%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN023^1 : TPTP v9.2.1. Released v6.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n025.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 08:42:48 AM UTC 2026 % Result : Theorem 0.52s 0.79s % Output : Proof 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : NUN023^1 : TPTP v9.2.1. Released v6.4.0. % 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.33 % Computer : n025.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue Jun 2 12:37:31 EDT 2026 % 0.16/0.33 % CPUTime : % 0.27/0.49 %----Proving TH0 % 0.52/0.79 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.52/0.79 % SZS status Theorem % 0.52/0.79 % SZS output start Proof % 0.52/0.79 ( % 0.52/0.79 (declare-sort $$unsorted 0) % 0.52/0.79 (declare-const tptp.ite (-> Bool $$unsorted $$unsorted $$unsorted)) % 0.52/0.79 (declare-const tptp.s (-> $$unsorted $$unsorted)) % 0.52/0.79 (declare-const tptp.zero $$unsorted) % 0.52/0.79 (define @t1 () (_ tptp.s tptp.zero)) % 0.52/0.79 (define @t2 () (@var "H" (-> $$unsorted $$unsorted))) % 0.52/0.79 (define @t3 () (_ @t2 @t1)) % 0.52/0.79 (define @t4 () (_ @t2 tptp.zero)) % 0.52/0.79 (define @t5 () (and (= @t4 @t1) (= @t3 tptp.zero))) % 0.52/0.79 (define @t6 () (@list @t2)) % 0.52/0.79 (define @t7 () (exists @t6 @t5)) % 0.52/0.79 (define @t8 () (@var "V" $$unsorted)) % 0.52/0.79 (define @t9 () (@var "U" $$unsorted)) % 0.52/0.79 (define @t10 () (@var "X" Bool)) % 0.52/0.79 (define @t11 () (_ (_ (_ tptp.ite @t10) @t9) @t8)) % 0.52/0.79 (define @t12 () (not @t10)) % 0.52/0.79 (define @t13 () (=> @t12 (= @t11 @t8))) % 0.52/0.79 (define @t14 () (@list @t10 @t9 @t8)) % 0.52/0.79 (define @t15 () (forall @t14 @t13)) % 0.52/0.79 (define @t16 () (=> @t10 (= @t11 @t9))) % 0.52/0.79 (define @t17 () (forall @t14 @t16)) % 0.52/0.79 (define @t18 () (and @t17 @t15)) % 0.52/0.79 (define @t19 () (=> @t18 @t7)) % 0.52/0.79 (define @t20 () (not @t19)) % 0.52/0.79 (define @t21 () (tptp.s tptp.zero)) % 0.52/0.79 (define @t22 () (_ @t2 @t21)) % 0.52/0.79 (define @t23 () (= @t1 @t21)) % 0.52/0.79 (define @t24 () (= tptp.zero @t3)) % 0.52/0.79 (define @t25 () (not @t24)) % 0.52/0.79 (define @t26 () (_ @t2 tptp.zero)) % 0.52/0.79 (define @t27 () (= @t1 @t4)) % 0.52/0.79 (define @t28 () (not @t27)) % 0.52/0.79 (define @t29 () (or @t28 @t25)) % 0.52/0.79 (define @t30 () (and @t27 @t24)) % 0.52/0.79 (define @t31 () (forall @t6 (not @t30))) % 0.52/0.79 (define @t32 () (not @t31)) % 0.52/0.79 (define @t33 () (= @t8 (tptp.ite false @t9 @t8))) % 0.52/0.79 (define @t34 () (or false @t33)) % 0.52/0.79 (define @t35 () (@list @t9 @t8)) % 0.52/0.79 (define @t36 () (tptp.ite @t10 @t9 @t8)) % 0.52/0.79 (define @t37 () (= @t8 @t36)) % 0.52/0.79 (define @t38 () (@list @t10)) % 0.52/0.79 (define @t39 () (not @t12)) % 0.52/0.79 (define @t40 () (or @t10 @t10 @t37)) % 0.52/0.79 (define @t41 () (or @t10 @t37)) % 0.52/0.79 (define @t42 () (forall @t38 @t41)) % 0.52/0.79 (define @t43 () (forall @t35 @t42)) % 0.52/0.79 (define @t44 () (@list @t9 @t8 @t10)) % 0.52/0.79 (define @t45 () (forall @t44 @t41)) % 0.52/0.79 (define @t46 () (= @t8 @t11)) % 0.52/0.79 (define @t47 () (or @t10 @t46)) % 0.52/0.79 (define @t48 () (= @t9 (tptp.ite true @t9 @t8))) % 0.52/0.79 (define @t49 () (not true)) % 0.52/0.79 (define @t50 () (or @t49 @t48)) % 0.52/0.79 (define @t51 () (= @t9 @t36)) % 0.52/0.79 (define @t52 () (or @t12 @t12 @t51)) % 0.52/0.79 (define @t53 () (or @t12 @t51)) % 0.52/0.79 (define @t54 () (forall @t38 @t53)) % 0.52/0.79 (define @t55 () (forall @t35 @t54)) % 0.52/0.79 (define @t56 () (forall @t44 @t53)) % 0.52/0.79 (define @t57 () (= @t9 @t11)) % 0.52/0.79 (define @t58 () (or @t12 @t57)) % 0.52/0.79 (define @t59 () (_ tptp.s @t21)) % 0.52/0.79 (define @t60 () (ite @t23 tptp.zero @t59)) % 0.52/0.79 (define @t61 () (= tptp.zero @t21)) % 0.52/0.79 (define @t62 () (ite @t61 @t1 @t60)) % 0.52/0.79 (define @t63 () (@purify @t62)) % 0.52/0.79 (define @t64 () (= tptp.zero @t63)) % 0.52/0.79 (define @t65 () (not @t64)) % 0.52/0.79 (define @t66 () (= tptp.zero @t62)) % 0.52/0.79 (define @t67 () (not @t66)) % 0.52/0.79 (define @t68 () (not @t23)) % 0.52/0.79 (define @t69 () (or @t68 @t67)) % 0.52/0.79 (define @t70 () (forall @t6 (or (not (= @t21 @t26)) (not (= tptp.zero @t22))))) % 0.52/0.79 (define @t71 () (@var "BOUND_VARIABLE_28820" $$unsorted)) % 0.52/0.79 (define @t72 () (lambda (@list @t71) (ite (= tptp.zero @t71) @t1 (ite (= @t1 @t71) tptp.zero @t59)))) % 0.52/0.79 (define @t73 () (_ @t72 @t21)) % 0.52/0.79 (define @t74 () (= tptp.zero @t73)) % 0.52/0.79 (define @t75 () (not @t74)) % 0.52/0.79 (define @t76 () (ite (= @t1 tptp.zero) tptp.zero @t59)) % 0.52/0.79 (define @t77 () (ite (= tptp.zero tptp.zero) @t1 @t76)) % 0.52/0.79 (define @t78 () (_ @t72 tptp.zero)) % 0.52/0.79 (define @t79 () (= @t21 @t78)) % 0.52/0.79 (define @t80 () (not @t79)) % 0.52/0.79 (define @t81 () (or @t80 @t75)) % 0.52/0.79 (define @t82 () (@list false)) % 0.52/0.79 (define @t83 () (@list @t70)) % 0.52/0.79 (define @t84 () (not @t61)) % 0.52/0.79 (define @t85 () (lambda (@list (@var "BOUND_VARIABLE_7561" $$unsorted)) @t21)) % 0.52/0.79 (define @t86 () (_ @t85 @t21)) % 0.52/0.79 (define @t87 () (= tptp.zero @t86)) % 0.52/0.79 (define @t88 () (not @t87)) % 0.52/0.79 (define @t89 () (_ @t85 tptp.zero)) % 0.52/0.79 (define @t90 () (= @t21 @t89)) % 0.52/0.79 (define @t91 () (not @t90)) % 0.52/0.79 (define @t92 () (or @t91 @t88)) % 0.52/0.79 (define @t93 () (@purify @t60)) % 0.52/0.79 (define @t94 () (= @t60 @t63)) % 0.52/0.79 (define @t95 () (= @t1 @t63)) % 0.52/0.79 (define @t96 () (= @t62 @t60)) % 0.52/0.79 (define @t97 () (= @t62 @t1)) % 0.52/0.79 (define @t98 () (= @t63 @t93)) % 0.52/0.79 (define @t99 () (= tptp.zero @t93)) % 0.52/0.79 (define @t100 () (tptp.s @t21)) % 0.52/0.79 (define @t101 () (= @t59 @t93)) % 0.52/0.79 (define @t102 () (= @t60 @t59)) % 0.52/0.79 (define @t103 () (= @t60 tptp.zero)) % 0.52/0.79 (define @t104 () (not @t99)) % 0.52/0.79 (define @t105 () (not @t98)) % 0.52/0.79 (define @t106 () (and @t65 @t98)) % 0.52/0.79 (assume @p1 @t20) % 0.52/0.79 (assume @p2 true) % 0.52/0.79 (step @p3 :rule refl :args ((_ @t2 @t1))) % 0.52/0.79 (step @p4 :rule refl :args (@t21)) % 0.52/0.79 (step @p5 :rule cong :premises (@p4) :args (@t22)) % 0.52/0.79 (step @p6 :rule trans :premises (@p5 @p3)) % 0.52/0.79 (step @p7 :rule refl :args (@t2)) % 0.52/0.79 (step @p8 :rule ho_cong :premises (@p7 @p4)) % 0.52/0.79 (step @p9 :rule cong :premises (@p8 @p6) :args ((= (_ @t2 @t21) @t22))) % 0.52/0.79 (step @p10 :rule symm :premises (@p9)) % 0.52/0.79 (step @p11 :rule refl :args (@t3)) % 0.52/0.79 (step @p12 :rule eq_resolve :premises (@p11 @p10)) % 0.52/0.79 (step @p13 :rule refl :args (@t1)) % 0.52/0.79 (step @p14 :rule cong :premises (@p13 @p4) :args (@t23)) % 0.52/0.79 (step @p15 :rule symm :premises (@p14)) % 0.52/0.79 (step @p16 :rule eq_resolve :premises (@p13 @p15)) % 0.52/0.79 (step @p17 :rule ho_cong :premises (@p7 @p16)) % 0.52/0.79 (step @p18 :rule trans :premises (@p17 @p12)) % 0.52/0.79 (step @p19 :rule refl :args (tptp.zero)) % 0.52/0.79 (step @p20 :rule cong :premises (@p19 @p18) :args (@t24)) % 0.52/0.79 (step @p21 :rule cong :premises (@p20) :args (@t25)) % 0.52/0.79 (step @p22 :rule refl :args (@t26)) % 0.52/0.79 (step @p23 :rule refl :args (@t4)) % 0.52/0.79 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t4 @t26))) % 0.52/0.79 (step @p25 :rule symm :premises (@p24)) % 0.52/0.79 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.52/0.79 (step @p27 :rule cong :premises (@p16 @p26) :args (@t27)) % 0.52/0.79 (step @p28 :rule cong :premises (@p27) :args (@t28)) % 0.52/0.79 (step @p29 :rule nary_cong :premises (@p28 @p21) :args (@t29)) % 0.52/0.79 (step @p30 :rule cong :premises (@p29) :args ((forall @t6 @t29))) % 0.52/0.79 (step @p31 :rule bool-and-de-morgan :args (@t27 @t24 true)) % 0.52/0.79 (step @p32 :rule cong :premises (@p31) :args (@t31)) % 0.52/0.79 (step @p33 :rule trans :premises (@p32 @p30)) % 0.52/0.79 (step @p34 :rule cong :premises (@p33) :args (@t32)) % 0.52/0.79 (step @p35 :rule exists-elim :args ((= (exists @t6 @t30) @t32))) % 0.52/0.79 (step @p36 :rule trans :premises (@p35 @p34)) % 0.52/0.79 (step @p37 :rule eq-symm :args (@t3 tptp.zero)) % 0.52/0.79 (step @p38 :rule eq-symm :args (@t4 @t1)) % 0.52/0.79 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t5)) % 0.52/0.79 (step @p40 :rule cong :premises (@p39) :args (@t7)) % 0.52/0.79 (step @p41 :rule trans :premises (@p40 @p36)) % 0.52/0.79 (step @p42 :rule aci_norm :args ((= @t34 @t33))) % 0.52/0.79 (step @p43 :rule cong :premises (@p42) :args ((forall @t35 @t34))) % 0.52/0.79 (step @p44 :rule quant-var-elim-eq :args ((= (forall @t38 (or (not (= @t10 false)) @t10 @t37)) @t34))) % 0.52/0.79 (step @p45 :rule refl :args (@t37)) % 0.52/0.79 (step @p46 :rule refl :args (@t10)) % 0.52/0.79 (step @p47 :rule bool-eq-false :args (@t10)) % 0.52/0.79 (step @p48 :rule symm :premises (@p47)) % 0.52/0.79 (step @p49 :rule cong :premises (@p48) :args (@t39)) % 0.52/0.79 (step @p50 :rule bool-double-not-elim :args (@t10)) % 0.52/0.79 (step @p51 :rule symm :premises (@p50)) % 0.52/0.79 (step @p52 :rule trans :premises (@p51 @p49)) % 0.52/0.79 (step @p53 :rule nary_cong :premises (@p52 @p46 @p45) :args (@t40)) % 0.52/0.79 (step @p54 :rule aci_norm :args ((= @t41 @t40))) % 0.52/0.79 (step @p55 :rule trans :premises (@p54 @p53)) % 0.52/0.79 (step @p56 :rule cong :premises (@p55) :args (@t42)) % 0.52/0.79 (step @p57 :rule trans :premises (@p56 @p44)) % 0.52/0.79 (step @p58 :rule cong :premises (@p57) :args (@t43)) % 0.52/0.79 (step @p59 :rule quant-merge-prenex :args ((= @t43 @t45))) % 0.52/0.79 (step @p60 :rule symm :premises (@p59)) % 0.52/0.79 (step @p61 :rule quant_var_reordering :args ((= (forall @t14 @t41) @t45))) % 0.52/0.79 (step @p62 :rule trans :premises (@p61 @p60 @p58)) % 0.52/0.79 (step @p63 :rule trans :premises (@p62 @p43)) % 0.52/0.79 (step @p64 :rule refl :args (@t36)) % 0.52/0.79 (step @p65 :rule refl :args (@t11)) % 0.52/0.79 (step @p66 :rule cong :premises (@p65 @p64) :args ((= @t11 @t36))) % 0.52/0.79 (step @p67 :rule symm :premises (@p66)) % 0.52/0.79 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 0.52/0.79 (step @p69 :rule refl :args (@t8)) % 0.52/0.79 (step @p70 :rule cong :premises (@p69 @p68) :args (@t46)) % 0.52/0.79 (step @p71 :rule nary_cong :premises (@p46 @p70) :args (@t47)) % 0.52/0.79 (step @p72 :rule cong :premises (@p71) :args ((forall @t14 @t47))) % 0.52/0.79 (step @p73 :rule trans :premises (@p72 @p63)) % 0.52/0.79 (step @p74 :rule refl :args (@t46)) % 0.52/0.79 (step @p75 :rule nary_cong :premises (@p50 @p74) :args ((or @t39 @t46))) % 0.52/0.79 (step @p76 :rule bool-impl-elim :args (@t12 @t46)) % 0.52/0.79 (step @p77 :rule trans :premises (@p76 @p75)) % 0.52/0.79 (step @p78 :rule cong :premises (@p77) :args ((forall @t14 (=> @t12 @t46)))) % 0.52/0.79 (step @p79 :rule trans :premises (@p78 @p73)) % 0.52/0.79 (step @p80 :rule eq-symm :args (@t11 @t8)) % 0.52/0.79 (step @p81 :rule refl :args (@t12)) % 0.52/0.79 (step @p82 :rule cong :premises (@p81 @p80) :args (@t13)) % 0.52/0.79 (step @p83 :rule cong :premises (@p82) :args (@t15)) % 0.52/0.79 (step @p84 :rule trans :premises (@p83 @p79)) % 0.52/0.79 (step @p85 :rule aci_norm :args ((= (or false @t48) @t48))) % 0.52/0.79 (step @p86 :rule refl :args (@t48)) % 0.52/0.79 (step @p87 :rule evaluate :args (@t49)) % 0.52/0.79 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t50)) % 0.52/0.79 (step @p89 :rule trans :premises (@p88 @p85)) % 0.52/0.79 (step @p90 :rule cong :premises (@p89) :args ((forall @t35 @t50))) % 0.52/0.79 (step @p91 :rule quant-var-elim-eq :args ((= (forall @t38 (or (not (= @t10 true)) @t12 @t51)) @t50))) % 0.52/0.79 (step @p92 :rule refl :args (@t51)) % 0.52/0.79 (step @p93 :rule refl :args (@t12)) % 0.52/0.79 (step @p94 :rule bool-eq-true :args (@t10)) % 0.52/0.79 (step @p95 :rule symm :premises (@p94)) % 0.52/0.79 (step @p96 :rule cong :premises (@p95) :args (@t12)) % 0.52/0.79 (step @p97 :rule nary_cong :premises (@p96 @p93 @p92) :args (@t52)) % 0.52/0.79 (step @p98 :rule aci_norm :args ((= @t53 @t52))) % 0.52/0.79 (step @p99 :rule trans :premises (@p98 @p97)) % 0.52/0.79 (step @p100 :rule cong :premises (@p99) :args (@t54)) % 0.52/0.79 (step @p101 :rule trans :premises (@p100 @p91)) % 0.52/0.79 (step @p102 :rule cong :premises (@p101) :args (@t55)) % 0.52/0.79 (step @p103 :rule quant-merge-prenex :args ((= @t55 @t56))) % 0.52/0.79 (step @p104 :rule symm :premises (@p103)) % 0.52/0.79 (step @p105 :rule quant_var_reordering :args ((= (forall @t14 @t53) @t56))) % 0.52/0.79 (step @p106 :rule trans :premises (@p105 @p104 @p102)) % 0.52/0.79 (step @p107 :rule trans :premises (@p106 @p90)) % 0.52/0.79 (step @p108 :rule refl :args (@t9)) % 0.52/0.79 (step @p109 :rule cong :premises (@p108 @p68) :args (@t57)) % 0.52/0.79 (step @p110 :rule nary_cong :premises (@p93 @p109) :args (@t58)) % 0.52/0.79 (step @p111 :rule cong :premises (@p110) :args ((forall @t14 @t58))) % 0.52/0.79 (step @p112 :rule trans :premises (@p111 @p107)) % 0.52/0.79 (step @p113 :rule bool-impl-elim :args (@t10 @t57)) % 0.52/0.79 (step @p114 :rule cong :premises (@p113) :args ((forall @t14 (=> @t10 @t57)))) % 0.52/0.79 (step @p115 :rule trans :premises (@p114 @p112)) % 0.52/0.79 (step @p116 :rule eq-symm :args (@t11 @t9)) % 0.52/0.79 (step @p117 :rule refl :args (@t10)) % 0.52/0.79 (step @p118 :rule cong :premises (@p117 @p116) :args (@t16)) % 0.52/0.79 (step @p119 :rule cong :premises (@p118) :args (@t17)) % 0.52/0.79 (step @p120 :rule trans :premises (@p119 @p115)) % 0.52/0.79 (step @p121 :rule nary_cong :premises (@p120 @p84) :args (@t18)) % 0.52/0.79 (step @p122 :rule cong :premises (@p121 @p41) :args (@t19)) % 0.52/0.79 (step @p123 :rule cong :premises (@p122) :args (@t20)) % 0.52/0.79 (step @p124 :rule eq_resolve :premises (@p1 @p123)) % 0.52/0.79 (step @p125 :rule not_implies_elim2 :premises (@p124)) % 0.52/0.79 (step @p126 :rule not_not_elim :premises (@p125)) % 0.52/0.79 (step @p127 :rule aci_norm :args ((= (or false @t65) @t65))) % 0.52/0.79 (step @p128 :rule eq-refl :args (@t62)) % 0.52/0.79 (step @p129 :rule skolem_intro :args (@t63)) % 0.52/0.79 (step @p130 :rule refl :args (@t62)) % 0.52/0.79 (step @p131 :rule cong :premises (@p130 @p129) :args ((= @t62 @t63))) % 0.52/0.79 (step @p132 :rule trans :premises (@p131 @p128)) % 0.52/0.79 (step @p133 :rule true_elim :premises (@p132)) % 0.52/0.79 (step @p134 :rule refl :args (tptp.zero)) % 0.52/0.79 (step @p135 :rule cong :premises (@p134 @p133) :args (@t66)) % 0.52/0.79 (step @p136 :rule cong :premises (@p135) :args (@t67)) % 0.52/0.79 (step @p137 :rule eq-refl :args (@t21)) % 0.52/0.79 (step @p138 :rule refl :args (@t21)) % 0.52/0.79 (step @p139 :rule cong :premises (@p16 @p138) :args (@t23)) % 0.52/0.79 (step @p140 :rule trans :premises (@p139 @p137)) % 0.52/0.79 (step @p141 :rule cong :premises (@p140) :args (@t68)) % 0.52/0.79 (step @p142 :rule trans :premises (@p141 @p87)) % 0.52/0.79 (step @p143 :rule nary_cong :premises (@p142 @p136) :args (@t69)) % 0.52/0.79 (step @p144 :rule trans :premises (@p143 @p127)) % 0.52/0.79 (step @p145 :rule refl :args (@t70)) % 0.52/0.79 (step @p146 :rule cong :premises (@p145 @p144) :args ((=> @t70 @t69))) % 0.52/0.79 (step @p147 :rule beta-reduce :args ((= @t73 @t62))) % 0.52/0.79 (step @p148 :rule cong :premises (@p134 @p147) :args (@t74)) % 0.52/0.79 (step @p149 :rule cong :premises (@p148) :args (@t75)) % 0.52/0.79 (step @p150 :rule eq-symm :args (@t21 @t1)) % 0.52/0.79 (step @p151 :rule ite-true-cond :args (@t1 (ite (= tptp.zero @t1) tptp.zero @t59))) % 0.52/0.79 (step @p152 :rule refl :args (@t59)) % 0.52/0.79 (step @p153 :rule eq-symm :args (@t1 tptp.zero)) % 0.52/0.79 (step @p154 :rule cong :premises (@p153 @p134 @p152) :args (@t76)) % 0.52/0.79 (step @p155 :rule refl :args (@t1)) % 0.52/0.79 (step @p156 :rule eq-refl :args (tptp.zero)) % 0.52/0.79 (step @p157 :rule cong :premises (@p156 @p155 @p154) :args (@t77)) % 0.52/0.79 (step @p158 :rule trans :premises (@p157 @p151)) % 0.52/0.79 (step @p159 :rule beta-reduce :args ((= @t78 @t77))) % 0.52/0.79 (step @p160 :rule trans :premises (@p159 @p158)) % 0.52/0.79 (step @p161 :rule cong :premises (@p138 @p160) :args (@t79)) % 0.52/0.79 (step @p162 :rule trans :premises (@p161 @p150)) % 0.52/0.79 (step @p163 :rule cong :premises (@p162) :args (@t80)) % 0.52/0.79 (step @p164 :rule nary_cong :premises (@p163 @p149) :args (@t81)) % 0.52/0.79 (step @p165 :rule cong :premises (@p145 @p164) :args ((=> @t70 @t81))) % 0.52/0.79 (assume-push @p263 @t70) % 0.52/0.79 (step @p167 :rule instantiate :premises (@p126) :args ((@list @t72))) % 0.52/0.79 (step-pop @p264 :rule scope :premises (@p167)) % 0.52/0.79 (step @p168 :rule process_scope :premises (@p264) :args (@t81)) % 0.52/0.79 (step @p170 :rule eq_resolve :premises (@p168 @p165)) % 0.52/0.79 (step @p171 :rule eq_resolve :premises (@p170 @p146)) % 0.52/0.79 (step @p172 :rule implies_elim :premises (@p171)) % 0.52/0.79 (step @p173 :rule chain_m_resolution :premises (@p172 @p126) :args (@t65 @t82 @t83)) % 0.52/0.79 (step @p174 :rule aci_norm :args ((= (or false @t84) @t84))) % 0.52/0.79 (step @p175 :rule beta-reduce :args ((= @t86 @t21))) % 0.52/0.79 (step @p176 :rule cong :premises (@p134 @p175) :args (@t87)) % 0.52/0.79 (step @p177 :rule cong :premises (@p176) :args (@t88)) % 0.52/0.79 (step @p178 :rule beta-reduce :args ((= @t89 @t21))) % 0.52/0.79 (step @p179 :rule cong :premises (@p138 @p178) :args (@t90)) % 0.52/0.79 (step @p180 :rule trans :premises (@p179 @p137)) % 0.52/0.79 (step @p181 :rule cong :premises (@p180) :args (@t91)) % 0.52/0.79 (step @p182 :rule trans :premises (@p181 @p87)) % 0.52/0.79 (step @p183 :rule nary_cong :premises (@p182 @p177) :args (@t92)) % 0.52/0.79 (step @p184 :rule trans :premises (@p183 @p174)) % 0.52/0.79 (step @p185 :rule cong :premises (@p145 @p184) :args ((=> @t70 @t92))) % 0.52/0.79 (assume-push @p265 @t70) % 0.52/0.79 (step @p187 :rule instantiate :premises (@p126) :args ((@list @t85))) % 0.52/0.79 (step-pop @p266 :rule scope :premises (@p187)) % 0.52/0.79 (step @p188 :rule process_scope :premises (@p266) :args (@t92)) % 0.52/0.79 (step @p190 :rule eq_resolve :premises (@p188 @p185)) % 0.52/0.79 (step @p191 :rule implies_elim :premises (@p190)) % 0.52/0.79 (step @p192 :rule chain_m_resolution :premises (@p191 @p126) :args (@t84 @t82 @t83)) % 0.52/0.79 (step @p193 :rule eq-symm :args (@t93 @t63)) % 0.52/0.79 (step @p194 :rule refl :args (@t63)) % 0.52/0.79 (step @p195 :rule eq-refl :args (@t60)) % 0.52/0.79 (step @p196 :rule skolem_intro :args (@t93)) % 0.52/0.79 (step @p197 :rule refl :args (@t60)) % 0.52/0.79 (step @p198 :rule cong :premises (@p197 @p196) :args ((= @t60 @t93))) % 0.52/0.79 (step @p199 :rule trans :premises (@p198 @p195)) % 0.52/0.79 (step @p200 :rule true_elim :premises (@p199)) % 0.52/0.79 (step @p201 :rule cong :premises (@p200 @p194) :args (@t94)) % 0.52/0.79 (step @p202 :rule trans :premises (@p201 @p193)) % 0.52/0.79 (step @p203 :rule cong :premises (@p16 @p194) :args (@t95)) % 0.52/0.79 (step @p204 :rule refl :args (@t61)) % 0.52/0.79 (step @p205 :rule cong :premises (@p204 @p203 @p202) :args ((ite @t61 @t95 @t94))) % 0.52/0.79 (step @p206 :rule eq-symm :args (@t63 @t60)) % 0.52/0.79 (step @p207 :rule eq-symm :args (@t63 @t1)) % 0.52/0.79 (step @p208 :rule cong :premises (@p204 @p207 @p206) :args ((ite @t61 (= @t63 @t1) (= @t63 @t60)))) % 0.52/0.79 (step @p209 :rule trans :premises (@p208 @p205)) % 0.52/0.79 (step @p210 :rule cong :premises (@p133 @p197) :args (@t96)) % 0.52/0.79 (step @p211 :rule cong :premises (@p133 @p155) :args (@t97)) % 0.52/0.79 (step @p212 :rule cong :premises (@p204 @p211 @p210) :args ((ite @t61 @t97 @t96))) % 0.52/0.79 (step @p213 :rule ite_eq :args (@t62)) % 0.52/0.79 (step @p214 :rule eq_resolve :premises (@p213 @p212)) % 0.52/0.79 (step @p215 :rule eq_resolve :premises (@p214 @p209)) % 0.52/0.79 (step @p216 :rule ite_elim2 :premises (@p215)) % 0.52/0.79 (step @p217 :rule chain_m_resolution :premises (@p216 @p192) :args (@t98 (@list true) (@list @t61))) % 0.52/0.79 (step @p218 :rule ite-true-cond :args (@t99 (= @t100 @t93))) % 0.52/0.79 (step @p219 :rule refl :args (@t93)) % 0.52/0.79 (step @p220 :rule refl :args ((tptp.s @t1))) % 0.52/0.79 (step @p221 :rule cong :premises (@p4) :args (@t100)) % 0.52/0.79 (step @p222 :rule trans :premises (@p221 @p220)) % 0.52/0.79 (step @p223 :rule refl :args (tptp.s)) % 0.52/0.79 (step @p224 :rule ho_cong :premises (@p223 @p4)) % 0.52/0.79 (step @p225 :rule cong :premises (@p224 @p222) :args ((= @t59 @t100))) % 0.52/0.79 (step @p226 :rule symm :premises (@p225)) % 0.52/0.79 (step @p227 :rule refl :args ((_ tptp.s @t1))) % 0.52/0.79 (step @p228 :rule eq_resolve :premises (@p227 @p226)) % 0.52/0.79 (step @p229 :rule cong :premises (@p228 @p219) :args (@t101)) % 0.52/0.79 (step @p230 :rule refl :args (@t99)) % 0.52/0.79 (step @p231 :rule cong :premises (@p140 @p230 @p229) :args ((ite @t23 @t99 @t101))) % 0.52/0.79 (step @p232 :rule trans :premises (@p231 @p218)) % 0.52/0.79 (step @p233 :rule eq-symm :args (@t93 @t59)) % 0.52/0.79 (step @p234 :rule eq-symm :args (@t93 tptp.zero)) % 0.52/0.79 (step @p235 :rule refl :args (@t23)) % 0.52/0.79 (step @p236 :rule cong :premises (@p235 @p234 @p233) :args ((ite @t23 (= @t93 tptp.zero) (= @t93 @t59)))) % 0.52/0.79 (step @p237 :rule trans :premises (@p236 @p232)) % 0.52/0.79 (step @p238 :rule cong :premises (@p200 @p152) :args (@t102)) % 0.52/0.79 (step @p239 :rule cong :premises (@p200 @p134) :args (@t103)) % 0.52/0.79 (step @p240 :rule cong :premises (@p235 @p239 @p238) :args ((ite @t23 @t103 @t102))) % 0.52/0.79 (step @p241 :rule ite_eq :args (@t60)) % 0.52/0.79 (step @p242 :rule eq_resolve :premises (@p241 @p240)) % 0.52/0.79 (step @p243 :rule eq_resolve :premises (@p242 @p237)) % 0.52/0.79 (step @p244 :rule refl :args (@t104)) % 0.52/0.79 (step @p245 :rule refl :args (@t105)) % 0.52/0.79 (step @p246 :rule bool-double-not-elim :args (@t64)) % 0.52/0.79 (step @p247 :rule nary_cong :premises (@p246 @p245 @p244) :args ((or (not @t65) @t105 @t104))) % 0.52/0.79 (assume-push @p267 @t65) % 0.52/0.79 (assume-push @p268 @t98) % 0.52/0.79 (step @p250 :rule false_intro :premises (@p173)) % 0.52/0.79 (step @p251 :rule symm :premises (@p217)) % 0.52/0.79 (step @p252 :rule cong :premises (@p134 @p251) :args (@t99)) % 0.52/0.79 (step @p253 :rule trans :premises (@p252 @p250)) % 0.52/0.79 (step @p254 :rule false_elim :premises (@p253)) % 0.52/0.79 (step-pop @p269 :rule scope :premises (@p254)) % 0.52/0.79 (step-pop @p270 :rule scope :premises (@p269)) % 0.52/0.79 (step @p255 :rule process_scope :premises (@p270) :args (@t104)) % 0.52/0.79 (step @p258 :rule implies_elim :premises (@p255)) % 0.52/0.79 (step @p259 :rule cnf_and_neg :args (@t106)) % 0.52/0.79 (step @p260 :rule resolution :premises (@p259 @p258) :args (true @t106)) % 0.52/0.79 (step @p261 :rule eq_resolve :premises (@p260 @p247)) % 0.52/0.79 (step @p262 false :rule chain_m_resolution :premises (@p261 @p243 @p217 @p173) :args (false (@list false false true) (@list @t99 @t98 @t64))) % 0.52/0.79 ) % 0.52/0.79 % SZS output end Proof % 0.52/0.79 % cvc5 exiting %------------------------------------------------------------------------------