%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU592^2 : 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 : n009.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 08:52:20 AM UTC 2026 % Result : Theorem 0.73s 1.00s % Output : Proof 0.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU592^2 : 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 % 0.18/0.34 % Computer : n009.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 17:42:29 EDT 2026 % 0.18/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.73/1.00 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.73/1.00 % SZS status Theorem % 0.73/1.00 % SZS output start Proof % 0.73/1.00 ( % 0.73/1.00 (declare-sort $$unsorted 0) % 0.73/1.00 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.73/1.00 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.73/1.00 (declare-const tptp.binintersectEL Bool) % 0.73/1.00 (declare-const tptp.subsetI2 Bool) % 0.73/1.00 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.73/1.00 (define tptp.binintersect () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_1) (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_2) (_ (_ tptp.in _let_2) _let_1)))))))) % 0.73/1.00 (define @t1 () (@var "B" $$unsorted)) % 0.73/1.00 (define @t2 () (@var "A" $$unsorted)) % 0.73/1.00 (define @t3 () (_ (_ tptp.subset @t2) @t1)) % 0.73/1.00 (define @t4 () (@var "Xx" $$unsorted)) % 0.73/1.00 (define @t5 () (_ tptp.in @t4)) % 0.73/1.00 (define @t6 () (_ @t5 @t1)) % 0.73/1.00 (define @t7 () (_ @t5 @t2)) % 0.73/1.00 (define @t8 () (@list @t4)) % 0.73/1.00 (define @t9 () (forall @t8 (=> @t7 @t6))) % 0.73/1.00 (define @t10 () (=> @t9 @t3)) % 0.73/1.00 (define @t11 () (@list @t2 @t1)) % 0.73/1.00 (define @t12 () (forall @t11 @t10)) % 0.73/1.00 (define @t13 () (= tptp.subsetI2 @t12)) % 0.73/1.00 (define @t14 () (_ (_ tptp.binintersect @t2) @t1)) % 0.73/1.00 (define @t15 () (=> (_ @t5 @t14) @t7)) % 0.73/1.00 (define @t16 () (@list @t2 @t1 @t4)) % 0.73/1.00 (define @t17 () (forall @t16 @t15)) % 0.73/1.00 (define @t18 () (= tptp.binintersectEL @t17)) % 0.73/1.00 (define @t19 () (forall @t11 (_ (_ tptp.subset @t14) @t2))) % 0.73/1.00 (define @t20 () (=> tptp.binintersectEL @t19)) % 0.73/1.00 (define @t21 () (=> tptp.subsetI2 @t20)) % 0.73/1.00 (define @t22 () (not @t21)) % 0.73/1.00 (define @t23 () (lambda @t8 @t6)) % 0.73/1.00 (define @t24 () (_ tptp.dsetconstr @t2)) % 0.73/1.00 (define @t25 () (_ @t24 @t23)) % 0.73/1.00 (define @t26 () (lambda @t11 @t25)) % 0.73/1.00 (define @t27 () (@var "BOUND_VARIABLE_7484" $$unsorted)) % 0.73/1.00 (define @t28 () (tptp.in @t4 @t1)) % 0.73/1.00 (define @t29 () (lambda @t8 @t28)) % 0.73/1.00 (define @t30 () (tptp.dsetconstr @t2 @t29)) % 0.73/1.00 (define @t31 () (tptp.subset @t30 @t2)) % 0.73/1.00 (define @t32 () (forall @t11 @t31)) % 0.73/1.00 (define @t33 () (@quantifiers_skolemize @t32 1)) % 0.73/1.00 (define @t34 () (tptp.in @t27 @t33)) % 0.73/1.00 (define @t35 () (@list @t27)) % 0.73/1.00 (define @t36 () (lambda @t35 @t34)) % 0.73/1.00 (define @t37 () (@purify @t36)) % 0.73/1.00 (define @t38 () (_ @t37 @t27)) % 0.73/1.00 (define @t39 () (_ @t36 @t27)) % 0.73/1.00 (define @t40 () (= @t38 @t39)) % 0.73/1.00 (define @t41 () (forall @t35 @t40)) % 0.73/1.00 (define @t42 () (@const 0 $$unsorted)) % 0.73/1.00 (define @t43 () (tptp.in @t42 @t33)) % 0.73/1.00 (define @t44 () (_ @t37 @t42)) % 0.73/1.00 (define @t45 () (forall @t35 (= @t34 @t38))) % 0.73/1.00 (define @t46 () (= @t43 @t44)) % 0.73/1.00 (define @t47 () (@list @t42)) % 0.73/1.00 (define @t48 () (= @t44 @t43)) % 0.73/1.00 (define @t49 () (@list false)) % 0.73/1.00 (define @t50 () (tptp.in @t4 @t2)) % 0.73/1.00 (define @t51 () (_ (_ tptp.in @t27) @t1)) % 0.73/1.00 (define @t52 () (lambda @t35 @t51)) % 0.73/1.00 (define @t53 () (_ @t24 @t52)) % 0.73/1.00 (define @t54 () (tptp.in @t27 @t1)) % 0.73/1.00 (define @t55 () (lambda @t35 @t54)) % 0.73/1.00 (define @t56 () (tptp.dsetconstr @t2 @t55)) % 0.73/1.00 (define @t57 () (tptp.in @t4 @t56)) % 0.73/1.00 (define @t58 () (_ @t5 @t53)) % 0.73/1.00 (define @t59 () (not @t58)) % 0.73/1.00 (define @t60 () (or @t59 @t7)) % 0.73/1.00 (define @t61 () (=> (_ @t5 @t25) @t7)) % 0.73/1.00 (define @t62 () (lambda (@list @t1) @t25)) % 0.73/1.00 (define @t63 () (_ @t26 @t2)) % 0.73/1.00 (define @t64 () (_ @t63 @t1)) % 0.73/1.00 (define @t65 () (=> (_ @t5 @t64) @t7)) % 0.73/1.00 (define @t66 () (forall @t16 @t65)) % 0.73/1.00 (define @t67 () (=> tptp.binintersectEL @t32)) % 0.73/1.00 (define @t68 () (tptp.subset @t2 @t1)) % 0.73/1.00 (define @t69 () (forall @t8 (or (not @t50) @t28))) % 0.73/1.00 (define @t70 () (not @t69)) % 0.73/1.00 (define @t71 () (or @t70 @t3)) % 0.73/1.00 (define @t72 () (not @t7)) % 0.73/1.00 (define @t73 () (or @t72 @t6)) % 0.73/1.00 (define @t74 () (=> tptp.subsetI2 @t67)) % 0.73/1.00 (define @t75 () (_ (_ tptp.subset @t25) @t2)) % 0.73/1.00 (define @t76 () (forall @t11 (_ (_ tptp.subset @t64) @t2))) % 0.73/1.00 (define @t77 () (=> tptp.binintersectEL @t76)) % 0.73/1.00 (define @t78 () (=> tptp.subsetI2 @t77)) % 0.73/1.00 (define @t79 () (@quantifiers_skolemize @t32 0)) % 0.73/1.00 (define @t80 () (tptp.in @t4 @t33)) % 0.73/1.00 (define @t81 () (lambda @t8 @t80)) % 0.73/1.00 (define @t82 () (@purify @t81)) % 0.73/1.00 (define @t83 () (tptp.dsetconstr @t79 @t82)) % 0.73/1.00 (define @t84 () (forall @t8 (or (not (tptp.in @t4 @t83)) (tptp.in @t4 @t79)))) % 0.73/1.00 (define @t85 () (@quantifiers_skolemize @t84 0)) % 0.73/1.00 (define @t86 () (tptp.in @t85 @t79)) % 0.73/1.00 (define @t87 () (tptp.dsetconstr @t79 @t36)) % 0.73/1.00 (define @t88 () (tptp.in @t85 @t87)) % 0.73/1.00 (define @t89 () (not @t88)) % 0.73/1.00 (define @t90 () (or @t89 @t86)) % 0.73/1.00 (define @t91 () (forall @t16 (or (not @t57) @t50))) % 0.73/1.00 (define @t92 () (tptp.in @t85 (tptp.dsetconstr @t79 @t37))) % 0.73/1.00 (define @t93 () (not @t92)) % 0.73/1.00 (define @t94 () (or @t93 @t86)) % 0.73/1.00 (define @t95 () (tptp.subset @t83 @t79)) % 0.73/1.00 (define @t96 () (not @t95)) % 0.73/1.00 (define @t97 () (not @t32)) % 0.73/1.00 (define @t98 () (tptp.dsetconstr @t79 @t81)) % 0.73/1.00 (define @t99 () (tptp.subset @t98 @t79)) % 0.73/1.00 (define @t100 () (not @t99)) % 0.73/1.00 (define @t101 () (@list true)) % 0.73/1.00 (define @t102 () (not @t84)) % 0.73/1.00 (define @t103 () (or @t102 @t95)) % 0.73/1.00 (define @t104 () (@list true false)) % 0.73/1.00 (define @t105 () (tptp.in @t85 @t83)) % 0.73/1.00 (define @t106 () (not @t105)) % 0.73/1.00 (define @t107 () (or @t106 @t86)) % 0.73/1.00 (define @t108 () (@list @t107)) % 0.73/1.00 (define @t109 () (= @t82 @t37)) % 0.73/1.00 (define @t110 () (not @t109)) % 0.73/1.00 (define @t111 () (and @t93 @t109 @t105)) % 0.73/1.00 (define @t112 () (_ @t82 @t42)) % 0.73/1.00 (define @t113 () (= @t112 @t44)) % 0.73/1.00 (define @t114 () (not @t113)) % 0.73/1.00 (define @t115 () (_ @t82 @t4)) % 0.73/1.00 (define @t116 () (_ @t81 @t4)) % 0.73/1.00 (define @t117 () (= @t115 @t116)) % 0.73/1.00 (define @t118 () (forall @t8 @t117)) % 0.73/1.00 (define @t119 () (forall @t8 (= @t80 @t115))) % 0.73/1.00 (define @t120 () (= @t43 @t112)) % 0.73/1.00 (define @t121 () (= @t112 @t43)) % 0.73/1.00 (define @t122 () (not @t121)) % 0.73/1.00 (define @t123 () (not @t112)) % 0.73/1.00 (define @t124 () (not @t48)) % 0.73/1.00 (define @t125 () (not @t43)) % 0.73/1.00 (assume @p1 @t13) % 0.73/1.00 (assume @p2 @t18) % 0.73/1.00 (assume @p3 @t22) % 0.73/1.00 (assume @p4 true) % 0.73/1.00 (step @p5 (= tptp.binintersect @t26) :rule refl :args (@t26)) % 0.73/1.00 (step @p6 :rule eq-symm :args (@t38 @t34)) % 0.73/1.00 (step @p7 :rule beta-reduce :args ((= @t39 @t34))) % 0.73/1.00 (step @p8 :rule refl :args (@t38)) % 0.73/1.00 (step @p9 :rule cong :premises (@p8 @p7) :args (@t40)) % 0.73/1.00 (step @p10 :rule trans :premises (@p9 @p6)) % 0.73/1.00 (step @p11 :rule cong :premises (@p10) :args (@t41)) % 0.73/1.00 (step @p12 :rule quant-unused-vars :args ((= (forall @t35 true) true))) % 0.73/1.00 (step @p13 :rule eq-refl :args (@t39)) % 0.73/1.00 (step @p14 :rule cong :premises (@p13) :args ((forall @t35 (= @t39 @t39)))) % 0.73/1.00 (step @p15 :rule trans :premises (@p14 @p12)) % 0.73/1.00 (step @p16 :rule refl :args (@t39)) % 0.73/1.00 (step @p17 :rule refl :args (@t27)) % 0.73/1.00 (step @p18 :rule skolem_intro :args (@t37)) % 0.73/1.00 (step @p19 :rule ho_cong :premises (@p18 @p17)) % 0.73/1.00 (step @p20 :rule cong :premises (@p19 @p16) :args (@t40)) % 0.73/1.00 (step @p21 :rule cong :premises (@p20) :args (@t41)) % 0.73/1.00 (step @p22 :rule trans :premises (@p21 @p15)) % 0.73/1.00 (step @p23 :rule true_elim :premises (@p22)) % 0.73/1.00 (step @p24 :rule eq_resolve :premises (@p23 @p11)) % 0.73/1.00 (step @p25 :rule eq-symm :args (@t43 @t44)) % 0.73/1.00 (step @p26 :rule refl :args (@t45)) % 0.73/1.00 (step @p27 :rule cong :premises (@p26 @p25) :args ((=> @t45 @t46))) % 0.73/1.00 (assume-push @p322 @t45) % 0.73/1.00 (step @p29 :rule instantiate :premises (@p24) :args (@t47)) % 0.73/1.00 (step-pop @p323 :rule scope :premises (@p29)) % 0.73/1.00 (step @p30 :rule process_scope :premises (@p323) :args (@t46)) % 0.73/1.00 (step @p32 :rule eq_resolve :premises (@p30 @p27)) % 0.73/1.00 (step @p33 :rule implies_elim :premises (@p32)) % 0.73/1.00 (step @p34 :rule chain_m_resolution :premises (@p33 @p24) :args (@t48 @t49 (@list @t45))) % 0.73/1.00 (step @p35 :rule refl :args (@t32)) % 0.73/1.00 (step @p36 :rule refl :args (@t50)) % 0.73/1.00 (step @p37 :rule refl :args (@t7)) % 0.73/1.00 (step @p38 :rule cong :premises (@p37 @p36) :args ((= @t7 @t50))) % 0.73/1.00 (step @p39 :rule symm :premises (@p38)) % 0.73/1.00 (step @p40 :rule eq_resolve :premises (@p37 @p39)) % 0.73/1.00 (step @p41 :rule refl :args ((tptp.in @t4 @t53))) % 0.73/1.00 (step @p42 :rule refl :args ((tptp.dsetconstr @t2 @t52))) % 0.73/1.00 (step @p43 :rule refl :args (@t54)) % 0.73/1.00 (step @p44 :rule cong :premises (@p43) :args (@t55)) % 0.73/1.00 (step @p45 :rule refl :args (@t2)) % 0.73/1.00 (step @p46 :rule cong :premises (@p45 @p44) :args (@t56)) % 0.73/1.00 (step @p47 :rule trans :premises (@p46 @p42)) % 0.73/1.00 (step @p48 :rule refl :args (@t4)) % 0.73/1.00 (step @p49 :rule cong :premises (@p48 @p47) :args (@t57)) % 0.73/1.00 (step @p50 :rule trans :premises (@p49 @p41)) % 0.73/1.00 (step @p51 :rule refl :args (@t5)) % 0.73/1.00 (step @p52 :rule ho_cong :premises (@p51 @p47)) % 0.73/1.00 (step @p53 :rule cong :premises (@p52 @p50) :args ((= (_ @t5 @t56) @t57))) % 0.73/1.00 (step @p54 :rule symm :premises (@p53)) % 0.73/1.00 (step @p55 :rule refl :args (@t58)) % 0.73/1.00 (step @p56 :rule eq_resolve :premises (@p55 @p54)) % 0.73/1.00 (step @p57 :rule refl :args (@t24)) % 0.73/1.00 (step @p58 :rule ho_cong :premises (@p57 @p44)) % 0.73/1.00 (step @p59 :rule cong :premises (@p58 @p47) :args ((= (_ @t24 @t55) @t56))) % 0.73/1.00 (step @p60 :rule symm :premises (@p59)) % 0.73/1.00 (step @p61 :rule refl :args (@t53)) % 0.73/1.00 (step @p62 :rule eq_resolve :premises (@p61 @p60)) % 0.73/1.00 (step @p63 :rule refl :args (@t51)) % 0.73/1.00 (step @p64 :rule cong :premises (@p63 @p43) :args ((= @t51 @t54))) % 0.73/1.00 (step @p65 :rule symm :premises (@p64)) % 0.73/1.00 (step @p66 :rule eq_resolve :premises (@p63 @p65)) % 0.73/1.00 (step @p67 :rule cong :premises (@p66) :args (@t52)) % 0.73/1.00 (step @p68 :rule ho_cong :premises (@p57 @p67)) % 0.73/1.00 (step @p69 :rule trans :premises (@p68 @p62)) % 0.73/1.00 (step @p70 :rule ho_cong :premises (@p51 @p69)) % 0.73/1.00 (step @p71 :rule trans :premises (@p70 @p56)) % 0.73/1.00 (step @p72 :rule cong :premises (@p71) :args (@t59)) % 0.73/1.00 (step @p73 :rule nary_cong :premises (@p72 @p40) :args (@t60)) % 0.73/1.00 (step @p74 :rule cong :premises (@p73) :args ((forall @t16 @t60))) % 0.73/1.00 (step @p75 :rule bool-impl-elim :args (@t58 @t7)) % 0.73/1.00 (step @p76 :rule cong :premises (@p75) :args ((forall @t16 (=> @t58 @t7)))) % 0.73/1.00 (step @p77 :rule trans :premises (@p76 @p74)) % 0.73/1.00 (step @p78 :rule alpha_equiv :args (@t23 (@list @t4) (@list @t27))) % 0.73/1.00 (step @p79 :rule ho_cong :premises (@p57 @p78)) % 0.73/1.00 (step @p80 :rule ho_cong :premises (@p51 @p79)) % 0.73/1.00 (step @p81 :rule cong :premises (@p80 @p37) :args (@t61)) % 0.73/1.00 (step @p82 :rule cong :premises (@p81) :args ((forall @t16 @t61))) % 0.73/1.00 (step @p83 :rule trans :premises (@p82 @p77)) % 0.73/1.00 (step @p84 :rule refl :args (@t7)) % 0.73/1.00 (step @p85 :rule beta-reduce :args ((= (_ @t62 @t1) @t25))) % 0.73/1.00 (step @p86 :rule refl :args (@t1)) % 0.73/1.00 (step @p87 :rule beta-reduce :args ((= @t63 @t62))) % 0.73/1.00 (step @p88 :rule ho_cong :premises (@p87 @p86)) % 0.73/1.00 (step @p89 :rule trans :premises (@p88 @p85)) % 0.73/1.00 (step @p90 :rule refl :args (@t5)) % 0.73/1.00 (step @p91 :rule ho_cong :premises (@p90 @p89)) % 0.73/1.00 (step @p92 :rule cong :premises (@p91 @p84) :args (@t65)) % 0.73/1.00 (step @p93 :rule cong :premises (@p92) :args (@t66)) % 0.73/1.00 (step @p94 :rule trans :premises (@p93 @p83)) % 0.73/1.00 (step @p95 :rule refl :args (tptp.binintersectEL)) % 0.73/1.00 (step @p96 :rule cong :premises (@p95 @p94) :args ((= tptp.binintersectEL @t66))) % 0.73/1.00 (step @p97 :rule refl :args (@t2)) % 0.73/1.00 (step @p98 :rule ho_cong :premises (@p5 @p97)) % 0.73/1.00 (step @p99 :rule ho_cong :premises (@p98 @p86)) % 0.73/1.00 (step @p100 :rule ho_cong :premises (@p90 @p99)) % 0.73/1.00 (step @p101 :rule cong :premises (@p100 @p84) :args (@t15)) % 0.73/1.00 (step @p102 :rule cong :premises (@p101) :args (@t17)) % 0.73/1.00 (step @p103 :rule cong :premises (@p95 @p102) :args (@t18)) % 0.73/1.00 (step @p104 :rule trans :premises (@p103 @p96)) % 0.73/1.00 (step @p105 :rule eq_resolve :premises (@p2 @p104)) % 0.73/1.00 (step @p106 :rule cong :premises (@p105 @p35) :args (@t67)) % 0.73/1.00 (step @p107 :rule refl :args (@t68)) % 0.73/1.00 (step @p108 :rule refl :args (@t3)) % 0.73/1.00 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t3 @t68))) % 0.73/1.00 (step @p110 :rule symm :premises (@p109)) % 0.73/1.00 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 0.73/1.00 (step @p112 :rule refl :args (@t70)) % 0.73/1.00 (step @p113 :rule nary_cong :premises (@p112 @p111) :args (@t71)) % 0.73/1.00 (step @p114 :rule cong :premises (@p113) :args ((forall @t11 @t71))) % 0.73/1.00 (step @p115 :rule bool-impl-elim :args (@t69 @t3)) % 0.73/1.00 (step @p116 :rule cong :premises (@p115) :args ((forall @t11 (=> @t69 @t3)))) % 0.73/1.00 (step @p117 :rule trans :premises (@p116 @p114)) % 0.73/1.00 (step @p118 :rule refl :args (@t3)) % 0.73/1.00 (step @p119 :rule refl :args (@t28)) % 0.73/1.00 (step @p120 :rule refl :args (@t6)) % 0.73/1.00 (step @p121 :rule cong :premises (@p120 @p119) :args ((= @t6 @t28))) % 0.73/1.00 (step @p122 :rule symm :premises (@p121)) % 0.73/1.00 (step @p123 :rule eq_resolve :premises (@p120 @p122)) % 0.73/1.00 (step @p124 :rule cong :premises (@p40) :args (@t72)) % 0.73/1.00 (step @p125 :rule nary_cong :premises (@p124 @p123) :args (@t73)) % 0.73/1.00 (step @p126 :rule cong :premises (@p125) :args ((forall @t8 @t73))) % 0.73/1.00 (step @p127 :rule bool-impl-elim :args (@t7 @t6)) % 0.73/1.00 (step @p128 :rule cong :premises (@p127) :args (@t9)) % 0.73/1.00 (step @p129 :rule trans :premises (@p128 @p126)) % 0.73/1.00 (step @p130 :rule cong :premises (@p129 @p118) :args (@t10)) % 0.73/1.00 (step @p131 :rule cong :premises (@p130) :args (@t12)) % 0.73/1.00 (step @p132 :rule trans :premises (@p131 @p117)) % 0.73/1.00 (step @p133 :rule refl :args (tptp.subsetI2)) % 0.73/1.00 (step @p134 :rule cong :premises (@p133 @p132) :args (@t13)) % 0.73/1.00 (step @p135 :rule eq_resolve :premises (@p1 @p134)) % 0.73/1.00 (step @p136 :rule cong :premises (@p135 @p106) :args (@t74)) % 0.73/1.00 (step @p137 :rule cong :premises (@p136) :args ((not @t74))) % 0.73/1.00 (step @p138 :rule refl :args ((tptp.subset @t25 @t2))) % 0.73/1.00 (step @p139 :rule refl :args ((tptp.dsetconstr @t2 @t23))) % 0.73/1.00 (step @p140 :rule cong :premises (@p119) :args (@t29)) % 0.73/1.00 (step @p141 :rule cong :premises (@p45 @p140) :args (@t30)) % 0.73/1.00 (step @p142 :rule trans :premises (@p141 @p139)) % 0.73/1.00 (step @p143 :rule cong :premises (@p142 @p45) :args (@t31)) % 0.73/1.00 (step @p144 :rule trans :premises (@p143 @p138)) % 0.73/1.00 (step @p145 :rule refl :args (tptp.subset)) % 0.73/1.00 (step @p146 :rule ho_cong :premises (@p145 @p142)) % 0.73/1.00 (step @p147 :rule ho_cong :premises (@p146 @p45)) % 0.73/1.00 (step @p148 :rule cong :premises (@p147 @p144) :args ((= (_ (_ tptp.subset @t30) @t2) @t31))) % 0.73/1.00 (step @p149 :rule symm :premises (@p148)) % 0.73/1.00 (step @p150 :rule refl :args (@t75)) % 0.73/1.00 (step @p151 :rule eq_resolve :premises (@p150 @p149)) % 0.73/1.00 (step @p152 :rule ho_cong :premises (@p57 @p140)) % 0.73/1.00 (step @p153 :rule cong :premises (@p152 @p142) :args ((= (_ @t24 @t29) @t30))) % 0.73/1.00 (step @p154 :rule symm :premises (@p153)) % 0.73/1.00 (step @p155 :rule refl :args (@t25)) % 0.73/1.00 (step @p156 :rule eq_resolve :premises (@p155 @p154)) % 0.73/1.00 (step @p157 :rule cong :premises (@p123) :args (@t23)) % 0.73/1.00 (step @p158 :rule ho_cong :premises (@p57 @p157)) % 0.73/1.00 (step @p159 :rule trans :premises (@p158 @p156)) % 0.73/1.00 (step @p160 :rule ho_cong :premises (@p145 @p159)) % 0.73/1.00 (step @p161 :rule ho_cong :premises (@p160 @p45)) % 0.73/1.00 (step @p162 :rule trans :premises (@p161 @p151)) % 0.73/1.00 (step @p163 :rule cong :premises (@p162) :args ((forall @t11 @t75))) % 0.73/1.00 (step @p164 :rule refl :args (tptp.subset)) % 0.73/1.00 (step @p165 :rule ho_cong :premises (@p164 @p89)) % 0.73/1.00 (step @p166 :rule ho_cong :premises (@p165 @p97)) % 0.73/1.00 (step @p167 :rule cong :premises (@p166) :args (@t76)) % 0.73/1.00 (step @p168 :rule trans :premises (@p167 @p163)) % 0.73/1.00 (step @p169 :rule cong :premises (@p95 @p168) :args (@t77)) % 0.73/1.00 (step @p170 :rule cong :premises (@p133 @p169) :args (@t78)) % 0.73/1.00 (step @p171 :rule cong :premises (@p170) :args ((not @t78))) % 0.73/1.00 (step @p172 :rule ho_cong :premises (@p164 @p99)) % 0.73/1.00 (step @p173 :rule ho_cong :premises (@p172 @p97)) % 0.73/1.00 (step @p174 :rule cong :premises (@p173) :args (@t19)) % 0.73/1.00 (step @p175 :rule cong :premises (@p95 @p174) :args (@t20)) % 0.73/1.00 (step @p176 :rule cong :premises (@p133 @p175) :args (@t21)) % 0.73/1.00 (step @p177 :rule cong :premises (@p176) :args (@t22)) % 0.73/1.00 (step @p178 :rule trans :premises (@p177 @p171)) % 0.73/1.00 (step @p179 :rule trans :premises (@p178 @p137)) % 0.73/1.00 (step @p180 :rule eq_resolve :premises (@p3 @p179)) % 0.73/1.00 (step @p181 :rule not_implies_elim2 :premises (@p180)) % 0.73/1.00 (step @p182 :rule not_implies_elim1 :premises (@p181)) % 0.73/1.00 (step @p183 :rule refl :args (@t86)) % 0.73/1.00 (step @p184 :rule eq-refl :args (@t36)) % 0.73/1.00 (step @p185 :rule refl :args (@t36)) % 0.73/1.00 (step @p186 :rule cong :premises (@p185 @p18) :args ((= @t36 @t37))) % 0.73/1.00 (step @p187 :rule trans :premises (@p186 @p184)) % 0.73/1.00 (step @p188 :rule true_elim :premises (@p187)) % 0.73/1.00 (step @p189 :rule refl :args (@t79)) % 0.73/1.00 (step @p190 :rule cong :premises (@p189 @p188) :args (@t87)) % 0.73/1.00 (step @p191 :rule refl :args (@t85)) % 0.73/1.00 (step @p192 :rule cong :premises (@p191 @p190) :args (@t88)) % 0.73/1.00 (step @p193 :rule cong :premises (@p192) :args (@t89)) % 0.73/1.00 (step @p194 :rule nary_cong :premises (@p193 @p183) :args (@t90)) % 0.73/1.00 (step @p195 :rule refl :args (@t91)) % 0.73/1.00 (step @p196 :rule cong :premises (@p195 @p194) :args ((=> @t91 @t90))) % 0.73/1.00 (assume-push @p324 @t91) % 0.73/1.00 (step @p198 :rule instantiate :premises (@p182) :args ((@list @t79 @t33 @t85))) % 0.73/1.00 (step-pop @p325 :rule scope :premises (@p198)) % 0.73/1.00 (step @p199 :rule process_scope :premises (@p325) :args (@t90)) % 0.73/1.00 (step @p201 :rule eq_resolve :premises (@p199 @p196)) % 0.73/1.00 (step @p202 :rule implies_elim :premises (@p201)) % 0.73/1.00 (step @p203 :rule chain_m_resolution :premises (@p202 @p182) :args (@t94 @t49 (@list @t91))) % 0.73/1.00 (step @p204 :rule not_implies_elim1 :premises (@p180)) % 0.73/1.00 (step @p205 :rule instantiate :premises (@p204) :args ((@list @t83 @t79))) % 0.73/1.00 (step @p206 :rule not_implies_elim2 :premises (@p181)) % 0.73/1.00 (step @p207 :rule refl :args (@t96)) % 0.73/1.00 (step @p208 :rule bool-double-not-elim :args (@t32)) % 0.73/1.00 (step @p209 :rule nary_cong :premises (@p208 @p207) :args ((or (not @t97) @t96))) % 0.73/1.00 (step @p210 :rule eq-refl :args (@t81)) % 0.73/1.00 (step @p211 :rule skolem_intro :args (@t82)) % 0.73/1.00 (step @p212 :rule refl :args (@t81)) % 0.73/1.00 (step @p213 :rule cong :premises (@p212 @p211) :args ((= @t81 @t82))) % 0.73/1.00 (step @p214 :rule trans :premises (@p213 @p210)) % 0.73/1.00 (step @p215 :rule true_elim :premises (@p214)) % 0.73/1.00 (step @p216 :rule cong :premises (@p189 @p215) :args (@t98)) % 0.73/1.00 (step @p217 :rule cong :premises (@p216 @p189) :args (@t99)) % 0.73/1.00 (step @p218 :rule cong :premises (@p217) :args (@t100)) % 0.73/1.00 (step @p219 :rule refl :args (@t97)) % 0.73/1.00 (step @p220 :rule cong :premises (@p219 @p218) :args ((=> @t97 @t100))) % 0.73/1.00 (assume-push @p326 @t97) % 0.73/1.00 (step @p222 :rule skolemize :premises (@p206)) % 0.73/1.00 (step-pop @p327 :rule scope :premises (@p222)) % 0.73/1.00 (step @p223 :rule process_scope :premises (@p327) :args (@t100)) % 0.73/1.00 (step @p225 :rule eq_resolve :premises (@p223 @p220)) % 0.73/1.00 (step @p226 :rule implies_elim :premises (@p225)) % 0.73/1.00 (step @p227 :rule eq_resolve :premises (@p226 @p209)) % 0.73/1.00 (step @p228 :rule chain_m_resolution :premises (@p227 @p206) :args (@t96 @t101 (@list @t32))) % 0.73/1.00 (step @p229 :rule cnf_or_pos :args (@t103)) % 0.73/1.00 (step @p230 :rule reordering :premises (@p229) :args ((or @t95 @t102 (not @t103)))) % 0.73/1.00 (step @p231 :rule chain_m_resolution :premises (@p230 @p228 @p205) :args (@t102 @t104 (@list @t95 @t103))) % 0.73/1.00 (step @p232 :rule skolemize :premises (@p231)) % 0.73/1.00 (step @p233 :rule cnf_or_neg :args (@t107 1)) % 0.73/1.00 (step @p234 :rule chain_m_resolution :premises (@p233 @p232) :args ((not @t86) @t101 @t108)) % 0.73/1.00 (step @p235 :rule cnf_or_pos :args (@t94)) % 0.73/1.00 (step @p236 :rule reordering :premises (@p235) :args ((or @t86 @t93 (not @t94)))) % 0.73/1.00 (step @p237 :rule chain_m_resolution :premises (@p236 @p234 @p203) :args (@t93 @t104 (@list @t86 @t94))) % 0.73/1.00 (step @p238 :rule bool-double-not-elim :args (@t105)) % 0.73/1.00 (step @p239 :rule refl :args (@t107)) % 0.73/1.00 (step @p240 :rule nary_cong :premises (@p239 @p238) :args ((or @t107 (not @t106)))) % 0.73/1.00 (step @p241 :rule cnf_or_neg :args (@t107 0)) % 0.73/1.00 (step @p242 :rule eq_resolve :premises (@p241 @p240)) % 0.73/1.00 (step @p243 :rule reordering :premises (@p242) :args ((or @t105 @t107))) % 0.73/1.00 (step @p244 :rule chain_m_resolution :premises (@p243 @p232) :args (@t105 @t101 @t108)) % 0.73/1.00 (step @p245 :rule refl :args (@t110)) % 0.73/1.00 (step @p246 :rule bool-double-not-elim :args (@t92)) % 0.73/1.00 (step @p247 :rule refl :args (@t106)) % 0.73/1.00 (step @p248 :rule nary_cong :premises (@p247 @p246 @p245) :args ((or @t106 (not @t93) @t110))) % 0.73/1.00 (assume-push @p328 @t93) % 0.73/1.00 (assume-push @p329 @t109) % 0.73/1.00 (assume-push @p330 @t105) % 0.73/1.00 (step @p252 :rule evaluate :args ((= true false))) % 0.73/1.00 (step @p253 :rule false_intro :premises (@p237)) % 0.73/1.00 (step @p254 :rule cong :premises (@p189 @p329) :args (@t83)) % 0.73/1.00 (step @p255 :rule cong :premises (@p191 @p254) :args (@t105)) % 0.73/1.00 (step @p256 :rule true_intro :premises (@p244)) % 0.73/1.00 (step @p257 :rule symm :premises (@p256)) % 0.73/1.00 (step @p258 :rule trans :premises (@p257 @p255 @p253)) % 0.73/1.00 (step @p259 false :rule eq_resolve :premises (@p258 @p252)) % 0.73/1.00 (step-pop @p331 :rule scope :premises (@p259)) % 0.73/1.00 (step-pop @p332 :rule scope :premises (@p331)) % 0.73/1.00 (step-pop @p333 :rule scope :premises (@p332)) % 0.73/1.00 (step @p260 :rule process_scope :premises (@p333) :args (false)) % 0.73/1.00 (assume-push @p334 @t105) % 0.73/1.00 (assume-push @p335 @t93) % 0.73/1.00 (assume-push @p336 @t109) % 0.73/1.00 (step @p267 :rule and_intro :premises (@p237 @p336 @p244)) % 0.73/1.00 (step-pop @p337 :rule scope :premises (@p267)) % 0.73/1.00 (step-pop @p338 :rule scope :premises (@p337)) % 0.73/1.00 (step-pop @p339 :rule scope :premises (@p338)) % 0.73/1.00 (step @p268 :rule process_scope :premises (@p339) :args (@t111)) % 0.73/1.00 (step @p272 :rule implies_elim :premises (@p268)) % 0.73/1.00 (step @p273 :rule resolution :premises (@p272 @p260) :args (true @t111)) % 0.73/1.00 (step @p274 :rule not_and :premises (@p273)) % 0.73/1.00 (step @p275 :rule eq_resolve :premises (@p274 @p248)) % 0.73/1.00 (step @p276 :rule chain_m_resolution :premises (@p275 @p244 @p237) :args (@t110 (@list false true) (@list @t105 @t92))) % 0.73/1.00 ; WARNING: add trust step for TRUST % 0.73/1.00 ; trust TRUST THEORY_LEMMA % 0.73/1.00 (step @p277 :rule trust :premises () :args ((or @t109 @t114))) % 0.73/1.00 (step @p278 :rule chain_m_resolution :premises (@p277 @p276) :args (@t114 @t101 (@list @t109))) % 0.73/1.00 (step @p279 :rule cnf_equiv_neg2 :args (@t113)) % 0.73/1.00 (step @p280 :rule eq-symm :args (@t115 @t80)) % 0.73/1.00 (step @p281 :rule beta-reduce :args ((= @t116 @t80))) % 0.73/1.00 (step @p282 :rule refl :args (@t115)) % 0.73/1.00 (step @p283 :rule cong :premises (@p282 @p281) :args (@t117)) % 0.73/1.00 (step @p284 :rule trans :premises (@p283 @p280)) % 0.73/1.00 (step @p285 :rule cong :premises (@p284) :args (@t118)) % 0.73/1.00 (step @p286 :rule quant-unused-vars :args ((= (forall @t8 true) true))) % 0.73/1.00 (step @p287 :rule eq-refl :args (@t116)) % 0.73/1.00 (step @p288 :rule cong :premises (@p287) :args ((forall @t8 (= @t116 @t116)))) % 0.73/1.00 (step @p289 :rule trans :premises (@p288 @p286)) % 0.73/1.00 (step @p290 :rule refl :args (@t116)) % 0.73/1.00 (step @p291 :rule refl :args (@t4)) % 0.73/1.00 (step @p292 :rule ho_cong :premises (@p211 @p291)) % 0.73/1.00 (step @p293 :rule cong :premises (@p292 @p290) :args (@t117)) % 0.73/1.00 (step @p294 :rule cong :premises (@p293) :args (@t118)) % 0.73/1.00 (step @p295 :rule trans :premises (@p294 @p289)) % 0.73/1.00 (step @p296 :rule true_elim :premises (@p295)) % 0.73/1.00 (step @p297 :rule eq_resolve :premises (@p296 @p285)) % 0.73/1.00 (step @p298 :rule eq-symm :args (@t43 @t112)) % 0.73/1.00 (step @p299 :rule refl :args (@t119)) % 0.73/1.00 (step @p300 :rule cong :premises (@p299 @p298) :args ((=> @t119 @t120))) % 0.73/1.00 (assume-push @p340 @t119) % 0.73/1.00 (step @p302 :rule instantiate :premises (@p297) :args (@t47)) % 0.73/1.00 (step-pop @p341 :rule scope :premises (@p302)) % 0.73/1.00 (step @p303 :rule process_scope :premises (@p341) :args (@t120)) % 0.73/1.00 (step @p305 :rule eq_resolve :premises (@p303 @p300)) % 0.73/1.00 (step @p306 :rule implies_elim :premises (@p305)) % 0.73/1.00 (step @p307 :rule chain_m_resolution :premises (@p306 @p297) :args (@t121 @t49 (@list @t119))) % 0.73/1.00 (step @p308 :rule cnf_equiv_pos1 :args (@t121)) % 0.73/1.00 (step @p309 :rule reordering :premises (@p308) :args ((or @t123 @t43 @t122))) % 0.73/1.00 (step @p310 :rule cnf_equiv_pos2 :args (@t48)) % 0.73/1.00 (step @p311 :rule reordering :premises (@p310) :args ((or @t44 @t125 @t124))) % 0.73/1.00 (step @p312 :rule chain_m_resolution :premises (@p311 @p34 @p309 @p307 @p279 @p278) :args (@t123 (@list false false false true true) (@list @t48 @t43 @t121 @t44 @t113))) % 0.73/1.00 (step @p313 :rule cnf_equiv_neg1 :args (@t113)) % 0.73/1.00 (step @p314 :rule reordering :premises (@p313) :args ((or @t112 @t44 @t113))) % 0.73/1.00 (step @p315 :rule chain_m_resolution :premises (@p314 @p312 @p278) :args (@t44 (@list true true) (@list @t112 @t113))) % 0.73/1.00 (step @p316 :rule cnf_equiv_pos2 :args (@t121)) % 0.73/1.00 (step @p317 :rule reordering :premises (@p316) :args ((or @t112 @t125 @t122))) % 0.73/1.00 (step @p318 :rule chain_m_resolution :premises (@p317 @p312 @p307) :args (@t125 @t104 (@list @t112 @t121))) % 0.73/1.00 (step @p319 :rule cnf_equiv_pos1 :args (@t48)) % 0.73/1.00 (step @p320 :rule reordering :premises (@p319) :args ((or (not @t44) @t43 @t124))) % 0.73/1.00 (step @p321 false :rule chain_m_resolution :premises (@p320 @p318 @p315 @p34) :args (false (@list true false false) (@list @t43 @t44 @t48))) % 0.73/1.00 ) % 0.73/1.00 % SZS output end Proof % 0.73/1.00 % cvc5 exiting %------------------------------------------------------------------------------