%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO109^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n002.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 09:12:03 AM UTC 2026 % Result : Theorem 2.52s 2.79s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO109^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n002.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 23:59:18 EDT 2026 % 0.16/0.35 % CPUTime : % 0.27/0.49 %----Proving TH0 % 2.52/2.79 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 2.52/2.79 % SZS status Theorem % 2.52/2.79 % SZS output start Proof % 2.52/2.79 ( % 2.52/2.79 (declare-sort $$unsorted 0) % 2.52/2.79 (declare-const tptp.cM (-> $$unsorted $$unsorted Bool)) % 2.52/2.79 (declare-const tptp.cN (-> $$unsorted $$unsorted Bool)) % 2.52/2.79 (declare-const tptp.cP (-> $$unsorted Bool)) % 2.52/2.79 (define @t1 () (@var "Xz" $$unsorted)) % 2.52/2.79 (define @t2 () (_ tptp.cP @t1)) % 2.52/2.79 (define @t3 () (@list @t1)) % 2.52/2.79 (define @t4 () (forall @t3 @t2)) % 2.52/2.79 (define @t5 () (_ tptp.cN @t1)) % 2.52/2.79 (define @t6 () (_ @t5 @t1)) % 2.52/2.79 (define @t7 () (_ tptp.cM @t1)) % 2.52/2.79 (define @t8 () (_ @t7 @t1)) % 2.52/2.79 (define @t9 () (@var "Xw" $$unsorted)) % 2.52/2.79 (define @t10 () (_ @t5 @t9)) % 2.52/2.79 (define @t11 () (_ @t7 @t9)) % 2.52/2.79 (define @t12 () (or @t11 @t10 @t8 @t6)) % 2.52/2.79 (define @t13 () (_ (_ tptp.cN @t9) @t1)) % 2.52/2.79 (define @t14 () (_ (_ tptp.cM @t9) @t1)) % 2.52/2.79 (define @t15 () (or @t14 @t13)) % 2.52/2.79 (define @t16 () (@list @t9 @t1)) % 2.52/2.79 (define @t17 () (forall @t16 (=> @t15 @t12))) % 2.52/2.79 (define @t18 () (@var "Xu" $$unsorted)) % 2.52/2.79 (define @t19 () (_ (_ tptp.cN @t18) @t9)) % 2.52/2.79 (define @t20 () (@var "Xv" $$unsorted)) % 2.52/2.79 (define @t21 () (_ (_ tptp.cM @t18) @t20)) % 2.52/2.79 (define @t22 () (@list @t20)) % 2.52/2.79 (define @t23 () (forall @t22 @t21)) % 2.52/2.79 (define @t24 () (or @t23 @t19)) % 2.52/2.79 (define @t25 () (@list @t18)) % 2.52/2.79 (define @t26 () (exists @t25 @t24)) % 2.52/2.79 (define @t27 () (@list @t9)) % 2.52/2.79 (define @t28 () (forall @t27 @t26)) % 2.52/2.79 (define @t29 () (@var "Xx" $$unsorted)) % 2.52/2.79 (define @t30 () (_ tptp.cP @t29)) % 2.52/2.79 (define @t31 () (@var "Xy" $$unsorted)) % 2.52/2.79 (define @t32 () (_ tptp.cN @t29)) % 2.52/2.79 (define @t33 () (_ @t32 @t31)) % 2.52/2.79 (define @t34 () (_ tptp.cM @t29)) % 2.52/2.79 (define @t35 () (_ @t34 @t31)) % 2.52/2.79 (define @t36 () (or @t35 @t33)) % 2.52/2.79 (define @t37 () (@list @t31)) % 2.52/2.79 (define @t38 () (exists @t37 @t36)) % 2.52/2.79 (define @t39 () (=> @t38 @t30)) % 2.52/2.79 (define @t40 () (@list @t29)) % 2.52/2.79 (define @t41 () (forall @t40 @t39)) % 2.52/2.79 (define @t42 () (and @t41 @t28 @t17)) % 2.52/2.79 (define @t43 () (=> @t42 @t4)) % 2.52/2.79 (define @t44 () (not @t43)) % 2.52/2.79 (define @t45 () (tptp.cP @t1)) % 2.52/2.79 (define @t46 () (tptp.cN @t1 @t1)) % 2.52/2.79 (define @t47 () (tptp.cM @t1 @t1)) % 2.52/2.79 (define @t48 () (tptp.cN @t1 @t9)) % 2.52/2.79 (define @t49 () (tptp.cM @t1 @t9)) % 2.52/2.79 (define @t50 () (tptp.cN @t9 @t1)) % 2.52/2.79 (define @t51 () (not @t13)) % 2.52/2.79 (define @t52 () (tptp.cM @t9 @t1)) % 2.52/2.79 (define @t53 () (not @t14)) % 2.52/2.79 (define @t54 () (and @t53 @t51)) % 2.52/2.79 (define @t55 () (or @t54 @t11 @t10 @t8 @t6)) % 2.52/2.79 (define @t56 () (@var "BOUND_VARIABLE_7525" $$unsorted)) % 2.52/2.79 (define @t57 () (tptp.cN @t56 @t9)) % 2.52/2.79 (define @t58 () (@list @t56)) % 2.52/2.79 (define @t59 () (forall @t58 (not @t57))) % 2.52/2.79 (define @t60 () (not @t59)) % 2.52/2.79 (define @t61 () (forall @t27 @t60)) % 2.52/2.79 (define @t62 () (@var "BOUND_VARIABLE_7518" $$unsorted)) % 2.52/2.79 (define @t63 () (forall (@list @t62) (not (forall @t22 (tptp.cM @t62 @t20))))) % 2.52/2.79 (define @t64 () (not @t63)) % 2.52/2.79 (define @t65 () (_ (_ tptp.cN @t56) @t9)) % 2.52/2.79 (define @t66 () (not @t65)) % 2.52/2.79 (define @t67 () (forall @t58 @t66)) % 2.52/2.79 (define @t68 () (not @t19)) % 2.52/2.79 (define @t69 () (forall @t25 @t68)) % 2.52/2.79 (define @t70 () (@list @t18)) % 2.52/2.79 (define @t71 () (tptp.cM @t18 @t20)) % 2.52/2.79 (define @t72 () (forall @t22 @t71)) % 2.52/2.79 (define @t73 () (not @t72)) % 2.52/2.79 (define @t74 () (forall @t25 @t73)) % 2.52/2.79 (define @t75 () (and @t74 @t69)) % 2.52/2.79 (define @t76 () (or @t72 @t19)) % 2.52/2.79 (define @t77 () (forall @t25 (not @t76))) % 2.52/2.79 (define @t78 () (not @t77)) % 2.52/2.79 (define @t79 () (tptp.cP @t29)) % 2.52/2.79 (define @t80 () (@var "BOUND_VARIABLE_7499" $$unsorted)) % 2.52/2.79 (define @t81 () (not (tptp.cN @t29 @t80))) % 2.52/2.79 (define @t82 () (@var "BOUND_VARIABLE_7495" $$unsorted)) % 2.52/2.79 (define @t83 () (not (tptp.cM @t29 @t82))) % 2.52/2.79 (define @t84 () (and @t83 @t81)) % 2.52/2.79 (define @t85 () (or @t84 @t79)) % 2.52/2.79 (define @t86 () (@list @t82 @t80)) % 2.52/2.79 (define @t87 () (forall @t86 @t85)) % 2.52/2.79 (define @t88 () (forall (@list @t80) @t81)) % 2.52/2.79 (define @t89 () (@var "BOUND_VARIABLE_7473" $$unsorted)) % 2.52/2.79 (define @t90 () (@list @t89)) % 2.52/2.79 (define @t91 () (forall @t86 @t81)) % 2.52/2.79 (define @t92 () (forall (@list @t82) @t83)) % 2.52/2.79 (define @t93 () (@var "BOUND_VARIABLE_7467" $$unsorted)) % 2.52/2.79 (define @t94 () (@list @t93)) % 2.52/2.79 (define @t95 () (forall @t86 @t83)) % 2.52/2.79 (define @t96 () (and @t95 @t91)) % 2.52/2.79 (define @t97 () (forall @t86 @t84)) % 2.52/2.79 (define @t98 () (or @t97 @t79)) % 2.52/2.79 (define @t99 () (tptp.cN @t29 @t89)) % 2.52/2.79 (define @t100 () (@list @t89)) % 2.52/2.79 (define @t101 () (tptp.cM @t29 @t93)) % 2.52/2.79 (define @t102 () (@list @t93)) % 2.52/2.79 (define @t103 () (and (forall @t102 (not @t101)) (forall @t100 (not @t99)))) % 2.52/2.80 (define @t104 () (or @t103 @t30)) % 2.52/2.80 (define @t105 () (not @t103)) % 2.52/2.80 (define @t106 () (_ @t32 @t89)) % 2.52/2.80 (define @t107 () (not @t106)) % 2.52/2.80 (define @t108 () (forall @t100 @t107)) % 2.52/2.80 (define @t109 () (_ @t34 @t93)) % 2.52/2.80 (define @t110 () (not @t109)) % 2.52/2.80 (define @t111 () (forall @t102 @t110)) % 2.52/2.80 (define @t112 () (not @t33)) % 2.52/2.80 (define @t113 () (forall @t37 @t112)) % 2.52/2.80 (define @t114 () (@list @t31)) % 2.52/2.80 (define @t115 () (not @t35)) % 2.52/2.80 (define @t116 () (forall @t37 @t115)) % 2.52/2.80 (define @t117 () (and @t116 @t113)) % 2.52/2.80 (define @t118 () (forall @t37 (not @t36))) % 2.52/2.80 (define @t119 () (not @t118)) % 2.52/2.80 (define @t120 () (@quantifiers_skolemize (forall @t3 @t45) 0)) % 2.52/2.80 (define @t121 () (forall @t58 (not (tptp.cN @t56 @t120)))) % 2.52/2.80 (define @t122 () (@quantifiers_skolemize @t121 0)) % 2.52/2.80 (define @t123 () (tptp.cP @t120)) % 2.52/2.80 (define @t124 () (tptp.cN @t120 @t120)) % 2.52/2.80 (define @t125 () (not @t124)) % 2.52/2.80 (define @t126 () (tptp.cM @t120 @t122)) % 2.52/2.80 (define @t127 () (not @t126)) % 2.52/2.80 (define @t128 () (and @t127 @t125)) % 2.52/2.80 (define @t129 () (or @t128 @t123)) % 2.52/2.80 (define @t130 () (@list true false)) % 2.52/2.80 (define @t131 () (@list false)) % 2.52/2.80 (define @t132 () (@quantifiers_skolemize @t63 0)) % 2.52/2.80 (define @t133 () (tptp.cM @t120 @t132)) % 2.52/2.80 (define @t134 () (not @t133)) % 2.52/2.80 (define @t135 () (and @t134 @t125)) % 2.52/2.80 (define @t136 () (or @t135 @t123)) % 2.52/2.80 (define @t137 () (not @t135)) % 2.52/2.80 (define @t138 () (@list @t135)) % 2.52/2.80 (define @t139 () (tptp.cN @t120 @t132)) % 2.52/2.80 (define @t140 () (not @t139)) % 2.52/2.80 (define @t141 () (tptp.cM @t120 @t120)) % 2.52/2.80 (define @t142 () (not @t141)) % 2.52/2.80 (define @t143 () (and @t142 @t140)) % 2.52/2.80 (define @t144 () (or @t143 @t123)) % 2.52/2.80 (define @t145 () (not @t143)) % 2.52/2.80 (define @t146 () (@list @t143)) % 2.52/2.80 (define @t147 () (tptp.cM @t132 @t120)) % 2.52/2.80 (define @t148 () (not @t147)) % 2.52/2.80 (define @t149 () (and @t148 (not (tptp.cN @t132 @t120)))) % 2.52/2.80 (define @t150 () (or @t149 @t133 @t139 @t141 @t124)) % 2.52/2.80 (define @t151 () (@list true true true true false)) % 2.52/2.80 (define @t152 () (forall @t22 (tptp.cM @t132 @t20))) % 2.52/2.80 (define @t153 () (@list @t120)) % 2.52/2.80 (define @t154 () (not @t152)) % 2.52/2.80 (define @t155 () (@list true)) % 2.52/2.80 (define @t156 () (not @t154)) % 2.52/2.80 (define @t157 () (not @t121)) % 2.52/2.80 (define @t158 () (tptp.cN @t122 @t120)) % 2.52/2.80 (define @t159 () (not @t158)) % 2.52/2.80 (define @t160 () (not @t159)) % 2.52/2.80 (define @t161 () (and (not (tptp.cM @t122 @t120)) @t159)) % 2.52/2.80 (define @t162 () (not @t161)) % 2.52/2.80 (define @t163 () (tptp.cN @t120 @t122)) % 2.52/2.80 (define @t164 () (or @t161 @t126 @t163 @t141 @t124)) % 2.52/2.80 (define @t165 () (not @t163)) % 2.52/2.80 (define @t166 () (and @t142 @t165)) % 2.52/2.80 (define @t167 () (not @t166)) % 2.52/2.80 (define @t168 () (or @t166 @t123)) % 2.52/2.80 (assume @p1 @t44) % 2.52/2.80 (assume @p2 true) % 2.52/2.80 (step @p3 :rule refl :args (@t45)) % 2.52/2.80 (step @p4 :rule refl :args (@t2)) % 2.52/2.80 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t2 @t45))) % 2.52/2.80 (step @p6 :rule symm :premises (@p5)) % 2.52/2.80 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 2.52/2.80 (step @p8 :rule cong :premises (@p7) :args (@t4)) % 2.52/2.80 (step @p9 :rule refl :args (@t46)) % 2.52/2.80 (step @p10 :rule refl :args (@t6)) % 2.52/2.80 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t6 @t46))) % 2.52/2.80 (step @p12 :rule symm :premises (@p11)) % 2.52/2.80 (step @p13 :rule eq_resolve :premises (@p10 @p12)) % 2.52/2.80 (step @p14 :rule refl :args (@t47)) % 2.52/2.80 (step @p15 :rule refl :args (@t8)) % 2.52/2.80 (step @p16 :rule cong :premises (@p15 @p14) :args ((= @t8 @t47))) % 2.52/2.80 (step @p17 :rule symm :premises (@p16)) % 2.52/2.80 (step @p18 :rule eq_resolve :premises (@p15 @p17)) % 2.52/2.80 (step @p19 :rule refl :args (@t48)) % 2.52/2.80 (step @p20 :rule refl :args (@t10)) % 2.52/2.80 (step @p21 :rule cong :premises (@p20 @p19) :args ((= @t10 @t48))) % 2.52/2.80 (step @p22 :rule symm :premises (@p21)) % 2.52/2.80 (step @p23 :rule eq_resolve :premises (@p20 @p22)) % 2.52/2.80 (step @p24 :rule refl :args (@t49)) % 2.52/2.80 (step @p25 :rule refl :args (@t11)) % 2.52/2.80 (step @p26 :rule cong :premises (@p25 @p24) :args ((= @t11 @t49))) % 2.52/2.80 (step @p27 :rule symm :premises (@p26)) % 2.52/2.80 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 2.52/2.80 (step @p29 :rule refl :args (@t50)) % 2.52/2.80 (step @p30 :rule refl :args (@t13)) % 2.52/2.80 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t13 @t50))) % 2.52/2.80 (step @p32 :rule symm :premises (@p31)) % 2.52/2.80 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 2.52/2.80 (step @p34 :rule cong :premises (@p33) :args (@t51)) % 2.52/2.80 (step @p35 :rule refl :args (@t52)) % 2.52/2.80 (step @p36 :rule refl :args (@t14)) % 2.52/2.80 (step @p37 :rule cong :premises (@p36 @p35) :args ((= @t14 @t52))) % 2.52/2.80 (step @p38 :rule symm :premises (@p37)) % 2.52/2.80 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 2.52/2.80 (step @p40 :rule cong :premises (@p39) :args (@t53)) % 2.52/2.80 (step @p41 :rule nary_cong :premises (@p40 @p34) :args (@t54)) % 2.52/2.80 (step @p42 :rule nary_cong :premises (@p41 @p28 @p23 @p18 @p13) :args (@t55)) % 2.52/2.80 (step @p43 :rule cong :premises (@p42) :args ((forall @t16 @t55))) % 2.52/2.80 (step @p44 :rule aci_norm :args ((= (or @t54 @t12) @t55))) % 2.52/2.80 (step @p45 :rule refl :args (@t12)) % 2.52/2.80 (step @p46 :rule bool-or-de-morgan :args (@t14 @t13 false)) % 2.52/2.80 (step @p47 :rule nary_cong :premises (@p46 @p45) :args ((or (not @t15) @t12))) % 2.52/2.80 (step @p48 :rule trans :premises (@p47 @p44)) % 2.52/2.80 (step @p49 :rule bool-impl-elim :args (@t15 @t12)) % 2.52/2.80 (step @p50 :rule trans :premises (@p49 @p48)) % 2.52/2.80 (step @p51 :rule cong :premises (@p50) :args (@t17)) % 2.52/2.80 (step @p52 :rule trans :premises (@p51 @p43)) % 2.52/2.80 (step @p53 :rule quant-miniscope-or :args ((= (forall @t27 (or @t64 @t60)) (or @t64 @t61)))) % 2.52/2.80 (step @p54 :rule bool-and-de-morgan :args (@t63 @t59 true)) % 2.52/2.80 (step @p55 :rule cong :premises (@p54) :args ((forall @t27 (not (and @t63 @t59))))) % 2.52/2.80 (step @p56 :rule trans :premises (@p55 @p53)) % 2.52/2.80 (step @p57 :rule refl :args (@t57)) % 2.52/2.80 (step @p58 :rule refl :args (@t65)) % 2.52/2.80 (step @p59 :rule cong :premises (@p58 @p57) :args ((= @t65 @t57))) % 2.52/2.80 (step @p60 :rule symm :premises (@p59)) % 2.52/2.80 (step @p61 :rule eq_resolve :premises (@p58 @p60)) % 2.52/2.80 (step @p62 :rule cong :premises (@p61) :args (@t66)) % 2.52/2.80 (step @p63 :rule cong :premises (@p62) :args (@t67)) % 2.52/2.80 (step @p64 :rule refl :args (@t63)) % 2.52/2.80 (step @p65 :rule nary_cong :premises (@p64 @p63) :args ((and @t63 @t67))) % 2.52/2.80 (step @p66 :rule alpha_equiv :args (@t69 @t70 (@list @t56))) % 2.52/2.80 (step @p67 :rule alpha_equiv :args (@t74 @t70 (@list @t62))) % 2.52/2.80 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t75)) % 2.52/2.80 (step @p69 :rule quant-miniscope-and :args ((= (forall @t25 (and @t73 @t68)) @t75))) % 2.52/2.80 (step @p70 :rule trans :premises (@p69 @p68)) % 2.52/2.80 (step @p71 :rule trans :premises (@p70 @p65)) % 2.52/2.80 (step @p72 :rule bool-or-de-morgan :args (@t72 @t19 false)) % 2.52/2.80 (step @p73 :rule cong :premises (@p72) :args (@t77)) % 2.52/2.80 (step @p74 :rule trans :premises (@p73 @p71)) % 2.52/2.80 (step @p75 :rule cong :premises (@p74) :args (@t78)) % 2.52/2.80 (step @p76 :rule exists-elim :args ((= (exists @t25 @t76) @t78))) % 2.52/2.80 (step @p77 :rule trans :premises (@p76 @p75)) % 2.52/2.80 (step @p78 :rule refl :args (@t19)) % 2.52/2.80 (step @p79 :rule refl :args (@t71)) % 2.52/2.80 (step @p80 :rule refl :args (@t21)) % 2.52/2.80 (step @p81 :rule cong :premises (@p80 @p79) :args ((= @t21 @t71))) % 2.52/2.80 (step @p82 :rule symm :premises (@p81)) % 2.52/2.80 (step @p83 :rule eq_resolve :premises (@p80 @p82)) % 2.52/2.80 (step @p84 :rule cong :premises (@p83) :args (@t23)) % 2.52/2.80 (step @p85 :rule nary_cong :premises (@p84 @p78) :args (@t24)) % 2.52/2.80 (step @p86 :rule cong :premises (@p85) :args (@t26)) % 2.52/2.80 (step @p87 :rule trans :premises (@p86 @p77)) % 2.52/2.80 (step @p88 :rule cong :premises (@p87) :args (@t28)) % 2.52/2.80 (step @p89 :rule trans :premises (@p88 @p56)) % 2.52/2.80 (step @p90 :rule quant-merge-prenex :args ((= (forall @t40 @t87) (forall (@list @t29 @t82 @t80) @t85)))) % 2.52/2.80 (step @p91 :rule refl :args (@t79)) % 2.52/2.80 (step @p92 :rule alpha_equiv :args (@t88 (@list @t80) @t90)) % 2.52/2.80 (step @p93 :rule quant-unused-vars :args ((= @t91 @t88))) % 2.52/2.80 (step @p94 :rule trans :premises (@p93 @p92)) % 2.52/2.80 (step @p95 :rule alpha_equiv :args (@t92 (@list @t82) @t94)) % 2.52/2.80 (step @p96 :rule quant-unused-vars :args ((= @t95 @t92))) % 2.52/2.80 (step @p97 :rule trans :premises (@p96 @p95)) % 2.52/2.80 (step @p98 :rule nary_cong :premises (@p97 @p94) :args (@t96)) % 2.52/2.80 (step @p99 :rule quant-miniscope-and :args ((= @t97 @t96))) % 2.52/2.80 (step @p100 :rule trans :premises (@p99 @p98)) % 2.52/2.80 (step @p101 :rule nary_cong :premises (@p100 @p91) :args (@t98)) % 2.52/2.80 (step @p102 :rule quant-miniscope-or :args ((= @t87 @t98))) % 2.52/2.80 (step @p103 :rule trans :premises (@p102 @p101)) % 2.52/2.80 (step @p104 :rule symm :premises (@p103)) % 2.52/2.80 (step @p105 :rule cong :premises (@p104) :args ((forall @t40 (or @t103 @t79)))) % 2.52/2.80 (step @p106 :rule trans :premises (@p105 @p90)) % 2.52/2.80 (step @p107 :rule refl :args (@t79)) % 2.52/2.80 (step @p108 :rule refl :args (@t30)) % 2.52/2.80 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t30 @t79))) % 2.52/2.80 (step @p110 :rule symm :premises (@p109)) % 2.52/2.80 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 2.52/2.80 (step @p112 :rule refl :args (@t103)) % 2.52/2.80 (step @p113 :rule nary_cong :premises (@p112 @p111) :args (@t104)) % 2.52/2.80 (step @p114 :rule cong :premises (@p113) :args ((forall @t40 @t104))) % 2.52/2.80 (step @p115 :rule trans :premises (@p114 @p106)) % 2.52/2.80 (step @p116 :rule bool-double-not-elim :args (@t103)) % 2.52/2.80 (step @p117 :rule nary_cong :premises (@p116 @p108) :args ((or (not @t105) @t30))) % 2.52/2.80 (step @p118 :rule bool-impl-elim :args (@t105 @t30)) % 2.52/2.80 (step @p119 :rule trans :premises (@p118 @p117)) % 2.52/2.80 (step @p120 :rule cong :premises (@p119) :args ((forall @t40 (=> @t105 @t30)))) % 2.52/2.80 (step @p121 :rule trans :premises (@p120 @p115)) % 2.52/2.80 (step @p122 :rule refl :args (@t30)) % 2.52/2.80 (step @p123 :rule refl :args (@t99)) % 2.52/2.80 (step @p124 :rule refl :args (@t106)) % 2.52/2.80 (step @p125 :rule cong :premises (@p124 @p123) :args ((= @t106 @t99))) % 2.52/2.80 (step @p126 :rule symm :premises (@p125)) % 2.52/2.80 (step @p127 :rule eq_resolve :premises (@p124 @p126)) % 2.52/2.80 (step @p128 :rule cong :premises (@p127) :args (@t107)) % 2.52/2.80 (step @p129 :rule cong :premises (@p128) :args (@t108)) % 2.52/2.80 (step @p130 :rule refl :args (@t101)) % 2.52/2.80 (step @p131 :rule refl :args (@t109)) % 2.52/2.80 (step @p132 :rule cong :premises (@p131 @p130) :args ((= @t109 @t101))) % 2.52/2.80 (step @p133 :rule symm :premises (@p132)) % 2.52/2.80 (step @p134 :rule eq_resolve :premises (@p131 @p133)) % 2.52/2.80 (step @p135 :rule cong :premises (@p134) :args (@t110)) % 2.52/2.80 (step @p136 :rule cong :premises (@p135) :args (@t111)) % 2.52/2.80 (step @p137 :rule nary_cong :premises (@p136 @p129) :args ((and @t111 @t108))) % 2.52/2.80 (step @p138 :rule alpha_equiv :args (@t113 @t114 @t90)) % 2.52/2.80 (step @p139 :rule alpha_equiv :args (@t116 @t114 @t94)) % 2.52/2.80 (step @p140 :rule nary_cong :premises (@p139 @p138) :args (@t117)) % 2.52/2.80 (step @p141 :rule quant-miniscope-and :args ((= (forall @t37 (and @t115 @t112)) @t117))) % 2.52/2.80 (step @p142 :rule trans :premises (@p141 @p140)) % 2.52/2.80 (step @p143 :rule trans :premises (@p142 @p137)) % 2.52/2.80 (step @p144 :rule bool-or-de-morgan :args (@t35 @t33 false)) % 2.52/2.80 (step @p145 :rule cong :premises (@p144) :args (@t118)) % 2.52/2.80 (step @p146 :rule trans :premises (@p145 @p143)) % 2.52/2.80 (step @p147 :rule cong :premises (@p146) :args (@t119)) % 2.52/2.80 (step @p148 :rule exists-elim :args ((= @t38 @t119))) % 2.52/2.80 (step @p149 :rule trans :premises (@p148 @p147)) % 2.52/2.80 (step @p150 :rule cong :premises (@p149 @p122) :args (@t39)) % 2.52/2.80 (step @p151 :rule cong :premises (@p150) :args (@t41)) % 2.52/2.80 (step @p152 :rule trans :premises (@p151 @p121)) % 2.52/2.80 (step @p153 :rule nary_cong :premises (@p152 @p89 @p52) :args (@t42)) % 2.52/2.80 (step @p154 :rule cong :premises (@p153 @p8) :args (@t43)) % 2.52/2.80 (step @p155 :rule cong :premises (@p154) :args (@t44)) % 2.52/2.80 (step @p156 :rule eq_resolve :premises (@p1 @p155)) % 2.52/2.80 (step @p157 :rule not_implies_elim2 :premises (@p156)) % 2.52/2.80 (step @p158 :rule skolemize :premises (@p157)) % 2.52/2.80 (step @p159 :rule not_implies_elim1 :premises (@p156)) % 2.52/2.80 (step @p160 :rule and_elim :premises (@p159) :args (2)) % 2.52/2.80 (step @p161 :rule instantiate :premises (@p160) :args ((@list @t122 @t120))) % 2.52/2.80 (step @p162 :rule and_elim :premises (@p159) :args (0)) % 2.52/2.80 (step @p163 :rule instantiate :premises (@p162) :args ((@list @t120 @t122 @t120))) % 2.52/2.80 (step @p164 :rule cnf_or_pos :args (@t129)) % 2.52/2.80 (step @p165 :rule reordering :premises (@p164) :args ((or @t123 @t128 (not @t129)))) % 2.52/2.80 (step @p166 :rule chain_m_resolution :premises (@p165 @p158 @p163) :args (@t128 @t130 (@list @t123 @t129))) % 2.52/2.80 (step @p167 :rule cnf_and_pos :args (@t128 0)) % 2.52/2.80 (step @p168 :rule reordering :premises (@p167) :args ((or @t127 (not @t128)))) % 2.52/2.80 (step @p169 :rule chain_m_resolution :premises (@p168 @p166) :args (@t127 @t131 (@list @t128))) % 2.52/2.80 (step @p170 :rule instantiate :premises (@p160) :args ((@list @t132 @t120))) % 2.52/2.80 (step @p171 :rule instantiate :premises (@p162) :args ((@list @t120 @t132 @t120))) % 2.52/2.80 (step @p172 :rule cnf_or_pos :args (@t136)) % 2.52/2.80 (step @p173 :rule reordering :premises (@p172) :args ((or @t123 @t135 (not @t136)))) % 2.52/2.80 (step @p174 :rule chain_m_resolution :premises (@p173 @p158 @p171) :args (@t135 @t130 (@list @t123 @t136))) % 2.52/2.80 (step @p175 :rule cnf_and_pos :args (@t135 1)) % 2.52/2.80 (step @p176 :rule reordering :premises (@p175) :args ((or @t125 @t137))) % 2.52/2.80 (step @p177 :rule chain_m_resolution :premises (@p176 @p174) :args (@t125 @t131 @t138)) % 2.52/2.80 (step @p178 :rule instantiate :premises (@p162) :args ((@list @t120 @t120 @t132))) % 2.52/2.80 (step @p179 :rule cnf_or_pos :args (@t144)) % 2.52/2.80 (step @p180 :rule reordering :premises (@p179) :args ((or @t123 @t143 (not @t144)))) % 2.52/2.80 (step @p181 :rule chain_m_resolution :premises (@p180 @p158 @p178) :args (@t143 @t130 (@list @t123 @t144))) % 2.52/2.80 (step @p182 :rule cnf_and_pos :args (@t143 0)) % 2.52/2.80 (step @p183 :rule reordering :premises (@p182) :args ((or @t142 @t145))) % 2.52/2.80 (step @p184 :rule chain_m_resolution :premises (@p183 @p181) :args (@t142 @t131 @t146)) % 2.52/2.80 (step @p185 :rule cnf_and_pos :args (@t143 1)) % 2.52/2.80 (step @p186 :rule reordering :premises (@p185) :args ((or @t140 @t145))) % 2.52/2.80 (step @p187 :rule chain_m_resolution :premises (@p186 @p181) :args (@t140 @t131 @t146)) % 2.52/2.80 (step @p188 :rule cnf_and_pos :args (@t135 0)) % 2.52/2.80 (step @p189 :rule reordering :premises (@p188) :args ((or @t134 @t137))) % 2.52/2.80 (step @p190 :rule chain_m_resolution :premises (@p189 @p174) :args (@t134 @t131 @t138)) % 2.52/2.80 (step @p191 :rule cnf_or_pos :args (@t150)) % 2.52/2.80 (step @p192 :rule reordering :premises (@p191) :args ((or @t149 @t133 @t139 @t141 @t124 (not @t150)))) % 2.52/2.80 (step @p193 :rule chain_m_resolution :premises (@p192 @p190 @p187 @p184 @p177 @p170) :args (@t149 @t151 (@list @t133 @t139 @t141 @t124 @t150))) % 2.52/2.80 (step @p194 :rule cnf_and_pos :args (@t149 0)) % 2.52/2.80 (step @p195 :rule reordering :premises (@p194) :args ((or @t148 (not @t149)))) % 2.52/2.80 (step @p196 :rule chain_m_resolution :premises (@p195 @p193) :args (@t148 @t131 (@list @t149))) % 2.52/2.80 (assume-push @p252 @t152) % 2.52/2.80 (step @p198 :rule instantiate :premises (@p252) :args (@t153)) % 2.52/2.80 (step-pop @p253 :rule scope :premises (@p198)) % 2.52/2.80 (step @p199 :rule process_scope :premises (@p253) :args (@t147)) % 2.52/2.80 (step @p201 :rule implies_elim :premises (@p199)) % 2.52/2.80 (step @p202 :rule chain_m_resolution :premises (@p201 @p196) :args (@t154 @t155 (@list @t147))) % 2.52/2.80 (step @p203 :rule refl :args (@t152)) % 2.52/2.80 (step @p204 :rule bool-double-not-elim :args (@t63)) % 2.52/2.80 (step @p205 :rule nary_cong :premises (@p204 @p203) :args ((or (not @t64) @t152))) % 2.52/2.80 (step @p206 :rule bool-double-not-elim :args (@t152)) % 2.52/2.80 (step @p207 :rule refl :args (@t64)) % 2.52/2.80 (step @p208 :rule cong :premises (@p207 @p206) :args ((=> @t64 @t156))) % 2.52/2.80 (assume-push @p254 @t64) % 2.52/2.80 (step @p210 :rule skolemize :premises (@p254)) % 2.52/2.80 (step-pop @p255 :rule scope :premises (@p210)) % 2.52/2.80 (step @p211 :rule process_scope :premises (@p255) :args (@t156)) % 2.52/2.80 (step @p213 :rule eq_resolve :premises (@p211 @p208)) % 2.52/2.80 (step @p214 :rule implies_elim :premises (@p213)) % 2.52/2.80 (step @p215 :rule eq_resolve :premises (@p214 @p205)) % 2.52/2.80 (step @p216 :rule chain_m_resolution :premises (@p215 @p202) :args (@t63 @t155 (@list @t152))) % 2.52/2.80 (step @p217 :rule and_elim :premises (@p159) :args (1)) % 2.52/2.80 (step @p218 :rule chain_m_resolution :premises (@p217 @p216) :args (@t61 @t131 (@list @t63))) % 2.52/2.80 (assume-push @p256 @t61) % 2.52/2.80 (step @p220 :rule instantiate :premises (@p256) :args (@t153)) % 2.52/2.80 (step-pop @p257 :rule scope :premises (@p220)) % 2.52/2.80 (step @p221 :rule process_scope :premises (@p257) :args (@t157)) % 2.52/2.80 (step @p223 :rule implies_elim :premises (@p221)) % 2.52/2.80 (step @p224 :rule chain_m_resolution :premises (@p223 @p218) :args (@t157 @t131 (@list @t61))) % 2.52/2.80 (step @p225 :rule refl :args (@t158)) % 2.52/2.80 (step @p226 :rule bool-double-not-elim :args (@t121)) % 2.52/2.80 (step @p227 :rule nary_cong :premises (@p226 @p225) :args ((or (not @t157) @t158))) % 2.52/2.80 (step @p228 :rule bool-double-not-elim :args (@t158)) % 2.52/2.80 (step @p229 :rule refl :args (@t157)) % 2.52/2.80 (step @p230 :rule cong :premises (@p229 @p228) :args ((=> @t157 @t160))) % 2.52/2.80 (assume-push @p258 @t157) % 2.52/2.80 (step @p232 :rule skolemize :premises (@p258)) % 2.52/2.80 (step-pop @p259 :rule scope :premises (@p232)) % 2.52/2.80 (step @p233 :rule process_scope :premises (@p259) :args (@t160)) % 2.52/2.80 (step @p235 :rule eq_resolve :premises (@p233 @p230)) % 2.52/2.80 (step @p236 :rule implies_elim :premises (@p235)) % 2.52/2.80 (step @p237 :rule eq_resolve :premises (@p236 @p227)) % 2.52/2.80 (step @p238 :rule chain_m_resolution :premises (@p237 @p224) :args (@t158 @t155 (@list @t121))) % 2.52/2.80 (step @p239 :rule cnf_and_pos :args (@t161 1)) % 2.52/2.80 (step @p240 :rule reordering :premises (@p239) :args ((or @t159 @t162))) % 2.52/2.80 (step @p241 :rule chain_m_resolution :premises (@p240 @p238) :args (@t162 @t131 (@list @t158))) % 2.52/2.80 (step @p242 :rule cnf_or_pos :args (@t164)) % 2.52/2.80 (step @p243 :rule reordering :premises (@p242) :args ((or @t141 @t124 @t161 @t126 @t163 (not @t164)))) % 2.52/2.80 (step @p244 :rule chain_m_resolution :premises (@p243 @p184 @p177 @p241 @p169 @p161) :args (@t163 @t151 (@list @t141 @t124 @t161 @t126 @t164))) % 0.35/2.80 (step @p245 :rule cnf_and_pos :args (@t166 1)) % 0.35/2.80 (step @p246 :rule reordering :premises (@p245) :args ((or @t165 @t167))) % 0.35/2.80 (step @p247 :rule chain_m_resolution :premises (@p246 @p244) :args (@t167 @t131 (@list @t163))) % 0.35/2.80 (step @p248 :rule instantiate :premises (@p162) :args ((@list @t120 @t120 @t122))) % 0.35/2.80 (step @p249 :rule cnf_or_pos :args (@t168)) % 0.35/2.80 (step @p250 :rule reordering :premises (@p249) :args ((or @t123 @t166 (not @t168)))) % 0.35/2.80 (step @p251 false :rule chain_m_resolution :premises (@p250 @p248 @p247 @p158) :args (false (@list false true true) (@list @t168 @t166 @t123))) % 0.35/2.80 ) % 0.35/2.80 % SZS output end Proof % 0.35/2.80 % cvc5 exiting %------------------------------------------------------------------------------