%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU540^2 : 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 : n019.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 08:52:07 AM UTC 2026 % Result : Theorem 0.39s 0.58s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU540^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n019.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 17:41:19 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.39/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.58 % SZS status Theorem % 0.39/0.58 % SZS output start Proof % 0.39/0.58 ( % 0.39/0.58 (declare-sort $$unsorted 0) % 0.39/0.58 (declare-const tptp.emptyset $$unsorted) % 0.39/0.58 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.39/0.58 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.39/0.58 (declare-const tptp.powersetI Bool) % 0.39/0.58 (declare-const tptp.dsetconstrI Bool) % 0.39/0.58 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.39/0.58 (define tptp.prop2set () (let ((_let_1 (@var "Xphi" Bool))) (lambda (@list _let_1) (_ (_ tptp.dsetconstr (_ tptp.powerset tptp.emptyset)) (lambda (@list (@var "Xx" $$unsorted)) _let_1))))) % 0.39/0.58 (define @t1 () (@var "Xy" $$unsorted)) % 0.39/0.58 (define @t2 () (@var "Xphi" (-> $$unsorted Bool))) % 0.39/0.58 (define @t3 () (_ @t2 @t1)) % 0.39/0.58 (define @t4 () (@list @t1)) % 0.39/0.58 (define @t5 () (lambda @t4 @t3)) % 0.39/0.58 (define @t6 () (@var "A" $$unsorted)) % 0.39/0.58 (define @t7 () (_ tptp.dsetconstr @t6)) % 0.39/0.58 (define @t8 () (_ @t7 @t5)) % 0.39/0.58 (define @t9 () (@var "Xx" $$unsorted)) % 0.39/0.58 (define @t10 () (_ tptp.in @t9)) % 0.39/0.58 (define @t11 () (_ @t10 @t8)) % 0.39/0.58 (define @t12 () (_ @t2 @t9)) % 0.39/0.58 (define @t13 () (=> @t12 @t11)) % 0.39/0.58 (define @t14 () (_ @t10 @t6)) % 0.39/0.58 (define @t15 () (@list @t6 @t2 @t9)) % 0.39/0.58 (define @t16 () (forall @t15 (=> @t14 @t13))) % 0.39/0.58 (define @t17 () (= tptp.dsetconstrI @t16)) % 0.39/0.58 (define @t18 () (_ tptp.powerset @t6)) % 0.39/0.58 (define @t19 () (@var "B" $$unsorted)) % 0.39/0.58 (define @t20 () (_ tptp.in @t19)) % 0.39/0.58 (define @t21 () (_ @t20 @t18)) % 0.39/0.58 (define @t22 () (_ @t10 @t19)) % 0.39/0.58 (define @t23 () (@list @t9)) % 0.39/0.58 (define @t24 () (forall @t23 (=> @t22 @t14))) % 0.39/0.58 (define @t25 () (=> @t24 @t21)) % 0.39/0.58 (define @t26 () (@list @t6 @t19)) % 0.39/0.58 (define @t27 () (forall @t26 @t25)) % 0.39/0.58 (define @t28 () (= tptp.powersetI @t27)) % 0.39/0.58 (define @t29 () (@var "Xphi" Bool)) % 0.39/0.58 (define @t30 () (_ tptp.in tptp.emptyset)) % 0.39/0.58 (define @t31 () (=> @t29 (_ @t30 (_ tptp.prop2set @t29)))) % 0.39/0.58 (define @t32 () (@list @t29)) % 0.39/0.58 (define @t33 () (forall @t32 @t31)) % 0.39/0.58 (define @t34 () (=> tptp.powersetI @t33)) % 0.39/0.58 (define @t35 () (=> tptp.dsetconstrI @t34)) % 0.39/0.58 (define @t36 () (not @t35)) % 0.39/0.58 (define @t37 () (lambda @t23 @t29)) % 0.39/0.58 (define @t38 () (_ tptp.powerset tptp.emptyset)) % 0.39/0.58 (define @t39 () (_ (_ tptp.dsetconstr @t38) @t37)) % 0.39/0.58 (define @t40 () (lambda @t32 @t39)) % 0.39/0.58 (define @t41 () (@var "BOUND_VARIABLE_7571" $$unsorted)) % 0.39/0.58 (define @t42 () (lambda (@list @t41) true)) % 0.39/0.58 (define @t43 () (@purify @t42)) % 0.39/0.58 (define @t44 () (tptp.powerset tptp.emptyset)) % 0.39/0.58 (define @t45 () (tptp.dsetconstr @t44 @t42)) % 0.39/0.58 (define @t46 () (tptp.in tptp.emptyset @t45)) % 0.39/0.58 (define @t47 () (tptp.powerset @t6)) % 0.39/0.58 (define @t48 () (tptp.in @t19 @t47)) % 0.39/0.58 (define @t49 () (tptp.in @t9 @t6)) % 0.39/0.58 (define @t50 () (tptp.in @t9 @t19)) % 0.39/0.58 (define @t51 () (forall @t23 (or (not @t50) @t49))) % 0.39/0.58 (define @t52 () (not @t51)) % 0.39/0.58 (define @t53 () (forall @t26 (or @t52 @t48))) % 0.39/0.58 (define @t54 () (=> @t53 @t46)) % 0.39/0.58 (define @t55 () (_ @t2 @t9)) % 0.39/0.58 (define @t56 () (not @t55)) % 0.39/0.58 (define @t57 () (not @t49)) % 0.39/0.58 (define @t58 () (forall @t15 (or @t57 @t56 (tptp.in @t9 (tptp.dsetconstr @t6 @t2))))) % 0.39/0.58 (define @t59 () (=> @t58 @t54)) % 0.39/0.58 (define @t60 () (or @t52 @t21)) % 0.39/0.58 (define @t61 () (not @t22)) % 0.39/0.58 (define @t62 () (or @t61 @t14)) % 0.39/0.58 (define @t63 () (=> tptp.powersetI @t46)) % 0.39/0.58 (define @t64 () (_ @t2 @t1)) % 0.39/0.58 (define @t65 () (lambda @t4 @t64)) % 0.39/0.58 (define @t66 () (tptp.dsetconstr @t6 @t65)) % 0.39/0.58 (define @t67 () (tptp.in @t9 @t66)) % 0.39/0.58 (define @t68 () (or @t57 @t56 @t67)) % 0.39/0.58 (define @t69 () (not @t12)) % 0.39/0.58 (define @t70 () (not @t14)) % 0.39/0.58 (define @t71 () (or @t70 @t69 @t11)) % 0.39/0.58 (define @t72 () (=> tptp.dsetconstrI @t63)) % 0.39/0.58 (define @t73 () (lambda @t23 true)) % 0.39/0.58 (define @t74 () (tptp.dsetconstr @t44 @t73)) % 0.39/0.58 (define @t75 () (tptp.in tptp.emptyset @t74)) % 0.39/0.58 (define @t76 () (not true)) % 0.39/0.58 (define @t77 () (or @t76 @t75)) % 0.39/0.58 (define @t78 () (tptp.dsetconstr @t44 @t37)) % 0.39/0.58 (define @t79 () (tptp.in tptp.emptyset @t78)) % 0.39/0.58 (define @t80 () (not @t29)) % 0.39/0.58 (define @t81 () (or @t80 @t80 @t79)) % 0.39/0.58 (define @t82 () (or @t80 @t79)) % 0.39/0.58 (define @t83 () (_ @t30 @t39)) % 0.39/0.58 (define @t84 () (or @t80 @t83)) % 0.39/0.58 (define @t85 () (_ @t40 @t29)) % 0.39/0.58 (define @t86 () (=> @t29 (_ @t30 @t85))) % 0.39/0.58 (define @t87 () (forall @t32 @t86)) % 0.39/0.58 (define @t88 () (=> tptp.powersetI @t87)) % 0.39/0.58 (define @t89 () (=> tptp.dsetconstrI @t88)) % 0.39/0.58 (define @t90 () (tptp.in tptp.emptyset (tptp.dsetconstr @t44 @t43))) % 0.39/0.58 (define @t91 () (tptp.in tptp.emptyset @t44)) % 0.39/0.58 (define @t92 () (not @t91)) % 0.39/0.58 (define @t93 () (or @t92 @t90)) % 0.39/0.58 (define @t94 () (_ @t43 tptp.emptyset)) % 0.39/0.58 (define @t95 () (not @t94)) % 0.39/0.58 (define @t96 () (or @t92 @t95 @t90)) % 0.39/0.58 (define @t97 () (@list true false)) % 0.39/0.58 (define @t98 () (tptp.in @t9 tptp.emptyset)) % 0.39/0.58 (define @t99 () (forall @t23 (or (not @t98) @t98))) % 0.39/0.58 (define @t100 () (not @t99)) % 0.39/0.58 (define @t101 () (or @t100 @t91)) % 0.39/0.58 (assume @p1 @t17) % 0.39/0.58 (assume @p2 @t28) % 0.39/0.58 (assume @p3 @t36) % 0.39/0.58 (assume @p4 true) % 0.39/0.58 (step @p5 (= tptp.prop2set @t40) :rule refl :args (@t40)) % 0.39/0.58 (step @p6 :rule eq-refl :args (@t42)) % 0.39/0.58 (step @p7 :rule refl :args (@t42)) % 0.39/0.58 (step @p8 :rule symm :premises (@p7)) % 0.39/0.58 (step @p9 :rule refl :args (@t42)) % 0.39/0.58 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t42 @t42))) % 0.39/0.58 (step @p11 :rule trans :premises (@p10 @p6)) % 0.39/0.58 (step @p12 :rule skolem_intro :args (@t43)) % 0.39/0.58 (step @p13 :rule cong :premises (@p9 @p12) :args ((= @t42 @t43))) % 0.39/0.58 (step @p14 :rule trans :premises (@p13 @p11)) % 0.39/0.58 (step @p15 :rule true_elim :premises (@p14)) % 0.39/0.58 (step @p16 :rule refl :args (@t44)) % 0.39/0.58 (step @p17 :rule cong :premises (@p16 @p15) :args (@t45)) % 0.39/0.58 (step @p18 :rule refl :args (tptp.emptyset)) % 0.39/0.58 (step @p19 :rule cong :premises (@p18 @p17) :args (@t46)) % 0.39/0.58 (step @p20 :rule refl :args (@t53)) % 0.39/0.58 (step @p21 :rule cong :premises (@p20 @p19) :args (@t54)) % 0.39/0.58 (step @p22 :rule refl :args (@t58)) % 0.39/0.58 (step @p23 :rule cong :premises (@p22 @p21) :args (@t59)) % 0.39/0.58 (step @p24 :rule cong :premises (@p23) :args ((not @t59))) % 0.39/0.58 (step @p25 :rule refl :args (@t46)) % 0.39/0.58 (step @p26 :rule refl :args ((tptp.in @t19 @t18))) % 0.39/0.58 (step @p27 :rule refl :args (@t47)) % 0.39/0.58 (step @p28 :rule refl :args (@t19)) % 0.39/0.58 (step @p29 :rule cong :premises (@p28 @p27) :args (@t48)) % 0.39/0.58 (step @p30 :rule trans :premises (@p29 @p26)) % 0.39/0.58 (step @p31 :rule refl :args (@t20)) % 0.39/0.58 (step @p32 :rule ho_cong :premises (@p31 @p27)) % 0.39/0.58 (step @p33 :rule cong :premises (@p32 @p30) :args ((= (_ @t20 @t47) @t48))) % 0.39/0.58 (step @p34 :rule symm :premises (@p33)) % 0.39/0.58 (step @p35 :rule refl :args (@t21)) % 0.39/0.58 (step @p36 :rule eq_resolve :premises (@p35 @p34)) % 0.39/0.58 (step @p37 :rule refl :args (@t18)) % 0.39/0.58 (step @p38 :rule cong :premises (@p37 @p27) :args ((= @t18 @t47))) % 0.39/0.58 (step @p39 :rule symm :premises (@p38)) % 0.39/0.58 (step @p40 :rule eq_resolve :premises (@p37 @p39)) % 0.39/0.58 (step @p41 :rule ho_cong :premises (@p31 @p40)) % 0.39/0.58 (step @p42 :rule trans :premises (@p41 @p36)) % 0.39/0.58 (step @p43 :rule refl :args (@t52)) % 0.39/0.58 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t60)) % 0.39/0.58 (step @p45 :rule cong :premises (@p44) :args ((forall @t26 @t60))) % 0.39/0.58 (step @p46 :rule bool-impl-elim :args (@t51 @t21)) % 0.39/0.58 (step @p47 :rule cong :premises (@p46) :args ((forall @t26 (=> @t51 @t21)))) % 0.39/0.58 (step @p48 :rule trans :premises (@p47 @p45)) % 0.39/0.58 (step @p49 :rule refl :args (@t21)) % 0.39/0.58 (step @p50 :rule refl :args (@t49)) % 0.39/0.58 (step @p51 :rule refl :args (@t14)) % 0.39/0.58 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t14 @t49))) % 0.39/0.58 (step @p53 :rule symm :premises (@p52)) % 0.39/0.58 (step @p54 :rule eq_resolve :premises (@p51 @p53)) % 0.39/0.58 (step @p55 :rule refl :args (@t50)) % 0.39/0.58 (step @p56 :rule refl :args (@t22)) % 0.39/0.58 (step @p57 :rule cong :premises (@p56 @p55) :args ((= @t22 @t50))) % 0.39/0.58 (step @p58 :rule symm :premises (@p57)) % 0.39/0.58 (step @p59 :rule eq_resolve :premises (@p56 @p58)) % 0.39/0.58 (step @p60 :rule cong :premises (@p59) :args (@t61)) % 0.39/0.58 (step @p61 :rule nary_cong :premises (@p60 @p54) :args (@t62)) % 0.39/0.58 (step @p62 :rule cong :premises (@p61) :args ((forall @t23 @t62))) % 0.39/0.58 (step @p63 :rule bool-impl-elim :args (@t22 @t14)) % 0.39/0.58 (step @p64 :rule cong :premises (@p63) :args (@t24)) % 0.39/0.58 (step @p65 :rule trans :premises (@p64 @p62)) % 0.39/0.58 (step @p66 :rule cong :premises (@p65 @p49) :args (@t25)) % 0.39/0.58 (step @p67 :rule cong :premises (@p66) :args (@t27)) % 0.39/0.58 (step @p68 :rule trans :premises (@p67 @p48)) % 0.39/0.58 (step @p69 :rule refl :args (tptp.powersetI)) % 0.39/0.58 (step @p70 :rule cong :premises (@p69 @p68) :args (@t28)) % 0.39/0.58 (step @p71 :rule eq_resolve :premises (@p2 @p70)) % 0.39/0.58 (step @p72 :rule cong :premises (@p71 @p25) :args (@t63)) % 0.39/0.58 (step @p73 :rule lambda-elim :args ((= @t65 @t2))) % 0.39/0.58 (step @p74 :rule refl :args (@t6)) % 0.39/0.58 (step @p75 :rule cong :premises (@p74 @p73) :args (@t66)) % 0.39/0.58 (step @p76 :rule refl :args (@t9)) % 0.39/0.58 (step @p77 :rule cong :premises (@p76 @p75) :args (@t67)) % 0.39/0.58 (step @p78 :rule refl :args (@t56)) % 0.39/0.58 (step @p79 :rule refl :args (@t57)) % 0.39/0.58 (step @p80 :rule nary_cong :premises (@p79 @p78 @p77) :args (@t68)) % 0.39/0.58 (step @p81 :rule cong :premises (@p80) :args ((forall @t15 @t68))) % 0.39/0.58 (step @p82 :rule refl :args ((tptp.in @t9 @t8))) % 0.39/0.58 (step @p83 :rule refl :args ((tptp.dsetconstr @t6 @t5))) % 0.39/0.58 (step @p84 :rule refl :args (@t64)) % 0.39/0.58 (step @p85 :rule cong :premises (@p84) :args (@t65)) % 0.39/0.58 (step @p86 :rule refl :args (@t6)) % 0.39/0.58 (step @p87 :rule cong :premises (@p86 @p85) :args (@t66)) % 0.39/0.58 (step @p88 :rule trans :premises (@p87 @p83)) % 0.39/0.58 (step @p89 :rule refl :args (@t9)) % 0.39/0.58 (step @p90 :rule cong :premises (@p89 @p88) :args (@t67)) % 0.39/0.58 (step @p91 :rule trans :premises (@p90 @p82)) % 0.39/0.58 (step @p92 :rule refl :args (@t10)) % 0.39/0.58 (step @p93 :rule ho_cong :premises (@p92 @p88)) % 0.39/0.58 (step @p94 :rule cong :premises (@p93 @p91) :args ((= (_ @t10 @t66) @t67))) % 0.39/0.58 (step @p95 :rule symm :premises (@p94)) % 0.39/0.58 (step @p96 :rule refl :args (@t11)) % 0.39/0.58 (step @p97 :rule eq_resolve :premises (@p96 @p95)) % 0.39/0.58 (step @p98 :rule refl :args (@t7)) % 0.39/0.58 (step @p99 :rule ho_cong :premises (@p98 @p85)) % 0.39/0.58 (step @p100 :rule cong :premises (@p99 @p88) :args ((= (_ @t7 @t65) @t66))) % 0.39/0.58 (step @p101 :rule symm :premises (@p100)) % 0.39/0.58 (step @p102 :rule refl :args (@t8)) % 0.39/0.58 (step @p103 :rule eq_resolve :premises (@p102 @p101)) % 0.39/0.58 (step @p104 :rule refl :args (@t3)) % 0.39/0.58 (step @p105 :rule cong :premises (@p104 @p84) :args ((= @t3 @t64))) % 0.39/0.58 (step @p106 :rule symm :premises (@p105)) % 0.39/0.58 (step @p107 :rule eq_resolve :premises (@p104 @p106)) % 0.39/0.58 (step @p108 :rule cong :premises (@p107) :args (@t5)) % 0.39/0.58 (step @p109 :rule ho_cong :premises (@p98 @p108)) % 0.39/0.58 (step @p110 :rule trans :premises (@p109 @p103)) % 0.39/0.58 (step @p111 :rule ho_cong :premises (@p92 @p110)) % 0.39/0.58 (step @p112 :rule trans :premises (@p111 @p97)) % 0.39/0.58 (step @p113 :rule refl :args (@t55)) % 0.39/0.58 (step @p114 :rule refl :args (@t12)) % 0.39/0.58 (step @p115 :rule cong :premises (@p114 @p113) :args ((= @t12 @t55))) % 0.39/0.58 (step @p116 :rule symm :premises (@p115)) % 0.39/0.58 (step @p117 :rule eq_resolve :premises (@p114 @p116)) % 0.39/0.58 (step @p118 :rule cong :premises (@p117) :args (@t69)) % 0.39/0.58 (step @p119 :rule cong :premises (@p54) :args (@t70)) % 0.39/0.58 (step @p120 :rule nary_cong :premises (@p119 @p118 @p112) :args (@t71)) % 0.39/0.58 (step @p121 :rule cong :premises (@p120) :args ((forall @t15 @t71))) % 0.39/0.58 (step @p122 :rule trans :premises (@p121 @p81)) % 0.39/0.58 (step @p123 :rule aci_norm :args ((= (or @t70 (or @t69 @t11)) @t71))) % 0.39/0.58 (step @p124 :rule bool-impl-elim :args (@t12 @t11)) % 0.39/0.58 (step @p125 :rule refl :args (@t70)) % 0.39/0.58 (step @p126 :rule nary_cong :premises (@p125 @p124) :args ((or @t70 @t13))) % 0.39/0.58 (step @p127 :rule trans :premises (@p126 @p123)) % 0.39/0.58 (step @p128 :rule bool-impl-elim :args (@t14 @t13)) % 0.39/0.58 (step @p129 :rule trans :premises (@p128 @p127)) % 0.39/0.58 (step @p130 :rule cong :premises (@p129) :args (@t16)) % 0.39/0.58 (step @p131 :rule trans :premises (@p130 @p122)) % 0.39/0.58 (step @p132 :rule refl :args (tptp.dsetconstrI)) % 0.39/0.58 (step @p133 :rule cong :premises (@p132 @p131) :args (@t17)) % 0.39/0.58 (step @p134 :rule eq_resolve :premises (@p1 @p133)) % 0.39/0.58 (step @p135 :rule cong :premises (@p134 @p72) :args (@t72)) % 0.39/0.58 (step @p136 :rule cong :premises (@p135) :args ((not @t72))) % 0.39/0.58 (step @p137 :rule aci_norm :args ((= (or false @t46) @t46))) % 0.39/0.58 (step @p138 :rule symm :premises (@p7)) % 0.39/0.58 (step @p139 :rule alpha_equiv :args (@t73 (@list @t9) (@list @t41))) % 0.39/0.58 (step @p140 :rule trans :premises (@p139 @p138)) % 0.39/0.58 (step @p141 :rule cong :premises (@p16 @p140) :args (@t74)) % 0.39/0.58 (step @p142 :rule cong :premises (@p18 @p141) :args (@t75)) % 0.39/0.58 (step @p143 :rule evaluate :args (@t76)) % 0.39/0.58 (step @p144 :rule nary_cong :premises (@p143 @p142) :args (@t77)) % 0.39/0.58 (step @p145 :rule trans :premises (@p144 @p137)) % 0.39/0.58 (step @p146 :rule quant-var-elim-eq :args ((= (forall @t32 (or (not (= @t29 true)) @t80 @t79)) @t77))) % 0.39/0.58 (step @p147 :rule refl :args (@t79)) % 0.39/0.58 (step @p148 :rule refl :args (@t80)) % 0.39/0.58 (step @p149 :rule bool-eq-true :args (@t29)) % 0.39/0.58 (step @p150 :rule symm :premises (@p149)) % 0.39/0.58 (step @p151 :rule cong :premises (@p150) :args (@t80)) % 0.39/0.58 (step @p152 :rule nary_cong :premises (@p151 @p148 @p147) :args (@t81)) % 0.39/0.58 (step @p153 :rule aci_norm :args ((= @t82 @t81))) % 0.39/0.58 (step @p154 :rule trans :premises (@p153 @p152)) % 0.39/0.58 (step @p155 :rule cong :premises (@p154) :args ((forall @t32 @t82))) % 0.39/0.58 (step @p156 :rule trans :premises (@p155 @p146)) % 0.39/0.58 (step @p157 :rule trans :premises (@p156 @p145)) % 0.39/0.58 (step @p158 :rule refl :args ((tptp.in tptp.emptyset @t39))) % 0.39/0.58 (step @p159 :rule refl :args ((tptp.dsetconstr @t38 @t37))) % 0.39/0.58 (step @p160 :rule refl :args (@t37)) % 0.39/0.58 (step @p161 :rule refl :args (@t44)) % 0.39/0.58 (step @p162 :rule cong :premises (@p161 @p160) :args (@t78)) % 0.39/0.58 (step @p163 :rule trans :premises (@p162 @p159)) % 0.39/0.58 (step @p164 :rule refl :args (tptp.emptyset)) % 0.39/0.58 (step @p165 :rule cong :premises (@p164 @p163) :args (@t79)) % 0.39/0.58 (step @p166 :rule trans :premises (@p165 @p158)) % 0.39/0.58 (step @p167 :rule refl :args (@t30)) % 0.39/0.58 (step @p168 :rule ho_cong :premises (@p167 @p163)) % 0.39/0.58 (step @p169 :rule cong :premises (@p168 @p166) :args ((= (_ @t30 @t78) @t79))) % 0.39/0.58 (step @p170 :rule symm :premises (@p169)) % 0.39/0.58 (step @p171 :rule refl :args (@t83)) % 0.39/0.58 (step @p172 :rule eq_resolve :premises (@p171 @p170)) % 0.39/0.58 (step @p173 :rule refl :args (tptp.dsetconstr)) % 0.39/0.58 (step @p174 :rule ho_cong :premises (@p173 @p161)) % 0.39/0.58 (step @p175 :rule ho_cong :premises (@p174 @p160)) % 0.39/0.58 (step @p176 :rule cong :premises (@p175 @p163) :args ((= (_ (_ tptp.dsetconstr @t44) @t37) @t78))) % 0.39/0.58 (step @p177 :rule symm :premises (@p176)) % 0.39/0.58 (step @p178 :rule refl :args (@t39)) % 0.39/0.58 (step @p179 :rule eq_resolve :premises (@p178 @p177)) % 0.39/0.58 (step @p180 :rule refl :args (@t38)) % 0.39/0.58 (step @p181 :rule cong :premises (@p180 @p161) :args ((= @t38 @t44))) % 0.39/0.58 (step @p182 :rule symm :premises (@p181)) % 0.39/0.58 (step @p183 :rule eq_resolve :premises (@p180 @p182)) % 0.39/0.58 (step @p184 :rule ho_cong :premises (@p173 @p183)) % 0.39/0.58 (step @p185 :rule ho_cong :premises (@p184 @p160)) % 0.39/0.58 (step @p186 :rule trans :premises (@p185 @p179)) % 0.39/0.58 (step @p187 :rule ho_cong :premises (@p167 @p186)) % 0.39/0.58 (step @p188 :rule trans :premises (@p187 @p172)) % 0.39/0.58 (step @p189 :rule nary_cong :premises (@p148 @p188) :args (@t84)) % 0.39/0.58 (step @p190 :rule cong :premises (@p189) :args ((forall @t32 @t84))) % 0.39/0.58 (step @p191 :rule trans :premises (@p190 @p157)) % 0.39/0.58 (step @p192 :rule bool-impl-elim :args (@t29 @t83)) % 0.39/0.58 (step @p193 :rule cong :premises (@p192) :args ((forall @t32 (=> @t29 @t83)))) % 0.39/0.58 (step @p194 :rule trans :premises (@p193 @p191)) % 0.39/0.58 (step @p195 :rule beta-reduce :args ((= @t85 @t39))) % 0.39/0.58 (step @p196 :rule refl :args (@t30)) % 0.39/0.58 (step @p197 :rule ho_cong :premises (@p196 @p195)) % 0.39/0.58 (step @p198 :rule refl :args (@t29)) % 0.39/0.58 (step @p199 :rule cong :premises (@p198 @p197) :args (@t86)) % 0.39/0.58 (step @p200 :rule cong :premises (@p199) :args (@t87)) % 0.39/0.58 (step @p201 :rule trans :premises (@p200 @p194)) % 0.39/0.58 (step @p202 :rule cong :premises (@p69 @p201) :args (@t88)) % 0.39/0.58 (step @p203 :rule cong :premises (@p132 @p202) :args (@t89)) % 0.39/0.58 (step @p204 :rule cong :premises (@p203) :args ((not @t89))) % 0.39/0.58 (step @p205 :rule ho_cong :premises (@p5 @p198)) % 0.39/0.58 (step @p206 :rule ho_cong :premises (@p196 @p205)) % 0.39/0.58 (step @p207 :rule cong :premises (@p198 @p206) :args (@t31)) % 0.39/0.58 (step @p208 :rule cong :premises (@p207) :args (@t33)) % 0.39/0.58 (step @p209 :rule cong :premises (@p69 @p208) :args (@t34)) % 0.39/0.58 (step @p210 :rule cong :premises (@p132 @p209) :args (@t35)) % 0.39/0.58 (step @p211 :rule cong :premises (@p210) :args (@t36)) % 0.39/0.58 (step @p212 :rule trans :premises (@p211 @p204)) % 0.39/0.58 (step @p213 :rule trans :premises (@p212 @p136 @p24)) % 0.39/0.58 (step @p214 :rule eq_resolve :premises (@p3 @p213)) % 0.39/0.58 (step @p215 :rule not_implies_elim2 :premises (@p214)) % 0.39/0.58 (step @p216 :rule not_implies_elim1 :premises (@p215)) % 0.39/0.58 (step @p217 :rule not_implies_elim1 :premises (@p214)) % 0.39/0.58 (step @p218 :rule aci_norm :args ((= (or @t92 false @t90) @t93))) % 0.39/0.58 (step @p219 :rule refl :args (@t90)) % 0.39/0.58 (step @p220 :rule beta-reduce :args ((= (_ @t42 tptp.emptyset) true))) % 0.39/0.58 (step @p221 :rule ho_cong :premises (@p12 @p18)) % 0.39/0.58 (step @p222 :rule bool-eq-true :args (@t94)) % 0.39/0.58 (step @p223 :rule trans :premises (@p222 @p221 @p220)) % 0.39/0.58 (step @p224 :rule true_elim :premises (@p223)) % 0.39/0.58 (step @p225 :rule cong :premises (@p224) :args (@t95)) % 0.39/0.58 (step @p226 :rule trans :premises (@p225 @p143)) % 0.39/0.58 (step @p227 :rule refl :args (@t92)) % 0.39/0.58 (step @p228 :rule nary_cong :premises (@p227 @p226 @p219) :args (@t96)) % 0.39/0.58 (step @p229 :rule trans :premises (@p228 @p218)) % 0.39/0.58 (step @p230 :rule cong :premises (@p22 @p229) :args ((=> @t58 @t96))) % 0.39/0.58 (assume-push @p260 @t58) % 0.39/0.58 (step @p232 :rule instantiate :premises (@p217) :args ((@list @t44 @t43 tptp.emptyset))) % 0.39/0.58 (step-pop @p261 :rule scope :premises (@p232)) % 0.39/0.58 (step @p233 :rule process_scope :premises (@p261) :args (@t96)) % 0.39/0.58 (step @p235 :rule eq_resolve :premises (@p233 @p230)) % 0.39/0.58 (step @p236 :rule implies_elim :premises (@p235)) % 0.39/0.58 (step @p237 :rule chain_m_resolution :premises (@p236 @p217) :args (@t93 (@list false) (@list @t58))) % 0.39/0.58 (step @p238 :rule not_implies_elim2 :premises (@p215)) % 0.39/0.58 (step @p239 :rule cnf_or_pos :args (@t93)) % 0.39/0.58 (step @p240 :rule reordering :premises (@p239) :args ((or @t90 @t92 (not @t93)))) % 0.39/0.58 (step @p241 :rule chain_m_resolution :premises (@p240 @p238 @p237) :args (@t92 @t97 (@list @t90 @t93))) % 0.39/0.58 (step @p242 :rule aci_norm :args ((= (or false @t91) @t91))) % 0.39/0.58 (step @p243 :rule refl :args (@t91)) % 0.39/0.58 (step @p244 :rule quant-unused-vars :args ((= (forall @t23 true) true))) % 0.39/0.58 (step @p245 :rule bool-or-taut2 :args (false @t98 false false)) % 0.39/0.58 (step @p246 :rule cong :premises (@p245) :args (@t99)) % 0.39/0.58 (step @p247 :rule trans :premises (@p246 @p244)) % 0.39/0.58 (step @p248 :rule cong :premises (@p247) :args (@t100)) % 0.39/0.58 (step @p249 :rule trans :premises (@p248 @p143)) % 0.39/0.58 (step @p250 :rule nary_cong :premises (@p249 @p243) :args (@t101)) % 0.39/0.58 (step @p251 :rule trans :premises (@p250 @p242)) % 0.39/0.58 (step @p252 :rule cong :premises (@p20 @p251) :args ((=> @t53 @t101))) % 0.39/0.58 (assume-push @p262 @t53) % 0.39/0.58 (step @p254 :rule instantiate :premises (@p216) :args ((@list tptp.emptyset tptp.emptyset))) % 0.39/0.58 (step-pop @p263 :rule scope :premises (@p254)) % 0.39/0.58 (step @p255 :rule process_scope :premises (@p263) :args (@t101)) % 0.39/0.58 (step @p257 :rule eq_resolve :premises (@p255 @p252)) % 0.39/0.58 (step @p258 :rule implies_elim :premises (@p257)) % 0.39/0.58 (step @p259 false :rule chain_m_resolution :premises (@p258 @p241 @p216) :args (false @t97 (@list @t91 @t53))) % 0.39/0.58 ) % 0.39/0.58 % SZS output end Proof % 0.39/0.58 % cvc5 exiting %------------------------------------------------------------------------------