%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU666^2 : 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 : n006.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 08:52:39 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 : SEU666^2 : TPTP v9.2.1. Released v3.7.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n006.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 17:45:19 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.49 %----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 $$unsorted 0) % 0.38/0.57 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.38/0.57 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.subsetI2 Bool) % 0.38/0.57 (declare-const tptp.dsetconstrEL Bool) % 0.38/0.57 (define tptp.dpsetconstr () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "Xu" $$unsorted))) (let ((_let_4 (@var "Xphi" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (@var "B" $$unsorted))) (let ((_let_6 (@var "A" $$unsorted))) (lambda (@list _let_6 _let_5 _let_4) (_ (_ tptp.dsetconstr (_ (_ tptp.cartprod _let_6) _let_5)) (lambda (@list _let_3) (exists (@list _let_2) (and (_ (_ tptp.in _let_2) _let_6) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_5) (_ (_ _let_4 _let_2) _let_1) (= _let_3 (_ (_ tptp.kpair _let_2) _let_1)))))))))))))))) % 0.38/0.57 (define @t1 () (@var "A" $$unsorted)) % 0.38/0.57 (define @t2 () (@var "Xx" $$unsorted)) % 0.38/0.57 (define @t3 () (_ tptp.in @t2)) % 0.38/0.57 (define @t4 () (_ @t3 @t1)) % 0.38/0.57 (define @t5 () (@var "Xy" $$unsorted)) % 0.38/0.57 (define @t6 () (@var "Xphi" (-> $$unsorted Bool))) % 0.38/0.57 (define @t7 () (_ @t6 @t5)) % 0.38/0.57 (define @t8 () (@list @t5)) % 0.38/0.57 (define @t9 () (lambda @t8 @t7)) % 0.38/0.57 (define @t10 () (_ tptp.dsetconstr @t1)) % 0.38/0.57 (define @t11 () (_ @t10 @t9)) % 0.38/0.57 (define @t12 () (_ @t3 @t11)) % 0.38/0.57 (define @t13 () (@list @t1 @t6 @t2)) % 0.38/0.57 (define @t14 () (forall @t13 (=> @t12 @t4))) % 0.38/0.57 (define @t15 () (= tptp.dsetconstrEL @t14)) % 0.38/0.57 (define @t16 () (@var "B" $$unsorted)) % 0.38/0.57 (define @t17 () (_ (_ tptp.subset @t1) @t16)) % 0.38/0.57 (define @t18 () (_ @t3 @t16)) % 0.38/0.57 (define @t19 () (@list @t2)) % 0.38/0.57 (define @t20 () (forall @t19 (=> @t4 @t18))) % 0.38/0.57 (define @t21 () (=> @t20 @t17)) % 0.38/0.57 (define @t22 () (@list @t1 @t16)) % 0.38/0.57 (define @t23 () (forall @t22 @t21)) % 0.38/0.57 (define @t24 () (= tptp.subsetI2 @t23)) % 0.38/0.57 (define @t25 () (_ (_ tptp.cartprod @t1) @t16)) % 0.38/0.57 (define @t26 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.38/0.57 (define @t27 () (_ @t26 @t2)) % 0.38/0.57 (define @t28 () (_ @t27 @t5)) % 0.38/0.57 (define @t29 () (lambda (@list @t2 @t5) @t28)) % 0.38/0.57 (define @t30 () (@list @t1 @t16 @t26)) % 0.38/0.57 (define @t31 () (forall @t30 (_ (_ tptp.subset (_ (_ (_ tptp.dpsetconstr @t1) @t16) @t29)) @t25))) % 0.38/0.57 (define @t32 () (=> tptp.subsetI2 @t31)) % 0.38/0.57 (define @t33 () (=> tptp.dsetconstrEL @t32)) % 0.38/0.57 (define @t34 () (not @t33)) % 0.38/0.57 (define @t35 () (_ tptp.kpair @t2)) % 0.38/0.57 (define @t36 () (_ @t35 @t5)) % 0.38/0.57 (define @t37 () (@var "Xu" $$unsorted)) % 0.38/0.57 (define @t38 () (= @t37 @t36)) % 0.38/0.57 (define @t39 () (_ (_ tptp.in @t5) @t16)) % 0.38/0.57 (define @t40 () (and @t39 @t28 @t38)) % 0.38/0.57 (define @t41 () (exists @t8 @t40)) % 0.38/0.57 (define @t42 () (and @t4 @t41)) % 0.38/0.57 (define @t43 () (exists @t19 @t42)) % 0.38/0.57 (define @t44 () (@list @t37)) % 0.38/0.57 (define @t45 () (lambda @t44 @t43)) % 0.38/0.57 (define @t46 () (_ tptp.dsetconstr @t25)) % 0.38/0.57 (define @t47 () (lambda @t30 (_ @t46 @t45))) % 0.38/0.57 (define @t48 () (tptp.cartprod @t1 @t16)) % 0.38/0.57 (define @t49 () (@var "BOUND_VARIABLE_7499" $$unsorted)) % 0.38/0.57 (define @t50 () (tptp.kpair @t2 @t49)) % 0.38/0.57 (define @t51 () (= @t37 @t50)) % 0.38/0.57 (define @t52 () (not @t51)) % 0.38/0.57 (define @t53 () (_ @t26 @t2 @t49)) % 0.38/0.57 (define @t54 () (not @t53)) % 0.38/0.57 (define @t55 () (tptp.in @t49 @t16)) % 0.38/0.57 (define @t56 () (not @t55)) % 0.38/0.57 (define @t57 () (tptp.in @t2 @t1)) % 0.38/0.57 (define @t58 () (not @t57)) % 0.38/0.57 (define @t59 () (or @t58 @t56 @t54 @t52)) % 0.38/0.57 (define @t60 () (@list @t2 @t49)) % 0.38/0.57 (define @t61 () (forall @t60 @t59)) % 0.38/0.57 (define @t62 () (not @t61)) % 0.38/0.57 (define @t63 () (lambda @t44 @t62)) % 0.38/0.57 (define @t64 () (tptp.dsetconstr @t48 @t63)) % 0.38/0.57 (define @t65 () (tptp.subset @t64 @t48)) % 0.38/0.57 (define @t66 () (forall @t30 @t65)) % 0.38/0.57 (define @t67 () (tptp.subset @t1 @t16)) % 0.38/0.57 (define @t68 () (tptp.in @t2 @t16)) % 0.38/0.57 (define @t69 () (forall @t19 (or @t58 @t68))) % 0.38/0.57 (define @t70 () (not @t69)) % 0.38/0.57 (define @t71 () (or @t70 @t17)) % 0.38/0.57 (define @t72 () (not @t4)) % 0.38/0.57 (define @t73 () (or @t72 @t18)) % 0.38/0.57 (define @t74 () (=> tptp.subsetI2 @t66)) % 0.38/0.57 (define @t75 () (_ @t6 @t5)) % 0.38/0.57 (define @t76 () (lambda @t8 @t75)) % 0.38/0.57 (define @t77 () (tptp.dsetconstr @t1 @t76)) % 0.38/0.57 (define @t78 () (tptp.in @t2 @t77)) % 0.38/0.57 (define @t79 () (not @t78)) % 0.38/0.57 (define @t80 () (or @t79 @t57)) % 0.38/0.57 (define @t81 () (not @t12)) % 0.38/0.57 (define @t82 () (or @t81 @t4)) % 0.38/0.57 (define @t83 () (=> tptp.dsetconstrEL @t74)) % 0.38/0.57 (define @t84 () (_ @t27 @t49)) % 0.38/0.57 (define @t85 () (not @t84)) % 0.38/0.57 (define @t86 () (lambda @t44 (not (forall @t60 (or @t72 (not (_ (_ tptp.in @t49) @t16)) @t85 (not (= @t37 (_ @t35 @t49)))))))) % 0.38/0.57 (define @t87 () (_ @t46 @t86)) % 0.38/0.57 (define @t88 () (_ @t46 @t63)) % 0.38/0.57 (define @t89 () (or @t58 @t56 @t85 @t52)) % 0.38/0.57 (define @t90 () (_ @t29 @t2 @t49)) % 0.38/0.57 (define @t91 () (not @t90)) % 0.38/0.57 (define @t92 () (or @t58 @t56 @t91 @t52)) % 0.38/0.57 (define @t93 () (forall @t60 @t92)) % 0.38/0.57 (define @t94 () (not @t93)) % 0.38/0.57 (define @t95 () (lambda @t44 @t94)) % 0.38/0.57 (define @t96 () (lambda (@list @t26) @t88)) % 0.38/0.57 (define @t97 () (lambda (@list @t16 @t26) @t88)) % 0.38/0.57 (define @t98 () (_ (lambda @t30 @t88) @t1)) % 0.38/0.57 (define @t99 () (forall @t30 (_ (_ tptp.subset (_ (_ @t98 @t16) @t29)) @t25))) % 0.38/0.57 (define @t100 () (=> tptp.subsetI2 @t99)) % 0.38/0.57 (define @t101 () (=> tptp.dsetconstrEL @t100)) % 0.38/0.57 (define @t102 () (or @t56 @t54 @t52)) % 0.38/0.57 (define @t103 () (or @t58 @t102)) % 0.38/0.57 (define @t104 () (forall @t60 @t103)) % 0.38/0.57 (define @t105 () (@list @t49)) % 0.38/0.57 (define @t106 () (forall @t105 @t103)) % 0.38/0.57 (define @t107 () (forall @t105 @t102)) % 0.38/0.57 (define @t108 () (or @t58 @t107)) % 0.38/0.57 (define @t109 () (tptp.kpair @t2 @t5)) % 0.38/0.57 (define @t110 () (_ @t26 @t2 @t5)) % 0.38/0.57 (define @t111 () (tptp.in @t5 @t16)) % 0.38/0.57 (define @t112 () (forall @t8 (or (not @t111) (not @t110) (not (= @t37 @t109))))) % 0.38/0.57 (define @t113 () (or @t72 @t112)) % 0.38/0.57 (define @t114 () (not @t112)) % 0.38/0.57 (define @t115 () (and @t4 @t114)) % 0.38/0.57 (define @t116 () (forall @t19 (not @t115))) % 0.38/0.57 (define @t117 () (not @t116)) % 0.38/0.57 (define @t118 () (not @t38)) % 0.38/0.57 (define @t119 () (not @t28)) % 0.38/0.57 (define @t120 () (not @t39)) % 0.38/0.57 (define @t121 () (or @t120 @t119 @t118)) % 0.38/0.57 (define @t122 () (forall @t8 (not @t40))) % 0.38/0.57 (define @t123 () (not @t122)) % 0.38/0.57 (define @t124 () (@quantifiers_skolemize @t66 1)) % 0.38/0.57 (define @t125 () (@quantifiers_skolemize @t66 0)) % 0.38/0.57 (define @t126 () (tptp.cartprod @t125 @t124)) % 0.38/0.57 (define @t127 () (lambda @t44 (not (forall @t60 (or (not (tptp.in @t2 @t125)) (not (tptp.in @t49 @t124)) (not (_ (@quantifiers_skolemize @t66 2) @t2 @t49)) @t52))))) % 0.38/0.57 (define @t128 () (@purify @t127)) % 0.38/0.57 (define @t129 () (tptp.dsetconstr @t126 @t128)) % 0.38/0.57 (define @t130 () (tptp.subset @t129 @t126)) % 0.38/0.57 (define @t131 () (not @t130)) % 0.38/0.57 (define @t132 () (not @t66)) % 0.38/0.57 (define @t133 () (tptp.dsetconstr @t126 @t127)) % 0.38/0.57 (define @t134 () (tptp.subset @t133 @t126)) % 0.38/0.57 (define @t135 () (not @t134)) % 0.38/0.57 (define @t136 () (forall @t19 (or (not (tptp.in @t2 @t129)) (tptp.in @t2 @t126)))) % 0.38/0.57 (define @t137 () (not @t136)) % 0.38/0.57 (define @t138 () (or @t137 @t130)) % 0.38/0.57 (define @t139 () (@list true false)) % 0.38/0.57 (define @t140 () (forall @t13 (or (not (tptp.in @t2 (tptp.dsetconstr @t1 @t6))) @t57))) % 0.38/0.57 (define @t141 () (@quantifiers_skolemize @t136 0)) % 0.38/0.57 (define @t142 () (or (not (tptp.in @t141 @t129)) (tptp.in @t141 @t126))) % 0.38/0.57 (assume @p1 @t15) % 0.38/0.57 (assume @p2 @t24) % 0.38/0.57 (assume @p3 @t34) % 0.38/0.57 (assume @p4 true) % 0.38/0.57 (step @p5 (= tptp.dpsetconstr @t47) :rule refl :args (@t47)) % 0.38/0.57 (step @p6 :rule refl :args (@t66)) % 0.38/0.57 (step @p7 :rule refl :args (@t67)) % 0.38/0.57 (step @p8 :rule refl :args (@t17)) % 0.38/0.57 (step @p9 :rule cong :premises (@p8 @p7) :args ((= @t17 @t67))) % 0.38/0.57 (step @p10 :rule symm :premises (@p9)) % 0.38/0.57 (step @p11 :rule eq_resolve :premises (@p8 @p10)) % 0.38/0.57 (step @p12 :rule refl :args (@t70)) % 0.38/0.57 (step @p13 :rule nary_cong :premises (@p12 @p11) :args (@t71)) % 0.38/0.57 (step @p14 :rule cong :premises (@p13) :args ((forall @t22 @t71))) % 0.38/0.57 (step @p15 :rule bool-impl-elim :args (@t69 @t17)) % 0.38/0.57 (step @p16 :rule cong :premises (@p15) :args ((forall @t22 (=> @t69 @t17)))) % 0.38/0.57 (step @p17 :rule trans :premises (@p16 @p14)) % 0.38/0.57 (step @p18 :rule refl :args (@t17)) % 0.38/0.57 (step @p19 :rule refl :args (@t68)) % 0.38/0.57 (step @p20 :rule refl :args (@t18)) % 0.38/0.57 (step @p21 :rule cong :premises (@p20 @p19) :args ((= @t18 @t68))) % 0.38/0.57 (step @p22 :rule symm :premises (@p21)) % 0.38/0.57 (step @p23 :rule eq_resolve :premises (@p20 @p22)) % 0.38/0.57 (step @p24 :rule refl :args (@t57)) % 0.38/0.57 (step @p25 :rule refl :args (@t4)) % 0.38/0.57 (step @p26 :rule cong :premises (@p25 @p24) :args ((= @t4 @t57))) % 0.38/0.57 (step @p27 :rule symm :premises (@p26)) % 0.38/0.57 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.38/0.57 (step @p29 :rule cong :premises (@p28) :args (@t72)) % 0.38/0.57 (step @p30 :rule nary_cong :premises (@p29 @p23) :args (@t73)) % 0.38/0.57 (step @p31 :rule cong :premises (@p30) :args ((forall @t19 @t73))) % 0.38/0.57 (step @p32 :rule bool-impl-elim :args (@t4 @t18)) % 0.38/0.57 (step @p33 :rule cong :premises (@p32) :args (@t20)) % 0.38/0.57 (step @p34 :rule trans :premises (@p33 @p31)) % 0.38/0.57 (step @p35 :rule cong :premises (@p34 @p18) :args (@t21)) % 0.38/0.57 (step @p36 :rule cong :premises (@p35) :args (@t23)) % 0.38/0.57 (step @p37 :rule trans :premises (@p36 @p17)) % 0.38/0.57 (step @p38 :rule refl :args (tptp.subsetI2)) % 0.38/0.57 (step @p39 :rule cong :premises (@p38 @p37) :args (@t24)) % 0.38/0.57 (step @p40 :rule eq_resolve :premises (@p2 @p39)) % 0.38/0.57 (step @p41 :rule cong :premises (@p40 @p6) :args (@t74)) % 0.38/0.57 (step @p42 :rule refl :args (@t57)) % 0.38/0.57 (step @p43 :rule lambda-elim :args ((= @t76 @t6))) % 0.38/0.57 (step @p44 :rule refl :args (@t1)) % 0.38/0.57 (step @p45 :rule cong :premises (@p44 @p43) :args (@t77)) % 0.38/0.57 (step @p46 :rule refl :args (@t2)) % 0.38/0.57 (step @p47 :rule cong :premises (@p46 @p45) :args (@t78)) % 0.38/0.57 (step @p48 :rule cong :premises (@p47) :args (@t79)) % 0.38/0.57 (step @p49 :rule nary_cong :premises (@p48 @p42) :args (@t80)) % 0.38/0.57 (step @p50 :rule cong :premises (@p49) :args ((forall @t13 @t80))) % 0.38/0.57 (step @p51 :rule refl :args ((tptp.in @t2 @t11))) % 0.38/0.57 (step @p52 :rule refl :args ((tptp.dsetconstr @t1 @t9))) % 0.38/0.57 (step @p53 :rule refl :args (@t75)) % 0.38/0.57 (step @p54 :rule cong :premises (@p53) :args (@t76)) % 0.38/0.57 (step @p55 :rule refl :args (@t1)) % 0.38/0.57 (step @p56 :rule cong :premises (@p55 @p54) :args (@t77)) % 0.38/0.57 (step @p57 :rule trans :premises (@p56 @p52)) % 0.38/0.57 (step @p58 :rule refl :args (@t2)) % 0.38/0.57 (step @p59 :rule cong :premises (@p58 @p57) :args (@t78)) % 0.38/0.57 (step @p60 :rule trans :premises (@p59 @p51)) % 0.38/0.57 (step @p61 :rule refl :args (@t3)) % 0.38/0.57 (step @p62 :rule ho_cong :premises (@p61 @p57)) % 0.38/0.57 (step @p63 :rule cong :premises (@p62 @p60) :args ((= (_ @t3 @t77) @t78))) % 0.38/0.57 (step @p64 :rule symm :premises (@p63)) % 0.38/0.57 (step @p65 :rule refl :args (@t12)) % 0.38/0.57 (step @p66 :rule eq_resolve :premises (@p65 @p64)) % 0.38/0.57 (step @p67 :rule refl :args (@t10)) % 0.38/0.57 (step @p68 :rule ho_cong :premises (@p67 @p54)) % 0.38/0.57 (step @p69 :rule cong :premises (@p68 @p57) :args ((= (_ @t10 @t76) @t77))) % 0.38/0.57 (step @p70 :rule symm :premises (@p69)) % 0.38/0.57 (step @p71 :rule refl :args (@t11)) % 0.38/0.57 (step @p72 :rule eq_resolve :premises (@p71 @p70)) % 0.38/0.57 (step @p73 :rule refl :args (@t7)) % 0.38/0.57 (step @p74 :rule cong :premises (@p73 @p53) :args ((= @t7 @t75))) % 0.38/0.57 (step @p75 :rule symm :premises (@p74)) % 0.38/0.57 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 0.38/0.57 (step @p77 :rule cong :premises (@p76) :args (@t9)) % 0.38/0.57 (step @p78 :rule ho_cong :premises (@p67 @p77)) % 0.38/0.57 (step @p79 :rule trans :premises (@p78 @p72)) % 0.38/0.57 (step @p80 :rule ho_cong :premises (@p61 @p79)) % 0.38/0.57 (step @p81 :rule trans :premises (@p80 @p66)) % 0.38/0.57 (step @p82 :rule cong :premises (@p81) :args (@t81)) % 0.38/0.57 (step @p83 :rule nary_cong :premises (@p82 @p28) :args (@t82)) % 0.38/0.57 (step @p84 :rule cong :premises (@p83) :args ((forall @t13 @t82))) % 0.38/0.57 (step @p85 :rule trans :premises (@p84 @p50)) % 0.38/0.57 (step @p86 :rule bool-impl-elim :args (@t12 @t4)) % 0.38/0.57 (step @p87 :rule cong :premises (@p86) :args (@t14)) % 0.38/0.57 (step @p88 :rule trans :premises (@p87 @p85)) % 0.38/0.57 (step @p89 :rule refl :args (tptp.dsetconstrEL)) % 0.38/0.57 (step @p90 :rule cong :premises (@p89 @p88) :args (@t15)) % 0.38/0.57 (step @p91 :rule eq_resolve :premises (@p1 @p90)) % 0.38/0.57 (step @p92 :rule cong :premises (@p91 @p41) :args (@t83)) % 0.38/0.57 (step @p93 :rule cong :premises (@p92) :args ((not @t83))) % 0.38/0.57 (step @p94 :rule refl :args ((tptp.subset @t87 @t25))) % 0.38/0.57 (step @p95 :rule refl :args (@t48)) % 0.38/0.57 (step @p96 :rule refl :args ((tptp.dsetconstr @t25 @t86))) % 0.38/0.57 (step @p97 :rule refl :args (@t50)) % 0.38/0.57 (step @p98 :rule refl :args (@t37)) % 0.38/0.57 (step @p99 :rule cong :premises (@p98 @p97) :args (@t51)) % 0.38/0.57 (step @p100 :rule cong :premises (@p99) :args (@t52)) % 0.38/0.57 (step @p101 :rule refl :args (@t53)) % 0.38/0.57 (step @p102 :rule cong :premises (@p101) :args (@t54)) % 0.38/0.57 (step @p103 :rule refl :args (@t55)) % 0.38/0.57 (step @p104 :rule cong :premises (@p103) :args (@t56)) % 0.38/0.57 (step @p105 :rule cong :premises (@p24) :args (@t58)) % 0.38/0.57 (step @p106 :rule nary_cong :premises (@p105 @p104 @p102 @p100) :args (@t59)) % 0.38/0.57 (step @p107 :rule cong :premises (@p106) :args (@t61)) % 0.38/0.57 (step @p108 :rule cong :premises (@p107) :args (@t62)) % 0.38/0.57 (step @p109 :rule cong :premises (@p108) :args (@t63)) % 0.38/0.57 (step @p110 :rule cong :premises (@p95 @p109) :args (@t64)) % 0.38/0.57 (step @p111 :rule trans :premises (@p110 @p96)) % 0.38/0.57 (step @p112 :rule cong :premises (@p111 @p95) :args (@t65)) % 0.38/0.57 (step @p113 :rule trans :premises (@p112 @p94)) % 0.38/0.57 (step @p114 :rule refl :args (tptp.subset)) % 0.38/0.57 (step @p115 :rule ho_cong :premises (@p114 @p111)) % 0.38/0.57 (step @p116 :rule ho_cong :premises (@p115 @p95)) % 0.38/0.57 (step @p117 :rule cong :premises (@p116 @p113) :args ((= (_ (_ tptp.subset @t64) @t48) @t65))) % 0.38/0.57 (step @p118 :rule symm :premises (@p117)) % 0.38/0.57 (step @p119 :rule refl :args ((_ (_ tptp.subset @t87) @t25))) % 0.38/0.57 (step @p120 :rule eq_resolve :premises (@p119 @p118)) % 0.38/0.57 (step @p121 :rule refl :args (@t25)) % 0.38/0.57 (step @p122 :rule cong :premises (@p121 @p95) :args ((= @t25 @t48))) % 0.38/0.57 (step @p123 :rule symm :premises (@p122)) % 0.38/0.57 (step @p124 :rule eq_resolve :premises (@p121 @p123)) % 0.38/0.57 (step @p125 :rule refl :args (tptp.dsetconstr)) % 0.38/0.57 (step @p126 :rule ho_cong :premises (@p125 @p95)) % 0.38/0.57 (step @p127 :rule ho_cong :premises (@p126 @p109)) % 0.38/0.57 (step @p128 :rule cong :premises (@p127 @p111) :args ((= (_ (_ tptp.dsetconstr @t48) @t63) @t64))) % 0.38/0.57 (step @p129 :rule symm :premises (@p128)) % 0.38/0.57 (step @p130 :rule refl :args (@t87)) % 0.38/0.57 (step @p131 :rule eq_resolve :premises (@p130 @p129)) % 0.38/0.57 (step @p132 :rule refl :args (@t63)) % 0.38/0.57 (step @p133 :rule ho_cong :premises (@p125 @p124)) % 0.38/0.57 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.38/0.57 (step @p135 :rule trans :premises (@p134 @p131)) % 0.38/0.57 (step @p136 :rule ho_cong :premises (@p114 @p135)) % 0.38/0.57 (step @p137 :rule ho_cong :premises (@p136 @p124)) % 0.38/0.57 (step @p138 :rule trans :premises (@p137 @p120)) % 0.38/0.57 (step @p139 :rule cong :premises (@p138) :args ((forall @t30 (_ (_ tptp.subset @t88) @t25)))) % 0.38/0.57 (step @p140 :rule refl :args (@t25)) % 0.38/0.57 (step @p141 :rule refl :args (@t52)) % 0.38/0.57 (step @p142 :rule refl :args (@t84)) % 0.38/0.57 (step @p143 :rule cong :premises (@p142 @p101) :args ((= @t84 @t53))) % 0.38/0.57 (step @p144 :rule symm :premises (@p143)) % 0.38/0.57 (step @p145 :rule eq_resolve :premises (@p142 @p144)) % 0.38/0.57 (step @p146 :rule cong :premises (@p145) :args (@t85)) % 0.38/0.57 (step @p147 :rule refl :args (@t56)) % 0.38/0.57 (step @p148 :rule refl :args (@t58)) % 0.38/0.57 (step @p149 :rule nary_cong :premises (@p148 @p147 @p146 @p141) :args (@t89)) % 0.38/0.57 (step @p150 :rule cong :premises (@p149) :args ((forall @t60 @t89))) % 0.38/0.57 (step @p151 :rule refl :args (@t52)) % 0.38/0.57 (step @p152 :rule beta-reduce :args ((= @t90 @t84))) % 0.38/0.57 (step @p153 :rule cong :premises (@p152) :args (@t91)) % 0.38/0.57 (step @p154 :rule refl :args (@t56)) % 0.38/0.57 (step @p155 :rule refl :args (@t58)) % 0.38/0.57 (step @p156 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@p165)) % 0.38/0.57 (step @p172 :rule trans :premises (@p171 @p164)) % 0.38/0.57 (step @p173 :rule refl :args (tptp.subset)) % 0.38/0.57 (step @p174 :rule ho_cong :premises (@p173 @p172)) % 0.38/0.57 (step @p175 :rule ho_cong :premises (@p174 @p140)) % 0.38/0.57 (step @p176 :rule cong :premises (@p175) :args (@t99)) % 0.38/0.57 (step @p177 :rule trans :premises (@p176 @p139)) % 0.38/0.57 (step @p178 :rule cong :premises (@p38 @p177) :args (@t100)) % 0.38/0.57 (step @p179 :rule cong :premises (@p89 @p178) :args (@t101)) % 0.38/0.57 (step @p180 :rule cong :premises (@p179) :args ((not @t101))) % 0.38/0.57 (step @p181 :rule aci_norm :args ((= @t103 @t59))) % 0.38/0.57 (step @p182 :rule cong :premises (@p181) :args (@t104)) % 0.38/0.57 (step @p183 :rule quant-merge-prenex :args ((= (forall @t19 @t106) @t104))) % 0.38/0.57 (step @p184 :rule alpha_equiv :args (@t107 (@list @t49) (@list @t5))) % 0.38/0.57 (step @p185 :rule nary_cong :premises (@p148 @p184) :args (@t108)) % 0.38/0.57 (step 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% 0.38/0.57 (step @p201 :rule cong :premises (@p200) :args (@t116)) % 0.38/0.57 (step @p202 :rule trans :premises (@p201 @p195)) % 0.38/0.57 (step @p203 :rule cong :premises (@p202) :args (@t117)) % 0.38/0.57 (step @p204 :rule exists-elim :args ((= (exists @t19 @t115) @t117))) % 0.38/0.57 (step @p205 :rule trans :premises (@p204 @p203)) % 0.38/0.57 (step @p206 :rule refl :args (@t109)) % 0.38/0.57 (step @p207 :rule refl :args (@t36)) % 0.38/0.57 (step @p208 :rule cong :premises (@p207 @p206) :args ((= @t36 @t109))) % 0.38/0.57 (step @p209 :rule symm :premises (@p208)) % 0.38/0.57 (step @p210 :rule eq_resolve :premises (@p207 @p209)) % 0.38/0.57 (step @p211 :rule cong :premises (@p98 @p210) :args (@t38)) % 0.38/0.57 (step @p212 :rule cong :premises (@p211) :args (@t118)) % 0.38/0.57 (step @p213 :rule refl :args (@t110)) % 0.38/0.57 (step @p214 :rule refl :args (@t28)) % 0.38/0.57 (step @p215 :rule cong :premises (@p214 @p213) :args ((= @t28 @t110))) % 0.38/0.57 (step @p216 :rule symm :premises (@p215)) % 0.38/0.57 (step @p217 :rule eq_resolve :premises (@p214 @p216)) % 0.38/0.57 (step @p218 :rule cong :premises (@p217) :args (@t119)) % 0.38/0.57 (step @p219 :rule refl :args (@t111)) % 0.38/0.57 (step @p220 :rule refl :args (@t39)) % 0.38/0.57 (step @p221 :rule cong :premises (@p220 @p219) :args ((= @t39 @t111))) % 0.38/0.57 (step @p222 :rule symm :premises (@p221)) % 0.38/0.57 (step @p223 :rule eq_resolve :premises (@p220 @p222)) % 0.38/0.57 (step @p224 :rule cong :premises (@p223) :args (@t120)) % 0.38/0.57 (step @p225 :rule nary_cong :premises (@p224 @p218 @p212) :args (@t121)) % 0.38/0.57 (step @p226 :rule cong :premises (@p225) :args ((forall @t8 @t121))) % 0.38/0.57 (step @p227 :rule aci_norm :args ((= (or @t120 (or @t119 @t118)) @t121))) % 0.38/0.57 (step @p228 :rule bool-and-de-morgan :args (@t28 @t38 true)) % 0.38/0.57 (step @p229 :rule refl :args (@t120)) % 0.38/0.57 (step @p230 :rule nary_cong :premises (@p229 @p228) :args ((or @t120 (not (and @t28 @t38))))) % 0.38/0.57 (step @p231 :rule bool-and-de-morgan :args (@t39 @t28 (and @t38))) % 0.38/0.57 (step @p232 :rule trans :premises (@p231 @p230)) % 0.38/0.57 (step @p233 :rule trans :premises (@p232 @p227)) % 0.38/0.57 (step @p234 :rule cong :premises (@p233) :args (@t122)) % 0.38/0.57 (step @p235 :rule trans :premises (@p234 @p226)) % 0.38/0.57 (step @p236 :rule cong :premises (@p235) :args (@t123)) % 0.38/0.57 (step @p237 :rule exists-elim :args ((= @t41 @t123))) % 0.38/0.57 (step @p238 :rule trans :premises (@p237 @p236)) % 0.38/0.57 (step @p239 :rule refl :args (@t4)) % 0.38/0.57 (step @p240 :rule nary_cong :premises (@p239 @p238) :args (@t42)) % 0.38/0.57 (step @p241 :rule cong :premises (@p240) :args (@t43)) % 0.38/0.57 (step @p242 :rule trans :premises (@p241 @p205)) % 0.38/0.57 (step @p243 :rule cong :premises (@p242) :args (@t45)) % 0.38/0.57 (step @p244 :rule ho_cong :premises (@p161 @p243)) % 0.38/0.57 (step @p245 :rule cong :premises (@p244) :args (@t47)) % 0.38/0.57 (step @p246 :rule trans :premises (@p5 @p245)) % 0.38/0.57 (step @p247 :rule ho_cong :premises (@p246 @p44)) % 0.38/0.57 (step @p248 :rule ho_cong :premises (@p247 @p167)) % 0.38/0.57 (step @p249 :rule ho_cong :premises (@p248 @p165)) % 0.38/0.57 (step @p250 :rule ho_cong :premises (@p173 @p249)) % 0.38/0.57 (step @p251 :rule ho_cong :premises (@p250 @p140)) % 0.38/0.57 (step @p252 :rule cong :premises (@p251) :args (@t31)) % 0.38/0.57 (step @p253 :rule cong :premises (@p38 @p252) :args (@t32)) % 0.38/0.57 (step @p254 :rule cong :premises (@p89 @p253) :args (@t33)) % 0.38/0.57 (step @p255 :rule cong :premises (@p254) :args (@t34)) % 0.38/0.57 (step @p256 :rule trans :premises (@p255 @p180)) % 0.38/0.57 (step @p257 :rule trans :premises (@p256 @p93)) % 0.38/0.57 (step @p258 :rule eq_resolve :premises (@p3 @p257)) % 0.38/0.57 (step @p259 :rule not_implies_elim1 :premises (@p258)) % 0.38/0.57 (step @p260 :rule not_implies_elim2 :premises (@p258)) % 0.38/0.57 (step @p261 :rule not_implies_elim1 :premises (@p260)) % 0.38/0.57 (step @p262 :rule instantiate :premises (@p261) :args ((@list @t129 @t126))) % 0.38/0.58 (step @p263 :rule not_implies_elim2 :premises (@p260)) % 0.38/0.58 (step @p264 :rule refl :args (@t131)) % 0.38/0.58 (step @p265 :rule bool-double-not-elim :args (@t66)) % 0.38/0.58 (step @p266 :rule nary_cong :premises (@p265 @p264) :args ((or (not @t132) @t131))) % 0.38/0.58 (step @p267 :rule refl :args (@t126)) % 0.38/0.58 (step @p268 :rule eq-refl :args (@t127)) % 0.38/0.58 (step @p269 :rule skolem_intro :args (@t128)) % 0.38/0.58 (step @p270 :rule refl :args (@t127)) % 0.38/0.58 (step @p271 :rule cong :premises (@p270 @p269) :args ((= @t127 @t128))) % 0.38/0.58 (step @p272 :rule trans :premises (@p271 @p268)) % 0.38/0.58 (step @p273 :rule true_elim :premises (@p272)) % 0.38/0.58 (step @p274 :rule cong :premises (@p267 @p273) :args (@t133)) % 0.38/0.58 (step @p275 :rule cong :premises (@p274 @p267) :args (@t134)) % 0.38/0.58 (step @p276 :rule cong :premises (@p275) :args (@t135)) % 0.38/0.58 (step @p277 :rule refl :args (@t132)) % 0.38/0.58 (step @p278 :rule cong :premises (@p277 @p276) :args ((=> @t132 @t135))) % 0.38/0.58 (assume-push @p297 @t132) % 0.38/0.58 (step @p280 :rule skolemize :premises (@p263)) % 0.38/0.58 (step-pop @p298 :rule scope :premises (@p280)) % 0.38/0.58 (step @p281 :rule process_scope :premises (@p298) :args (@t135)) % 0.38/0.58 (step @p283 :rule eq_resolve :premises (@p281 @p278)) % 0.38/0.58 (step @p284 :rule implies_elim :premises (@p283)) % 0.38/0.58 (step @p285 :rule eq_resolve :premises (@p284 @p266)) % 0.38/0.58 (step @p286 :rule chain_m_resolution :premises (@p285 @p263) :args (@t131 (@list true) (@list @t66))) % 0.38/0.58 (step @p287 :rule cnf_or_pos :args (@t138)) % 0.38/0.58 (step @p288 :rule reordering :premises (@p287) :args ((or @t130 @t137 (not @t138)))) % 0.38/0.58 (step @p289 :rule chain_m_resolution :premises (@p288 @p286 @p262) :args (@t137 @t139 (@list @t130 @t138))) % 0.38/0.58 (step @p290 :rule skolemize :premises (@p289)) % 0.38/0.58 (assume-push @p299 @t140) % 0.38/0.58 (step @p292 :rule instantiate :premises (@p259) :args ((@list @t126 @t128 @t141))) % 0.38/0.58 (step-pop @p300 :rule scope :premises (@p292)) % 0.38/0.58 (step @p293 :rule process_scope :premises (@p300) :args (@t142)) % 0.38/0.58 (step @p295 :rule implies_elim :premises (@p293)) % 0.38/0.58 (step @p296 false :rule chain_m_resolution :premises (@p295 @p290 @p259) :args (false @t139 (@list @t142 @t140))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------