%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG227+1 : TPTP v9.2.1. Released v3.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n012.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 08:05:35 AM UTC 2026 % Result : Theorem 0.17s 15.55s % Output : Proof 0.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : ALG227+1 : TPTP v9.2.1. Released v3.4.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Wed Jun 3 01:49:48 EDT 2026 % 0.07/0.25 % CPUTime : % 0.16/0.34 %----Proving TF0_NAR, FOF, or CNF % 0.17/15.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.17/15.55 --- Run --no-e-matching --full-saturate-quant at 6... % 0.17/15.55 % SZS status Theorem % 0.17/15.55 % SZS output start Proof % 0.17/15.55 ( % 0.17/15.55 (declare-sort $$unsorted 0) % 0.17/15.55 (declare-const tptp.a_2_0_closure3 (-> $$unsorted $$unsorted $$unsorted)) % 0.17/15.55 (declare-const tptp.v1_finset_1 (-> $$unsorted Bool)) % 0.17/15.55 (declare-const tptp.v1_xboole_0 (-> $$unsorted Bool)) % 0.17/15.55 (declare-const tptp.v1_funct_1 (-> $$unsorted Bool)) % 0.17/15.55 (declare-const tptp.m1_pboole (-> $$unsorted $$unsorted Bool)) % 0.17/15.55 (declare-const tptp.m1_subset_1 (-> $$unsorted $$unsorted Bool)) % 0.17/15.55 (declare-const tptp.v1_relat_1 (-> $$unsorted Bool)) % 0.17/15.55 (declare-const tptp.r2_hidden (-> $$unsorted $$unsorted Bool)) % 0.17/15.55 (declare-const tptp.k1_closure3 (-> $$unsorted $$unsorted $$unsorted)) % 0.17/15.55 (declare-const tptp.k1_funct_1 (-> $$unsorted $$unsorted $$unsorted)) % 0.17/15.55 (declare-const tptp.v2_funct_1 (-> $$unsorted Bool)) % 0.17/15.55 (declare-const tptp.v1_fraenkel (-> $$unsorted Bool)) % 0.17/15.55 (declare-const tptp.k1_xboole_0 $$unsorted) % 0.17/15.55 (define @t1 () (@var "C" $$unsorted)) % 0.17/15.55 (define @t2 () (@var "B" $$unsorted)) % 0.17/15.55 (define @t3 () (tptp.k1_funct_1 @t2 @t1)) % 0.17/15.55 (define @t4 () (@var "A" $$unsorted)) % 0.17/15.55 (define @t5 () (tptp.k1_closure3 @t4 @t2)) % 0.17/15.55 (define @t6 () (tptp.r2_hidden @t1 @t5)) % 0.17/15.55 (define @t7 () (not @t6)) % 0.17/15.55 (define @t8 () (=> @t7 (= @t3 tptp.k1_xboole_0))) % 0.17/15.55 (define @t9 () (tptp.m1_subset_1 @t1 @t4)) % 0.17/15.55 (define @t10 () (=> @t9 @t8)) % 0.17/15.55 (define @t11 () (@list @t1)) % 0.17/15.55 (define @t12 () (forall @t11 @t10)) % 0.17/15.55 (define @t13 () (tptp.m1_pboole @t2 @t4)) % 0.17/15.55 (define @t14 () (=> @t13 @t12)) % 0.17/15.55 (define @t15 () (@list @t2)) % 0.17/15.55 (define @t16 () (forall @t15 @t14)) % 0.17/15.55 (define @t17 () (tptp.v1_xboole_0 @t4)) % 0.17/15.55 (define @t18 () (not @t17)) % 0.17/15.55 (define @t19 () (=> @t18 @t16)) % 0.17/15.55 (define @t20 () (@list @t4)) % 0.17/15.55 (define @t21 () (forall @t20 @t19)) % 0.17/15.55 (define @t22 () (not @t21)) % 0.17/15.55 (define @t23 () (tptp.r2_hidden @t4 @t2)) % 0.17/15.55 (define @t24 () (@list @t4 @t2)) % 0.17/15.55 (define @t25 () (tptp.v1_fraenkel @t4)) % 0.17/15.55 (define @t26 () (tptp.v1_finset_1 @t4)) % 0.17/15.55 (define @t27 () (tptp.v1_funct_1 @t4)) % 0.17/15.55 (define @t28 () (tptp.v2_funct_1 @t4)) % 0.17/15.55 (define @t29 () (tptp.v1_relat_1 @t4)) % 0.17/15.55 (define @t30 () (and @t29 @t27 @t28)) % 0.17/15.55 (define @t31 () (and @t29 @t17 @t27)) % 0.17/15.55 (define @t32 () (tptp.a_2_0_closure3 @t4 @t2)) % 0.17/15.55 (define @t33 () (forall @t11 (= (= @t1 @t5) (= @t1 @t32)))) % 0.17/15.55 (define @t34 () (forall @t15 (=> @t13 @t33))) % 0.17/15.55 (define @t35 () (=> @t18 @t34)) % 0.17/15.55 (define @t36 () (forall @t20 @t35)) % 0.17/15.55 (define @t37 () (@var "D" $$unsorted)) % 0.17/15.55 (define @t38 () (tptp.k1_funct_1 @t1 @t37)) % 0.17/15.55 (define @t39 () (not (= @t38 tptp.k1_xboole_0))) % 0.17/15.55 (define @t40 () (= @t4 @t37)) % 0.17/15.55 (define @t41 () (tptp.m1_subset_1 @t37 @t2)) % 0.17/15.55 (define @t42 () (and @t41 @t40 @t39)) % 0.17/15.55 (define @t43 () (@list @t37)) % 0.17/15.55 (define @t44 () (exists @t43 @t42)) % 0.17/15.55 (define @t45 () (tptp.r2_hidden @t4 (tptp.a_2_0_closure3 @t2 @t1))) % 0.17/15.55 (define @t46 () (= @t45 @t44)) % 0.17/15.55 (define @t47 () (tptp.m1_pboole @t1 @t2)) % 0.17/15.55 (define @t48 () (tptp.v1_xboole_0 @t2)) % 0.17/15.55 (define @t49 () (not @t48)) % 0.17/15.55 (define @t50 () (and @t49 @t47)) % 0.17/15.55 (define @t51 () (=> @t50 @t46)) % 0.17/15.55 (define @t52 () (@list @t4 @t2 @t1)) % 0.17/15.55 (define @t53 () (forall @t52 @t51)) % 0.17/15.55 (define @t54 () (tptp.m1_subset_1 @t4 @t2)) % 0.17/15.55 (define @t55 () (= @t4 @t2)) % 0.17/15.55 (define @t56 () (@var "BOUND_VARIABLE_7571" $$unsorted)) % 0.17/15.55 (define @t57 () (@var "BOUND_VARIABLE_7569" $$unsorted)) % 0.17/15.55 (define @t58 () (= tptp.k1_xboole_0 (tptp.k1_funct_1 @t57 @t56))) % 0.17/15.55 (define @t59 () (tptp.r2_hidden @t56 (tptp.k1_closure3 @t4 @t57))) % 0.17/15.55 (define @t60 () (not (tptp.m1_subset_1 @t56 @t4))) % 0.17/15.55 (define @t61 () (not (tptp.m1_pboole @t57 @t4))) % 0.17/15.55 (define @t62 () (or @t17 @t61 @t60 @t59 @t58)) % 0.17/15.55 (define @t63 () (or @t61 @t60 @t59 @t58)) % 0.17/15.55 (define @t64 () (or @t17 @t63)) % 0.17/15.55 (define @t65 () (@list @t4 @t57 @t56)) % 0.17/15.55 (define @t66 () (forall @t65 @t64)) % 0.17/15.55 (define @t67 () (@list @t57 @t56)) % 0.17/15.55 (define @t68 () (forall @t67 @t64)) % 0.17/15.55 (define @t69 () (forall @t67 @t63)) % 0.17/15.55 (define @t70 () (@var "BOUND_VARIABLE_7552" $$unsorted)) % 0.17/15.55 (define @t71 () (or @t17 @t69)) % 0.17/15.55 (define @t72 () (= tptp.k1_xboole_0 (tptp.k1_funct_1 @t2 @t70))) % 0.17/15.55 (define @t73 () (tptp.r2_hidden @t70 @t5)) % 0.17/15.55 (define @t74 () (not (tptp.m1_subset_1 @t70 @t4))) % 0.17/15.55 (define @t75 () (not @t13)) % 0.17/15.55 (define @t76 () (or @t75 @t74 @t73 @t72)) % 0.17/15.55 (define @t77 () (@list @t2 @t70)) % 0.17/15.55 (define @t78 () (forall @t77 @t76)) % 0.17/15.55 (define @t79 () (not @t18)) % 0.17/15.55 (define @t80 () (or @t74 @t73 @t72)) % 0.17/15.55 (define @t81 () (or @t75 @t80)) % 0.17/15.55 (define @t82 () (forall @t77 @t81)) % 0.17/15.55 (define @t83 () (@list @t70)) % 0.17/15.55 (define @t84 () (forall @t83 @t81)) % 0.17/15.55 (define @t85 () (forall @t83 @t80)) % 0.17/15.55 (define @t86 () (@list @t1)) % 0.17/15.55 (define @t87 () (or @t75 @t85)) % 0.17/15.55 (define @t88 () (= tptp.k1_xboole_0 @t3)) % 0.17/15.55 (define @t89 () (not @t9)) % 0.17/15.55 (define @t90 () (or @t89 @t6 @t88)) % 0.17/15.55 (define @t91 () (forall @t11 @t90)) % 0.17/15.55 (define @t92 () (=> @t7 @t88)) % 0.17/15.55 (define @t93 () (forall @t65 @t62)) % 0.17/15.55 (define @t94 () (@quantifiers_skolemize @t93 2)) % 0.17/15.55 (define @t95 () (@quantifiers_skolemize @t93 1)) % 0.17/15.55 (define @t96 () (= tptp.k1_xboole_0 (tptp.k1_funct_1 @t95 @t94))) % 0.17/15.55 (define @t97 () (@quantifiers_skolemize @t93 0)) % 0.17/15.55 (define @t98 () (tptp.k1_closure3 @t97 @t95)) % 0.17/15.55 (define @t99 () (tptp.r2_hidden @t94 @t98)) % 0.17/15.55 (define @t100 () (tptp.m1_subset_1 @t94 @t97)) % 0.17/15.55 (define @t101 () (not @t100)) % 0.17/15.55 (define @t102 () (tptp.m1_pboole @t95 @t97)) % 0.17/15.55 (define @t103 () (not @t102)) % 0.17/15.55 (define @t104 () (tptp.v1_xboole_0 @t97)) % 0.17/15.55 (define @t105 () (or @t104 @t103 @t101 @t99 @t96)) % 0.17/15.55 (define @t106 () (@list true)) % 0.17/15.55 (define @t107 () (@list @t105)) % 0.17/15.55 (define @t108 () (@var "BOUND_VARIABLE_7628" $$unsorted)) % 0.17/15.55 (define @t109 () (tptp.a_2_0_closure3 @t4 @t108)) % 0.17/15.55 (define @t110 () (@var "BOUND_VARIABLE_7630" $$unsorted)) % 0.17/15.55 (define @t111 () (tptp.k1_closure3 @t4 @t108)) % 0.17/15.55 (define @t112 () (= (= @t111 @t110) (= @t109 @t110))) % 0.17/15.55 (define @t113 () (not (tptp.m1_pboole @t108 @t4))) % 0.17/15.55 (define @t114 () (or @t17 @t113 @t112)) % 0.17/15.55 (define @t115 () (or @t113 @t112)) % 0.17/15.55 (define @t116 () (or @t17 @t115)) % 0.17/15.55 (define @t117 () (@list @t4 @t108 @t110)) % 0.17/15.55 (define @t118 () (forall @t117 @t116)) % 0.17/15.55 (define @t119 () (@list @t108 @t110)) % 0.17/15.55 (define @t120 () (forall @t119 @t116)) % 0.17/15.55 (define @t121 () (forall @t119 @t115)) % 0.17/15.55 (define @t122 () (@var "BOUND_VARIABLE_7611" $$unsorted)) % 0.17/15.55 (define @t123 () (or @t17 @t121)) % 0.17/15.55 (define @t124 () (@list @t2 @t122)) % 0.17/15.55 (define @t125 () (forall @t124 (or @t75 (= (= @t5 @t122) (= @t32 @t122))))) % 0.17/15.55 (define @t126 () (= (= @t122 @t5) (= @t122 @t32))) % 0.17/15.55 (define @t127 () (or @t75 @t126)) % 0.17/15.55 (define @t128 () (forall @t124 @t127)) % 0.17/15.55 (define @t129 () (@list @t122)) % 0.17/15.55 (define @t130 () (forall @t129 @t127)) % 0.17/15.55 (define @t131 () (forall @t129 @t126)) % 0.17/15.55 (define @t132 () (or @t75 @t131)) % 0.17/15.55 (define @t133 () (tptp.a_2_0_closure3 @t97 @t95)) % 0.17/15.55 (define @t134 () (= @t98 @t133)) % 0.17/15.55 (define @t135 () (= @t98 @t98)) % 0.17/15.55 (define @t136 () (or @t104 @t103 (= @t135 @t134))) % 0.17/15.55 (define @t137 () (forall @t117 (or @t17 @t113 (= (= @t110 @t111) (= @t110 @t109))))) % 0.17/15.55 (define @t138 () (or @t104 @t103 @t134)) % 0.17/15.55 (define @t139 () (@list true false false)) % 0.17/15.55 (define @t140 () (tptp.r2_hidden @t94 @t133)) % 0.17/15.55 (define @t141 () (= tptp.k1_xboole_0 (tptp.k1_funct_1 @t1 @t4))) % 0.17/15.55 (define @t142 () (not @t141)) % 0.17/15.55 (define @t143 () (= @t45 (and @t54 @t142))) % 0.17/15.55 (define @t144 () (not @t47)) % 0.17/15.55 (define @t145 () (not @t54)) % 0.17/15.55 (define @t146 () (or @t145 @t141)) % 0.17/15.55 (define @t147 () (= @t45 (not @t146))) % 0.17/15.55 (define @t148 () (not (= @t4 @t4))) % 0.17/15.55 (define @t149 () (or @t145 @t148 @t141)) % 0.17/15.55 (define @t150 () (= tptp.k1_xboole_0 @t38)) % 0.17/15.55 (define @t151 () (not @t40)) % 0.17/15.55 (define @t152 () (not @t41)) % 0.17/15.55 (define @t153 () (or @t151 @t152 @t151 @t150)) % 0.17/15.55 (define @t154 () (or @t152 @t151 @t150)) % 0.17/15.55 (define @t155 () (not @t150)) % 0.17/15.55 (define @t156 () (not @t155)) % 0.17/15.55 (define @t157 () (or @t152 @t151 @t156)) % 0.17/15.55 (define @t158 () (and @t41 @t40 @t155)) % 0.17/15.55 (define @t159 () (forall @t43 (not @t158))) % 0.17/15.55 (define @t160 () (not @t159)) % 0.17/15.55 (define @t161 () (not @t96)) % 0.17/15.55 (define @t162 () (and @t100 @t161)) % 0.17/15.55 (define @t163 () (= @t140 @t162)) % 0.17/15.55 (define @t164 () (or @t104 @t103 @t163)) % 0.17/15.55 (assume @p1 @t22) % 0.17/15.55 (assume @p2 (forall @t24 (=> @t23 (not (tptp.r2_hidden @t2 @t4))))) % 0.17/15.55 (assume @p3 (forall @t20 (=> @t17 @t25))) % 0.17/15.55 (assume @p4 (forall @t20 (=> @t17 @t26))) % 0.17/15.55 (assume @p5 (forall @t20 (=> @t17 @t27))) % 0.17/15.55 (assume @p6 (forall @t20 (=> @t31 @t30))) % 0.17/15.55 (assume @p7 @t36) % 0.17/15.55 (assume @p8 true) % 0.17/15.55 (assume @p9 (forall @t24 (=> @t13 (and (tptp.v1_relat_1 @t2) (tptp.v1_funct_1 @t2))))) % 0.17/15.55 (assume @p10 (forall @t20 (exists @t15 @t13))) % 0.17/15.55 (assume @p11 (forall @t20 (exists @t15 (tptp.m1_subset_1 @t2 @t4)))) % 0.17/15.55 (assume @p12 (tptp.v1_xboole_0 tptp.k1_xboole_0)) % 0.17/15.55 (assume @p13 @t53) % 0.17/15.55 (assume @p14 (exists @t20 (and @t17 @t29 @t27 @t28 @t26 @t25))) % 0.17/15.55 (assume @p15 (exists @t20 (and @t18 @t26))) % 0.17/15.55 (assume @p16 (exists @t20 (and @t29 @t27))) % 0.17/15.55 (assume @p17 (exists @t20 @t17)) % 0.17/15.55 (assume @p18 (exists @t20 @t31)) % 0.17/15.55 (assume @p19 (exists @t20 @t18)) % 0.17/15.55 (assume @p20 (exists @t20 @t30)) % 0.17/15.55 (assume @p21 (forall @t24 (=> @t23 @t54))) % 0.17/15.55 (assume @p22 (forall @t24 (=> @t54 (or @t48 @t23)))) % 0.17/15.55 (assume @p23 (forall @t24 (=> (forall @t11 (= (tptp.r2_hidden @t1 @t4) (tptp.r2_hidden @t1 @t2))) @t55))) % 0.17/15.55 (assume @p24 (forall @t20 (=> @t17 (= @t4 tptp.k1_xboole_0)))) % 0.17/15.55 (assume @p25 (forall @t24 (not (and @t23 @t48)))) % 0.17/15.55 (assume @p26 (forall @t24 (not (and @t17 (not @t55) @t48)))) % 0.17/15.55 (step @p27 :rule evaluate :args ((= true false))) % 0.17/15.55 (step @p28 :rule aci_norm :args ((= @t64 @t62))) % 0.17/15.55 (step @p29 :rule cong :premises (@p28) :args (@t66)) % 0.17/15.55 (step @p30 :rule quant-merge-prenex :args ((= (forall @t20 @t68) @t66))) % 0.17/15.55 (step @p31 :rule alpha_equiv :args (@t69 (@list @t57 @t56) (@list @t2 @t70))) % 0.17/15.55 (step @p32 :rule refl :args (@t17)) % 0.17/15.55 (step @p33 :rule nary_cong :premises (@p32 @p31) :args (@t71)) % 0.17/15.55 (step @p34 :rule quant-miniscope-or :args ((= @t68 @t71))) % 0.17/15.55 (step @p35 :rule trans :premises (@p34 @p33)) % 0.17/15.55 (step @p36 :rule symm :premises (@p35)) % 0.17/15.55 (step @p37 :rule cong :premises (@p36) :args ((forall @t20 (or @t17 @t78)))) % 0.17/15.55 (step @p38 :rule trans :premises (@p37 @p30)) % 0.17/15.55 (step @p39 :rule trans :premises (@p38 @p29)) % 0.17/15.55 (step @p40 :rule refl :args (@t78)) % 0.17/15.55 (step @p41 :rule bool-double-not-elim :args (@t17)) % 0.17/15.55 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or @t79 @t78))) % 0.17/15.55 (step @p43 :rule bool-impl-elim :args (@t18 @t78)) % 0.17/15.55 (step @p44 :rule trans :premises (@p43 @p42)) % 0.17/15.55 (step @p45 :rule cong :premises (@p44) :args ((forall @t20 (=> @t18 @t78)))) % 0.17/15.55 (step @p46 :rule trans :premises (@p45 @p39)) % 0.17/15.55 (step @p47 :rule aci_norm :args ((= @t81 @t76))) % 0.17/15.55 (step @p48 :rule cong :premises (@p47) :args (@t82)) % 0.17/15.55 (step @p49 :rule quant-merge-prenex :args ((= (forall @t15 @t84) @t82))) % 0.17/15.55 (step @p50 :rule alpha_equiv :args (@t85 (@list @t70) @t86)) % 0.17/15.55 (step @p51 :rule refl :args (@t75)) % 0.17/15.55 (step @p52 :rule nary_cong :premises (@p51 @p50) :args (@t87)) % 0.17/15.55 (step @p53 :rule quant-miniscope-or :args ((= @t84 @t87))) % 0.17/15.55 (step @p54 :rule trans :premises (@p53 @p52)) % 0.17/15.55 (step @p55 :rule symm :premises (@p54)) % 0.17/15.55 (step @p56 :rule cong :premises (@p55) :args ((forall @t15 (or @t75 @t91)))) % 0.17/15.55 (step @p57 :rule trans :premises (@p56 @p49)) % 0.17/15.55 (step @p58 :rule trans :premises (@p57 @p48)) % 0.17/15.55 (step @p59 :rule bool-impl-elim :args (@t13 @t91)) % 0.17/15.55 (step @p60 :rule cong :premises (@p59) :args ((forall @t15 (=> @t13 @t91)))) % 0.17/15.55 (step @p61 :rule trans :premises (@p60 @p58)) % 0.17/15.55 (step @p62 :rule aci_norm :args ((= (or @t89 (or @t6 @t88)) @t90))) % 0.17/15.55 (step @p63 :rule refl :args (@t88)) % 0.17/15.55 (step @p64 :rule bool-double-not-elim :args (@t6)) % 0.17/15.55 (step @p65 :rule nary_cong :premises (@p64 @p63) :args ((or (not @t7) @t88))) % 0.17/15.55 (step @p66 :rule bool-impl-elim :args (@t7 @t88)) % 0.17/15.55 (step @p67 :rule trans :premises (@p66 @p65)) % 0.17/15.55 (step @p68 :rule refl :args (@t89)) % 0.17/15.55 (step @p69 :rule nary_cong :premises (@p68 @p67) :args ((or @t89 @t92))) % 0.17/15.55 (step @p70 :rule trans :premises (@p69 @p62)) % 0.17/15.55 (step @p71 :rule bool-impl-elim :args (@t9 @t92)) % 0.17/15.55 (step @p72 :rule trans :premises (@p71 @p70)) % 0.17/15.55 (step @p73 :rule cong :premises (@p72) :args ((forall @t11 (=> @t9 @t92)))) % 0.17/15.55 (step @p74 :rule eq-symm :args (@t3 tptp.k1_xboole_0)) % 0.17/15.55 (step @p75 :rule refl :args (@t7)) % 0.17/15.55 (step @p76 :rule cong :premises (@p75 @p74) :args (@t8)) % 0.17/15.55 (step @p77 :rule refl :args (@t9)) % 0.17/15.55 (step @p78 :rule cong :premises (@p77 @p76) :args (@t10)) % 0.17/15.55 (step @p79 :rule cong :premises (@p78) :args (@t12)) % 0.17/15.55 (step @p80 :rule trans :premises (@p79 @p73)) % 0.17/15.55 (step @p81 :rule refl :args (@t13)) % 0.17/15.55 (step @p82 :rule cong :premises (@p81 @p80) :args (@t14)) % 0.17/15.55 (step @p83 :rule cong :premises (@p82) :args (@t16)) % 0.17/15.55 (step @p84 :rule trans :premises (@p83 @p61)) % 0.17/15.55 (step @p85 :rule refl :args (@t18)) % 0.17/15.55 (step @p86 :rule cong :premises (@p85 @p84) :args (@t19)) % 0.17/15.55 (step @p87 :rule cong :premises (@p86) :args (@t21)) % 0.17/15.55 (step @p88 :rule trans :premises (@p87 @p46)) % 0.17/15.55 (step @p89 :rule cong :premises (@p88) :args (@t22)) % 0.17/15.55 (step @p90 :rule eq_resolve :premises (@p1 @p89)) % 0.17/15.55 (step @p91 :rule skolemize :premises (@p90)) % 0.17/15.55 (step @p92 :rule cnf_or_neg :args (@t105 3)) % 0.17/15.55 (step @p93 :rule chain_m_resolution :premises (@p92 @p91) :args ((not @t99) @t106 @t107)) % 0.17/15.55 (step @p94 :rule false_intro :premises (@p93)) % 0.17/15.55 (step @p95 :rule eq-symm :args (@t109 @t110)) % 0.17/15.55 (step @p96 :rule eq-symm :args (@t111 @t110)) % 0.17/15.55 (step @p97 :rule cong :premises (@p96 @p95) :args (@t112)) % 0.17/15.55 (step @p98 :rule refl :args (@t113)) % 0.17/15.55 (step @p99 :rule refl :args (@t17)) % 0.17/15.55 (step @p100 :rule nary_cong :premises (@p99 @p98 @p97) :args (@t114)) % 0.17/15.55 (step @p101 :rule aci_norm :args ((= @t116 @t114))) % 0.17/15.55 (step @p102 :rule trans :premises (@p101 @p100)) % 0.17/15.55 (step @p103 :rule cong :premises (@p102) :args (@t118)) % 0.17/15.55 (step @p104 :rule quant-merge-prenex :args ((= (forall @t20 @t120) @t118))) % 0.17/15.55 (step @p105 :rule alpha_equiv :args (@t121 (@list @t108 @t110) (@list @t2 @t122))) % 0.17/15.55 (step @p106 :rule nary_cong :premises (@p32 @p105) :args (@t123)) % 0.17/15.55 (step @p107 :rule quant-miniscope-or :args ((= @t120 @t123))) % 0.17/15.55 (step @p108 :rule trans :premises (@p107 @p106)) % 0.17/15.55 (step @p109 :rule symm :premises (@p108)) % 0.17/15.55 (step @p110 :rule cong :premises (@p109) :args ((forall @t20 (or @t17 @t125)))) % 0.17/15.55 (step @p111 :rule trans :premises (@p110 @p104)) % 0.17/15.55 (step @p112 :rule trans :premises (@p111 @p103)) % 0.17/15.55 (step @p113 :rule refl :args (@t125)) % 0.17/15.55 (step @p114 :rule nary_cong :premises (@p41 @p113) :args ((or @t79 @t125))) % 0.17/15.55 (step @p115 :rule bool-impl-elim :args (@t18 @t125)) % 0.17/15.55 (step @p116 :rule trans :premises (@p115 @p114)) % 0.17/15.55 (step @p117 :rule cong :premises (@p116) :args ((forall @t20 (=> @t18 @t125)))) % 0.17/15.55 (step @p118 :rule trans :premises (@p117 @p112)) % 0.17/15.55 (step @p119 :rule eq-symm :args (@t122 @t32)) % 0.17/15.55 (step @p120 :rule eq-symm :args (@t122 @t5)) % 0.17/15.55 (step @p121 :rule cong :premises (@p120 @p119) :args (@t126)) % 0.17/15.55 (step @p122 :rule refl :args (@t75)) % 0.17/15.55 (step @p123 :rule nary_cong :premises (@p122 @p121) :args (@t127)) % 0.17/15.55 (step @p124 :rule cong :premises (@p123) :args (@t128)) % 0.17/15.55 (step @p125 :rule quant-merge-prenex :args ((= (forall @t15 @t130) @t128))) % 0.17/15.55 (step @p126 :rule alpha_equiv :args (@t131 (@list @t122) @t86)) % 0.17/15.55 (step @p127 :rule nary_cong :premises (@p51 @p126) :args (@t132)) % 0.17/15.55 (step @p128 :rule quant-miniscope-or :args ((= @t130 @t132))) % 0.17/15.55 (step @p129 :rule trans :premises (@p128 @p127)) % 0.17/15.55 (step @p130 :rule symm :premises (@p129)) % 0.17/15.55 (step @p131 :rule cong :premises (@p130) :args ((forall @t15 (or @t75 @t33)))) % 0.17/15.55 (step @p132 :rule trans :premises (@p131 @p125)) % 0.17/15.55 (step @p133 :rule trans :premises (@p132 @p124)) % 0.17/15.55 (step @p134 :rule bool-impl-elim :args (@t13 @t33)) % 0.17/15.55 (step @p135 :rule cong :premises (@p134) :args (@t34)) % 0.17/15.55 (step @p136 :rule trans :premises (@p135 @p133)) % 0.17/15.55 (step @p137 :rule cong :premises (@p85 @p136) :args (@t35)) % 0.17/15.55 (step @p138 :rule cong :premises (@p137) :args (@t36)) % 0.17/15.55 (step @p139 :rule trans :premises (@p138 @p118)) % 0.17/15.55 (step @p140 :rule eq_resolve :premises (@p7 @p139)) % 0.17/15.55 (step @p141 :rule bool-eq-true :args (@t134)) % 0.17/15.55 (step @p142 :rule eq-refl :args (@t98)) % 0.17/15.55 (step @p143 :rule refl :args (@t134)) % 0.17/15.55 (step @p144 :rule cong :premises (@p143 @p142) :args ((= @t134 @t135))) % 0.17/15.55 (step @p145 :rule trans :premises (@p144 @p141)) % 0.17/15.55 (step @p146 :rule eq-symm :args (@t135 @t134)) % 0.17/15.55 (step @p147 :rule trans :premises (@p146 @p145)) % 0.17/15.55 (step @p148 :rule refl :args (@t103)) % 0.17/15.55 (step @p149 :rule refl :args (@t104)) % 0.17/15.55 (step @p150 :rule nary_cong :premises (@p149 @p148 @p147) :args (@t136)) % 0.17/15.55 (step @p151 :rule refl :args (@t137)) % 0.17/15.55 (step @p152 :rule cong :premises (@p151 @p150) :args ((=> @t137 @t136))) % 0.17/15.55 (assume-push @p269 @t137) % 0.17/15.55 (step @p154 :rule instantiate :premises (@p140) :args ((@list @t97 @t95 @t98))) % 0.17/15.55 (step-pop @p270 :rule scope :premises (@p154)) % 0.17/15.55 (step @p155 :rule process_scope :premises (@p270) :args (@t136)) % 0.17/15.55 (step @p157 :rule eq_resolve :premises (@p155 @p152)) % 0.17/15.55 (step @p158 :rule implies_elim :premises (@p157)) % 0.17/15.55 (step @p159 :rule chain_m_resolution :premises (@p158 @p140) :args (@t138 (@list false) (@list @t137))) % 0.17/15.55 (step @p160 :rule bool-double-not-elim :args (@t102)) % 0.17/15.55 (step @p161 :rule refl :args (@t105)) % 0.17/15.55 (step @p162 :rule nary_cong :premises (@p161 @p160) :args ((or @t105 (not @t103)))) % 0.17/15.55 (step @p163 :rule cnf_or_neg :args (@t105 1)) % 0.17/15.55 (step @p164 :rule eq_resolve :premises (@p163 @p162)) % 0.17/15.55 (step @p165 :rule reordering :premises (@p164) :args ((or @t102 @t105))) % 0.17/15.55 (step @p166 :rule chain_m_resolution :premises (@p165 @p91) :args (@t102 @t106 @t107)) % 0.17/15.55 (step @p167 :rule cnf_or_neg :args (@t105 0)) % 0.17/15.55 (step @p168 :rule chain_m_resolution :premises (@p167 @p91) :args ((not @t104) @t106 @t107)) % 0.17/15.55 (step @p169 :rule cnf_or_pos :args (@t138)) % 0.17/15.55 (step @p170 :rule reordering :premises (@p169) :args ((or @t104 @t103 @t134 (not @t138)))) % 0.17/15.55 (step @p171 :rule chain_m_resolution :premises (@p170 @p168 @p166 @p159) :args (@t134 @t139 (@list @t104 @t102 @t138))) % 0.17/15.55 (step @p172 :rule symm :premises (@p171)) % 0.17/15.55 (step @p173 :rule refl :args (@t94)) % 0.17/15.55 (step @p174 :rule cong :premises (@p173 @p172) :args (@t140)) % 0.17/15.55 (step @p175 :rule aci_norm :args ((= (or (or @t48 @t144) @t143) (or @t48 @t144 @t143)))) % 0.17/15.55 (step @p176 :rule refl :args (@t142)) % 0.17/15.55 (step @p177 :rule bool-double-not-elim :args (@t54)) % 0.17/15.55 (step @p178 :rule nary_cong :premises (@p177 @p176) :args ((and (not @t145) @t142))) % 0.17/15.55 (step @p179 :rule bool-or-de-morgan :args (@t145 @t141 false)) % 0.17/15.55 (step @p180 :rule trans :premises (@p179 @p178)) % 0.17/15.55 (step @p181 :rule refl :args (@t45)) % 0.17/15.55 (step @p182 :rule cong :premises (@p181 @p180) :args (@t147)) % 0.17/15.55 (step @p183 :rule refl :args (@t144)) % 0.17/15.55 (step @p184 :rule bool-double-not-elim :args (@t48)) % 0.17/15.55 (step @p185 :rule nary_cong :premises (@p184 @p183) :args ((or (not @t49) @t144))) % 0.17/15.55 (step @p186 :rule bool-and-de-morgan :args (@t49 @t47 true)) % 0.17/15.55 (step @p187 :rule trans :premises (@p186 @p185)) % 0.17/15.55 (step @p188 :rule nary_cong :premises (@p187 @p182) :args ((or (not @t50) @t147))) % 0.17/15.55 (step @p189 :rule trans :premises (@p188 @p175)) % 0.17/15.55 (step @p190 :rule bool-impl-elim :args (@t50 @t147)) % 0.17/15.55 (step @p191 :rule trans :premises (@p190 @p189)) % 0.17/15.55 (step @p192 :rule cong :premises (@p191) :args ((forall @t52 (=> @t50 @t147)))) % 0.17/15.55 (step @p193 :rule aci_norm :args ((= (or @t145 false @t141) @t146))) % 0.17/15.55 (step @p194 :rule refl :args (@t141)) % 0.17/15.55 (step @p195 :rule evaluate :args ((not true))) % 0.17/15.55 (step @p196 :rule eq-refl :args (@t4)) % 0.17/15.55 (step @p197 :rule cong :premises (@p196) :args (@t148)) % 0.17/15.55 (step @p198 :rule trans :premises (@p197 @p195)) % 0.17/15.55 (step @p199 :rule refl :args (@t145)) % 0.17/15.55 (step @p200 :rule nary_cong :premises (@p199 @p198 @p194) :args (@t149)) % 0.17/15.55 (step @p201 :rule trans :premises (@p200 @p193)) % 0.17/15.55 (step @p202 :rule quant-var-elim-eq :args ((= (forall @t43 (or (not (= @t37 @t4)) @t152 @t151 @t150)) @t149))) % 0.17/15.55 (step @p203 :rule refl :args (@t150)) % 0.17/15.55 (step @p204 :rule refl :args (@t151)) % 0.17/15.55 (step @p205 :rule refl :args (@t152)) % 0.17/15.55 (step @p206 :rule eq-symm :args (@t4 @t37)) % 0.17/15.55 (step @p207 :rule cong :premises (@p206) :args (@t151)) % 0.17/15.55 (step @p208 :rule nary_cong :premises (@p207 @p205 @p204 @p203) :args (@t153)) % 0.17/15.55 (step @p209 :rule aci_norm :args ((= @t154 @t153))) % 0.17/15.55 (step @p210 :rule trans :premises (@p209 @p208)) % 0.17/15.55 (step @p211 :rule cong :premises (@p210) :args ((forall @t43 @t154))) % 0.17/15.55 (step @p212 :rule trans :premises (@p211 @p202)) % 0.17/15.55 (step @p213 :rule trans :premises (@p212 @p201)) % 0.17/15.55 (step @p214 :rule bool-double-not-elim :args (@t150)) % 0.17/15.55 (step @p215 :rule nary_cong :premises (@p205 @p204 @p214) :args (@t157)) % 0.17/15.55 (step @p216 :rule aci_norm :args ((= (or @t152 (or @t151 @t156)) @t157))) % 0.17/15.55 (step @p217 :rule trans :premises (@p216 @p215)) % 0.17/15.55 (step @p218 :rule bool-and-de-morgan :args (@t40 @t155 true)) % 0.17/15.55 (step @p219 :rule nary_cong :premises (@p205 @p218) :args ((or @t152 (not (and @t40 @t155))))) % 0.17/15.55 (step @p220 :rule bool-and-de-morgan :args (@t41 @t40 (and @t155))) % 0.17/15.55 (step @p221 :rule trans :premises (@p220 @p219)) % 0.17/15.55 (step @p222 :rule trans :premises (@p221 @p217)) % 0.17/15.55 (step @p223 :rule cong :premises (@p222) :args (@t159)) % 0.17/15.55 (step @p224 :rule trans :premises (@p223 @p213)) % 0.17/15.55 (step @p225 :rule cong :premises (@p224) :args (@t160)) % 0.17/15.55 (step @p226 :rule exists-elim :args ((= (exists @t43 @t158) @t160))) % 0.17/15.55 (step @p227 :rule trans :premises (@p226 @p225)) % 0.17/15.55 (step @p228 :rule eq-symm :args (@t38 tptp.k1_xboole_0)) % 0.17/15.55 (step @p229 :rule cong :premises (@p228) :args (@t39)) % 0.17/15.55 (step @p230 :rule refl :args (@t40)) % 0.17/15.55 (step @p231 :rule refl :args (@t41)) % 0.17/15.55 (step @p232 :rule nary_cong :premises (@p231 @p230 @p229) :args (@t42)) % 0.17/15.55 (step @p233 :rule cong :premises (@p232) :args (@t44)) % 0.17/15.55 (step @p234 :rule trans :premises (@p233 @p227)) % 0.17/15.55 (step @p235 :rule refl :args (@t45)) % 0.17/15.55 (step @p236 :rule cong :premises (@p235 @p234) :args (@t46)) % 0.17/15.55 (step @p237 :rule refl :args (@t50)) % 0.17/15.55 (step @p238 :rule cong :premises (@p237 @p236) :args (@t51)) % 0.17/15.55 (step @p239 :rule cong :premises (@p238) :args (@t53)) % 0.17/15.55 (step @p240 :rule trans :premises (@p239 @p192)) % 0.17/15.55 (step @p241 :rule eq_resolve :premises (@p13 @p240)) % 0.17/15.55 (step @p242 :rule instantiate :premises (@p241) :args ((@list @t94 @t97 @t95))) % 0.17/15.55 (step @p243 :rule cnf_or_pos :args (@t164)) % 0.17/15.55 (step @p244 :rule reordering :premises (@p243) :args ((or @t104 @t103 @t163 (not @t164)))) % 0.17/15.55 (step @p245 :rule chain_m_resolution :premises (@p244 @p168 @p166 @p242) :args (@t163 @t139 (@list @t104 @t102 @t164))) % 0.17/15.55 (step @p246 :rule cnf_or_neg :args (@t105 4)) % 0.17/15.55 (step @p247 :rule chain_m_resolution :premises (@p246 @p91) :args (@t161 @t106 @t107)) % 0.17/15.55 (step @p248 :rule bool-double-not-elim :args (@t100)) % 0.17/15.55 (step @p249 :rule nary_cong :premises (@p161 @p248) :args ((or @t105 (not @t101)))) % 0.17/15.55 (step @p250 :rule cnf_or_neg :args (@t105 2)) % 0.17/15.55 (step @p251 :rule eq_resolve :premises (@p250 @p249)) % 0.17/15.55 (step @p252 :rule reordering :premises (@p251) :args ((or @t100 @t105))) % 0.17/15.55 (step @p253 :rule chain_m_resolution :premises (@p252 @p91) :args (@t100 @t106 @t107)) % 0.17/15.55 (step @p254 :rule bool-double-not-elim :args (@t96)) % 0.17/15.55 (step @p255 :rule refl :args (@t101)) % 0.17/15.55 (step @p256 :rule refl :args (@t162)) % 0.17/15.55 (step @p257 :rule nary_cong :premises (@p256 @p255 @p254) :args ((or @t162 @t101 (not @t161)))) % 0.17/15.55 (step @p258 :rule cnf_and_neg :args (@t162)) % 0.17/15.55 (step @p259 :rule eq_resolve :premises (@p258 @p257)) % 0.17/15.55 (step @p260 :rule reordering :premises (@p259) :args ((or @t101 @t96 @t162))) % 0.17/15.55 (step @p261 :rule chain_m_resolution :premises (@p260 @p253 @p247) :args (@t162 (@list false true) (@list @t100 @t96))) % 0.17/15.55 (step @p262 :rule cnf_equiv_pos2 :args (@t163)) % 0.17/15.55 (step @p263 :rule reordering :premises (@p262) :args ((or @t140 (not @t162) (not @t163)))) % 0.17/15.55 (step @p264 :rule chain_m_resolution :premises (@p263 @p261 @p245) :args (@t140 (@list false false) (@list @t162 @t163))) % 0.17/15.55 (step @p265 :rule true_intro :premises (@p264)) % 0.17/15.55 (step @p266 :rule symm :premises (@p265)) % 0.17/15.55 (step @p267 :rule trans :premises (@p266 @p174 @p94)) % 0.17/15.55 (step @p268 false :rule eq_resolve :premises (@p267 @p27)) % 0.17/15.55 ) % 0.17/15.55 % SZS output end Proof % 0.17/15.55 % cvc5 exiting %------------------------------------------------------------------------------