (step @p48 :rule eq_resolve :premises (@p45 @p47)) % 0.39/0.61 (step @p49 :rule refl :args ((tptp.in @t14 @t31))) % 0.39/0.61 (step @p50 :rule refl :args ((tptp.setminus @t1 @t5))) % 0.39/0.61 (step @p51 :rule refl :args (@t44)) % 0.39/0.61 (step @p52 :rule refl :args (@t1)) % 0.39/0.61 (step @p53 :rule cong :premises (@p52 @p51) :args (@t45)) % 0.39/0.61 (step @p54 :rule trans :premises (@p53 @p50)) % 0.39/0.61 (step @p55 :rule refl :args (@t14)) % 0.39/0.61 (step @p56 :rule cong :premises (@p55 @p54) :args (@t65)) % 0.39/0.61 (step @p57 :rule trans :premises (@p56 @p49)) % 0.39/0.61 (step @p58 :rule refl :args (@t15)) % 0.39/0.61 (step @p59 :rule ho_cong :premises (@p58 @p54)) % 0.39/0.61 (step @p60 :rule cong :premises (@p59 @p57) :args ((= (_ @t15 @t45) @t65))) % 0.39/0.61 (step @p61 :rule symm :premises (@p60)) % 0.39/0.61 (step @p62 :rule refl :args (@t32)) % 0.39/0.61 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 0.39/0.61 (step @p64 :rule refl :args (@t4)) % 0.39/0.61 (step @p65 :rule ho_cong :premises (@p64 @p51)) % 0.39/0.61 (step @p66 :rule cong :premises (@p65 @p54) :args ((= (_ @t4 @t44) @t45))) % 0.39/0.61 (step @p67 :rule symm :premises (@p66)) % 0.39/0.61 (step @p68 :rule refl :args (@t31)) % 0.39/0.61 (step @p69 :rule eq_resolve :premises (@p68 @p67)) % 0.39/0.61 (step @p70 :rule refl :args (@t5)) % 0.39/0.61 (step @p71 :rule cong :premises (@p70 @p51) :args ((= @t5 @t44))) % 0.39/0.61 (step @p72 :rule symm :premises (@p71)) % 0.39/0.61 (step @p73 :rule eq_resolve :premises (@p70 @p72)) % 0.39/0.61 (step @p74 :rule ho_cong :premises (@p64 @p73)) % 0.39/0.61 (step @p75 :rule trans :premises (@p74 @p69)) % 0.39/0.61 (step @p76 :rule ho_cong :premises (@p58 @p75)) % 0.39/0.61 (step @p77 :rule trans :premises (@p76 @p63)) % 0.39/0.61 (step @p78 :rule cong :premises (@p77) :args (@t71)) % 0.39/0.61 (step @p79 :rule refl :args (@t66)) % 0.39/0.61 (step @p80 :rule refl :args (@t19)) % 0.39/0.61 (step @p81 :rule cong :premises (@p80 @p79) :args ((= @t19 @t66))) % 0.39/0.61 (step @p82 :rule symm :premises (@p81)) % 0.39/0.61 (step @p83 :rule eq_resolve :premises (@p80 @p82)) % 0.39/0.61 (step @p84 :rule cong :premises (@p83) :args (@t72)) % 0.39/0.61 (step @p85 :rule nary_cong :premises (@p84 @p78 @p48) :args (@t73)) % 0.39/0.61 (step @p86 :rule cong :premises (@p85) :args ((forall @t20 @t73))) % 0.39/0.61 (step @p87 :rule aci_norm :args ((= (or @t72 (or @t71 @t17)) @t73))) % 0.39/0.61 (step @p88 :rule bool-impl-elim :args (@t32 @t17)) % 0.39/0.61 (step @p89 :rule refl :args (@t72)) % 0.39/0.61 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or @t72 @t33))) % 0.39/0.61 (step @p91 :rule trans :premises (@p90 @p87)) % 0.39/0.61 (step @p92 :rule bool-impl-elim :args (@t19 @t33)) % 0.39/0.61 (step @p93 :rule trans :premises (@p92 @p91)) % 0.39/0.61 (step @p94 :rule cong :premises (@p93) :args (@t34)) % 0.39/0.61 (step @p95 :rule trans :premises (@p94 @p86)) % 0.39/0.61 (step @p96 :rule refl :args (@t8)) % 0.39/0.61 (step @p97 :rule cong :premises (@p96 @p95) :args (@t35)) % 0.39/0.61 (step @p98 :rule cong :premises (@p97) :args (@t36)) % 0.39/0.61 (step @p99 :rule trans :premises (@p98 @p43)) % 0.39/0.61 (step @p100 :rule refl :args (tptp.doubleComplementE1)) % 0.39/0.61 (step @p101 :rule cong :premises (@p100 @p99) :args (@t37)) % 0.39/0.61 (step @p102 :rule eq_resolve :premises (@p3 @p101)) % 0.39/0.61 (step @p103 :rule cong :premises (@p102 @p6) :args (@t74)) % 0.39/0.61 (step @p104 :rule aci_norm :args ((= @t81 (or @t49 @t79 @t78 @t76)))) % 0.39/0.61 (step @p105 :rule cong :premises (@p104) :args (@t82)) % 0.39/0.61 (step @p106 :rule quant-merge-prenex :args ((= (forall @t9 @t84) @t82))) % 0.39/0.61 (step @p107 :rule alpha_equiv :args (@t85 (@list @t75) (@list @t12))) % 0.39/0.61 (step @p108 :rule nary_cong :premises (@p11 @p107) :args (@t86)) % 0.39/0.61 (step @p109 :rule quant-miniscope-or :args ((= @t84 @t86))) % 0.39/0.61 (step @p110 :rule trans :premises (@p109 @p108)) % 0.39/0.61 (step @p111 :rule symm :premises (@p110)) % 0.39/0.61 (step @p112 :rule cong :premises (@p111) :args ((forall @t9 (or @t49 @t92)))) % 0.39/0.61 (step @p113 :rule trans :premises (@p112 @p106)) % 0.39/0.61 (step @p114 :rule trans :premises (@p113 @p105)) % 0.39/0.61 (step @p115 :rule refl :args (@t92)) % 0.39/0.61 (step @p116 :rule nary_cong :premises (@p37 @p115) :args (@t93)) % 0.39/0.61 (step @p117 :rule cong :premises (@p116) :args ((forall @t9 @t93))) % 0.39/0.61 (step @p118 :rule trans :premises (@p117 @p114)) % 0.39/0.61 (step @p119 :rule bool-impl-elim :args (@t8 @t92)) % 0.39/0.61 (step @p120 :rule cong :premises (@p119) :args ((forall @t9 (=> @t8 @t92)))) % 0.39/0.61 (step @p121 :rule trans :premises (@p120 @p118)) % 0.39/0.61 (step @p122 :rule refl :args (@t87)) % 0.39/0.61 (step @p123 :rule refl :args (@t13)) % 0.39/0.61 (step @p124 :rule cong :premises (@p123 @p122) :args ((= @t13 @t87))) % 0.39/0.61 (step @p125 :rule symm :premises (@p124)) % 0.39/0.61 (step @p126 :rule eq_resolve :premises (@p123 @p125)) % 0.39/0.61 (step @p127 :rule refl :args (@t90)) % 0.39/0.61 (step @p128 :rule refl :args ((tptp.in @t12 @t2))) % 0.39/0.61 (step @p129 :rule refl :args (@t12)) % 0.39/0.61 (step @p130 :rule cong :premises (@p129 @p21) :args (@t91)) % 0.39/0.61 (step @p131 :rule trans :premises (@p130 @p128)) % 0.39/0.61 (step @p132 :rule refl :args (@t23)) % 0.39/0.61 (step @p133 :rule ho_cong :premises (@p132 @p21)) % 0.39/0.61 (step @p134 :rule cong :premises (@p133 @p131) :args ((= (_ @t23 @t47) @t91))) % 0.39/0.61 (step @p135 :rule symm :premises (@p134)) % 0.39/0.61 (step @p136 :rule refl :args (@t24)) % 0.39/0.61 (step @p137 :rule eq_resolve :premises (@p136 @p135)) % 0.39/0.61 (step @p138 :rule ho_cong :premises (@p132 @p34)) % 0.39/0.61 (step @p139 :rule trans :premises (@p138 @p137)) % 0.39/0.61 (step @p140 :rule cong :premises (@p139) :args (@t94)) % 0.39/0.61 (step @p141 :rule nary_cong :premises (@p140 @p127 @p126) :args (@t95)) % 0.39/0.61 (step @p142 :rule cong :premises (@p141) :args ((forall @t26 @t95))) % 0.39/0.61 (step @p143 :rule aci_norm :args ((= (or @t94 (or @t90 @t13)) @t95))) % 0.39/0.61 (step @p144 :rule bool-impl-elim :args (@t89 @t13)) % 0.39/0.61 (step @p145 :rule refl :args (@t94)) % 0.39/0.61 (step @p146 :rule nary_cong :premises (@p145 @p144) :args ((or @t94 @t96))) % 0.39/0.61 (step @p147 :rule trans :premises (@p146 @p143)) % 0.39/0.61 (step @p148 :rule bool-impl-elim :args (@t24 @t96)) % 0.39/0.61 (step @p149 :rule trans :premises (@p148 @p147)) % 0.39/0.61 (step @p150 :rule cong :premises (@p149) :args ((forall @t26 (=> @t24 @t96)))) % 0.39/0.61 (step @p151 :rule trans :premises (@p150 @p142)) % 0.39/0.61 (step @p152 :rule refl :args (@t13)) % 0.39/0.61 (step @p153 :rule refl :args (@t88)) % 0.39/0.61 (step @p154 :rule refl :args (@t16)) % 0.39/0.61 (step @p155 :rule cong :premises (@p154 @p153) :args ((= @t16 @t88))) % 0.39/0.61 (step @p156 :rule symm :premises (@p155)) % 0.39/0.61 (step @p157 :rule eq_resolve :premises (@p154 @p156)) % 0.39/0.61 (step @p158 :rule cong :premises (@p48) :args (@t97)) % 0.39/0.61 (step @p159 :rule nary_cong :premises (@p84 @p158 @p157) :args (@t98)) % 0.39/0.61 (step @p160 :rule cong :premises (@p159) :args ((forall @t20 @t98))) % 0.39/0.61 (step @p161 :rule aci_norm :args ((= (or @t72 (or @t97 @t16)) @t98))) % 0.39/0.61 (step @p162 :rule bool-impl-elim :args (@t17 @t16)) % 0.39/0.61 (step @p163 :rule nary_cong :premises (@p89 @p162) :args ((or @t72 @t18))) % 0.39/0.61 (step @p164 :rule trans :premises (@p163 @p161)) % 0.39/0.61 (step @p165 :rule bool-impl-elim :args (@t19 @t18)) % 0.39/0.61 (step @p166 :rule trans :premises (@p165 @p164)) % 0.39/0.61 (step @p167 :rule cong :premises (@p166) :args (@t21)) % 0.39/0.61 (step @p168 :rule trans :premises (@p167 @p160)) % 0.39/0.61 (step @p169 :rule cong :premises (@p168 @p152) :args (@t22)) % 0.39/0.61 (step @p170 :rule refl :args (@t24)) % 0.39/0.61 (step @p171 :rule cong :premises (@p170 @p169) :args (@t25)) % 0.39/0.61 (step @p172 :rule cong :premises (@p171) :args (@t27)) % 0.39/0.61 (step @p173 :rule trans :premises (@p172 @p151)) % 0.39/0.61 (step @p174 :rule cong :premises (@p96 @p173) :args (@t28)) % 0.39/0.61 (step @p175 :rule cong :premises (@p174) :args (@t29)) % 0.39/0.61 (step @p176 :rule trans :premises (@p175 @p121)) % 0.39/0.61 (step @p177 :rule refl :args (tptp.subsetTI)) % 0.39/0.61 (step @p178 :rule cong :premises (@p177 @p176) :args (@t30)) % 0.39/0.61 (step @p179 :rule eq_resolve :premises (@p2 @p178)) % 0.39/0.61 (step @p180 :rule cong :premises (@p179 @p103) :args (@t99)) % 0.39/0.61 (step @p181 :rule refl :args ((tptp.in @t5 @t2))) % 0.39/0.61 (step @p182 :rule cong :premises (@p51 @p21) :args (@t100)) % 0.39/0.61 (step @p183 :rule trans :premises (@p182 @p181)) % 0.39/0.61 (step @p184 :rule refl :args (tptp.in)) % 0.39/0.61 (step @p185 :rule ho_cong :premises (@p184 @p51)) % 0.39/0.61 (step @p186 :rule ho_cong :premises (@p185 @p21)) % 0.39/0.61 (step @p187 :rule cong :premises (@p186 @p183) :args ((= (_ (_ tptp.in @t44) @t47) @t100))) % 0.39/0.61 (step @p188 :rule symm :premises (@p187)) % 0.39/0.61 (step @p189 :rule refl :args (@t6)) % 0.39/0.61 (step @p190 :rule eq_resolve :premises (@p189 @p188)) % 0.39/0.61 (step @p191 :rule ho_cong :premises (@p184 @p73)) % 0.39/0.61 (step @p192 :rule ho_cong :premises (@p191 @p34)) % 0.39/0.61 (step @p193 :rule trans :premises (@p192 @p190)) % 0.39/0.61 (step @p194 :rule nary_cong :premises (@p37 @p193) :args (@t101)) % 0.39/0.61 (step @p195 :rule cong :premises (@p194) :args ((forall @t9 @t101))) % 0.39/0.61 (step @p196 :rule bool-impl-elim :args (@t8 @t6)) % 0.39/0.61 (step @p197 :rule cong :premises (@p196) :args (@t10)) % 0.39/0.61 (step @p198 :rule trans :premises (@p197 @p195)) % 0.39/0.61 (step @p199 :rule refl :args (tptp.complementT_lem)) % 0.39/0.61 (step @p200 :rule cong :premises (@p199 @p198) :args (@t11)) % 0.39/0.61 (step @p201 :rule eq_resolve :premises (@p1 @p200)) % 0.39/0.61 (step @p202 :rule cong :premises (@p201 @p180) :args (@t102)) % 0.39/0.61 (step @p203 :rule cong :premises (@p202) :args ((not @t102))) % 0.39/0.61 (step @p204 :rule refl :args ((tptp.subset @t31 @t3))) % 0.39/0.61 (step @p205 :rule cong :premises (@p54 @p22) :args (@t46)) % 0.39/0.61 (step @p206 :rule trans :premises (@p205 @p204)) % 0.39/0.61 (step @p207 :rule refl :args (tptp.subset)) % 0.39/0.61 (step @p208 :rule ho_cong :premises (@p207 @p54)) % 0.39/0.61 (step @p209 :rule ho_cong :premises (@p208 @p22)) % 0.39/0.61 (step @p210 :rule cong :premises (@p209 @p206) :args ((= (_ (_ tptp.subset @t45) @t3) @t46))) % 0.39/0.61 (step @p211 :rule symm :premises (@p210)) % 0.39/0.61 (step @p212 :rule refl :args (@t38)) % 0.39/0.61 (step @p213 :rule eq_resolve :premises (@p212 @p211)) % 0.39/0.61 (step @p214 :rule ho_cong :premises (@p207 @p75)) % 0.39/0.61 (step @p215 :rule ho_cong :premises (@p214 @p22)) % 0.39/0.61 (step @p216 :rule trans :premises (@p215 @p213)) % 0.39/0.61 (step @p217 :rule nary_cong :premises (@p37 @p216) :args (@t103)) % 0.39/0.61 (step @p218 :rule cong :premises (@p217) :args ((forall @t9 @t103))) % 0.39/0.61 (step @p219 :rule bool-impl-elim :args (@t8 @t38)) % 0.39/0.61 (step @p220 :rule cong :premises (@p219) :args (@t39)) % 0.39/0.61 (step @p221 :rule trans :premises (@p220 @p218)) % 0.39/0.61 (step @p222 :rule cong :premises (@p100 @p221) :args (@t40)) % 0.39/0.61 (step @p223 :rule cong :premises (@p177 @p222) :args (@t41)) % 0.39/0.61 (step @p224 :rule cong :premises (@p199 @p223) :args (@t42)) % 0.39/0.61 (step @p225 :rule cong :premises (@p224) :args (@t43)) % 0.39/0.61 (step @p226 :rule trans :premises (@p225 @p203)) % 0.39/0.61 (step @p227 :rule eq_resolve :premises (@p4 @p226)) % 0.39/0.61 (step @p228 :rule not_implies_elim2 :premises (@p227)) % 0.39/0.61 (step @p229 :rule not_implies_elim2 :premises (@p228)) % 0.39/0.61 (step @p230 :rule not_implies_elim1 :premises (@p229)) % 0.39/0.61 (step @p231 :rule not_implies_elim1 :premises (@p228)) % 0.39/0.61 (step @p232 :rule instantiate :premises (@p231) :args ((@list @t105 @t107 @t104))) % 0.39/0.61 (step @p233 :rule not_implies_elim1 :premises (@p227)) % 0.39/0.61 (step @p234 :rule instantiate :premises (@p233) :args ((@list @t105 @t106))) % 0.39/0.61 (step @p235 :rule instantiate :premises (@p233) :args ((@list @t105 @t104))) % 0.39/0.61 (step @p236 :rule not_implies_elim2 :premises (@p229)) % 0.39/0.61 (step @p237 :rule skolemize :premises (@p236)) % 0.39/0.61 (step @p238 :rule bool-double-not-elim :args (@t109)) % 0.39/0.61 (step @p239 :rule refl :args (@t112)) % 0.39/0.61 (step @p240 :rule nary_cong :premises (@p239 @p238) :args ((or @t112 (not @t111)))) % 0.39/0.61 (step @p241 :rule cnf_or_neg :args (@t112 0)) % 0.39/0.61 (step @p242 :rule eq_resolve :premises (@p241 @p240)) % 0.39/0.61 (step @p243 :rule reordering :premises (@p242) :args ((or @t109 @t112))) % 0.39/0.61 (step @p244 :rule chain_m_resolution :premises (@p243 @p237) :args (@t109 @t113 @t114)) % 0.39/0.61 (step @p245 :rule cnf_or_pos :args (@t116)) % 0.39/0.61 (step @p246 :rule reordering :premises (@p245) :args ((or @t111 @t115 (not @t116)))) % 0.39/0.61 (step @p247 :rule chain_m_resolution :premises (@p246 @p244 @p235) :args (@t115 @t117 (@list @t109 @t116))) % 0.39/0.61 (step @p248 :rule cnf_or_pos :args (@t120)) % 0.39/0.61 (step @p249 :rule reordering :premises (@p248) :args ((or @t119 @t118 (not @t120)))) % 0.39/0.61 (step @p250 :rule chain_m_resolution :premises (@p249 @p247 @p234) :args (@t118 @t117 (@list @t115 @t120))) % 0.39/0.61 (step @p251 :rule cnf_or_neg :args (@t112 1)) % 0.39/0.61 (step @p252 :rule chain_m_resolution :premises (@p251 @p237) :args ((not @t110) @t113 @t114)) % 0.39/0.61 (step @p253 :rule cnf_or_pos :args (@t124)) % 0.39/0.61 (step @p254 :rule reordering :premises (@p253) :args ((or @t111 @t110 @t123 @t122 (not @t124)))) % 0.39/0.61 (step @p255 :rule chain_m_resolution :premises (@p254 @p244 @p252 @p250 @p232) :args (@t122 (@list false true false false) (@list @t109 @t110 @t118 @t124))) % 0.39/0.61 (step @p256 :rule skolemize :premises (@p255)) % 0.39/0.61 (step @p257 :rule cnf_or_neg :args (@t131 2)) % 0.39/0.61 (step @p258 :rule chain_m_resolution :premises (@p257 @p256) :args ((not @t126) @t113 @t132)) % 0.39/0.61 (step @p259 :rule bool-double-not-elim :args (@t127)) % 0.39/0.61 (step @p260 :rule refl :args (@t131)) % 0.39/0.61 (step @p261 :rule nary_cong :premises (@p260 @p259) :args ((or @t131 (not @t128)))) % 0.39/0.61 (step @p262 :rule cnf_or_neg :args (@t131 1)) % 0.39/0.61 (step @p263 :rule eq_resolve :premises (@p262 @p261)) % 0.39/0.61 (step @p264 :rule reordering :premises (@p263) :args ((or @t127 @t131))) % 0.39/0.61 (step @p265 :rule chain_m_resolution :premises (@p264 @p256) :args (@t127 @t113 @t132)) % 0.39/0.61 (step @p266 :rule bool-double-not-elim :args (@t129)) % 0.39/0.61 (step @p267 :rule nary_cong :premises (@p260 @p266) :args ((or @t131 (not @t130)))) % 0.39/0.61 (step @p268 :rule cnf_or_neg :args (@t131 0)) % 0.39/0.61 (step @p269 :rule eq_resolve :premises (@p268 @p267)) % 0.39/0.61 (step @p270 :rule reordering :premises (@p269) :args ((or @t129 @t131))) % 0.39/0.61 (step @p271 :rule chain_m_resolution :premises (@p270 @p256) :args (@t129 @t113 @t132)) % 0.39/0.61 (step @p272 :rule cnf_or_pos :args (@t133)) % 0.39/0.61 (step @p273 :rule reordering :premises (@p272) :args ((or @t111 @t130 @t128 @t126 @t134))) % 0.39/0.61 (step @p274 :rule chain_m_resolution :premises (@p273 @p244 @p271 @p265 @p258) :args (@t134 (@list false false false true) (@list @t109 @t129 @t127 @t126))) % 0.39/0.61 (assume-push @p281 @t135) % 0.39/0.61 (step @p276 :rule instantiate :premises (@p230) :args ((@list @t105 @t104 @t125))) % 0.39/0.61 (step-pop @p282 :rule scope :premises (@p276)) % 0.39/0.61 (step @p277 :rule process_scope :premises (@p282) :args (@t133)) % 0.39/0.61 (step @p279 :rule implies_elim :premises (@p277)) % 0.39/0.61 (step @p280 false :rule chain_m_resolution :premises (@p279 @p274 @p230) :args (false (@list true false) (@list @t133 @t135))) % 0.39/0.61 ) % 0.39/0.61 % SZS output end Proof % 0.39/0.61 % cvc5 exiting %------------------------------------------------------------------------------