%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN025^3 : 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 : n010.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 0.51s 0.72s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUN025^3 : 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 % 0.14/0.34 % Computer : n010.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 12:37:25 EDT 2026 % 0.14/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 0.51/0.72 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.51/0.72 % SZS status Theorem % 0.51/0.72 % SZS output start Proof % 0.51/0.72 ( % 0.51/0.72 (declare-sort $$unsorted 0) % 0.51/0.72 (declare-const tptp.h (-> $$unsorted $$unsorted)) % 0.51/0.72 (declare-const tptp.ite (-> Bool $$unsorted $$unsorted $$unsorted)) % 0.51/0.72 (declare-const tptp.s (-> $$unsorted $$unsorted)) % 0.51/0.72 (declare-const tptp.zero $$unsorted) % 0.51/0.72 (define @t1 () (_ tptp.s tptp.zero)) % 0.51/0.72 (define @t2 () (_ tptp.s @t1)) % 0.51/0.72 (define @t3 () (@var "H" (-> $$unsorted $$unsorted))) % 0.51/0.72 (define @t4 () (_ @t3 @t2)) % 0.51/0.72 (define @t5 () (_ @t3 @t1)) % 0.51/0.72 (define @t6 () (_ @t3 tptp.zero)) % 0.51/0.72 (define @t7 () (and (= @t6 @t1) (= @t5 tptp.zero) (= @t4 @t1))) % 0.51/0.72 (define @t8 () (@list @t3)) % 0.51/0.72 (define @t9 () (exists @t8 @t7)) % 0.51/0.72 (define @t10 () (@var "X" $$unsorted)) % 0.51/0.72 (define @t11 () (= @t10 @t1)) % 0.51/0.72 (define @t12 () (_ (_ (_ tptp.ite @t11) tptp.zero) @t1)) % 0.51/0.72 (define @t13 () (_ tptp.h @t10)) % 0.51/0.72 (define @t14 () (= @t13 (_ (_ (_ tptp.ite (= @t10 tptp.zero)) @t1) @t12))) % 0.51/0.72 (define @t15 () (@list @t10)) % 0.51/0.72 (define @t16 () (forall @t15 @t14)) % 0.51/0.72 (define @t17 () (_ tptp.s @t10)) % 0.51/0.72 (define @t18 () (not (= @t17 @t10))) % 0.51/0.72 (define @t19 () (forall @t15 @t18)) % 0.51/0.72 (define @t20 () (not (= @t17 tptp.zero))) % 0.51/0.72 (define @t21 () (forall @t15 @t20)) % 0.51/0.72 (define @t22 () (@var "V" $$unsorted)) % 0.51/0.72 (define @t23 () (@var "U" $$unsorted)) % 0.51/0.72 (define @t24 () (@var "X100" Bool)) % 0.51/0.72 (define @t25 () (_ (_ (_ tptp.ite @t24) @t23) @t22)) % 0.51/0.72 (define @t26 () (not @t24)) % 0.51/0.72 (define @t27 () (=> @t26 (= @t25 @t22))) % 0.51/0.72 (define @t28 () (@list @t24 @t23 @t22)) % 0.51/0.72 (define @t29 () (forall @t28 @t27)) % 0.51/0.72 (define @t30 () (=> @t24 (= @t25 @t23))) % 0.51/0.72 (define @t31 () (forall @t28 @t30)) % 0.51/0.72 (define @t32 () (and @t31 @t29 @t21 @t19 @t16)) % 0.51/0.72 (define @t33 () (=> @t32 @t9)) % 0.51/0.72 (define @t34 () (not @t33)) % 0.51/0.72 (define @t35 () (tptp.s tptp.zero)) % 0.51/0.72 (define @t36 () (tptp.s @t35)) % 0.51/0.72 (define @t37 () (_ @t3 @t36)) % 0.51/0.72 (define @t38 () (_ tptp.s @t35)) % 0.51/0.72 (define @t39 () (= @t38 @t36)) % 0.51/0.72 (define @t40 () (= @t1 @t35)) % 0.51/0.72 (define @t41 () (= @t1 @t4)) % 0.51/0.72 (define @t42 () (not @t41)) % 0.51/0.72 (define @t43 () (_ @t3 @t35)) % 0.51/0.72 (define @t44 () (= tptp.zero @t5)) % 0.51/0.72 (define @t45 () (not @t44)) % 0.51/0.72 (define @t46 () (_ @t3 tptp.zero)) % 0.51/0.72 (define @t47 () (= @t1 @t6)) % 0.51/0.72 (define @t48 () (not @t47)) % 0.51/0.72 (define @t49 () (or @t48 @t45 @t42)) % 0.51/0.72 (define @t50 () (and @t47 @t44 @t41)) % 0.51/0.72 (define @t51 () (forall @t8 (not @t50))) % 0.51/0.72 (define @t52 () (not @t51)) % 0.51/0.72 (define @t53 () (= tptp.zero @t10)) % 0.51/0.72 (define @t54 () (= @t10 @t35)) % 0.51/0.72 (define @t55 () (tptp.ite @t54 tptp.zero @t35)) % 0.51/0.72 (define @t56 () (tptp.ite @t53 @t35 @t55)) % 0.51/0.72 (define @t57 () (_ tptp.ite @t53)) % 0.51/0.72 (define @t58 () (_ (_ @t57 @t1) @t12)) % 0.51/0.72 (define @t59 () (tptp.h @t10)) % 0.51/0.72 (define @t60 () (= @t13 @t58)) % 0.51/0.72 (define @t61 () (tptp.s @t10)) % 0.51/0.72 (define @t62 () (= @t10 @t17)) % 0.51/0.72 (define @t63 () (not @t62)) % 0.51/0.72 (define @t64 () (= tptp.zero @t17)) % 0.51/0.72 (define @t65 () (not @t64)) % 0.51/0.72 (define @t66 () (= @t22 (tptp.ite false @t23 @t22))) % 0.51/0.72 (define @t67 () (or false @t66)) % 0.51/0.72 (define @t68 () (@list @t23 @t22)) % 0.51/0.72 (define @t69 () (tptp.ite @t24 @t23 @t22)) % 0.51/0.72 (define @t70 () (= @t22 @t69)) % 0.51/0.72 (define @t71 () (@list @t24)) % 0.51/0.72 (define @t72 () (not @t26)) % 0.51/0.72 (define @t73 () (or @t24 @t24 @t70)) % 0.51/0.72 (define @t74 () (or @t24 @t70)) % 0.51/0.72 (define @t75 () (forall @t71 @t74)) % 0.51/0.72 (define @t76 () (forall @t68 @t75)) % 0.51/0.72 (define @t77 () (@list @t23 @t22 @t24)) % 0.51/0.72 (define @t78 () (forall @t77 @t74)) % 0.51/0.72 (define @t79 () (= @t22 @t25)) % 0.51/0.72 (define @t80 () (or @t24 @t79)) % 0.51/0.72 (define @t81 () (= @t23 (tptp.ite true @t23 @t22))) % 0.51/0.72 (define @t82 () (not true)) % 0.51/0.72 (define @t83 () (or @t82 @t81)) % 0.51/0.72 (define @t84 () (= @t23 @t69)) % 0.51/0.72 (define @t85 () (or @t26 @t26 @t84)) % 0.51/0.72 (define @t86 () (or @t26 @t84)) % 0.51/0.72 (define @t87 () (forall @t71 @t86)) % 0.51/0.72 (define @t88 () (forall @t68 @t87)) % 0.51/0.72 (define @t89 () (forall @t77 @t86)) % 0.51/0.72 (define @t90 () (= @t23 @t25)) % 0.51/0.72 (define @t91 () (or @t26 @t90)) % 0.51/0.72 (define @t92 () (@list @t35)) % 0.51/0.72 (define @t93 () (ite @t39 @t1 @t38)) % 0.51/0.72 (define @t94 () (= tptp.zero @t36)) % 0.51/0.72 (define @t95 () (ite @t94 @t1 @t93)) % 0.51/0.72 (define @t96 () (@purify @t95)) % 0.51/0.72 (define @t97 () (= @t1 @t36)) % 0.51/0.72 (define @t98 () (ite @t97 tptp.zero @t95)) % 0.51/0.72 (define @t99 () (@purify @t98)) % 0.51/0.72 (define @t100 () (= @t95 @t99)) % 0.51/0.72 (define @t101 () (= tptp.zero @t99)) % 0.51/0.72 (define @t102 () (= @t98 @t95)) % 0.51/0.72 (define @t103 () (= @t98 tptp.zero)) % 0.51/0.72 (define @t104 () (= @t99 @t96)) % 0.51/0.72 (define @t105 () (@list true)) % 0.51/0.72 (define @t106 () (@purify @t93)) % 0.51/0.72 (define @t107 () (= @t93 @t96)) % 0.51/0.72 (define @t108 () (= @t1 @t96)) % 0.51/0.72 (define @t109 () (= @t95 @t93)) % 0.51/0.72 (define @t110 () (= @t95 @t1)) % 0.51/0.72 (define @t111 () (= @t96 @t106)) % 0.51/0.72 (define @t112 () (= @t35 @t106)) % 0.51/0.72 (define @t113 () (= @t38 @t106)) % 0.51/0.72 (define @t114 () (= @t1 @t106)) % 0.51/0.72 (define @t115 () (= @t93 @t38)) % 0.51/0.72 (define @t116 () (= @t93 @t1)) % 0.51/0.72 (define @t117 () (= @t35 @t98)) % 0.51/0.72 (define @t118 () (not @t117)) % 0.51/0.72 (define @t119 () (= tptp.zero @t35)) % 0.51/0.72 (define @t120 () (ite @t119 @t1 (ite (= @t35 @t38) @t1 @t38))) % 0.51/0.72 (define @t121 () (ite @t40 tptp.zero @t120)) % 0.51/0.72 (define @t122 () (@purify @t121)) % 0.51/0.72 (define @t123 () (= tptp.zero @t121)) % 0.51/0.72 (define @t124 () (not @t123)) % 0.51/0.72 (define @t125 () (= tptp.zero @t1)) % 0.51/0.72 (define @t126 () (ite @t125 tptp.zero @t1)) % 0.51/0.72 (define @t127 () (@purify @t126)) % 0.51/0.72 (define @t128 () (= @t35 @t126)) % 0.51/0.72 (define @t129 () (not @t128)) % 0.51/0.72 (define @t130 () (or @t129 @t124 @t118)) % 0.51/0.72 (define @t131 () (forall @t8 (or (not (= @t35 @t46)) (not (= tptp.zero @t43)) (not (= @t35 @t37))))) % 0.51/0.72 (define @t132 () (@var "BOUND_VARIABLE_43315" $$unsorted)) % 0.51/0.72 (define @t133 () (lambda (@list @t132) (ite (= @t1 @t132) tptp.zero (ite (= tptp.zero @t132) @t1 (ite (= @t38 @t132) @t1 @t38))))) % 0.51/0.72 (define @t134 () (_ @t133 @t36)) % 0.51/0.72 (define @t135 () (= @t35 @t134)) % 0.51/0.72 (define @t136 () (not @t135)) % 0.51/0.72 (define @t137 () (ite (= @t38 @t35) @t1 @t38)) % 0.51/0.72 (define @t138 () (ite @t119 @t1 @t137)) % 0.51/0.72 (define @t139 () (ite @t40 tptp.zero @t138)) % 0.51/0.72 (define @t140 () (_ @t133 @t35)) % 0.51/0.72 (define @t141 () (= tptp.zero @t140)) % 0.51/0.72 (define @t142 () (not @t141)) % 0.51/0.72 (define @t143 () (ite (= @t38 tptp.zero) @t1 @t38)) % 0.51/0.72 (define @t144 () (ite (= tptp.zero tptp.zero) @t1 @t143)) % 0.51/0.72 (define @t145 () (ite (= @t1 tptp.zero) tptp.zero @t144)) % 0.51/0.72 (define @t146 () (_ @t133 tptp.zero)) % 0.51/0.72 (define @t147 () (= @t35 @t146)) % 0.51/0.72 (define @t148 () (not @t147)) % 0.51/0.72 (define @t149 () (or @t148 @t142 @t136)) % 0.51/0.72 (define @t150 () (= @t35 @t99)) % 0.51/0.72 (define @t151 () (not @t150)) % 0.51/0.72 (define @t152 () (= tptp.zero @t122)) % 0.51/0.72 (define @t153 () (not @t152)) % 0.51/0.72 (define @t154 () (= @t35 @t127)) % 0.51/0.72 (define @t155 () (not @t154)) % 0.51/0.72 (define @t156 () (or @t155 @t153 @t151)) % 0.51/0.72 (define @t157 () (= @t1 @t127)) % 0.51/0.72 (define @t158 () (= tptp.zero @t127)) % 0.51/0.72 (define @t159 () (= @t126 @t1)) % 0.51/0.72 (define @t160 () (= @t126 tptp.zero)) % 0.51/0.72 (define @t161 () (@purify @t120)) % 0.51/0.72 (define @t162 () (= @t120 @t122)) % 0.51/0.72 (define @t163 () (= @t121 @t120)) % 0.51/0.72 (define @t164 () (= @t121 tptp.zero)) % 0.51/0.72 (define @t165 () (and @t104 @t111 @t112)) % 0.51/0.72 (assume @p1 @t34) % 0.51/0.72 (assume @p2 true) % 0.51/0.72 (step @p3 :rule refl :args ((_ @t3 @t2))) % 0.51/0.72 (step @p4 :rule refl :args ((tptp.s @t1))) % 0.51/0.72 (step @p5 :rule refl :args (@t35)) % 0.51/0.72 (step @p6 :rule cong :premises (@p5) :args (@t36)) % 0.51/0.72 (step @p7 :rule trans :premises (@p6 @p4)) % 0.51/0.72 (step @p8 :rule cong :premises (@p7) :args (@t37)) % 0.51/0.72 (step @p9 :rule trans :premises (@p8 @p3)) % 0.51/0.72 (step @p10 :rule refl :args (@t3)) % 0.51/0.72 (step @p11 :rule ho_cong :premises (@p10 @p7)) % 0.51/0.72 (step @p12 :rule cong :premises (@p11 @p9) :args ((= (_ @t3 @t36) @t37))) % 0.51/0.72 (step @p13 :rule symm :premises (@p12)) % 0.51/0.72 (step @p14 :rule refl :args (@t4)) % 0.51/0.72 (step @p15 :rule eq_resolve :premises (@p14 @p13)) % 0.51/0.72 (step @p16 :rule refl :args (tptp.s)) % 0.51/0.72 (step @p17 :rule ho_cong :premises (@p16 @p5)) % 0.51/0.72 (step @p18 :rule cong :premises (@p17 @p7) :args (@t39)) % 0.51/0.72 (step @p19 :rule symm :premises (@p18)) % 0.51/0.72 (step @p20 :rule refl :args (@t2)) % 0.51/0.72 (step @p21 :rule eq_resolve :premises (@p20 @p19)) % 0.51/0.72 (step @p22 :rule refl :args (@t1)) % 0.51/0.72 (step @p23 :rule cong :premises (@p22 @p5) :args (@t40)) % 0.51/0.72 (step @p24 :rule symm :premises (@p23)) % 0.51/0.72 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.51/0.72 (step @p26 :rule ho_cong :premises (@p16 @p25)) % 0.51/0.72 (step @p27 :rule trans :premises (@p26 @p21)) % 0.51/0.72 (step @p28 :rule ho_cong :premises (@p10 @p27)) % 0.51/0.72 (step @p29 :rule trans :premises (@p28 @p15)) % 0.51/0.72 (step @p30 :rule cong :premises (@p25 @p29) :args (@t41)) % 0.51/0.72 (step @p31 :rule cong :premises (@p30) :args (@t42)) % 0.51/0.72 (step @p32 :rule refl :args ((_ @t3 @t1))) % 0.51/0.72 (step @p33 :rule cong :premises (@p5) :args (@t43)) % 0.51/0.72 (step @p34 :rule trans :premises (@p33 @p32)) % 0.51/0.72 (step @p35 :rule ho_cong :premises (@p10 @p5)) % 0.51/0.72 (step @p36 :rule cong :premises (@p35 @p34) :args ((= (_ @t3 @t35) @t43))) % 0.51/0.72 (step @p37 :rule symm :premises (@p36)) % 0.51/0.72 (step @p38 :rule refl :args (@t5)) % 0.51/0.72 (step @p39 :rule eq_resolve :premises (@p38 @p37)) % 0.51/0.72 (step @p40 :rule ho_cong :premises (@p10 @p25)) % 0.51/0.72 (step @p41 :rule trans :premises (@p40 @p39)) % 0.51/0.72 (step @p42 :rule refl :args (tptp.zero)) % 0.51/0.72 (step @p43 :rule cong :premises (@p42 @p41) :args (@t44)) % 0.51/0.72 (step @p44 :rule cong :premises (@p43) :args (@t45)) % 0.51/0.72 (step @p45 :rule refl :args (@t46)) % 0.51/0.72 (step @p46 :rule refl :args (@t6)) % 0.51/0.72 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t6 @t46))) % 0.51/0.72 (step @p48 :rule symm :premises (@p47)) % 0.51/0.72 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.51/0.72 (step @p50 :rule cong :premises (@p25 @p49) :args (@t47)) % 0.51/0.72 (step @p51 :rule cong :premises (@p50) :args (@t48)) % 0.51/0.72 (step @p52 :rule nary_cong :premises (@p51 @p44 @p31) :args (@t49)) % 0.51/0.72 (step @p53 :rule cong :premises (@p52) :args ((forall @t8 @t49))) % 0.51/0.72 (step @p54 :rule aci_norm :args ((= (or @t48 (or @t45 @t42)) @t49))) % 0.51/0.72 (step @p55 :rule bool-and-de-morgan :args (@t44 @t41 true)) % 0.51/0.72 (step @p56 :rule refl :args (@t48)) % 0.51/0.72 (step @p57 :rule nary_cong :premises (@p56 @p55) :args ((or @t48 (not (and @t44 @t41))))) % 0.51/0.72 (step @p58 :rule bool-and-de-morgan :args (@t47 @t44 (and @t41))) % 0.51/0.72 (step @p59 :rule trans :premises (@p58 @p57)) % 0.51/0.72 (step @p60 :rule trans :premises (@p59 @p54)) % 0.51/0.72 (step @p61 :rule cong :premises (@p60) :args (@t51)) % 0.51/0.72 (step @p62 :rule trans :premises (@p61 @p53)) % 0.51/0.72 (step @p63 :rule cong :premises (@p62) :args (@t52)) % 0.51/0.72 (step @p64 :rule exists-elim :args ((= (exists @t8 @t50) @t52))) % 0.51/0.72 (step @p65 :rule trans :premises (@p64 @p63)) % 0.51/0.72 (step @p66 :rule eq-symm :args (@t4 @t1)) % 0.51/0.72 (step @p67 :rule eq-symm :args (@t5 tptp.zero)) % 0.51/0.72 (step @p68 :rule eq-symm :args (@t6 @t1)) % 0.51/0.72 (step @p69 :rule nary_cong :premises (@p68 @p67 @p66) :args (@t7)) % 0.51/0.72 (step @p70 :rule cong :premises (@p69) :args (@t9)) % 0.51/0.72 (step @p71 :rule trans :premises (@p70 @p65)) % 0.51/0.72 (step @p72 :rule refl :args ((tptp.ite @t53 @t1 @t12))) % 0.51/0.72 (step @p73 :rule refl :args ((tptp.ite @t11 tptp.zero @t1))) % 0.51/0.72 (step @p74 :rule refl :args (@t10)) % 0.51/0.72 (step @p75 :rule cong :premises (@p74 @p5) :args (@t54)) % 0.51/0.72 (step @p76 :rule cong :premises (@p75 @p42 @p5) :args (@t55)) % 0.51/0.72 (step @p77 :rule trans :premises (@p76 @p73)) % 0.51/0.72 (step @p78 :rule refl :args (@t53)) % 0.51/0.72 (step @p79 :rule cong :premises (@p78 @p5 @p77) :args (@t56)) % 0.51/0.72 (step @p80 :rule trans :premises (@p79 @p72)) % 0.51/0.72 (step @p81 :rule refl :args (@t57)) % 0.51/0.72 (step @p82 :rule ho_cong :premises (@p81 @p5)) % 0.51/0.72 (step @p83 :rule ho_cong :premises (@p82 @p77)) % 0.51/0.72 (step @p84 :rule cong :premises (@p83 @p80) :args ((= (_ (_ @t57 @t35) @t55) @t56))) % 0.51/0.72 (step @p85 :rule symm :premises (@p84)) % 0.51/0.72 (step @p86 :rule refl :args (@t58)) % 0.51/0.72 (step @p87 :rule eq_resolve :premises (@p86 @p85)) % 0.51/0.72 (step @p88 :rule refl :args (tptp.ite)) % 0.51/0.72 (step @p89 :rule ho_cong :premises (@p88 @p75)) % 0.51/0.72 (step @p90 :rule ho_cong :premises (@p89 @p42)) % 0.51/0.72 (step @p91 :rule ho_cong :premises (@p90 @p5)) % 0.51/0.72 (step @p92 :rule cong :premises (@p91 @p77) :args ((= (_ (_ (_ tptp.ite @t54) tptp.zero) @t35) @t55))) % 0.51/0.72 (step @p93 :rule symm :premises (@p92)) % 0.51/0.72 (step @p94 :rule refl :args (@t12)) % 0.51/0.72 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 0.51/0.72 (step @p96 :rule cong :premises (@p74 @p25) :args (@t11)) % 0.51/0.72 (step @p97 :rule ho_cong :premises (@p88 @p96)) % 0.51/0.72 (step @p98 :rule ho_cong :premises (@p97 @p42)) % 0.51/0.72 (step @p99 :rule ho_cong :premises (@p98 @p25)) % 0.51/0.72 (step @p100 :rule trans :premises (@p99 @p95)) % 0.51/0.72 (step @p101 :rule ho_cong :premises (@p81 @p25)) % 0.51/0.72 (step @p102 :rule ho_cong :premises (@p101 @p100)) % 0.51/0.72 (step @p103 :rule trans :premises (@p102 @p87)) % 0.51/0.72 (step @p104 :rule refl :args (@t59)) % 0.51/0.72 (step @p105 :rule refl :args (@t13)) % 0.51/0.72 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t13 @t59))) % 0.51/0.72 (step @p107 :rule symm :premises (@p106)) % 0.51/0.72 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.51/0.72 (step @p109 :rule cong :premises (@p108 @p103) :args (@t60)) % 0.51/0.72 (step @p110 :rule cong :premises (@p109) :args ((forall @t15 @t60))) % 0.51/0.72 (step @p111 :rule refl :args 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(step @p323 :rule skolem_intro :args (@t127)) % 0.51/0.72 (step @p324 :rule refl :args (@t126)) % 0.51/0.72 (step @p325 :rule cong :premises (@p324 @p323) :args ((= @t126 @t127))) % 0.51/0.72 (step @p326 :rule trans :premises (@p325 @p322)) % 0.51/0.72 (step @p327 :rule true_elim :premises (@p326)) % 0.51/0.72 (step @p328 :rule cong :premises (@p311 @p327) :args (@t128)) % 0.51/0.72 (step @p329 :rule cong :premises (@p328) :args (@t129)) % 0.51/0.72 (step @p330 :rule nary_cong :premises (@p329 @p321 @p313) :args (@t130)) % 0.51/0.72 (step @p331 :rule refl :args (@t131)) % 0.51/0.72 (step @p332 :rule cong :premises (@p331 @p330) :args ((=> @t131 @t130))) % 0.51/0.72 (step @p333 :rule beta-reduce :args ((= @t134 @t98))) % 0.51/0.72 (step @p334 :rule cong :premises (@p311 @p333) :args (@t135)) % 0.51/0.72 (step @p335 :rule cong :premises (@p334) :args (@t136)) % 0.51/0.72 (step @p336 :rule eq-symm :args (@t38 @t35)) % 0.51/0.72 (step @p337 :rule cong :premises (@p336 @p112 @p302) :args (@t137)) % 0.51/0.72 (step @p338 :rule refl :args (@t119)) % 0.51/0.72 (step @p339 :rule cong :premises (@p338 @p112 @p337) :args (@t138)) % 0.51/0.72 (step @p340 :rule refl :args (@t40)) % 0.51/0.72 (step @p341 :rule cong :premises (@p340 @p253 @p339) :args (@t139)) % 0.51/0.72 (step @p342 :rule beta-reduce :args ((= @t140 @t139))) % 0.51/0.72 (step @p343 :rule trans :premises (@p342 @p341)) % 0.51/0.72 (step @p344 :rule cong :premises (@p253 @p343) :args (@t141)) % 0.51/0.72 (step @p345 :rule cong :premises (@p344) :args (@t142)) % 0.51/0.72 (step @p346 :rule ite-true-cond :args (@t1 (ite (= tptp.zero @t38) @t1 @t38))) % 0.51/0.72 (step @p347 :rule eq-symm :args (@t38 tptp.zero)) % 0.51/0.72 (step @p348 :rule cong :premises (@p347 @p112 @p302) :args (@t143)) % 0.51/0.72 (step @p349 :rule eq-refl :args (tptp.zero)) % 0.51/0.72 (step @p350 :rule cong :premises (@p349 @p112 @p348) :args (@t144)) % 0.51/0.72 (step @p351 :rule trans :premises (@p350 @p346)) % 0.51/0.72 (step @p352 :rule eq-symm :args (@t1 tptp.zero)) % 0.51/0.72 (step @p353 :rule cong :premises (@p352 @p253 @p351) :args (@t145)) % 0.51/0.72 (step @p354 :rule beta-reduce :args ((= @t146 @t145))) % 0.51/0.72 (step @p355 :rule trans :premises (@p354 @p353)) % 0.51/0.72 (step @p356 :rule cong :premises (@p311 @p355) :args (@t147)) % 0.51/0.72 (step @p357 :rule cong :premises (@p356) :args (@t148)) % 0.51/0.72 (step @p358 :rule nary_cong :premises (@p357 @p345 @p335) :args (@t149)) % 0.51/0.72 (step @p359 :rule cong :premises (@p331 @p358) :args ((=> @t131 @t149))) % 0.51/0.72 (assume-push @p432 @t131) % 0.51/0.72 (step @p361 :rule instantiate :premises (@p310) :args ((@list @t133))) % 0.51/0.72 (step-pop @p433 :rule scope :premises (@p361)) % 0.51/0.72 (step @p362 :rule process_scope :premises (@p433) :args (@t149)) % 0.51/0.72 (step @p364 :rule eq_resolve :premises (@p362 @p359)) % 0.51/0.72 (step @p365 :rule eq_resolve :premises (@p364 @p332)) % 0.51/0.72 (step @p366 :rule implies_elim :premises (@p365)) % 0.51/0.72 (step @p367 :rule chain_m_resolution :premises (@p366 @p310) :args (@t156 (@list false) (@list @t131))) % 0.51/0.72 (step @p368 :rule instantiate :premises (@p261) :args ((@list tptp.zero))) % 0.51/0.72 (step @p369 :rule refl :args (@t127)) % 0.51/0.72 (step @p370 :rule cong :premises (@p25 @p369) :args (@t157)) % 0.51/0.72 (step @p371 :rule refl :args (@t158)) % 0.51/0.72 (step @p372 :rule cong :premises (@p253 @p25) :args (@t125)) % 0.51/0.72 (step @p373 :rule cong :premises (@p372 @p371 @p370) :args ((ite @t125 @t158 @t157))) % 0.51/0.72 (step @p374 :rule eq-symm :args (@t127 @t1)) % 0.51/0.72 (step @p375 :rule eq-symm :args (@t127 tptp.zero)) % 0.51/0.72 (step @p376 :rule refl :args (@t125)) % 0.51/0.72 (step @p377 :rule cong :premises (@p376 @p375 @p374) :args ((ite @t125 (= @t127 tptp.zero) (= @t127 @t1)))) % 0.51/0.72 (step @p378 :rule trans :premises (@p377 @p373)) % 0.51/0.72 (step @p379 :rule cong :premises (@p327 @p112) :args (@t159)) % 0.51/0.72 (step @p380 :rule cong :premises (@p327 @p253) :args (@t160)) % 0.51/0.72 (step @p381 :rule cong :premises (@p376 @p380 @p379) :args ((ite @t125 @t160 @t159))) % 0.51/0.72 (step @p382 :rule ite_eq :args (@t126)) % 0.51/0.72 (step @p383 :rule eq_resolve :premises (@p382 @p381)) % 0.51/0.72 (step @p384 :rule eq_resolve :premises (@p383 @p378)) % 0.51/0.72 (step @p385 :rule ite_elim2 :premises (@p384)) % 0.51/0.72 (step @p386 :rule chain_m_resolution :premises (@p385 @p368) :args (@t154 @t105 (@list @t119))) % 0.51/0.72 (step @p387 :rule ite-true-cond :args (@t152 (= @t122 @t161))) % 0.51/0.72 (step @p388 :rule eq-symm :args (@t161 @t122)) % 0.51/0.72 (step @p389 :rule refl :args (@t122)) % 0.51/0.72 (step @p390 :rule eq-refl :args (@t120)) % 0.51/0.72 (step @p391 :rule skolem_intro :args (@t161)) % 0.51/0.72 (step @p392 :rule refl :args (@t120)) % 0.51/0.72 (step @p393 :rule cong :premises (@p392 @p391) :args ((= @t120 @t161))) % 0.51/0.72 (step @p394 :rule trans :premises (@p393 @p390)) % 0.51/0.72 (step @p395 :rule true_elim :premises (@p394)) % 0.51/0.72 (step @p396 :rule cong :premises (@p395 @p389) :args (@t162)) % 0.51/0.72 (step @p397 :rule trans :premises (@p396 @p388)) % 0.51/0.72 (step @p398 :rule refl :args (@t152)) % 0.51/0.72 (step @p399 :rule eq-refl :args (@t35)) % 0.51/0.72 (step @p400 :rule cong :premises (@p25 @p311) :args (@t40)) % 0.51/0.72 (step @p401 :rule trans :premises (@p400 @p399)) % 0.51/0.72 (step @p402 :rule cong :premises (@p401 @p398 @p397) :args ((ite @t40 @t152 @t162))) % 0.51/0.72 (step @p403 :rule trans :premises (@p402 @p387)) % 0.51/0.72 (step @p404 :rule eq-symm :args (@t122 @t120)) % 0.51/0.72 (step @p405 :rule eq-symm :args (@t122 tptp.zero)) % 0.51/0.72 (step @p406 :rule cong :premises (@p340 @p405 @p404) :args ((ite @t40 (= @t122 tptp.zero) (= @t122 @t120)))) % 0.51/0.72 (step @p407 :rule trans :premises (@p406 @p403)) % 0.51/0.72 (step @p408 :rule cong :premises (@p319 @p392) :args (@t163)) % 0.51/0.72 (step @p409 :rule cong :premises (@p319 @p253) :args (@t164)) % 0.51/0.72 (step @p410 :rule cong :premises (@p340 @p409 @p408) :args ((ite @t40 @t164 @t163))) % 0.51/0.72 (step @p411 :rule ite_eq :args (@t121)) % 0.51/0.72 (step @p412 :rule eq_resolve :premises (@p411 @p410)) % 0.51/0.72 (step @p413 :rule eq_resolve :premises (@p412 @p407)) % 0.51/0.72 (step @p414 :rule cnf_or_pos :args (@t156)) % 0.51/0.73 (step @p415 :rule reordering :premises (@p414) :args ((or @t151 @t153 @t155 (not @t156)))) % 0.51/0.73 (step @p416 :rule chain_m_resolution :premises (@p415 @p413 @p386 @p367) :args (@t151 (@list false false false) (@list @t152 @t154 @t156))) % 0.51/0.73 (assume-push @p434 @t104) % 0.51/0.73 (assume-push @p435 @t111) % 0.51/0.73 (assume-push @p436 @t112) % 0.51/0.73 (step @p420 :rule symm :premises (@p260)) % 0.51/0.73 (step @p421 :rule symm :premises (@p287)) % 0.51/0.73 (step @p422 :rule trans :premises (@p308 @p421 @p420)) % 0.51/0.73 (step-pop @p437 :rule scope :premises (@p422)) % 0.51/0.73 (step-pop @p438 :rule scope :premises (@p437)) % 0.51/0.73 (step-pop @p439 :rule scope :premises (@p438)) % 0.51/0.73 (step @p423 :rule process_scope :premises (@p439) :args (@t150)) % 0.51/0.73 (step @p427 :rule implies_elim :premises (@p423)) % 0.51/0.73 (step @p428 :rule cnf_and_neg :args (@t165)) % 0.51/0.73 (step @p429 :rule resolution :premises (@p428 @p427) :args (true @t165)) % 0.51/0.73 (step @p430 :rule reordering :premises (@p429) :args ((or @t150 (not @t104) (not @t111) (not @t112)))) % 0.51/0.73 (step @p431 false :rule chain_m_resolution :premises (@p430 @p416 @p308 @p287 @p260) :args (false (@list true false false false) (@list @t150 @t112 @t111 @t104))) % 0.51/0.73 ) % 0.51/0.73 % SZS output end Proof % 0.51/0.73 % cvc5 exiting %------------------------------------------------------------------------------