%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM404+1 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n006.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 08:39:19 AM UTC 2026 % Result : Theorem 1.02s 1.29s % Output : Proof 1.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM404+1 : TPTP v9.2.1. Released v3.2.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n006.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 11:16:34 EDT 2026 % 0.16/0.35 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 1.02/1.29 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.02/1.29 % SZS status Theorem % 1.02/1.29 % SZS output start Proof % 1.02/1.29 ( % 1.02/1.29 (declare-sort $$unsorted 0) % 1.02/1.29 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 1.02/1.29 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 1.02/1.29 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 1.02/1.29 (declare-const tptp.function (-> $$unsorted Bool)) % 1.02/1.29 (declare-const tptp.empty (-> $$unsorted Bool)) % 1.02/1.29 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 1.02/1.29 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 1.02/1.29 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 1.02/1.29 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 1.02/1.29 (declare-const tptp.relation_non_empty (-> $$unsorted Bool)) % 1.02/1.29 (declare-const tptp.relation (-> $$unsorted Bool)) % 1.02/1.29 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 1.02/1.29 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 1.02/1.29 (declare-const tptp.empty_set $$unsorted) % 1.02/1.29 (define @t1 () (@var "A" $$unsorted)) % 1.02/1.29 (define @t2 () (@var "B" $$unsorted)) % 1.02/1.29 (define @t3 () (tptp.in @t2 @t1)) % 1.02/1.29 (define @t4 () (not @t3)) % 1.02/1.29 (define @t5 () (tptp.in @t1 @t2)) % 1.02/1.29 (define @t6 () (@list @t1 @t2)) % 1.02/1.29 (define @t7 () (forall @t6 (=> @t5 @t4))) % 1.02/1.29 (define @t8 () (tptp.function @t1)) % 1.02/1.29 (define @t9 () (tptp.empty @t1)) % 1.02/1.29 (define @t10 () (@list @t1)) % 1.02/1.29 (define @t11 () (tptp.epsilon_connected @t1)) % 1.02/1.29 (define @t12 () (tptp.epsilon_transitive @t1)) % 1.02/1.29 (define @t13 () (and @t12 @t11)) % 1.02/1.29 (define @t14 () (tptp.ordinal @t1)) % 1.02/1.29 (define @t15 () (tptp.relation @t1)) % 1.02/1.29 (define @t16 () (tptp.one_to_one @t1)) % 1.02/1.29 (define @t17 () (and @t15 @t8 @t16)) % 1.02/1.29 (define @t18 () (and @t15 @t9 @t8)) % 1.02/1.29 (define @t19 () (forall @t10 (=> @t13 @t14))) % 1.02/1.29 (define @t20 () (and @t12 @t11 @t14)) % 1.02/1.29 (define @t21 () (tptp.subset @t2 @t1)) % 1.02/1.29 (define @t22 () (@list @t2)) % 1.02/1.29 (define @t23 () (forall @t22 (=> @t3 @t21))) % 1.02/1.29 (define @t24 () (= @t12 @t23)) % 1.02/1.29 (define @t25 () (forall @t10 @t24)) % 1.02/1.29 (define @t26 () (@var "C" $$unsorted)) % 1.02/1.29 (define @t27 () (tptp.in @t26 @t2)) % 1.02/1.29 (define @t28 () (not @t27)) % 1.02/1.29 (define @t29 () (= @t2 @t26)) % 1.02/1.29 (define @t30 () (not @t29)) % 1.02/1.29 (define @t31 () (tptp.in @t2 @t26)) % 1.02/1.29 (define @t32 () (not @t31)) % 1.02/1.29 (define @t33 () (tptp.in @t26 @t1)) % 1.02/1.29 (define @t34 () (@list @t2 @t26)) % 1.02/1.29 (define @t35 () (forall @t34 (not (and @t3 @t33 @t32 @t30 @t28)))) % 1.02/1.29 (define @t36 () (= @t11 @t35)) % 1.02/1.29 (define @t37 () (forall @t10 @t36)) % 1.02/1.29 (define @t38 () (@list @t26)) % 1.02/1.29 (define @t39 () (forall @t38 (=> @t33 @t27))) % 1.02/1.29 (define @t40 () (tptp.subset @t1 @t2)) % 1.02/1.29 (define @t41 () (= @t40 @t39)) % 1.02/1.29 (define @t42 () (forall @t6 @t41)) % 1.02/1.29 (define @t43 () (tptp.relation_empty_yielding tptp.empty_set)) % 1.02/1.29 (define @t44 () (tptp.relation tptp.empty_set)) % 1.02/1.29 (define @t45 () (tptp.empty tptp.empty_set)) % 1.02/1.29 (define @t46 () (not @t9)) % 1.02/1.29 (define @t47 () (tptp.relation_empty_yielding @t1)) % 1.02/1.29 (define @t48 () (tptp.element @t1 @t2)) % 1.02/1.29 (define @t49 () (=> @t5 @t14)) % 1.02/1.29 (define @t50 () (tptp.ordinal @t2)) % 1.02/1.29 (define @t51 () (forall @t6 (=> @t50 @t49))) % 1.02/1.29 (define @t52 () (= @t1 @t2)) % 1.02/1.29 (define @t53 () (not @t52)) % 1.02/1.29 (define @t54 () (not @t5)) % 1.02/1.29 (define @t55 () (not (and @t54 @t53 @t4))) % 1.02/1.29 (define @t56 () (forall @t22 (=> @t50 @t55))) % 1.02/1.29 (define @t57 () (=> @t14 @t56)) % 1.02/1.29 (define @t58 () (forall @t10 @t57)) % 1.02/1.29 (define @t59 () (tptp.empty @t2)) % 1.02/1.29 (define @t60 () (forall @t10 (not (forall @t22 (= @t3 @t50))))) % 1.02/1.29 (define @t61 () (not @t60)) % 1.02/1.29 (define @t62 () (tptp.element @t2 (tptp.powerset @t26))) % 1.02/1.29 (define @t63 () (@list @t1 @t2 @t26)) % 1.02/1.29 (define @t64 () (@quantifiers_skolemize @t60 0)) % 1.02/1.29 (define @t65 () (tptp.in @t2 @t64)) % 1.02/1.29 (define @t66 () (forall @t22 (= @t50 @t65))) % 1.02/1.29 (define @t67 () (forall @t22 (= @t65 @t50))) % 1.02/1.29 (define @t68 () (not (not @t67))) % 1.02/1.29 (define @t69 () (@list true)) % 1.02/1.29 (define @t70 () (tptp.in @t26 @t64)) % 1.02/1.29 (define @t71 () (not @t65)) % 1.02/1.29 (define @t72 () (forall @t22 (or @t71 (tptp.subset @t2 @t64)))) % 1.02/1.29 (define @t73 () (@quantifiers_skolemize @t72 0)) % 1.02/1.29 (define @t74 () (forall @t38 (or (not (tptp.in @t26 @t73)) @t70))) % 1.02/1.29 (define @t75 () (@quantifiers_skolemize @t74 0)) % 1.02/1.29 (define @t76 () (tptp.ordinal @t75)) % 1.02/1.29 (define @t77 () (tptp.in @t75 @t64)) % 1.02/1.29 (define @t78 () (= @t76 @t77)) % 1.02/1.29 (define @t79 () (= @t77 @t76)) % 1.02/1.29 (define @t80 () (@list false)) % 1.02/1.29 (define @t81 () (@list @t66)) % 1.02/1.29 (define @t82 () (@list @t64)) % 1.02/1.29 (define @t83 () (not @t11)) % 1.02/1.29 (define @t84 () (not @t12)) % 1.02/1.29 (define @t85 () (not @t33)) % 1.02/1.29 (define @t86 () (not @t28)) % 1.02/1.29 (define @t87 () (not @t30)) % 1.02/1.29 (define @t88 () (not @t32)) % 1.02/1.29 (define @t89 () (or @t4 @t85 @t88 @t87 @t86)) % 1.02/1.29 (define @t90 () (forall @t34 (or @t71 (not @t70) @t31 @t29 @t27))) % 1.02/1.29 (define @t91 () (@quantifiers_skolemize @t90 0)) % 1.02/1.29 (define @t92 () (tptp.in @t91 @t64)) % 1.02/1.29 (define @t93 () (@quantifiers_skolemize @t90 1)) % 1.02/1.29 (define @t94 () (tptp.in @t93 @t91)) % 1.02/1.29 (define @t95 () (= @t91 @t93)) % 1.02/1.29 (define @t96 () (tptp.in @t91 @t93)) % 1.02/1.29 (define @t97 () (tptp.in @t93 @t64)) % 1.02/1.29 (define @t98 () (not @t97)) % 1.02/1.29 (define @t99 () (not @t92)) % 1.02/1.29 (define @t100 () (or @t99 @t98 @t96 @t95 @t94)) % 1.02/1.29 (define @t101 () (tptp.ordinal @t91)) % 1.02/1.29 (define @t102 () (= @t101 @t92)) % 1.02/1.29 (define @t103 () (= @t92 @t101)) % 1.02/1.29 (define @t104 () (tptp.ordinal @t93)) % 1.02/1.29 (define @t105 () (= @t104 @t97)) % 1.02/1.29 (define @t106 () (= @t97 @t104)) % 1.02/1.29 (define @t107 () (@var "BOUND_VARIABLE_7732" $$unsorted)) % 1.02/1.29 (define @t108 () (tptp.in @t107 @t1)) % 1.02/1.29 (define @t109 () (= @t1 @t107)) % 1.02/1.29 (define @t110 () (tptp.in @t1 @t107)) % 1.02/1.29 (define @t111 () (not (tptp.ordinal @t107))) % 1.02/1.29 (define @t112 () (not @t14)) % 1.02/1.29 (define @t113 () (or @t111 @t110 @t109 @t108)) % 1.02/1.29 (define @t114 () (or @t112 @t113)) % 1.02/1.29 (define @t115 () (forall (@list @t1 @t107) @t114)) % 1.02/1.29 (define @t116 () (@list @t107)) % 1.02/1.29 (define @t117 () (forall @t116 @t114)) % 1.02/1.29 (define @t118 () (forall @t116 @t113)) % 1.02/1.29 (define @t119 () (or @t112 @t118)) % 1.02/1.29 (define @t120 () (not @t50)) % 1.02/1.29 (define @t121 () (or @t120 @t5 @t52 @t3)) % 1.02/1.29 (define @t122 () (forall @t22 @t121)) % 1.02/1.29 (define @t123 () (not @t4)) % 1.02/1.29 (define @t124 () (not @t53)) % 1.02/1.29 (define @t125 () (not @t54)) % 1.02/1.29 (define @t126 () (or @t125 @t124 @t123)) % 1.02/1.29 (define @t127 () (not @t104)) % 1.02/1.29 (define @t128 () (not @t101)) % 1.02/1.29 (define @t129 () (or @t128 @t127 @t96 @t95 @t94)) % 1.02/1.29 (define @t130 () (not @t100)) % 1.02/1.29 (define @t131 () (not @t90)) % 1.02/1.29 (define @t132 () (tptp.epsilon_connected @t64)) % 1.02/1.29 (define @t133 () (= @t132 @t90)) % 1.02/1.29 (define @t134 () (@list false false)) % 1.02/1.29 (define @t135 () (tptp.in @t64 @t64)) % 1.02/1.29 (define @t136 () (not @t135)) % 1.02/1.29 (define @t137 () (or @t136 @t136)) % 1.02/1.29 (define @t138 () (forall @t6 (or @t54 @t4))) % 1.02/1.29 (define @t139 () (tptp.ordinal @t64)) % 1.02/1.29 (define @t140 () (= @t139 @t135)) % 1.02/1.29 (define @t141 () (not @t139)) % 1.02/1.29 (define @t142 () (@list true false)) % 1.02/1.29 (define @t143 () (not @t132)) % 1.02/1.29 (define @t144 () (tptp.epsilon_transitive @t64)) % 1.02/1.29 (define @t145 () (not @t144)) % 1.02/1.29 (define @t146 () (or @t145 @t143 @t139)) % 1.02/1.29 (define @t147 () (= @t144 @t72)) % 1.02/1.29 (define @t148 () (not @t72)) % 1.02/1.29 (define @t149 () (tptp.subset @t73 @t64)) % 1.02/1.29 (define @t150 () (tptp.in @t73 @t64)) % 1.02/1.29 (define @t151 () (not @t150)) % 1.02/1.29 (define @t152 () (or @t151 @t149)) % 1.02/1.29 (define @t153 () (not @t152)) % 1.02/1.29 (define @t154 () (@list @t152)) % 1.02/1.29 (define @t155 () (= @t149 @t74)) % 1.02/1.29 (define @t156 () (not @t74)) % 1.02/1.29 (define @t157 () (tptp.in @t75 @t73)) % 1.02/1.29 (define @t158 () (not @t157)) % 1.02/1.29 (define @t159 () (or @t158 @t77)) % 1.02/1.29 (define @t160 () (not @t159)) % 1.02/1.29 (define @t161 () (@list @t159)) % 1.02/1.29 (define @t162 () (tptp.ordinal @t73)) % 1.02/1.29 (define @t163 () (= @t162 @t150)) % 1.02/1.29 (define @t164 () (= @t150 @t162)) % 1.02/1.29 (define @t165 () (not @t162)) % 1.02/1.29 (define @t166 () (or @t165 @t158 @t76)) % 1.02/1.29 (assume @p1 @t7) % 1.02/1.29 (assume @p2 (forall @t10 (=> @t9 @t8))) % 1.02/1.29 (assume @p3 (forall @t10 (=> @t14 @t13))) % 1.02/1.29 (assume @p4 (forall @t10 (=> @t9 @t15))) % 1.02/1.29 (assume @p5 (forall @t10 (=> @t18 @t17))) % 1.02/1.29 (assume @p6 @t19) % 1.02/1.29 (assume @p7 (forall @t10 (=> @t9 @t20))) % 1.02/1.29 (assume @p8 @t25) % 1.02/1.29 (assume @p9 @t37) % 1.02/1.29 (assume @p10 @t42) % 1.02/1.29 (assume @p11 (forall @t10 (= @t14 @t13))) % 1.02/1.29 (assume @p12 (forall @t10 (exists @t22 (tptp.element @t2 @t1)))) % 1.02/1.29 (assume @p13 (and @t45 @t44 @t43)) % 1.02/1.29 (assume @p14 @t45) % 1.02/1.29 (assume @p15 (and @t44 @t43 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) @t45 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set))) % 1.02/1.29 (assume @p16 (and @t45 @t44)) % 1.02/1.29 (assume @p17 (exists @t10 (and @t15 @t8))) % 1.02/1.29 (assume @p18 (exists @t10 @t20)) % 1.02/1.29 (assume @p19 (exists @t10 (and @t9 @t15))) % 1.02/1.29 (assume @p20 (exists @t10 @t9)) % 1.02/1.29 (assume @p21 (exists @t10 @t18)) % 1.02/1.29 (assume @p22 (exists @t10 (and @t15 @t8 @t16 @t9 @t12 @t11 @t14))) % 1.02/1.29 (assume @p23 (exists @t10 (and @t46 @t15))) % 1.02/1.29 (assume @p24 (exists @t10 @t46)) % 1.02/1.29 (assume @p25 (exists @t10 @t17)) % 1.02/1.29 (assume @p26 (exists @t10 (and @t46 @t12 @t11 @t14))) % 1.02/1.29 (assume @p27 (exists @t10 (and @t15 @t47))) % 1.02/1.29 (assume @p28 (exists @t10 (and @t15 @t47 @t8))) % 1.02/1.29 (assume @p29 (exists @t10 (and @t15 (tptp.relation_non_empty @t1) @t8))) % 1.02/1.29 (assume @p30 (forall @t6 (tptp.subset @t1 @t1))) % 1.02/1.29 (assume @p31 (forall @t6 (=> @t5 @t48))) % 1.02/1.29 (assume @p32 @t51) % 1.02/1.29 (assume @p33 @t58) % 1.02/1.29 (assume @p34 (forall @t6 (=> @t48 (or @t59 @t5)))) % 1.02/1.29 (assume @p35 @t61) % 1.02/1.29 (assume @p36 (forall @t6 (= (tptp.element @t1 (tptp.powerset @t2)) @t40))) % 1.02/1.29 (assume @p37 (forall @t63 (=> (and @t5 @t62) (tptp.element @t1 @t26)))) % 1.02/1.29 (assume @p38 (forall @t63 (not (and @t5 @t62 (tptp.empty @t26))))) % 1.02/1.29 (assume @p39 (forall @t10 (=> @t9 (= @t1 tptp.empty_set)))) % 1.02/1.29 (assume @p40 (forall @t6 (not (and @t5 @t59)))) % 1.02/1.29 (assume @p41 (forall @t6 (not (and @t9 @t53 @t59)))) % 1.02/1.29 (assume @p42 true) % 1.02/1.29 (step @p43 :rule refl :args (@t66)) % 1.02/1.29 (step @p44 :rule bool-double-not-elim :args (@t60)) % 1.02/1.29 (step @p45 :rule nary_cong :premises (@p44 @p43) :args ((or (not @t61) @t66))) % 1.02/1.29 (step @p46 :rule eq-symm :args (@t65 @t50)) % 1.02/1.29 (step @p47 :rule cong :premises (@p46) :args (@t67)) % 1.02/1.29 (step @p48 :rule bool-double-not-elim :args (@t67)) % 1.02/1.29 (step @p49 :rule trans :premises (@p48 @p47)) % 1.02/1.29 (step @p50 :rule refl :args (@t61)) % 1.02/1.29 (step @p51 :rule cong :premises (@p50 @p49) :args ((=> @t61 @t68))) % 1.02/1.29 (assume-push @p302 @t61) % 1.02/1.29 (step @p53 :rule skolemize :premises (@p35)) % 1.02/1.29 (step-pop @p303 :rule scope :premises (@p53)) % 1.02/1.29 (step @p54 :rule process_scope :premises (@p303) :args (@t68)) % 1.02/1.29 (step @p56 :rule eq_resolve :premises (@p54 @p51)) % 1.02/1.29 (step @p57 :rule implies_elim :premises (@p56)) % 1.02/1.29 (step @p58 :rule eq_resolve :premises (@p57 @p45)) % 1.02/1.29 (step @p59 :rule chain_m_resolution :premises (@p58 @p35) :args (@t66 @t69 (@list @t60))) % 1.02/1.29 (step @p60 :rule eq-symm :args (@t76 @t77)) % 1.02/1.29 (step @p61 :rule cong :premises (@p43 @p60) :args ((=> @t66 @t78))) % 1.02/1.29 (assume-push @p304 @t66) % 1.02/1.29 (step @p63 :rule instantiate :premises (@p59) :args ((@list @t75))) % 1.02/1.29 (step-pop @p305 :rule scope :premises (@p63)) % 1.02/1.29 (step @p64 :rule process_scope :premises (@p305) :args (@t78)) % 1.02/1.29 (step @p66 :rule eq_resolve :premises (@p64 @p61)) % 1.02/1.29 (step @p67 :rule implies_elim :premises (@p66)) % 1.02/1.29 (step @p68 :rule chain_m_resolution :premises (@p67 @p59) :args (@t79 @t80 @t81)) % 1.02/1.29 (step @p69 :rule bool-impl-elim :args (@t33 @t27)) % 1.02/1.29 (step @p70 :rule cong :premises (@p69) :args (@t39)) % 1.02/1.29 (step @p71 :rule refl :args (@t40)) % 1.02/1.29 (step @p72 :rule cong :premises (@p71 @p70) :args (@t41)) % 1.02/1.29 (step @p73 :rule cong :premises (@p72) :args (@t42)) % 1.02/1.29 (step @p74 :rule eq_resolve :premises (@p10 @p73)) % 1.02/1.29 (step @p75 :rule instantiate :premises (@p74) :args ((@list @t73 @t64))) % 1.02/1.29 (step @p76 :rule bool-impl-elim :args (@t3 @t21)) % 1.02/1.29 (step @p77 :rule cong :premises (@p76) :args (@t23)) % 1.02/1.29 (step @p78 :rule refl :args (@t12)) % 1.02/1.29 (step @p79 :rule cong :premises (@p78 @p77) :args (@t24)) % 1.02/1.29 (step @p80 :rule cong :premises (@p79) :args (@t25)) % 1.02/1.29 (step @p81 :rule eq_resolve :premises (@p8 @p80)) % 1.02/1.29 (step @p82 :rule instantiate :premises (@p81) :args (@t82)) % 1.02/1.29 (step @p83 :rule aci_norm :args ((= (or (or @t84 @t83) @t14) (or @t84 @t83 @t14)))) % 1.02/1.29 (step @p84 :rule refl :args (@t14)) % 1.02/1.29 (step @p85 :rule bool-and-de-morgan :args (@t12 @t11 true)) % 1.02/1.29 (step @p86 :rule nary_cong :premises (@p85 @p84) :args ((or (not @t13) @t14))) % 1.02/1.29 (step @p87 :rule trans :premises (@p86 @p83)) % 1.02/1.29 (step @p88 :rule bool-impl-elim :args (@t13 @t14)) % 1.02/1.29 (step @p89 :rule trans :premises (@p88 @p87)) % 1.02/1.29 (step @p90 :rule cong :premises (@p89) :args (@t19)) % 1.02/1.29 (step @p91 :rule eq_resolve :premises (@p6 @p90)) % 1.02/1.29 (step @p92 :rule instantiate :premises (@p91) :args (@t82)) % 1.02/1.29 (step @p93 :rule bool-double-not-elim :args (@t27)) % 1.02/1.29 (step @p94 :rule bool-double-not-elim :args (@t29)) % 1.02/1.29 (step @p95 :rule bool-double-not-elim :args (@t31)) % 1.02/1.29 (step @p96 :rule refl :args (@t85)) % 1.02/1.29 (step @p97 :rule refl :args (@t4)) % 1.02/1.29 (step @p98 :rule nary_cong :premises (@p97 @p96 @p95 @p94 @p93) :args (@t89)) % 1.02/1.29 (step @p99 :rule aci_norm :args ((= (or @t4 (or @t85 (or @t88 (or @t87 @t86)))) @t89))) % 1.02/1.29 (step @p100 :rule trans :premises (@p99 @p98)) % 1.02/1.29 (step @p101 :rule bool-and-de-morgan :args (@t30 @t28 true)) % 1.02/1.29 (step @p102 :rule refl :args (@t88)) % 1.02/1.29 (step @p103 :rule nary_cong :premises (@p102 @p101) :args ((or @t88 (not (and @t30 @t28))))) % 1.02/1.29 (step @p104 :rule bool-and-de-morgan :args (@t32 @t30 (and @t28))) % 1.02/1.29 (step @p105 :rule trans :premises (@p104 @p103)) % 1.02/1.29 (step @p106 :rule nary_cong :premises (@p96 @p105) :args ((or @t85 (not (and @t32 @t30 @t28))))) % 1.02/1.29 (step @p107 :rule bool-and-de-morgan :args (@t33 @t32 (and @t30 @t28))) % 1.02/1.29 (step @p108 :rule trans :premises (@p107 @p106)) % 1.02/1.29 (step @p109 :rule nary_cong :premises (@p97 @p108) :args ((or @t4 (not (and @t33 @t32 @t30 @t28))))) % 1.02/1.29 (step @p110 :rule bool-and-de-morgan :args (@t3 @t33 (and @t32 @t30 @t28))) % 1.02/1.29 (step @p111 :rule trans :premises (@p110 @p109)) % 1.02/1.29 (step @p112 :rule trans :premises (@p111 @p100)) % 1.02/1.29 (step @p113 :rule cong :premises (@p112) :args (@t35)) % 1.02/1.29 (step @p114 :rule refl :args (@t11)) % 1.02/1.29 (step @p115 :rule cong :premises (@p114 @p113) :args (@t36)) % 1.02/1.29 (step @p116 :rule cong :premises (@p115) :args (@t37)) % 1.02/1.29 (step @p117 :rule eq_resolve :premises (@p9 @p116)) % 1.02/1.29 (step @p118 :rule instantiate :premises (@p117) :args (@t82)) % 1.02/1.29 (step @p119 :rule bool-double-not-elim :args (@t92)) % 1.02/1.29 (step @p120 :rule refl :args (@t100)) % 1.02/1.29 (step @p121 :rule nary_cong :premises (@p120 @p119) :args ((or @t100 (not @t99)))) % 1.02/1.29 (step @p122 :rule cnf_or_neg :args (@t100 0)) % 1.02/1.29 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 1.02/1.29 (step @p124 :rule reordering :premises (@p123) :args ((or @t92 @t100))) % 1.02/1.29 (step @p125 :rule bool-double-not-elim :args (@t97)) % 1.02/1.29 (step @p126 :rule nary_cong :premises (@p120 @p125) :args ((or @t100 (not @t98)))) % 1.02/1.29 (step @p127 :rule cnf_or_neg :args (@t100 1)) % 1.02/1.29 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 1.02/1.29 (step @p129 :rule reordering :premises (@p128) :args ((or @t97 @t100))) % 1.02/1.29 (step @p130 :rule cnf_or_neg :args (@t100 2)) % 1.02/1.29 (step @p131 :rule cnf_or_neg :args (@t100 3)) % 1.02/1.29 (step @p132 :rule cnf_or_neg :args (@t100 4)) % 1.02/1.29 (step @p133 :rule eq-symm :args (@t101 @t92)) % 1.02/1.29 (step @p134 :rule cong :premises (@p43 @p133) :args ((=> @t66 @t102))) % 1.02/1.29 (assume-push @p306 @t66) % 1.02/1.29 (step @p136 :rule instantiate :premises (@p59) :args ((@list @t91))) % 1.02/1.29 (step-pop @p307 :rule scope :premises (@p136)) % 1.02/1.29 (step @p137 :rule process_scope :premises (@p307) :args (@t102)) % 1.02/1.29 (step @p139 :rule eq_resolve :premises (@p137 @p134)) % 1.02/1.29 (step @p140 :rule implies_elim :premises (@p139)) % 1.02/1.29 (step @p141 :rule chain_m_resolution :premises (@p140 @p59) :args (@t103 @t80 @t81)) % 1.02/1.29 (step @p142 :rule cnf_equiv_pos1 :args (@t103)) % 1.02/1.29 (step @p143 :rule reordering :premises (@p142) :args ((or @t99 @t101 (not @t103)))) % 1.02/1.29 (step @p144 :rule eq-symm :args (@t104 @t97)) % 1.02/1.29 (step @p145 :rule cong :premises (@p43 @p144) :args ((=> @t66 @t105))) % 1.02/1.29 (assume-push @p308 @t66) % 1.02/1.29 (step @p147 :rule instantiate :premises (@p59) :args ((@list @t93))) % 1.02/1.29 (step-pop @p309 :rule scope :premises (@p147)) % 1.02/1.29 (step @p148 :rule process_scope :premises (@p309) :args (@t105)) % 1.02/1.29 (step @p150 :rule eq_resolve :premises (@p148 @p145)) % 1.02/1.29 (step @p151 :rule implies_elim :premises (@p150)) % 1.02/1.29 (step @p152 :rule chain_m_resolution :premises (@p151 @p59) :args (@t106 @t80 @t81)) % 1.02/1.29 (step @p153 :rule cnf_equiv_pos1 :args (@t106)) % 1.02/1.29 (step @p154 :rule reordering :premises (@p153) :args ((or @t98 @t104 (not @t106)))) % 1.02/1.29 (step @p155 :rule aci_norm :args ((= @t114 (or @t112 @t111 @t110 @t109 @t108)))) % 1.02/1.29 (step @p156 :rule cong :premises (@p155) :args (@t115)) % 1.02/1.29 (step @p157 :rule quant-merge-prenex :args ((= (forall @t10 @t117) @t115))) % 1.02/1.29 (step @p158 :rule alpha_equiv :args (@t118 (@list @t107) (@list @t2))) % 1.02/1.29 (step @p159 :rule refl :args (@t112)) % 1.02/1.29 (step @p160 :rule nary_cong :premises (@p159 @p158) :args (@t119)) % 1.02/1.29 (step @p161 :rule quant-miniscope-or :args ((= @t117 @t119))) % 1.02/1.29 (step @p162 :rule trans :premises (@p161 @p160)) % 1.02/1.29 (step @p163 :rule symm :premises (@p162)) % 1.02/1.29 (step @p164 :rule cong :premises (@p163) :args ((forall @t10 (or @t112 @t122)))) % 1.02/1.29 (step @p165 :rule trans :premises (@p164 @p157)) % 1.02/1.29 (step @p166 :rule trans :premises (@p165 @p156)) % 1.02/1.29 (step @p167 :rule bool-impl-elim :args (@t14 @t122)) % 1.02/1.29 (step @p168 :rule cong :premises (@p167) :args ((forall @t10 (=> @t14 @t122)))) % 1.02/1.29 (step @p169 :rule trans :premises (@p168 @p166)) % 1.02/1.29 (step @p170 :rule aci_norm :args ((= (or @t120 (or @t5 @t52 @t3)) @t121))) % 1.02/1.29 (step @p171 :rule bool-double-not-elim :args (@t3)) % 1.02/1.29 (step @p172 :rule bool-double-not-elim :args (@t52)) % 1.02/1.29 (step @p173 :rule bool-double-not-elim :args (@t5)) % 1.02/1.29 (step @p174 :rule nary_cong :premises (@p173 @p172 @p171) :args (@t126)) % 1.02/1.29 (step @p175 :rule aci_norm :args ((= (or @t125 (or @t124 @t123)) @t126))) % 1.02/1.29 (step @p176 :rule trans :premises (@p175 @p174)) % 1.02/1.29 (step @p177 :rule bool-and-de-morgan :args (@t53 @t4 true)) % 1.02/1.29 (step @p178 :rule refl :args (@t125)) % 1.02/1.29 (step @p179 :rule nary_cong :premises (@p178 @p177) :args ((or @t125 (not (and @t53 @t4))))) % 1.02/1.29 (step @p180 :rule bool-and-de-morgan :args (@t54 @t53 (and @t4))) % 1.02/1.29 (step @p181 :rule trans :premises (@p180 @p179)) % 1.02/1.29 (step @p182 :rule trans :premises (@p181 @p176)) % 1.02/1.29 (step @p183 :rule refl :args (@t120)) % 1.02/1.29 (step @p184 :rule nary_cong :premises (@p183 @p182) :args ((or @t120 @t55))) % 1.02/1.29 (step @p185 :rule trans :premises (@p184 @p170)) % 1.02/1.29 (step @p186 :rule bool-impl-elim :args (@t50 @t55)) % 1.02/1.29 (step @p187 :rule trans :premises (@p186 @p185)) % 1.02/1.29 (step @p188 :rule cong :premises (@p187) :args (@t56)) % 1.02/1.29 (step @p189 :rule refl :args (@t14)) % 1.02/1.29 (step @p190 :rule cong :premises (@p189 @p188) :args (@t57)) % 1.02/1.29 (step @p191 :rule cong :premises (@p190) :args (@t58)) % 1.02/1.29 (step @p192 :rule trans :premises (@p191 @p169)) % 1.02/1.29 (step @p193 :rule eq_resolve :premises (@p33 @p192)) % 1.02/1.29 (step @p194 :rule instantiate :premises (@p193) :args ((@list @t91 @t93))) % 1.02/1.29 (step @p195 :rule cnf_or_pos :args (@t129)) % 1.02/1.29 (step @p196 :rule reordering :premises (@p195) :args ((or @t96 @t95 @t94 @t128 @t127 (not @t129)))) % 1.02/1.29 (step @p197 :rule chain_m_resolution :premises (@p196 @p194 @p154 @p152 @p143 @p141 @p132 @p131 @p130 @p129 @p124) :args (@t100 (@list false false false false false true true true false false) (@list @t129 @t104 @t106 @t101 @t103 @t94 @t95 @t96 @t97 @t92))) % 1.02/1.29 (step @p198 :rule refl :args (@t130)) % 1.02/1.29 (step @p199 :rule bool-double-not-elim :args (@t90)) % 1.02/1.29 (step @p200 :rule nary_cong :premises (@p199 @p198) :args ((or (not @t131) @t130))) % 1.02/1.29 (assume-push @p310 @t131) % 1.02/1.29 (step @p202 :rule skolemize :premises (@p310)) % 1.02/1.29 (step-pop @p311 :rule scope :premises (@p202)) % 1.02/1.29 (step @p203 :rule process_scope :premises (@p311) :args (@t130)) % 1.02/1.29 (step @p205 :rule implies_elim :premises (@p203)) % 1.02/1.29 (step @p206 :rule eq_resolve :premises (@p205 @p200)) % 1.02/1.29 (step @p207 :rule chain_m_resolution :premises (@p206 @p197) :args (@t90 @t80 (@list @t100))) % 1.02/1.29 (step @p208 :rule cnf_equiv_pos2 :args (@t133)) % 1.02/1.29 (step @p209 :rule reordering :premises (@p208) :args ((or @t132 @t131 (not @t133)))) % 1.02/1.29 (step @p210 :rule chain_m_resolution :premises (@p209 @p207 @p118) :args (@t132 @t134 (@list @t90 @t133))) % 1.02/1.29 (step @p211 :rule instantiate :premises (@p59) :args (@t82)) % 1.02/1.29 (step @p212 :rule bool-impl-elim :args (@t5 @t4)) % 1.02/1.29 (step @p213 :rule cong :premises (@p212) :args (@t7)) % 1.02/1.29 (step @p214 :rule eq_resolve :premises (@p1 @p213)) % 1.02/1.29 (step @p215 :rule aci_norm :args ((= @t137 @t136))) % 1.02/1.29 (step @p216 :rule refl :args (@t138)) % 1.02/1.29 (step @p217 :rule cong :premises (@p216 @p215) :args ((=> @t138 @t137))) % 1.02/1.29 (assume-push @p312 @t138) % 1.02/1.29 (step @p219 :rule instantiate :premises (@p214) :args ((@list @t64 @t64))) % 1.02/1.29 (step-pop @p313 :rule scope :premises (@p219)) % 1.02/1.29 (step @p220 :rule process_scope :premises (@p313) :args (@t137)) % 1.02/1.29 (step @p222 :rule eq_resolve :premises (@p220 @p217)) % 1.02/1.29 (step @p223 :rule implies_elim :premises (@p222)) % 1.02/1.29 (step @p224 :rule chain_m_resolution :premises (@p223 @p214) :args (@t136 @t80 (@list @t138))) % 1.02/1.29 (step @p225 :rule cnf_equiv_pos1 :args (@t140)) % 1.02/1.29 (step @p226 :rule reordering :premises (@p225) :args ((or @t141 @t135 (not @t140)))) % 1.02/1.29 (step @p227 :rule chain_m_resolution :premises (@p226 @p224 @p211) :args (@t141 @t142 (@list @t135 @t140))) % 1.02/1.29 (step @p228 :rule cnf_or_pos :args (@t146)) % 1.02/1.29 (step @p229 :rule reordering :premises (@p228) :args ((or @t139 @t145 @t143 (not @t146)))) % 1.02/1.29 (step @p230 :rule chain_m_resolution :premises (@p229 @p227 @p210 @p92) :args (@t145 (@list true false false) (@list @t139 @t132 @t146))) % 1.02/1.29 (step @p231 :rule cnf_equiv_pos2 :args (@t147)) % 1.02/1.29 (step @p232 :rule reordering :premises (@p231) :args ((or @t144 @t148 (not @t147)))) % 1.02/1.29 (step @p233 :rule chain_m_resolution :premises (@p232 @p230 @p82) :args (@t148 @t142 (@list @t144 @t147))) % 1.02/1.29 (step @p234 :rule refl :args (@t153)) % 1.02/1.29 (step @p235 :rule bool-double-not-elim :args (@t72)) % 1.02/1.29 (step @p236 :rule nary_cong :premises (@p235 @p234) :args ((or (not @t148) @t153))) % 1.02/1.29 (assume-push @p314 @t148) % 1.02/1.29 (step @p238 :rule skolemize :premises (@p314)) % 1.02/1.29 (step-pop @p315 :rule scope :premises (@p238)) % 1.02/1.29 (step @p239 :rule process_scope :premises (@p315) :args (@t153)) % 1.02/1.29 (step @p241 :rule implies_elim :premises (@p239)) % 1.02/1.29 (step @p242 :rule eq_resolve :premises (@p241 @p236)) % 1.02/1.29 (step @p243 :rule chain_m_resolution :premises (@p242 @p233) :args (@t153 @t69 (@list @t72))) % 1.02/1.29 (step @p244 :rule cnf_or_neg :args (@t152 1)) % 1.02/1.29 (step @p245 :rule chain_m_resolution :premises (@p244 @p243) :args ((not @t149) @t69 @t154)) % 1.02/1.29 (step @p246 :rule cnf_equiv_pos2 :args (@t155)) % 1.02/1.29 (step @p247 :rule reordering :premises (@p246) :args ((or @t149 @t156 (not @t155)))) % 1.02/1.29 (step @p248 :rule chain_m_resolution :premises (@p247 @p245 @p75) :args (@t156 @t142 (@list @t149 @t155))) % 1.02/1.29 (step @p249 :rule refl :args (@t160)) % 1.02/1.29 (step @p250 :rule bool-double-not-elim :args (@t74)) % 1.02/1.29 (step @p251 :rule nary_cong :premises (@p250 @p249) :args ((or (not @t156) @t160))) % 1.02/1.29 (assume-push @p316 @t156) % 1.02/1.29 (step @p253 :rule skolemize :premises (@p316)) % 1.02/1.29 (step-pop @p317 :rule scope :premises (@p253)) % 1.02/1.29 (step @p254 :rule process_scope :premises (@p317) :args (@t160)) % 1.02/1.29 (step @p256 :rule implies_elim :premises (@p254)) % 1.02/1.29 (step @p257 :rule eq_resolve :premises (@p256 @p251)) % 1.02/1.29 (step @p258 :rule chain_m_resolution :premises (@p257 @p248) :args (@t160 @t69 (@list @t74))) % 1.02/1.29 (step @p259 :rule cnf_or_neg :args (@t159 1)) % 1.02/1.29 (step @p260 :rule chain_m_resolution :premises (@p259 @p258) :args ((not @t77) @t69 @t161)) % 1.02/1.29 (step @p261 :rule aci_norm :args ((= (or @t120 (or @t54 @t14)) (or @t120 @t54 @t14)))) % 1.02/1.29 (step @p262 :rule bool-impl-elim :args (@t5 @t14)) % 1.02/1.29 (step @p263 :rule nary_cong :premises (@p183 @p262) :args ((or @t120 @t49))) % 1.02/1.29 (step @p264 :rule trans :premises (@p263 @p261)) % 1.02/1.29 (step @p265 :rule bool-impl-elim :args (@t50 @t49)) % 1.02/1.29 (step @p266 :rule trans :premises (@p265 @p264)) % 1.02/1.29 (step @p267 :rule cong :premises (@p266) :args (@t51)) % 1.02/1.29 (step @p268 :rule eq_resolve :premises (@p32 @p267)) % 1.02/1.29 (step @p269 :rule instantiate :premises (@p268) :args ((@list @t75 @t73))) % 1.02/1.29 (step @p270 :rule bool-double-not-elim :args (@t157)) % 1.02/1.29 (step @p271 :rule refl :args (@t159)) % 1.02/1.29 (step @p272 :rule nary_cong :premises (@p271 @p270) :args ((or @t159 (not @t158)))) % 1.02/1.29 (step @p273 :rule cnf_or_neg :args (@t159 0)) % 1.02/1.29 (step @p274 :rule eq_resolve :premises (@p273 @p272)) % 1.02/1.29 (step @p275 :rule reordering :premises (@p274) :args ((or @t157 @t159))) % 1.02/1.29 (step @p276 :rule chain_m_resolution :premises (@p275 @p258) :args (@t157 @t69 @t161)) % 1.02/1.29 (step @p277 :rule eq-symm :args (@t162 @t150)) % 1.02/1.29 (step @p278 :rule cong :premises (@p43 @p277) :args ((=> @t66 @t163))) % 1.02/1.29 (assume-push @p318 @t66) % 1.02/1.29 (step @p280 :rule instantiate :premises (@p59) :args ((@list @t73))) % 1.02/1.29 (step-pop @p319 :rule scope :premises (@p280)) % 1.02/1.29 (step @p281 :rule process_scope :premises (@p319) :args (@t163)) % 1.02/1.29 (step @p283 :rule eq_resolve :premises (@p281 @p278)) % 1.02/1.29 (step @p284 :rule implies_elim :premises (@p283)) % 1.02/1.29 (step @p285 :rule chain_m_resolution :premises (@p284 @p59) :args (@t164 @t80 @t81)) % 1.02/1.29 (step @p286 :rule bool-double-not-elim :args (@t150)) % 1.02/1.29 (step @p287 :rule refl :args (@t152)) % 1.02/1.29 (step @p288 :rule nary_cong :premises (@p287 @p286) :args ((or @t152 (not @t151)))) % 1.02/1.29 (step @p289 :rule cnf_or_neg :args (@t152 0)) % 1.02/1.29 (step @p290 :rule eq_resolve :premises (@p289 @p288)) % 1.02/1.29 (step @p291 :rule reordering :premises (@p290) :args ((or @t150 @t152))) % 1.02/1.29 (step @p292 :rule chain_m_resolution :premises (@p291 @p243) :args (@t150 @t69 @t154)) % 1.02/1.29 (step @p293 :rule cnf_equiv_pos1 :args (@t164)) % 1.02/1.29 (step @p294 :rule reordering :premises (@p293) :args ((or @t151 @t162 (not @t164)))) % 1.02/1.29 (step @p295 :rule chain_m_resolution :premises (@p294 @p292 @p285) :args (@t162 @t134 (@list @t150 @t164))) % 1.02/1.29 (step @p296 :rule cnf_or_pos :args (@t166)) % 1.02/1.29 (step @p297 :rule reordering :premises (@p296) :args ((or @t165 @t158 @t76 (not @t166)))) % 1.02/1.29 (step @p298 :rule chain_m_resolution :premises (@p297 @p295 @p276 @p269) :args (@t76 (@list false false false) (@list @t162 @t157 @t166))) % 1.02/1.29 (step @p299 :rule cnf_equiv_pos2 :args (@t79)) % 1.02/1.29 (step @p300 :rule reordering :premises (@p299) :args ((or @t77 (not @t76) (not @t79)))) % 1.02/1.29 (step @p301 false :rule chain_m_resolution :premises (@p300 @p298 @p260 @p68) :args (false (@list false true false) (@list @t76 @t77 @t79))) % 1.02/1.29 ) % 1.02/1.29 % SZS output end Proof % 1.02/1.29 % cvc5 exiting %------------------------------------------------------------------------------