%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN023^2 : 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 : n014.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 0.47s 0.69s % Output : Proof 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUN023^2 : TPTP v9.2.1. Released v6.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n014.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 12:37:43 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.47/0.69 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.47/0.69 % SZS status Theorem % 0.47/0.69 % SZS output start Proof % 0.47/0.69 ( % 0.47/0.69 (declare-sort $$unsorted 0) % 0.47/0.69 (declare-const tptp.h (-> $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.ite (-> Bool $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.s (-> $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.zero $$unsorted) % 0.47/0.69 (define @t1 () (_ tptp.s tptp.zero)) % 0.47/0.69 (define @t2 () (@var "H" (-> $$unsorted $$unsorted))) % 0.47/0.69 (define @t3 () (_ @t2 @t1)) % 0.47/0.69 (define @t4 () (_ @t2 tptp.zero)) % 0.47/0.69 (define @t5 () (and (= @t4 @t1) (= @t3 tptp.zero))) % 0.47/0.69 (define @t6 () (@list @t2)) % 0.47/0.69 (define @t7 () (exists @t6 @t5)) % 0.47/0.69 (define @t8 () (@var "X" $$unsorted)) % 0.47/0.69 (define @t9 () (_ tptp.h @t8)) % 0.47/0.69 (define @t10 () (= @t9 (_ (_ (_ tptp.ite (= @t8 tptp.zero)) @t1) tptp.zero))) % 0.47/0.69 (define @t11 () (@list @t8)) % 0.47/0.69 (define @t12 () (forall @t11 @t10)) % 0.47/0.69 (define @t13 () (@var "V" $$unsorted)) % 0.47/0.69 (define @t14 () (@var "U" $$unsorted)) % 0.47/0.69 (define @t15 () (@var "X100" Bool)) % 0.47/0.69 (define @t16 () (_ (_ (_ tptp.ite @t15) @t14) @t13)) % 0.47/0.69 (define @t17 () (not @t15)) % 0.47/0.69 (define @t18 () (=> @t17 (= @t16 @t13))) % 0.47/0.69 (define @t19 () (@list @t15 @t14 @t13)) % 0.47/0.69 (define @t20 () (forall @t19 @t18)) % 0.47/0.69 (define @t21 () (=> @t15 (= @t16 @t14))) % 0.47/0.69 (define @t22 () (forall @t19 @t21)) % 0.47/0.69 (define @t23 () (and @t22 @t20 @t12)) % 0.47/0.69 (define @t24 () (=> @t23 @t7)) % 0.47/0.69 (define @t25 () (not @t24)) % 0.47/0.69 (define @t26 () (tptp.s tptp.zero)) % 0.47/0.69 (define @t27 () (_ @t2 @t26)) % 0.47/0.69 (define @t28 () (= @t1 @t26)) % 0.47/0.69 (define @t29 () (= tptp.zero @t3)) % 0.47/0.69 (define @t30 () (not @t29)) % 0.47/0.69 (define @t31 () (_ @t2 tptp.zero)) % 0.47/0.69 (define @t32 () (= @t1 @t4)) % 0.47/0.69 (define @t33 () (not @t32)) % 0.47/0.69 (define @t34 () (or @t33 @t30)) % 0.47/0.69 (define @t35 () (and @t32 @t29)) % 0.47/0.69 (define @t36 () (forall @t6 (not @t35))) % 0.47/0.69 (define @t37 () (not @t36)) % 0.47/0.69 (define @t38 () (= tptp.zero @t8)) % 0.47/0.69 (define @t39 () (tptp.ite @t38 @t26 tptp.zero)) % 0.47/0.69 (define @t40 () (_ tptp.ite @t38)) % 0.47/0.69 (define @t41 () (_ (_ @t40 @t1) tptp.zero)) % 0.47/0.69 (define @t42 () (tptp.h @t8)) % 0.47/0.69 (define @t43 () (= @t9 @t41)) % 0.47/0.69 (define @t44 () (= @t13 (tptp.ite false @t14 @t13))) % 0.47/0.69 (define @t45 () (or false @t44)) % 0.47/0.69 (define @t46 () (@list @t14 @t13)) % 0.47/0.69 (define @t47 () (tptp.ite @t15 @t14 @t13)) % 0.47/0.69 (define @t48 () (= @t13 @t47)) % 0.47/0.69 (define @t49 () (@list @t15)) % 0.47/0.69 (define @t50 () (not @t17)) % 0.47/0.69 (define @t51 () (or @t15 @t15 @t48)) % 0.47/0.69 (define @t52 () (or @t15 @t48)) % 0.47/0.69 (define @t53 () (forall @t49 @t52)) % 0.47/0.69 (define @t54 () (forall @t46 @t53)) % 0.47/0.69 (define @t55 () (@list @t14 @t13 @t15)) % 0.47/0.69 (define @t56 () (forall @t55 @t52)) % 0.47/0.69 (define @t57 () (= @t13 @t16)) % 0.47/0.69 (define @t58 () (or @t15 @t57)) % 0.47/0.69 (define @t59 () (= @t14 (tptp.ite true @t14 @t13))) % 0.47/0.69 (define @t60 () (not true)) % 0.47/0.69 (define @t61 () (or @t60 @t59)) % 0.47/0.69 (define @t62 () (= @t14 @t47)) % 0.47/0.69 (define @t63 () (or @t17 @t17 @t62)) % 0.47/0.69 (define @t64 () (or @t17 @t62)) % 0.47/0.69 (define @t65 () (forall @t49 @t64)) % 0.47/0.69 (define @t66 () (forall @t46 @t65)) % 0.47/0.69 (define @t67 () (forall @t55 @t64)) % 0.47/0.69 (define @t68 () (= @t14 @t16)) % 0.47/0.69 (define @t69 () (or @t17 @t68)) % 0.47/0.69 (define @t70 () (_ tptp.s @t26)) % 0.47/0.69 (define @t71 () (ite @t28 tptp.zero @t70)) % 0.47/0.69 (define @t72 () (= tptp.zero @t26)) % 0.47/0.69 (define @t73 () (ite @t72 @t1 @t71)) % 0.47/0.69 (define @t74 () (@purify @t73)) % 0.47/0.69 (define @t75 () (= tptp.zero @t74)) % 0.47/0.69 (define @t76 () (not @t75)) % 0.47/0.69 (define @t77 () (= tptp.zero @t73)) % 0.47/0.69 (define @t78 () (not @t77)) % 0.47/0.69 (define @t79 () (not @t28)) % 0.47/0.69 (define @t80 () (or @t79 @t78)) % 0.47/0.69 (define @t81 () (forall @t6 (or (not (= @t26 @t31)) (not (= tptp.zero @t27))))) % 0.47/0.69 (define @t82 () (@var "BOUND_VARIABLE_28876" $$unsorted)) % 0.47/0.69 (define @t83 () (lambda (@list @t82) (ite (= tptp.zero @t82) @t1 (ite (= @t1 @t82) tptp.zero @t70)))) % 0.47/0.69 (define @t84 () (_ @t83 @t26)) % 0.47/0.69 (define @t85 () (= tptp.zero @t84)) % 0.47/0.69 (define @t86 () (not @t85)) % 0.47/0.69 (define @t87 () (ite (= @t1 tptp.zero) tptp.zero @t70)) % 0.47/0.69 (define @t88 () (ite (= tptp.zero tptp.zero) @t1 @t87)) % 0.47/0.69 (define @t89 () (_ @t83 tptp.zero)) % 0.47/0.69 (define @t90 () (= @t26 @t89)) % 0.47/0.69 (define @t91 () (not @t90)) % 0.47/0.69 (define @t92 () (or @t91 @t86)) % 0.47/0.69 (define @t93 () (@list false)) % 0.47/0.69 (define @t94 () (@list @t81)) % 0.47/0.69 (define @t95 () (not @t72)) % 0.47/0.69 (define @t96 () (lambda (@list (@var "BOUND_VARIABLE_7599" $$unsorted)) @t26)) % 0.47/0.69 (define @t97 () (_ @t96 @t26)) % 0.47/0.69 (define @t98 () (= tptp.zero @t97)) % 0.47/0.69 (define @t99 () (not @t98)) % 0.47/0.69 (define @t100 () (_ @t96 tptp.zero)) % 0.47/0.69 (define @t101 () (= @t26 @t100)) % 0.47/0.69 (define @t102 () (not @t101)) % 0.47/0.69 (define @t103 () (or @t102 @t99)) % 0.47/0.69 (define @t104 () (@purify @t71)) % 0.47/0.69 (define @t105 () (= @t71 @t74)) % 0.47/0.69 (define @t106 () (= @t1 @t74)) % 0.47/0.69 (define @t107 () (= @t73 @t71)) % 0.47/0.69 (define @t108 () (= @t73 @t1)) % 0.47/0.69 (define @t109 () (= @t74 @t104)) % 0.47/0.69 (define @t110 () (= tptp.zero @t104)) % 0.47/0.69 (define @t111 () (tptp.s @t26)) % 0.47/0.69 (define @t112 () (= @t70 @t104)) % 0.47/0.69 (define @t113 () (= @t71 @t70)) % 0.47/0.69 (define @t114 () (= @t71 tptp.zero)) % 0.47/0.69 (define @t115 () (not @t110)) % 0.47/0.69 (define @t116 () (not @t109)) % 0.47/0.69 (define @t117 () (and @t76 @t109)) % 0.47/0.69 (assume @p1 @t25) % 0.47/0.69 (assume @p2 true) % 0.47/0.69 (step @p3 :rule refl :args ((_ @t2 @t1))) % 0.47/0.69 (step @p4 :rule refl :args (@t26)) % 0.47/0.69 (step @p5 :rule cong :premises (@p4) :args (@t27)) % 0.47/0.69 (step @p6 :rule trans :premises (@p5 @p3)) % 0.47/0.69 (step @p7 :rule refl :args (@t2)) % 0.47/0.69 (step @p8 :rule ho_cong :premises (@p7 @p4)) % 0.47/0.69 (step @p9 :rule cong :premises (@p8 @p6) :args ((= (_ @t2 @t26) @t27))) % 0.47/0.69 (step @p10 :rule symm :premises (@p9)) % 0.47/0.69 (step @p11 :rule refl :args (@t3)) % 0.47/0.69 (step @p12 :rule eq_resolve :premises (@p11 @p10)) % 0.47/0.69 (step @p13 :rule refl :args (@t1)) % 0.47/0.69 (step @p14 :rule cong :premises (@p13 @p4) :args (@t28)) % 0.47/0.69 (step @p15 :rule symm :premises (@p14)) % 0.47/0.69 (step @p16 :rule eq_resolve :premises (@p13 @p15)) % 0.47/0.69 (step @p17 :rule ho_cong :premises (@p7 @p16)) % 0.47/0.69 (step @p18 :rule trans :premises (@p17 @p12)) % 0.47/0.69 (step @p19 :rule refl :args (tptp.zero)) % 0.47/0.69 (step @p20 :rule cong :premises (@p19 @p18) :args (@t29)) % 0.47/0.69 (step @p21 :rule cong :premises (@p20) :args (@t30)) % 0.47/0.69 (step @p22 :rule refl :args (@t31)) % 0.47/0.69 (step @p23 :rule refl :args (@t4)) % 0.47/0.69 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t4 @t31))) % 0.47/0.69 (step @p25 :rule symm :premises (@p24)) % 0.47/0.69 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.47/0.69 (step @p27 :rule cong :premises (@p16 @p26) :args (@t32)) % 0.47/0.69 (step @p28 :rule cong :premises (@p27) :args (@t33)) % 0.47/0.69 (step @p29 :rule nary_cong :premises (@p28 @p21) :args (@t34)) % 0.47/0.69 (step @p30 :rule cong :premises (@p29) :args ((forall @t6 @t34))) % 0.47/0.69 (step @p31 :rule bool-and-de-morgan :args (@t32 @t29 true)) % 0.47/0.69 (step @p32 :rule cong :premises (@p31) :args (@t36)) % 0.47/0.69 (step @p33 :rule trans :premises (@p32 @p30)) % 0.47/0.69 (step @p34 :rule cong :premises (@p33) :args (@t37)) % 0.47/0.69 (step @p35 :rule exists-elim :args ((= (exists @t6 @t35) @t37))) % 0.47/0.69 (step @p36 :rule trans :premises (@p35 @p34)) % 0.47/0.69 (step @p37 :rule eq-symm :args (@t3 tptp.zero)) % 0.47/0.69 (step @p38 :rule eq-symm :args (@t4 @t1)) % 0.47/0.69 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t5)) % 0.47/0.69 (step @p40 :rule cong :premises (@p39) :args (@t7)) % 0.47/0.69 (step @p41 :rule trans :premises (@p40 @p36)) % 0.47/0.69 (step @p42 :rule refl :args ((tptp.ite @t38 @t1 tptp.zero))) % 0.47/0.69 (step @p43 :rule refl :args (@t38)) % 0.47/0.69 (step @p44 :rule cong :premises (@p43 @p4 @p19) :args (@t39)) % 0.47/0.69 (step @p45 :rule trans :premises (@p44 @p42)) % 0.47/0.69 (step @p46 :rule refl :args (@t40)) % 0.47/0.69 (step @p47 :rule ho_cong :premises (@p46 @p4)) % 0.47/0.69 (step @p48 :rule ho_cong :premises (@p47 @p19)) % 0.47/0.69 (step @p49 :rule cong :premises (@p48 @p45) :args ((= (_ (_ @t40 @t26) tptp.zero) @t39))) % 0.47/0.69 (step @p50 :rule symm :premises (@p49)) % 0.47/0.69 (step @p51 :rule refl :args (@t41)) % 0.47/0.69 (step @p52 :rule eq_resolve :premises (@p51 @p50)) % 0.47/0.69 (step @p53 :rule ho_cong :premises (@p46 @p16)) % 0.47/0.69 (step @p54 :rule ho_cong :premises (@p53 @p19)) % 0.47/0.69 (step @p55 :rule trans :premises (@p54 @p52)) % 0.47/0.69 (step @p56 :rule refl :args (@t42)) % 0.47/0.69 (step @p57 :rule refl :args (@t9)) % 0.47/0.69 (step @p58 :rule cong :premises (@p57 @p56) :args ((= @t9 @t42))) % 0.47/0.69 (step @p59 :rule symm :premises (@p58)) % 0.47/0.69 (step @p60 :rule eq_resolve :premises (@p57 @p59)) % 0.47/0.69 (step @p61 :rule cong :premises (@p60 @p55) :args (@t43)) % 0.47/0.69 (step @p62 :rule cong :premises (@p61) :args ((forall @t11 @t43))) % 0.47/0.69 (step @p63 :rule refl :args (tptp.zero)) % 0.47/0.69 (step @p64 :rule refl :args (@t1)) % 0.47/0.69 (step @p65 :rule eq-symm :args (@t8 tptp.zero)) % 0.47/0.69 (step @p66 :rule refl :args (tptp.ite)) % 0.47/0.69 (step @p67 :rule ho_cong :premises (@p66 @p65)) % 0.47/0.69 (step @p68 :rule ho_cong :premises (@p67 @p64)) % 0.47/0.69 (step @p69 :rule ho_cong :premises (@p68 @p63)) % 0.47/0.69 (step @p70 :rule refl :args (@t9)) % 0.47/0.69 (step @p71 :rule cong :premises (@p70 @p69) :args (@t10)) % 0.47/0.69 (step @p72 :rule cong :premises (@p71) :args (@t12)) % 0.47/0.69 (step @p73 :rule trans :premises (@p72 @p62)) % 0.47/0.69 (step @p74 :rule aci_norm :args ((= @t45 @t44))) % 0.47/0.69 (step @p75 :rule cong :premises (@p74) :args ((forall @t46 @t45))) % 0.47/0.69 (step @p76 :rule quant-var-elim-eq :args ((= (forall @t49 (or (not (= @t15 false)) @t15 @t48)) @t45))) % 0.47/0.69 (step @p77 :rule refl :args (@t48)) % 0.47/0.69 (step @p78 :rule refl :args (@t15)) % 0.47/0.69 (step @p79 :rule bool-eq-false :args (@t15)) % 0.47/0.69 (step @p80 :rule symm :premises (@p79)) % 0.47/0.69 (step @p81 :rule cong :premises (@p80) :args (@t50)) % 0.47/0.69 (step @p82 :rule bool-double-not-elim :args (@t15)) % 0.47/0.69 (step @p83 :rule symm :premises (@p82)) % 0.47/0.69 (step @p84 :rule trans :premises (@p83 @p81)) % 0.47/0.69 (step @p85 :rule nary_cong :premises (@p84 @p78 @p77) :args (@t51)) % 0.47/0.69 (step @p86 :rule aci_norm :args ((= @t52 @t51))) % 0.47/0.69 (step @p87 :rule trans :premises (@p86 @p85)) % 0.47/0.69 (step @p88 :rule cong :premises (@p87) :args (@t53)) % 0.47/0.69 (step @p89 :rule trans :premises (@p88 @p76)) % 0.47/0.69 (step @p90 :rule cong :premises (@p89) :args (@t54)) % 0.47/0.69 (step @p91 :rule quant-merge-prenex :args ((= @t54 @t56))) % 0.47/0.69 (step @p92 :rule symm :premises (@p91)) % 0.47/0.69 (step @p93 :rule quant_var_reordering :args ((= (forall @t19 @t52) @t56))) % 0.47/0.69 (step @p94 :rule trans :premises (@p93 @p92 @p90)) % 0.47/0.69 (step @p95 :rule trans :premises (@p94 @p75)) % 0.47/0.69 (step @p96 :rule refl :args (@t47)) % 0.47/0.69 (step @p97 :rule refl :args (@t16)) % 0.47/0.69 (step @p98 :rule cong :premises (@p97 @p96) :args ((= @t16 @t47))) % 0.47/0.69 (step @p99 :rule symm :premises (@p98)) % 0.47/0.69 (step @p100 :rule eq_resolve :premises (@p97 @p99)) % 0.47/0.69 (step @p101 :rule refl :args (@t13)) % 0.47/0.69 (step @p102 :rule cong :premises (@p101 @p100) :args (@t57)) % 0.47/0.69 (step @p103 :rule nary_cong :premises (@p78 @p102) :args (@t58)) % 0.47/0.69 (step @p104 :rule cong :premises (@p103) :args ((forall @t19 @t58))) % 0.47/0.69 (step @p105 :rule trans :premises (@p104 @p95)) % 0.47/0.69 (step @p106 :rule refl :args (@t57)) % 0.47/0.69 (step @p107 :rule nary_cong :premises (@p82 @p106) :args ((or @t50 @t57))) % 0.47/0.69 (step @p108 :rule bool-impl-elim :args (@t17 @t57)) % 0.47/0.69 (step @p109 :rule trans :premises (@p108 @p107)) % 0.47/0.69 (step @p110 :rule cong :premises (@p109) :args ((forall @t19 (=> @t17 @t57)))) % 0.47/0.69 (step @p111 :rule trans :premises (@p110 @p105)) % 0.47/0.69 (step @p112 :rule eq-symm :args (@t16 @t13)) % 0.47/0.69 (step @p113 :rule refl :args (@t17)) % 0.47/0.69 (step @p114 :rule cong :premises (@p113 @p112) :args (@t18)) % 0.47/0.69 (step @p115 :rule cong :premises (@p114) :args (@t20)) % 0.47/0.69 (step @p116 :rule trans :premises (@p115 @p111)) % 0.47/0.69 (step @p117 :rule aci_norm :args ((= (or false @t59) @t59))) % 0.47/0.69 (step @p118 :rule refl :args (@t59)) % 0.47/0.69 (step @p119 :rule evaluate :args (@t60)) % 0.47/0.69 (step @p120 :rule nary_cong :premises (@p119 @p118) :args (@t61)) % 0.47/0.69 (step @p121 :rule trans :premises (@p120 @p117)) % 0.47/0.69 (step @p122 :rule cong :premises (@p121) :args ((forall @t46 @t61))) % 0.47/0.69 (step @p123 :rule quant-var-elim-eq :args ((= (forall @t49 (or (not (= @t15 true)) @t17 @t62)) @t61))) % 0.47/0.69 (step @p124 :rule refl :args (@t62)) % 0.47/0.69 (step @p125 :rule refl :args (@t17)) % 0.47/0.69 (step @p126 :rule bool-eq-true :args (@t15)) % 0.47/0.69 (step @p127 :rule symm :premises (@p126)) % 0.47/0.69 (step @p128 :rule cong :premises (@p127) :args (@t17)) % 0.47/0.69 (step @p129 :rule nary_cong :premises (@p128 @p125 @p124) :args (@t63)) % 0.47/0.69 (step @p130 :rule aci_norm :args ((= @t64 @t63))) % 0.47/0.69 (step @p131 :rule trans :premises (@p130 @p129)) % 0.47/0.69 (step @p132 :rule cong :premises (@p131) :args (@t65)) % 0.47/0.69 (step @p133 :rule trans :premises (@p132 @p123)) % 0.47/0.69 (step @p134 :rule cong :premises (@p133) :args (@t66)) % 0.47/0.69 (step @p135 :rule quant-merge-prenex :args ((= @t66 @t67))) % 0.47/0.69 (step @p136 :rule symm :premises (@p135)) % 0.47/0.69 (step @p137 :rule quant_var_reordering :args ((= (forall @t19 @t64) @t67))) % 0.47/0.69 (step @p138 :rule trans :premises (@p137 @p136 @p134)) % 0.47/0.69 (step @p139 :rule trans :premises (@p138 @p122)) % 0.47/0.69 (step @p140 :rule refl :args (@t14)) % 0.47/0.69 (step @p141 :rule cong :premises (@p140 @p100) :args (@t68)) % 0.47/0.69 (step @p142 :rule nary_cong :premises (@p125 @p141) :args (@t69)) % 0.47/0.69 (step @p143 :rule cong :premises (@p142) :args ((forall @t19 @t69))) % 0.47/0.69 (step @p144 :rule trans :premises (@p143 @p139)) % 0.47/0.69 (step @p145 :rule bool-impl-elim :args (@t15 @t68)) % 0.47/0.69 (step @p146 :rule cong :premises (@p145) :args ((forall @t19 (=> @t15 @t68)))) % 0.47/0.69 (step @p147 :rule trans :premises (@p146 @p144)) % 0.47/0.69 (step @p148 :rule eq-symm :args (@t16 @t14)) % 0.47/0.69 (step @p149 :rule refl :args (@t15)) % 0.47/0.69 (step @p150 :rule cong :premises (@p149 @p148) :args (@t21)) % 0.47/0.69 (step @p151 :rule cong :premises (@p150) :args (@t22)) % 0.47/0.69 (step @p152 :rule trans :premises (@p151 @p147)) % 0.47/0.69 (step @p153 :rule nary_cong :premises (@p152 @p116 @p73) :args (@t23)) % 0.47/0.69 (step @p154 :rule cong :premises (@p153 @p41) :args (@t24)) % 0.47/0.69 (step @p155 :rule cong :premises (@p154) :args (@t25)) % 0.47/0.69 (step @p156 :rule eq_resolve :premises (@p1 @p155)) % 0.47/0.69 (step @p157 :rule not_implies_elim2 :premises (@p156)) % 0.47/0.69 (step @p158 :rule not_not_elim :premises (@p157)) % 0.47/0.69 (step @p159 :rule aci_norm :args ((= (or false @t76) @t76))) % 0.47/0.69 (step @p160 :rule eq-refl :args (@t73)) % 0.47/0.69 (step @p161 :rule skolem_intro :args (@t74)) % 0.47/0.69 (step @p162 :rule refl :args (@t73)) % 0.47/0.69 (step @p163 :rule cong :premises (@p162 @p161) :args ((= @t73 @t74))) % 0.47/0.69 (step @p164 :rule trans :premises (@p163 @p160)) % 0.47/0.69 (step @p165 :rule true_elim :premises (@p164)) % 0.47/0.69 (step @p166 :rule cong :premises (@p63 @p165) :args (@t77)) % 0.47/0.69 (step @p167 :rule cong :premises (@p166) :args (@t78)) % 0.47/0.69 (step @p168 :rule eq-refl :args (@t26)) % 0.47/0.69 (step @p169 :rule refl :args (@t26)) % 0.47/0.69 (step @p170 :rule cong :premises (@p16 @p169) :args (@t28)) % 0.47/0.69 (step @p171 :rule trans :premises (@p170 @p168)) % 0.47/0.69 (step @p172 :rule cong :premises (@p171) :args (@t79)) % 0.47/0.69 (step @p173 :rule trans :premises (@p172 @p119)) % 0.47/0.69 (step @p174 :rule nary_cong :premises (@p173 @p167) :args (@t80)) % 0.47/0.69 (step @p175 :rule trans :premises (@p174 @p159)) % 0.47/0.69 (step @p176 :rule refl :args (@t81)) % 0.47/0.69 (step @p177 :rule cong :premises (@p176 @p175) :args ((=> @t81 @t80))) % 0.47/0.69 (step @p178 :rule beta-reduce 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:premises (@p192) :args (@t91)) % 0.47/0.69 (step @p194 :rule nary_cong :premises (@p193 @p180) :args (@t92)) % 0.47/0.69 (step @p195 :rule cong :premises (@p176 @p194) :args ((=> @t81 @t92))) % 0.47/0.69 (assume-push @p293 @t81) % 0.47/0.69 (step @p197 :rule instantiate :premises (@p158) :args ((@list @t83))) % 0.47/0.69 (step-pop @p294 :rule scope :premises (@p197)) % 0.47/0.69 (step @p198 :rule process_scope :premises (@p294) :args (@t92)) % 0.47/0.69 (step @p200 :rule eq_resolve :premises (@p198 @p195)) % 0.47/0.69 (step @p201 :rule eq_resolve :premises (@p200 @p177)) % 0.47/0.69 (step @p202 :rule implies_elim :premises (@p201)) % 0.47/0.69 (step @p203 :rule chain_m_resolution :premises (@p202 @p158) :args (@t76 @t93 @t94)) % 0.47/0.69 (step @p204 :rule aci_norm :args ((= (or false @t95) @t95))) % 0.47/0.69 (step @p205 :rule beta-reduce :args ((= @t97 @t26))) % 0.47/0.69 (step @p206 :rule cong :premises (@p63 @p205) :args (@t98)) % 0.47/0.69 (step @p207 :rule cong :premises (@p206) :args (@t99)) % 0.47/0.69 (step @p208 :rule beta-reduce :args ((= @t100 @t26))) % 0.47/0.69 (step @p209 :rule cong :premises (@p169 @p208) :args (@t101)) % 0.47/0.69 (step @p210 :rule trans :premises (@p209 @p168)) % 0.47/0.69 (step @p211 :rule cong :premises (@p210) :args (@t102)) % 0.47/0.69 (step @p212 :rule trans :premises (@p211 @p119)) % 0.47/0.69 (step @p213 :rule nary_cong :premises (@p212 @p207) :args (@t103)) % 0.47/0.69 (step @p214 :rule trans :premises (@p213 @p204)) % 0.47/0.69 (step @p215 :rule cong :premises (@p176 @p214) :args ((=> @t81 @t103))) % 0.47/0.69 (assume-push @p295 @t81) % 0.47/0.69 (step @p217 :rule instantiate :premises (@p158) :args ((@list @t96))) % 0.47/0.69 (step-pop @p296 :rule scope :premises (@p217)) % 0.47/0.69 (step @p218 :rule process_scope :premises (@p296) :args (@t103)) % 0.47/0.69 (step @p220 :rule eq_resolve :premises (@p218 @p215)) % 0.47/0.69 (step @p221 :rule implies_elim :premises (@p220)) % 0.47/0.69 (step @p222 :rule chain_m_resolution :premises (@p221 @p158) :args (@t95 @t93 @t94)) % 0.47/0.69 (step @p223 :rule eq-symm :args (@t104 @t74)) % 0.47/0.69 (step @p224 :rule refl :args (@t74)) % 0.47/0.69 (step @p225 :rule eq-refl :args (@t71)) % 0.47/0.69 (step @p226 :rule skolem_intro :args (@t104)) % 0.47/0.69 (step @p227 :rule refl :args (@t71)) % 0.47/0.69 (step @p228 :rule cong :premises (@p227 @p226) :args ((= @t71 @t104))) % 0.47/0.69 (step @p229 :rule trans :premises (@p228 @p225)) % 0.47/0.69 (step @p230 :rule true_elim :premises (@p229)) % 0.47/0.69 (step @p231 :rule cong :premises (@p230 @p224) :args (@t105)) % 0.47/0.69 (step @p232 :rule trans :premises (@p231 @p223)) % 0.47/0.69 (step @p233 :rule cong :premises (@p16 @p224) :args (@t106)) % 0.47/0.69 (step @p234 :rule refl :args (@t72)) % 0.47/0.69 (step @p235 :rule cong :premises (@p234 @p233 @p232) :args ((ite @t72 @t106 @t105))) % 0.47/0.69 (step @p236 :rule eq-symm :args (@t74 @t71)) % 0.47/0.69 (step @p237 :rule eq-symm :args (@t74 @t1)) % 0.47/0.69 (step @p238 :rule cong :premises (@p234 @p237 @p236) :args ((ite @t72 (= @t74 @t1) (= @t74 @t71)))) % 0.47/0.69 (step @p239 :rule trans :premises (@p238 @p235)) % 0.47/0.69 (step @p240 :rule cong :premises (@p165 @p227) :args (@t107)) % 0.47/0.69 (step @p241 :rule cong :premises (@p165 @p64) :args (@t108)) % 0.47/0.69 (step @p242 :rule cong :premises (@p234 @p241 @p240) :args ((ite @t72 @t108 @t107))) % 0.47/0.69 (step @p243 :rule ite_eq :args (@t73)) % 0.47/0.69 (step @p244 :rule eq_resolve :premises (@p243 @p242)) % 0.47/0.69 (step @p245 :rule eq_resolve :premises (@p244 @p239)) % 0.47/0.69 (step @p246 :rule ite_elim2 :premises (@p245)) % 0.47/0.69 (step @p247 :rule chain_m_resolution :premises (@p246 @p222) :args (@t109 (@list true) (@list @t72))) % 0.47/0.69 (step @p248 :rule ite-true-cond :args (@t110 (= @t111 @t104))) % 0.47/0.69 (step @p249 :rule refl :args (@t104)) % 0.47/0.69 (step @p250 :rule refl :args ((tptp.s @t1))) % 0.47/0.69 (step @p251 :rule cong :premises (@p4) :args (@t111)) % 0.47/0.69 (step @p252 :rule trans :premises (@p251 @p250)) % 0.47/0.69 (step @p253 :rule refl :args (tptp.s)) % 0.47/0.69 (step @p254 :rule ho_cong :premises (@p253 @p4)) % 0.47/0.69 (step @p255 :rule cong :premises (@p254 @p252) :args ((= @t70 @t111))) % 0.47/0.69 (step @p256 :rule symm :premises (@p255)) % 0.47/0.69 (step @p257 :rule refl :args ((_ tptp.s @t1))) % 0.47/0.69 (step @p258 :rule eq_resolve :premises (@p257 @p256)) % 0.47/0.69 (step @p259 :rule cong :premises (@p258 @p249) :args (@t112)) % 0.47/0.69 (step @p260 :rule refl :args (@t110)) % 0.47/0.69 (step @p261 :rule cong :premises (@p171 @p260 @p259) :args ((ite @t28 @t110 @t112))) % 0.47/0.70 (step @p262 :rule trans :premises (@p261 @p248)) % 0.47/0.70 (step @p263 :rule eq-symm :args (@t104 @t70)) % 0.47/0.70 (step @p264 :rule eq-symm :args (@t104 tptp.zero)) % 0.47/0.70 (step @p265 :rule refl :args (@t28)) % 0.47/0.70 (step @p266 :rule cong :premises (@p265 @p264 @p263) :args ((ite @t28 (= @t104 tptp.zero) (= @t104 @t70)))) % 0.47/0.70 (step @p267 :rule trans :premises (@p266 @p262)) % 0.47/0.70 (step @p268 :rule cong :premises (@p230 @p183) :args (@t113)) % 0.47/0.70 (step @p269 :rule cong :premises (@p230 @p63) :args (@t114)) % 0.47/0.70 (step @p270 :rule cong :premises (@p265 @p269 @p268) :args ((ite @t28 @t114 @t113))) % 0.47/0.70 (step @p271 :rule ite_eq :args (@t71)) % 0.47/0.70 (step @p272 :rule eq_resolve :premises (@p271 @p270)) % 0.47/0.70 (step @p273 :rule eq_resolve :premises (@p272 @p267)) % 0.47/0.70 (step @p274 :rule refl :args (@t115)) % 0.47/0.70 (step @p275 :rule refl :args (@t116)) % 0.47/0.70 (step @p276 :rule bool-double-not-elim :args (@t75)) % 0.47/0.70 (step @p277 :rule nary_cong :premises (@p276 @p275 @p274) :args ((or (not @t76) @t116 @t115))) % 0.47/0.70 (assume-push @p297 @t76) % 0.47/0.70 (assume-push @p298 @t109) % 0.47/0.70 (step @p280 :rule false_intro :premises (@p203)) % 0.47/0.70 (step @p281 :rule symm :premises (@p247)) % 0.47/0.70 (step @p282 :rule cong :premises (@p63 @p281) :args (@t110)) % 0.47/0.70 (step @p283 :rule trans :premises (@p282 @p280)) % 0.47/0.70 (step @p284 :rule false_elim :premises (@p283)) % 0.47/0.70 (step-pop @p299 :rule scope :premises (@p284)) % 0.47/0.70 (step-pop @p300 :rule scope :premises (@p299)) % 0.47/0.70 (step @p285 :rule process_scope :premises (@p300) :args (@t115)) % 0.47/0.70 (step @p288 :rule implies_elim :premises (@p285)) % 0.47/0.70 (step @p289 :rule cnf_and_neg :args (@t117)) % 0.47/0.70 (step @p290 :rule resolution :premises (@p289 @p288) :args (true @t117)) % 0.47/0.70 (step @p291 :rule eq_resolve :premises (@p290 @p277)) % 0.47/0.70 (step @p292 false :rule chain_m_resolution :premises (@p291 @p273 @p247 @p203) :args (false (@list false false true) (@list @t110 @t109 @t75))) % 0.47/0.70 ) % 0.47/0.70 % SZS output end Proof % 0.47/0.70 % cvc5 exiting %------------------------------------------------------------------------------