%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU651^2 : 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 : n008.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 08:52:35 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU651^2 : 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 % 0.14/0.34 % Computer : n008.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Jun 2 17:44:48 EDT 2026 % 0.14/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 0.37/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (declare-sort $$unsorted 0) % 0.37/0.57 (declare-const tptp.setukpairinjR12 Bool) % 0.37/0.57 (declare-const tptp.secondinupair Bool) % 0.37/0.57 (declare-const tptp.uniqinunit Bool) % 0.37/0.57 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.emptyset $$unsorted) % 0.37/0.57 (define @t1 () (@var "Xy" $$unsorted)) % 0.37/0.57 (define @t2 () (@var "Xx" $$unsorted)) % 0.37/0.57 (define @t3 () (= @t2 @t1)) % 0.37/0.57 (define @t4 () (_ (_ tptp.setadjoin @t1) tptp.emptyset)) % 0.37/0.57 (define @t5 () (_ tptp.in @t2)) % 0.37/0.57 (define @t6 () (_ @t5 @t4)) % 0.37/0.57 (define @t7 () (@list @t2 @t1)) % 0.37/0.57 (define @t8 () (forall @t7 (=> @t6 @t3))) % 0.37/0.57 (define @t9 () (= tptp.uniqinunit @t8)) % 0.37/0.57 (define @t10 () (_ tptp.setadjoin @t2)) % 0.37/0.57 (define @t11 () (_ @t10 @t4)) % 0.37/0.57 (define @t12 () (_ tptp.in @t1)) % 0.37/0.57 (define @t13 () (_ @t12 @t11)) % 0.37/0.57 (define @t14 () (forall @t7 @t13)) % 0.37/0.57 (define @t15 () (= tptp.secondinupair @t14)) % 0.37/0.57 (define @t16 () (_ @t10 tptp.emptyset)) % 0.37/0.57 (define @t17 () (_ tptp.setadjoin @t16)) % 0.37/0.57 (define @t18 () (_ @t17 tptp.emptyset)) % 0.37/0.57 (define @t19 () (_ (_ tptp.setadjoin @t11) tptp.emptyset)) % 0.37/0.57 (define @t20 () (_ @t17 @t19)) % 0.37/0.57 (define @t21 () (= @t20 @t18)) % 0.37/0.57 (define @t22 () (forall @t7 (=> @t3 @t21))) % 0.37/0.57 (define @t23 () (= tptp.setukpairinjR12 @t22)) % 0.37/0.57 (define @t24 () (@var "Xu" $$unsorted)) % 0.37/0.57 (define @t25 () (= @t1 @t24)) % 0.37/0.57 (define @t26 () (@var "Xz" $$unsorted)) % 0.37/0.57 (define @t27 () (= @t26 @t24)) % 0.37/0.57 (define @t28 () (=> @t27 @t25)) % 0.37/0.57 (define @t29 () (_ (_ tptp.setadjoin @t24) tptp.emptyset)) % 0.37/0.57 (define @t30 () (_ tptp.setadjoin @t26)) % 0.37/0.57 (define @t31 () (_ @t30 @t29)) % 0.37/0.57 (define @t32 () (_ (_ tptp.setadjoin @t31) tptp.emptyset)) % 0.37/0.57 (define @t33 () (_ @t30 tptp.emptyset)) % 0.37/0.57 (define @t34 () (_ (_ tptp.setadjoin @t33) @t32)) % 0.37/0.57 (define @t35 () (= @t20 @t34)) % 0.37/0.57 (define @t36 () (@list @t2 @t1 @t26 @t24)) % 0.37/0.57 (define @t37 () (forall @t36 (=> @t35 @t28))) % 0.37/0.57 (define @t38 () (=> tptp.setukpairinjR12 @t37)) % 0.37/0.57 (define @t39 () (=> tptp.secondinupair @t38)) % 0.37/0.57 (define @t40 () (=> tptp.uniqinunit @t39)) % 0.37/0.57 (define @t41 () (not @t40)) % 0.37/0.57 (define @t42 () (tptp.setadjoin @t24 tptp.emptyset)) % 0.37/0.57 (define @t43 () (tptp.setadjoin @t1 tptp.emptyset)) % 0.37/0.57 (define @t44 () (tptp.setadjoin @t2 @t43)) % 0.37/0.57 (define @t45 () (tptp.setadjoin @t44 tptp.emptyset)) % 0.37/0.57 (define @t46 () (tptp.setadjoin @t2 tptp.emptyset)) % 0.37/0.57 (define @t47 () (tptp.setadjoin @t46 @t45)) % 0.37/0.57 (define @t48 () (not (= @t47 (tptp.setadjoin @t42 (tptp.setadjoin (tptp.setadjoin @t24 @t42) tptp.emptyset))))) % 0.37/0.57 (define @t49 () (or @t48 @t25)) % 0.37/0.57 (define @t50 () (@list @t2 @t1 @t24)) % 0.37/0.57 (define @t51 () (forall @t50 @t49)) % 0.37/0.57 (define @t52 () (= (tptp.setadjoin @t43 (tptp.setadjoin (tptp.setadjoin @t1 @t43) tptp.emptyset)) (tptp.setadjoin @t43 tptp.emptyset))) % 0.37/0.57 (define @t53 () (not (= @t1 @t1))) % 0.37/0.57 (define @t54 () (or @t53 @t52)) % 0.37/0.57 (define @t55 () (@list @t1)) % 0.37/0.57 (define @t56 () (tptp.setadjoin @t46 tptp.emptyset)) % 0.37/0.57 (define @t57 () (= @t47 @t56)) % 0.37/0.57 (define @t58 () (not @t3)) % 0.37/0.57 (define @t59 () (or @t58 @t58 @t57)) % 0.37/0.57 (define @t60 () (@list @t2)) % 0.37/0.57 (define @t61 () (or @t58 @t57)) % 0.37/0.57 (define @t62 () (forall @t60 @t61)) % 0.37/0.57 (define @t63 () (forall @t55 @t62)) % 0.37/0.57 (define @t64 () (forall (@list @t1 @t2) @t61)) % 0.37/0.57 (define @t65 () (_ tptp.setadjoin @t46)) % 0.37/0.57 (define @t66 () (or @t58 @t21)) % 0.37/0.57 (define @t67 () (=> tptp.setukpairinjR12 @t51)) % 0.37/0.57 (define @t68 () (tptp.in @t1 @t44)) % 0.37/0.57 (define @t69 () (=> tptp.secondinupair @t67)) % 0.37/0.57 (define @t70 () (tptp.in @t2 @t43)) % 0.37/0.57 (define @t71 () (not @t6)) % 0.37/0.57 (define @t72 () (or @t71 @t3)) % 0.37/0.57 (define @t73 () (=> tptp.uniqinunit @t69)) % 0.37/0.57 (define @t74 () (not (= @t24 @t24))) % 0.37/0.57 (define @t75 () (or @t48 @t74 @t25)) % 0.37/0.57 (define @t76 () (not @t27)) % 0.37/0.57 (define @t77 () (tptp.setadjoin @t26 @t42)) % 0.37/0.57 (define @t78 () (tptp.setadjoin @t77 tptp.emptyset)) % 0.37/0.57 (define @t79 () (tptp.setadjoin @t26 tptp.emptyset)) % 0.37/0.57 (define @t80 () (tptp.setadjoin @t79 @t78)) % 0.37/0.57 (define @t81 () (not (= @t47 @t80))) % 0.37/0.57 (define @t82 () (or @t76 @t81 @t76 @t25)) % 0.37/0.57 (define @t83 () (@list @t26)) % 0.37/0.57 (define @t84 () (or @t81 @t76 @t25)) % 0.37/0.57 (define @t85 () (forall @t83 @t84)) % 0.37/0.57 (define @t86 () (forall @t50 @t85)) % 0.37/0.57 (define @t87 () (forall (@list @t2 @t1 @t24 @t26) @t84)) % 0.37/0.57 (define @t88 () (not @t35)) % 0.37/0.57 (define @t89 () (or @t88 @t76 @t25)) % 0.37/0.57 (define @t90 () (@quantifiers_skolemize @t51 1)) % 0.37/0.57 (define @t91 () (@quantifiers_skolemize @t51 0)) % 0.37/0.57 (define @t92 () (@quantifiers_skolemize @t51 2)) % 0.37/0.57 (define @t93 () (tptp.setadjoin @t92 tptp.emptyset)) % 0.37/0.57 (define @t94 () (tptp.setadjoin @t91 (tptp.setadjoin @t90 tptp.emptyset))) % 0.37/0.57 (define @t95 () (tptp.setadjoin @t91 tptp.emptyset)) % 0.37/0.57 (define @t96 () (= (tptp.setadjoin @t95 (tptp.setadjoin @t94 tptp.emptyset)) (tptp.setadjoin @t93 (tptp.setadjoin (tptp.setadjoin @t92 @t93) tptp.emptyset)))) % 0.37/0.57 (define @t97 () (= @t90 @t92)) % 0.37/0.57 (define @t98 () (not @t96)) % 0.37/0.57 (define @t99 () (or @t98 @t97)) % 0.37/0.57 (define @t100 () (@list true)) % 0.37/0.57 (define @t101 () (@list @t99)) % 0.37/0.57 (define @t102 () (tptp.in @t94 (tptp.setadjoin @t93 tptp.emptyset))) % 0.37/0.57 (define @t103 () (= @t94 @t93)) % 0.37/0.57 (define @t104 () (not @t102)) % 0.37/0.57 (define @t105 () (or @t104 @t103)) % 0.37/0.57 (define @t106 () (tptp.in @t90 @t93)) % 0.37/0.57 (define @t107 () (not @t106)) % 0.37/0.57 (define @t108 () (or @t107 @t97)) % 0.37/0.57 (define @t109 () (not @t108)) % 0.37/0.57 (define @t110 () (@list true false)) % 0.37/0.57 (define @t111 () (forall @t7 (or (not @t70) @t3))) % 0.37/0.57 (assume @p1 @t9) % 0.37/0.57 (assume @p2 @t15) % 0.37/0.57 (assume @p3 @t23) % 0.37/0.57 (assume @p4 @t41) % 0.37/0.57 (assume @p5 true) % 0.37/0.57 (step @p6 :rule refl :args (@t51)) % 0.37/0.57 (step @p7 :rule aci_norm :args ((= (or false @t52) @t52))) % 0.37/0.57 (step @p8 :rule refl :args (@t52)) % 0.37/0.57 (step @p9 :rule evaluate :args ((not true))) % 0.37/0.57 (step @p10 :rule eq-refl :args (@t1)) % 0.37/0.57 (step @p11 :rule cong :premises (@p10) :args (@t53)) % 0.37/0.57 (step @p12 :rule trans :premises (@p11 @p9)) % 0.37/0.57 (step @p13 :rule nary_cong :premises (@p12 @p8) :args (@t54)) % 0.37/0.57 (step @p14 :rule trans :premises (@p13 @p7)) % 0.37/0.57 (step @p15 :rule cong :premises (@p14) :args ((forall @t55 @t54))) % 0.37/0.57 (step @p16 :rule quant-var-elim-eq :args ((= (forall @t60 @t59) @t54))) % 0.37/0.57 (step @p17 :rule aci_norm :args ((= @t61 @t59))) % 0.37/0.57 (step @p18 :rule cong :premises (@p17) :args (@t62)) % 0.37/0.57 (step @p19 :rule trans :premises (@p18 @p16)) % 0.37/0.57 (step @p20 :rule cong :premises (@p19) :args (@t63)) % 0.37/0.57 (step @p21 :rule quant-merge-prenex :args ((= @t63 @t64))) % 0.37/0.57 (step @p22 :rule symm :premises (@p21)) % 0.37/0.57 (step @p23 :rule quant_var_reordering :args ((= (forall @t7 @t61) @t64))) % 0.37/0.57 (step @p24 :rule trans :premises (@p23 @p22 @p20)) % 0.37/0.57 (step @p25 :rule trans :premises (@p24 @p15)) % 0.37/0.57 (step @p26 :rule refl :args ((tptp.setadjoin @t16 tptp.emptyset))) % 0.37/0.57 (step @p27 :rule refl :args (tptp.emptyset)) % 0.37/0.57 (step @p28 :rule refl :args (@t46)) % 0.37/0.57 (step @p29 :rule cong :premises (@p28 @p27) :args (@t56)) % 0.37/0.57 (step @p30 :rule trans :premises (@p29 @p26)) % 0.37/0.57 (step @p31 :rule refl :args (tptp.setadjoin)) % 0.37/0.57 (step @p32 :rule ho_cong :premises (@p31 @p28)) % 0.37/0.57 (step @p33 :rule ho_cong :premises (@p32 @p27)) % 0.37/0.57 (step @p34 :rule cong :premises (@p33 @p30) :args ((= (_ @t65 tptp.emptyset) @t56))) % 0.37/0.57 (step @p35 :rule symm :premises (@p34)) % 0.37/0.57 (step @p36 :rule refl :args (@t18)) % 0.37/0.57 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 0.37/0.57 (step @p38 :rule refl :args (@t16)) % 0.37/0.57 (step @p39 :rule cong :premises (@p38 @p28) :args ((= @t16 @t46))) % 0.37/0.57 (step @p40 :rule symm :premises (@p39)) % 0.37/0.57 (step @p41 :rule eq_resolve :premises (@p38 @p40)) % 0.37/0.57 (step @p42 :rule ho_cong :premises (@p31 @p41)) % 0.37/0.57 (step @p43 :rule ho_cong :premises (@p42 @p27)) % 0.37/0.57 (step @p44 :rule trans :premises (@p43 @p37)) % 0.37/0.57 (step @p45 :rule refl :args ((tptp.setadjoin @t16 @t19))) % 0.37/0.57 (step @p46 :rule refl :args ((tptp.setadjoin @t11 tptp.emptyset))) % 0.37/0.57 (step @p47 :rule refl :args ((tptp.setadjoin @t2 @t4))) % 0.37/0.57 (step @p48 :rule refl :args (@t43)) % 0.37/0.57 (step @p49 :rule refl :args (@t2)) % 0.37/0.57 (step @p50 :rule cong :premises (@p49 @p48) :args (@t44)) % 0.37/0.57 (step @p51 :rule trans :premises (@p50 @p47)) % 0.37/0.57 (step @p52 :rule cong :premises (@p51 @p27) :args (@t45)) % 0.37/0.57 (step @p53 :rule trans :premises (@p52 @p46)) % 0.37/0.57 (step @p54 :rule cong :premises (@p28 @p53) :args (@t47)) % 0.37/0.57 (step @p55 :rule trans :premises (@p54 @p45)) % 0.37/0.57 (step @p56 :rule ho_cong :premises (@p32 @p53)) % 0.37/0.57 (step @p57 :rule cong :premises (@p56 @p55) :args ((= (_ @t65 @t45) @t47))) % 0.37/0.57 (step @p58 :rule symm :premises (@p57)) % 0.37/0.57 (step @p59 :rule refl :args (@t20)) % 0.37/0.57 (step @p60 :rule eq_resolve :premises (@p59 @p58)) % 0.37/0.57 (step @p61 :rule ho_cong :premises (@p31 @p51)) % 0.37/0.57 (step @p62 :rule ho_cong :premises (@p61 @p27)) % 0.37/0.57 (step @p63 :rule cong :premises (@p62 @p53) :args ((= (_ (_ tptp.setadjoin @t44) tptp.emptyset) @t45))) % 0.37/0.57 (step @p64 :rule symm :premises (@p63)) % 0.37/0.57 (step @p65 :rule refl :args (@t19)) % 0.37/0.57 (step @p66 :rule eq_resolve :premises (@p65 @p64)) % 0.37/0.57 (step @p67 :rule refl :args (@t10)) % 0.37/0.57 (step @p68 :rule ho_cong :premises (@p67 @p48)) % 0.37/0.57 (step @p69 :rule cong :premises (@p68 @p51) :args ((= (_ @t10 @t43) @t44))) % 0.37/0.57 (step @p70 :rule symm :premises (@p69)) % 0.37/0.57 (step @p71 :rule refl :args (@t11)) % 0.37/0.57 (step @p72 :rule eq_resolve :premises (@p71 @p70)) % 0.37/0.57 (step @p73 :rule refl :args (@t4)) % 0.37/0.57 (step @p74 :rule cong :premises (@p73 @p48) :args ((= @t4 @t43))) % 0.37/0.57 (step @p75 :rule symm :premises (@p74)) % 0.37/0.57 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 0.37/0.57 (step @p77 :rule ho_cong :premises (@p67 @p76)) % 0.37/0.57 (step @p78 :rule trans :premises (@p77 @p72)) % 0.37/0.57 (step @p79 :rule ho_cong :premises (@p31 @p78)) % 0.37/0.57 (step @p80 :rule ho_cong :premises (@p79 @p27)) % 0.37/0.57 (step @p81 :rule trans :premises (@p80 @p66)) % 0.37/0.57 (step @p82 :rule ho_cong :premises (@p42 @p81)) % 0.37/0.57 (step @p83 :rule trans :premises (@p82 @p60)) % 0.37/0.57 (step @p84 :rule cong :premises (@p83 @p44) :args (@t21)) % 0.37/0.57 (step @p85 :rule refl :args (@t58)) % 0.37/0.57 (step @p86 :rule nary_cong :premises (@p85 @p84) :args (@t66)) % 0.37/0.57 (step @p87 :rule cong :premises (@p86) :args ((forall @t7 @t66))) % 0.37/0.57 (step @p88 :rule trans :premises (@p87 @p25)) % 0.37/0.57 (step @p89 :rule bool-impl-elim :args (@t3 @t21)) % 0.37/0.57 (step @p90 :rule cong :premises (@p89) :args (@t22)) % 0.37/0.57 (step @p91 :rule trans :premises (@p90 @p88)) % 0.37/0.57 (step @p92 :rule refl :args (tptp.setukpairinjR12)) % 0.37/0.57 (step @p93 :rule cong :premises (@p92 @p91) :args (@t23)) % 0.37/0.57 (step @p94 :rule eq_resolve :premises (@p3 @p93)) % 0.37/0.57 (step @p95 :rule cong :premises (@p94 @p6) :args (@t67)) % 0.37/0.57 (step @p96 :rule refl :args ((tptp.in @t1 @t11))) % 0.37/0.57 (step @p97 :rule refl :args (@t1)) % 0.37/0.57 (step @p98 :rule cong :premises (@p97 @p51) :args (@t68)) % 0.37/0.57 (step @p99 :rule trans :premises (@p98 @p96)) % 0.37/0.57 (step @p100 :rule refl :args (@t12)) % 0.37/0.57 (step @p101 :rule ho_cong :premises (@p100 @p51)) % 0.37/0.57 (step @p102 :rule cong :premises (@p101 @p99) :args ((= (_ @t12 @t44) @t68))) % 0.37/0.57 (step @p103 :rule symm :premises (@p102)) % 0.37/0.57 (step @p104 :rule refl :args (@t13)) % 0.37/0.57 (step @p105 :rule eq_resolve :premises (@p104 @p103)) % 0.37/0.57 (step @p106 :rule ho_cong :premises (@p100 @p78)) % 0.37/0.57 (step @p107 :rule trans :premises (@p106 @p105)) % 0.37/0.57 (step @p108 :rule cong :premises (@p107) :args (@t14)) % 0.37/0.57 (step @p109 :rule refl :args (tptp.secondinupair)) % 0.37/0.57 (step @p110 :rule cong :premises (@p109 @p108) :args (@t15)) % 0.37/0.57 (step @p111 :rule eq_resolve :premises (@p2 @p110)) % 0.37/0.57 (step @p112 :rule cong :premises (@p111 @p95) :args (@t69)) % 0.37/0.57 (step @p113 :rule refl :args (@t3)) % 0.37/0.57 (step @p114 :rule refl :args ((tptp.in @t2 @t4))) % 0.37/0.57 (step @p115 :rule cong :premises (@p49 @p48) :args (@t70)) % 0.37/0.57 (step @p116 :rule trans :premises (@p115 @p114)) % 0.37/0.57 (step @p117 :rule refl :args (@t5)) % 0.37/0.57 (step @p118 :rule ho_cong :premises (@p117 @p48)) % 0.37/0.57 (step @p119 :rule cong :premises (@p118 @p116) :args ((= (_ @t5 @t43) @t70))) % 0.37/0.57 (step @p120 :rule symm :premises (@p119)) % 0.37/0.57 (step @p121 :rule refl :args (@t6)) % 0.37/0.57 (step @p122 :rule eq_resolve :premises (@p121 @p120)) % 0.37/0.57 (step @p123 :rule ho_cong :premises (@p117 @p76)) % 0.37/0.57 (step @p124 :rule trans :premises (@p123 @p122)) % 0.37/0.57 (step @p125 :rule cong :premises (@p124) :args (@t71)) % 0.37/0.57 (step @p126 :rule nary_cong :premises (@p125 @p113) :args (@t72)) % 0.37/0.57 (step @p127 :rule cong :premises (@p126) :args ((forall @t7 @t72))) % 0.37/0.57 (step @p128 :rule bool-impl-elim :args (@t6 @t3)) % 0.37/0.57 (step @p129 :rule cong :premises (@p128) :args (@t8)) % 0.37/0.57 (step @p130 :rule trans :premises (@p129 @p127)) % 0.37/0.57 (step @p131 :rule refl :args (tptp.uniqinunit)) % 0.37/0.57 (step @p132 :rule cong :premises (@p131 @p130) :args (@t9)) % 0.37/0.57 (step @p133 :rule eq_resolve :premises (@p1 @p132)) % 0.37/0.57 (step @p134 :rule cong :premises (@p133 @p112) :args (@t73)) % 0.37/0.57 (step @p135 :rule cong :premises (@p134) :args ((not @t73))) % 0.37/0.57 (step @p136 :rule aci_norm :args ((= (or @t48 false @t25) @t49))) % 0.37/0.57 (step @p137 :rule refl :args (@t25)) % 0.37/0.57 (step @p138 :rule eq-refl :args (@t24)) % 0.37/0.57 (step @p139 :rule cong :premises (@p138) :args (@t74)) % 0.37/0.57 (step @p140 :rule trans :premises (@p139 @p9)) % 0.37/0.57 (step @p141 :rule refl :args (@t48)) % 0.37/0.57 (step @p142 :rule nary_cong :premises (@p141 @p140 @p137) :args (@t75)) % 0.37/0.57 (step @p143 :rule trans :premises (@p142 @p136)) % 0.37/0.57 (step @p144 :rule cong :premises (@p143) :args ((forall @t50 @t75))) % 0.37/0.57 (step @p145 :rule quant-var-elim-eq :args ((= (forall @t83 @t82) @t75))) % 0.37/0.57 (step @p146 :rule aci_norm :args ((= @t84 @t82))) % 0.37/0.57 (step @p147 :rule cong :premises (@p146) :args (@t85)) % 0.37/0.57 (step @p148 :rule trans :premises (@p147 @p145)) % 0.37/0.57 (step @p149 :rule cong :premises (@p148) :args (@t86)) % 0.37/0.57 (step @p150 :rule quant-merge-prenex :args ((= @t86 @t87))) % 0.37/0.57 (step @p151 :rule symm :premises (@p150)) % 0.37/0.57 (step @p152 :rule quant_var_reordering :args ((= (forall @t36 @t84) @t87))) % 0.37/0.57 (step @p153 :rule trans :premises (@p152 @p151 @p149)) % 0.37/0.57 (step @p154 :rule trans :premises (@p153 @p144)) % 0.37/0.57 (step @p155 :rule refl :args (@t25)) % 0.37/0.57 (step @p156 :rule refl :args (@t76)) % 0.37/0.57 (step @p157 :rule refl :args ((tptp.setadjoin @t33 @t32))) % 0.37/0.57 (step @p158 :rule refl :args ((tptp.setadjoin @t31 tptp.emptyset))) % 0.37/0.57 (step @p159 :rule refl :args ((tptp.setadjoin @t26 @t29))) % 0.37/0.57 (step @p160 :rule refl :args (@t42)) % 0.37/0.57 (step @p161 :rule refl :args (@t26)) % 0.37/0.57 (step @p162 :rule cong :premises (@p161 @p160) :args (@t77)) % 0.37/0.57 (step @p163 :rule trans :premises (@p162 @p159)) % 0.37/0.57 (step @p164 :rule cong :premises (@p163 @p27) :args (@t78)) % 0.37/0.57 (step @p165 :rule trans :premises (@p164 @p158)) % 0.37/0.57 (step @p166 :rule refl :args (@t79)) % 0.37/0.57 (step @p167 :rule cong :premises (@p166 @p165) :args (@t80)) % 0.37/0.57 (step @p168 :rule trans :premises (@p167 @p157)) % 0.37/0.57 (step @p169 :rule ho_cong :premises (@p31 @p166)) % 0.37/0.57 (step @p170 :rule ho_cong :premises (@p169 @p165)) % 0.37/0.57 (step @p171 :rule cong :premises (@p170 @p168) :args ((= (_ (_ tptp.setadjoin @t79) @t78) @t80))) % 0.37/0.57 (step @p172 :rule symm :premises (@p171)) % 0.37/0.57 (step @p173 :rule refl :args (@t34)) % 0.37/0.57 (step @p174 :rule eq_resolve :premises (@p173 @p172)) % 0.37/0.57 (step @p175 :rule ho_cong :premises (@p31 @p163)) % 0.37/0.57 (step @p176 :rule ho_cong :premises (@p175 @p27)) % 0.37/0.57 (step @p177 :rule cong :premises (@p176 @p165) :args ((= (_ (_ tptp.setadjoin @t77) tptp.emptyset) @t78))) % 0.37/0.57 (step @p178 :rule symm :premises (@p177)) % 0.37/0.57 (step @p179 :rule refl :args (@t32)) % 0.37/0.57 (step @p180 :rule eq_resolve :premises (@p179 @p178)) % 0.37/0.57 (step @p181 :rule refl :args (@t30)) % 0.37/0.57 (step @p182 :rule ho_cong :premises (@p181 @p160)) % 0.37/0.57 (step @p183 :rule cong :premises (@p182 @p163) :args ((= (_ @t30 @t42) @t77))) % 0.37/0.57 (step @p184 :rule symm :premises (@p183)) % 0.37/0.57 (step @p185 :rule refl :args (@t31)) % 0.37/0.57 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.37/0.57 (step @p187 :rule refl :args (@t29)) % 0.37/0.57 (step @p188 :rule cong :premises (@p187 @p160) :args ((= @t29 @t42))) % 0.37/0.57 (step @p189 :rule symm :premises (@p188)) % 0.37/0.57 (step @p190 :rule eq_resolve :premises (@p187 @p189)) % 0.37/0.57 (step @p191 :rule ho_cong :premises (@p181 @p190)) % 0.37/0.57 (step @p192 :rule trans :premises (@p191 @p186)) % 0.37/0.57 (step @p193 :rule ho_cong :premises (@p31 @p192)) % 0.37/0.57 (step @p194 :rule ho_cong :premises (@p193 @p27)) % 0.37/0.57 (step @p195 :rule trans :premises (@p194 @p180)) % 0.37/0.57 (step @p196 :rule refl :args (@t33)) % 0.37/0.57 (step @p197 :rule cong :premises (@p196 @p166) :args ((= @t33 @t79))) % 0.37/0.57 (step @p198 :rule symm :premises (@p197)) % 0.37/0.57 (step @p199 :rule eq_resolve :premises (@p196 @p198)) % 0.37/0.57 (step @p200 :rule ho_cong :premises (@p31 @p199)) % 0.37/0.57 (step @p201 :rule ho_cong :premises (@p200 @p195)) % 0.37/0.57 (step @p202 :rule trans :premises (@p201 @p174)) % 0.37/0.57 (step @p203 :rule cong :premises (@p83 @p202) :args (@t35)) % 0.37/0.57 (step @p204 :rule cong :premises (@p203) :args (@t88)) % 0.37/0.57 (step @p205 :rule nary_cong :premises (@p204 @p156 @p155) :args (@t89)) % 0.37/0.57 (step @p206 :rule cong :premises (@p205) :args ((forall @t36 @t89))) % 0.37/0.57 (step @p207 :rule trans :premises (@p206 @p154)) % 0.37/0.57 (step @p208 :rule aci_norm :args ((= (or @t88 (or @t76 @t25)) @t89))) % 0.37/0.57 (step @p209 :rule bool-impl-elim :args (@t27 @t25)) % 0.37/0.57 (step @p210 :rule refl :args (@t88)) % 0.37/0.57 (step @p211 :rule nary_cong :premises (@p210 @p209) :args ((or @t88 @t28))) % 0.37/0.57 (step @p212 :rule trans :premises (@p211 @p208)) % 0.37/0.57 (step @p213 :rule bool-impl-elim :args (@t35 @t28)) % 0.37/0.57 (step @p214 :rule trans :premises (@p213 @p212)) % 0.37/0.57 (step @p215 :rule cong :premises (@p214) :args (@t37)) % 0.37/0.57 (step @p216 :rule trans :premises (@p215 @p207)) % 0.37/0.57 (step @p217 :rule cong :premises (@p92 @p216) :args (@t38)) % 0.37/0.57 (step @p218 :rule cong :premises (@p109 @p217) :args (@t39)) % 0.37/0.57 (step @p219 :rule cong :premises (@p131 @p218) :args (@t40)) % 0.37/0.57 (step @p220 :rule cong :premises (@p219) :args (@t41)) % 0.37/0.57 (step @p221 :rule trans :premises (@p220 @p135)) % 0.37/0.57 (step @p222 :rule eq_resolve :premises (@p4 @p221)) % 0.37/0.57 (step @p223 :rule not_implies_elim1 :premises (@p222)) % 0.37/0.57 (step @p224 :rule not_implies_elim2 :premises (@p222)) % 0.37/0.57 (step @p225 :rule not_implies_elim1 :premises (@p224)) % 0.37/0.57 (step @p226 :rule instantiate :premises (@p225) :args ((@list @t91 @t90))) % 0.37/0.57 (step @p227 :rule true_intro :premises (@p226)) % 0.37/0.57 (step @p228 :rule instantiate :premises (@p223) :args ((@list @t94 @t93))) % 0.37/0.57 (step @p229 :rule instantiate :premises (@p225) :args ((@list @t95 @t94))) % 0.37/0.57 (step @p230 :rule true_intro :premises (@p229)) % 0.37/0.57 (step @p231 :rule not_implies_elim2 :premises (@p224)) % 0.37/0.57 (step @p232 :rule not_implies_elim2 :premises (@p231)) % 0.37/0.57 (step @p233 :rule skolemize :premises (@p232)) % 0.37/0.57 (step @p234 :rule bool-double-not-elim :args (@t96)) % 0.37/0.57 (step @p235 :rule refl :args (@t99)) % 0.37/0.57 (step @p236 :rule nary_cong :premises (@p235 @p234) :args ((or @t99 (not @t98)))) % 0.37/0.57 (step @p237 :rule cnf_or_neg :args (@t99 0)) % 0.37/0.57 (step @p238 :rule eq_resolve :premises (@p237 @p236)) % 0.37/0.57 (step @p239 :rule reordering :premises (@p238) :args ((or @t96 @t99))) % 0.37/0.57 (step @p240 :rule chain_m_resolution :premises (@p239 @p233) :args (@t96 @t100 @t101)) % 0.37/0.57 (step @p241 :rule symm :premises (@p240)) % 0.37/0.57 (step @p242 :rule not_implies_elim1 :premises (@p231)) % 0.37/0.57 (step @p243 :rule instantiate :premises (@p242) :args ((@list @t92))) % 0.37/0.57 (step @p244 :rule symm :premises (@p243)) % 0.37/0.57 (step @p245 :rule trans :premises (@p244 @p241)) % 0.37/0.57 (step @p246 :rule refl :args (@t94)) % 0.37/0.57 (step @p247 :rule cong :premises (@p246 @p245) :args (@t102)) % 0.37/0.57 (step @p248 :rule trans :premises (@p247 @p230)) % 0.37/0.57 (step @p249 :rule true_elim :premises (@p248)) % 0.37/0.57 (step @p250 :rule cnf_or_pos :args (@t105)) % 0.37/0.57 (step @p251 :rule reordering :premises (@p250) :args ((or @t104 @t103 (not @t105)))) % 0.37/0.57 (step @p252 :rule chain_m_resolution :premises (@p251 @p249 @p228) :args (@t103 (@list false false) (@list @t102 @t105))) % 0.37/0.57 (step @p253 :rule symm :premises (@p252)) % 0.37/0.57 (step @p254 :rule refl :args (@t90)) % 0.37/0.57 (step @p255 :rule cong :premises (@p254 @p253) :args (@t106)) % 0.37/0.57 (step @p256 :rule trans :premises (@p255 @p227)) % 0.37/0.57 (step @p257 :rule true_elim :premises (@p256)) % 0.37/0.57 (step @p258 :rule cnf_or_neg :args (@t99 1)) % 0.37/0.57 (step @p259 :rule chain_m_resolution :premises (@p258 @p233) :args ((not @t97) @t100 @t101)) % 0.37/0.57 (step @p260 :rule cnf_or_pos :args (@t108)) % 0.37/0.57 (step @p261 :rule reordering :premises (@p260) :args ((or @t97 @t107 @t109))) % 0.37/0.57 (step @p262 :rule chain_m_resolution :premises (@p261 @p259 @p257) :args (@t109 @t110 (@list @t97 @t106))) % 0.37/0.57 (assume-push @p269 @t111) % 0.37/0.57 (step @p264 :rule instantiate :premises (@p223) :args ((@list @t90 @t92))) % 0.37/0.57 (step-pop @p270 :rule scope :premises (@p264)) % 0.37/0.57 (step @p265 :rule process_scope :premises (@p270) :args (@t108)) % 0.37/0.57 (step @p267 :rule implies_elim :premises (@p265)) % 0.37/0.57 (step @p268 false :rule chain_m_resolution :premises (@p267 @p262 @p223) :args (false @t110 (@list @t108 @t111))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------