%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET815+4 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n029.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 08:48:42 AM UTC 2026 % Result : Theorem 34.00s 34.59s % Output : Proof 34.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET815+4 : TPTP v9.2.1. Released v3.2.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n029.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 16:13:02 EDT 2026 % 0.15/0.34 % CPUTime : % 0.27/0.49 %----Proving TF0_NAR, FOF, or CNF % 34.00/34.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 34.00/34.59 --- Run --no-e-matching --full-saturate-quant at 6... % 34.00/34.59 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 34.00/34.59 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 34.00/34.59 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 34.00/34.59 % SZS status Theorem % 34.00/34.59 % SZS output start Proof % 34.00/34.59 ( % 34.00/34.59 (declare-sort $$unsorted 0) % 34.00/34.59 (declare-const tptp.strict_order (-> $$unsorted $$unsorted Bool)) % 34.00/34.59 (declare-const tptp.on $$unsorted) % 34.00/34.59 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 34.00/34.59 (declare-const tptp.set (-> $$unsorted Bool)) % 34.00/34.59 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 34.00/34.59 (declare-const tptp.suc (-> $$unsorted $$unsorted)) % 34.00/34.59 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 34.00/34.59 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 34.00/34.59 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 34.00/34.59 (declare-const tptp.initial_segment (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 34.00/34.59 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 34.00/34.59 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 34.00/34.59 (declare-const tptp.empty_set $$unsorted) % 34.00/34.59 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 34.00/34.59 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 34.00/34.59 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 34.00/34.59 (declare-const tptp.least (-> $$unsorted $$unsorted $$unsorted Bool)) % 34.00/34.59 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 34.00/34.59 (declare-const tptp.strict_well_order (-> $$unsorted $$unsorted Bool)) % 34.00/34.59 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 34.00/34.59 (declare-const tptp.member_predicate $$unsorted) % 34.00/34.59 (define @t1 () (@var "B" $$unsorted)) % 34.00/34.59 (define @t2 () (@var "X" $$unsorted)) % 34.00/34.59 (define @t3 () (tptp.member @t2 @t1)) % 34.00/34.59 (define @t4 () (@var "A" $$unsorted)) % 34.00/34.59 (define @t5 () (tptp.member @t2 @t4)) % 34.00/34.59 (define @t6 () (@list @t2)) % 34.00/34.59 (define @t7 () (forall @t6 (=> @t5 @t3))) % 34.00/34.59 (define @t8 () (tptp.subset @t4 @t1)) % 34.00/34.59 (define @t9 () (= @t8 @t7)) % 34.00/34.59 (define @t10 () (@list @t4 @t1)) % 34.00/34.59 (define @t11 () (forall @t10 @t9)) % 34.00/34.59 (define @t12 () (tptp.subset @t2 @t4)) % 34.00/34.59 (define @t13 () (@list @t2 @t4)) % 34.00/34.59 (define @t14 () (@list @t2 @t4 @t1)) % 34.00/34.59 (define @t15 () (@var "E" $$unsorted)) % 34.00/34.59 (define @t16 () (= @t2 @t4)) % 34.00/34.59 (define @t17 () (tptp.singleton @t4)) % 34.00/34.59 (define @t18 () (tptp.member @t2 @t17)) % 34.00/34.59 (define @t19 () (= @t18 @t16)) % 34.00/34.59 (define @t20 () (forall @t13 @t19)) % 34.00/34.59 (define @t21 () (@var "Y" $$unsorted)) % 34.00/34.59 (define @t22 () (tptp.member @t2 @t21)) % 34.00/34.59 (define @t23 () (tptp.member @t21 @t4)) % 34.00/34.59 (define @t24 () (and @t23 @t22)) % 34.00/34.59 (define @t25 () (@list @t21)) % 34.00/34.59 (define @t26 () (exists @t25 @t24)) % 34.00/34.59 (define @t27 () (tptp.member @t2 (tptp.sum @t4))) % 34.00/34.59 (define @t28 () (= @t27 @t26)) % 34.00/34.59 (define @t29 () (forall @t13 @t28)) % 34.00/34.59 (define @t30 () (forall @t6 (=> @t5 @t12))) % 34.00/34.59 (define @t31 () (tptp.strict_well_order tptp.member_predicate @t4)) % 34.00/34.59 (define @t32 () (tptp.set @t4)) % 34.00/34.59 (define @t33 () (and @t32 @t31 @t30)) % 34.00/34.59 (define @t34 () (tptp.member @t4 tptp.on)) % 34.00/34.59 (define @t35 () (= @t34 @t33)) % 34.00/34.59 (define @t36 () (@list @t4)) % 34.00/34.59 (define @t37 () (forall @t36 @t35)) % 34.00/34.59 (define @t38 () (@var "R" $$unsorted)) % 34.00/34.59 (define @t39 () (tptp.strict_order @t38 @t15)) % 34.00/34.59 (define @t40 () (@list @t38 @t15)) % 34.00/34.59 (define @t41 () (@var "M" $$unsorted)) % 34.00/34.59 (define @t42 () (tptp.member @t2 @t15)) % 34.00/34.59 (define @t43 () (@list @t2 @t21)) % 34.00/34.59 (define @t44 () (@var "Z" $$unsorted)) % 34.00/34.59 (define @t45 () (tptp.apply @t38 @t2 @t21)) % 34.00/34.59 (define @t46 () (tptp.member @t21 @t15)) % 34.00/34.59 (define @t47 () (tptp.apply @t38 @t21 @t2)) % 34.00/34.59 (define @t48 () (tptp.suc @t4)) % 34.00/34.59 (define @t49 () (@list @t4 @t2)) % 34.00/34.59 (define @t50 () (tptp.equal_set (tptp.sum @t48) @t4)) % 34.00/34.59 (define @t51 () (forall @t36 (=> @t34 @t50))) % 34.00/34.59 (define @t52 () (not @t51)) % 34.00/34.59 (define @t53 () (@quantifiers_skolemize (forall @t36 (or (not @t34) @t50)) 0)) % 34.00/34.59 (define @t54 () (tptp.singleton @t53)) % 34.00/34.59 (define @t55 () (@list @t53 @t53)) % 34.00/34.59 (define @t56 () (forall @t25 (not @t24))) % 34.00/34.59 (define @t57 () (not @t56)) % 34.00/34.59 (define @t58 () (tptp.suc @t53)) % 34.00/34.59 (define @t59 () (tptp.sum @t58)) % 34.00/34.59 (define @t60 () (tptp.member @t2 @t59)) % 34.00/34.59 (define @t61 () (tptp.member @t2 @t53)) % 34.00/34.59 (define @t62 () (not @t61)) % 34.00/34.59 (define @t63 () (forall @t6 (or @t62 @t60))) % 34.00/34.59 (define @t64 () (@quantifiers_skolemize @t63 0)) % 34.00/34.59 (define @t65 () (@list @t59 @t53)) % 34.00/34.59 (define @t66 () (forall @t6 (or (not @t60) @t61))) % 34.00/34.59 (define @t67 () (@quantifiers_skolemize @t66 0)) % 34.00/34.59 (define @t68 () (tptp.member @t67 @t59)) % 34.00/34.59 (define @t69 () (tptp.member @t67 @t53)) % 34.00/34.59 (define @t70 () (not @t68)) % 34.00/34.59 (define @t71 () (or @t70 @t69)) % 34.00/34.59 (define @t72 () (not (tptp.member @t21 @t58))) % 34.00/34.59 (define @t73 () (forall @t25 (or @t72 (not (tptp.member @t67 @t21))))) % 34.00/34.59 (define @t74 () (not @t73)) % 34.00/34.59 (define @t75 () (= @t68 @t74)) % 34.00/34.59 (define @t76 () (@quantifiers_skolemize @t73 0)) % 34.00/34.59 (define @t77 () (tptp.member @t67 @t76)) % 34.00/34.59 (define @t78 () (not @t77)) % 34.00/34.59 (define @t79 () (tptp.member @t76 @t58)) % 34.00/34.59 (define @t80 () (not @t79)) % 34.00/34.59 (define @t81 () (or @t80 @t78)) % 34.00/34.59 (define @t82 () (not @t81)) % 34.00/34.59 (define @t83 () (tptp.union @t53 @t54)) % 34.00/34.59 (define @t84 () (tptp.member @t76 @t83)) % 34.00/34.59 (define @t85 () (= @t79 @t84)) % 34.00/34.59 (define @t86 () (tptp.member @t76 @t54)) % 34.00/34.59 (define @t87 () (tptp.member @t76 @t53)) % 34.00/34.59 (define @t88 () (or @t87 @t86)) % 34.00/34.59 (define @t89 () (= @t84 @t88)) % 34.00/34.59 (define @t90 () (@list @t76 @t53)) % 34.00/34.59 (define @t91 () (forall @t6 (or (not (tptp.member @t2 @t76)) @t61))) % 34.00/34.59 (define @t92 () (tptp.subset @t76 @t53)) % 34.00/34.59 (define @t93 () (= @t92 @t91)) % 34.00/34.59 (define @t94 () (not @t93)) % 34.00/34.59 (define @t95 () (not @t91)) % 34.00/34.59 (define @t96 () (@list @t53)) % 34.00/34.59 (define @t97 () (tptp.member @t53 tptp.on)) % 34.00/34.59 (define @t98 () (tptp.equal_set @t59 @t53)) % 34.00/34.59 (define @t99 () (not @t97)) % 34.00/34.59 (define @t100 () (or @t99 @t98)) % 34.00/34.59 (define @t101 () (@list true)) % 34.00/34.59 (define @t102 () (@list @t100)) % 34.00/34.59 (define @t103 () (forall @t6 (or @t62 (tptp.subset @t2 @t53)))) % 34.00/34.59 (define @t104 () (and (tptp.set @t53) (tptp.strict_well_order tptp.member_predicate @t53) @t103)) % 34.00/34.59 (define @t105 () (= @t97 @t104)) % 34.00/34.59 (define @t106 () (@list false false)) % 34.00/34.59 (define @t107 () (@list false)) % 34.00/34.59 (define @t108 () (not @t87)) % 34.00/34.59 (define @t109 () (or @t108 @t92)) % 34.00/34.59 (define @t110 () (@quantifiers_skolemize @t91 0)) % 34.00/34.59 (define @t111 () (tptp.member @t110 @t53)) % 34.00/34.59 (define @t112 () (tptp.member @t110 @t76)) % 34.00/34.59 (define @t113 () (not @t112)) % 34.00/34.59 (define @t114 () (or @t113 @t111)) % 34.00/34.59 (define @t115 () (not @t114)) % 34.00/34.59 (define @t116 () (not @t88)) % 34.00/34.59 (define @t117 () (= @t53 @t76)) % 34.00/34.59 (define @t118 () (= @t86 @t117)) % 34.00/34.59 (define @t119 () (not @t117)) % 34.00/34.59 (define @t120 () (not @t111)) % 34.00/34.59 (define @t121 () (and @t120 @t117 @t112)) % 34.00/34.59 (define @t122 () (or @t78 @t69)) % 34.00/34.59 (define @t123 () (not @t71)) % 34.00/34.59 (define @t124 () (not @t66)) % 34.00/34.59 (define @t125 () (tptp.subset @t59 @t53)) % 34.00/34.59 (define @t126 () (= @t125 @t66)) % 34.00/34.59 (define @t127 () (tptp.subset @t53 @t59)) % 34.00/34.59 (define @t128 () (and @t125 @t127)) % 34.00/34.59 (define @t129 () (= @t98 @t128)) % 34.00/34.59 (define @t130 () (not @t128)) % 34.00/34.59 (define @t131 () (@list true false)) % 34.00/34.59 (define @t132 () (= @t127 @t63)) % 34.00/34.59 (define @t133 () (not @t63)) % 34.00/34.59 (define @t134 () (tptp.member @t64 @t59)) % 34.00/34.59 (define @t135 () (tptp.member @t64 @t53)) % 34.00/34.59 (define @t136 () (not @t135)) % 34.00/34.59 (define @t137 () (or @t136 @t134)) % 34.00/34.59 (define @t138 () (not @t137)) % 34.00/34.59 (define @t139 () (@list @t137)) % 34.00/34.59 (define @t140 () (forall @t25 (or @t72 (not (tptp.member @t64 @t21))))) % 34.00/34.59 (define @t141 () (not @t140)) % 34.00/34.59 (define @t142 () (= @t134 @t141)) % 34.00/34.59 (define @t143 () (not @t142)) % 34.00/34.59 (define @t144 () (tptp.member @t53 @t58)) % 34.00/34.59 (define @t145 () (not @t144)) % 34.00/34.59 (define @t146 () (or @t145 @t136)) % 34.00/34.59 (define @t147 () (tptp.member @t53 @t83)) % 34.00/34.59 (define @t148 () (= @t144 @t147)) % 34.00/34.59 (define @t149 () (not @t147)) % 34.00/34.59 (define @t150 () (tptp.member @t53 @t54)) % 34.00/34.59 (define @t151 () (or (tptp.member @t53 @t53) @t150)) % 34.00/34.59 (define @t152 () (= @t147 @t151)) % 34.00/34.59 (define @t153 () (not @t151)) % 34.00/34.59 (define @t154 () (not @t150)) % 34.00/34.59 (define @t155 () (= @t150 (= @t53 @t53))) % 34.00/34.59 (define @t156 () (forall @t13 (= @t18 (= @t4 @t2)))) % 34.00/34.59 (assume @p1 @t11) % 34.00/34.59 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 34.00/34.59 (assume @p3 (forall @t13 (= (tptp.member @t2 (tptp.power_set @t4)) @t12))) % 34.00/34.59 (assume @p4 (forall @t14 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 34.00/34.59 (assume @p5 (forall @t14 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 34.00/34.59 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 34.00/34.59 (assume @p7 (forall (@list @t1 @t4 @t15) (= (tptp.member @t1 (tptp.difference @t15 @t4)) (and (tptp.member @t1 @t15) (not (tptp.member @t1 @t4)))))) % 34.00/34.59 (assume @p8 @t20) % 34.00/34.59 (assume @p9 (forall @t14 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t16 (= @t2 @t1))))) % 34.00/34.59 (assume @p10 @t29) % 34.00/34.59 (assume @p11 (forall @t13 (= (tptp.member @t2 (tptp.product @t4)) (forall @t25 (=> @t23 @t22))))) % 34.00/34.59 (assume @p12 @t37) % 34.00/34.59 (assume @p13 (forall @t40 (= (tptp.strict_well_order @t38 @t15) (and @t39 (forall @t36 (=> (and (tptp.subset @t4 @t15) (exists @t6 @t5)) (exists @t25 (tptp.least @t21 @t38 @t4)))))))) % 34.00/34.59 (assume @p14 (forall (@list @t38 @t15 @t41) (= (tptp.least @t41 @t38 @t15) (and (tptp.member @t41 @t15) (forall @t6 (=> @t42 (or (= @t41 @t2) (tptp.apply @t38 @t41 @t2)))))))) % 34.00/34.59 (assume @p15 (forall @t43 (= (tptp.apply tptp.member_predicate @t2 @t21) @t22))) % 34.00/34.59 (assume @p16 (forall @t40 (= @t39 (and (forall @t43 (=> (and @t42 @t46) (not (and @t45 @t47)))) (forall (@list @t2 @t21 @t44) (=> (and @t42 @t46 (tptp.member @t44 @t15)) (=> (and @t45 (tptp.apply @t38 @t21 @t44)) (tptp.apply @t38 @t2 @t44)))))))) % 34.00/34.59 (assume @p17 (forall @t6 (=> (tptp.set @t2) (forall @t25 (=> (tptp.member @t21 @t2) (tptp.set @t21)))))) % 34.00/34.59 (assume @p18 (forall (@list @t2 @t38 @t4 @t21) (= (tptp.member @t21 (tptp.initial_segment @t2 @t38 @t4)) (and @t23 @t47)))) % 34.00/34.59 (assume @p19 (forall @t49 (= (tptp.member @t2 @t48) (tptp.member @t2 (tptp.union @t4 @t17))))) % 34.00/34.59 (assume @p20 (forall @t49 (=> @t5 (tptp.subset (tptp.singleton @t2) @t4)))) % 34.00/34.59 (assume @p21 @t52) % 34.00/34.59 (assume @p22 true) % 34.00/34.59 (step @p23 :rule eq-symm :args (@t2 @t4)) % 34.00/34.59 (step @p24 :rule refl :args (@t18)) % 34.00/34.59 (step @p25 :rule cong :premises (@p24 @p23) :args (@t19)) % 34.00/34.59 (step @p26 :rule cong :premises (@p25) :args (@t20)) % 34.00/34.59 (step @p27 :rule eq_resolve :premises (@p8 @p26)) % 34.00/34.59 (step @p28 :rule instantiate :premises (@p5) :args ((@list @t53 @t53 @t54))) % 34.00/34.59 (step @p29 :rule instantiate :premises (@p19) :args (@t55)) % 34.00/34.59 (step @p30 :rule bool-and-de-morgan :args (@t23 @t22 true)) % 34.00/34.59 (step @p31 :rule cong :premises (@p30) :args (@t56)) % 34.00/34.59 (step @p32 :rule cong :premises (@p31) :args (@t57)) % 34.00/34.59 (step @p33 :rule exists-elim :args ((= @t26 @t57))) % 34.00/34.59 (step @p34 :rule trans :premises (@p33 @p32)) % 34.00/34.59 (step @p35 :rule refl :args (@t27)) % 34.00/34.59 (step @p36 :rule cong :premises (@p35 @p34) :args (@t28)) % 34.00/34.59 (step @p37 :rule cong :premises (@p36) :args (@t29)) % 34.00/34.59 (step @p38 :rule eq_resolve :premises (@p10 @p37)) % 34.00/34.59 (step @p39 :rule instantiate :premises (@p38) :args ((@list @t64 @t58))) % 34.00/34.59 (step @p40 :rule bool-impl-elim :args (@t5 @t3)) % 34.00/34.59 (step @p41 :rule cong :premises (@p40) :args (@t7)) % 34.00/34.59 (step @p42 :rule refl :args (@t8)) % 34.00/34.59 (step @p43 :rule cong :premises (@p42 @p41) :args (@t9)) % 34.00/34.59 (step @p44 :rule cong :premises (@p43) :args (@t11)) % 34.00/34.59 (step @p45 :rule eq_resolve :premises (@p1 @p44)) % 34.00/34.59 (step @p46 :rule instantiate :premises (@p45) :args ((@list @t53 @t59))) % 34.00/34.59 (step @p47 :rule instantiate :premises (@p45) :args (@t65)) % 34.00/34.59 (step @p48 :rule bool-double-not-elim :args (@t68)) % 34.00/34.59 (step @p49 :rule refl :args (@t71)) % 34.00/34.59 (step @p50 :rule nary_cong :premises (@p49 @p48) :args ((or @t71 (not @t70)))) % 34.00/34.59 (step @p51 :rule cnf_or_neg :args (@t71 0)) % 34.00/34.59 (step @p52 :rule eq_resolve :premises (@p51 @p50)) % 34.00/34.59 (step @p53 :rule reordering :premises (@p52) :args ((or @t68 @t71))) % 34.00/34.59 (step @p54 :rule cnf_or_neg :args (@t71 1)) % 34.00/34.59 (step @p55 :rule instantiate :premises (@p38) :args ((@list @t67 @t58))) % 34.00/34.59 (step @p56 :rule cnf_equiv_pos1 :args (@t75)) % 34.00/34.59 (step @p57 :rule reordering :premises (@p56) :args ((or @t70 @t74 (not @t75)))) % 34.00/34.59 (step @p58 :rule refl :args (@t82)) % 34.00/34.59 (step @p59 :rule bool-double-not-elim :args (@t73)) % 34.00/34.59 (step @p60 :rule nary_cong :premises (@p59 @p58) :args ((or (not @t74) @t82))) % 34.00/34.59 (assume-push @p265 @t74) % 34.00/34.59 (step @p62 :rule skolemize :premises (@p265)) % 34.00/34.59 (step-pop @p266 :rule scope :premises (@p62)) % 34.00/34.59 (step @p63 :rule process_scope :premises (@p266) :args (@t82)) % 34.00/34.59 (step @p65 :rule implies_elim :premises (@p63)) % 34.00/34.59 (step @p66 :rule eq_resolve :premises (@p65 @p60)) % 34.00/34.59 (step @p67 :rule bool-double-not-elim :args (@t79)) % 34.00/34.59 (step @p68 :rule refl :args (@t81)) % 34.00/34.59 (step @p69 :rule nary_cong :premises (@p68 @p67) :args ((or @t81 (not @t80)))) % 34.00/34.59 (step @p70 :rule cnf_or_neg :args (@t81 0)) % 34.00/34.59 (step @p71 :rule eq_resolve :premises (@p70 @p69)) % 34.00/34.59 (step @p72 :rule reordering :premises (@p71) :args ((or @t79 @t81))) % 34.00/34.59 (step @p73 :rule bool-double-not-elim :args (@t77)) % 34.00/34.59 (step @p74 :rule nary_cong :premises (@p68 @p73) :args ((or @t81 (not @t78)))) % 34.00/34.59 (step @p75 :rule cnf_or_neg :args (@t81 1)) % 34.00/34.59 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 34.00/34.59 (step @p77 :rule reordering :premises (@p76) :args ((or @t77 @t81))) % 34.00/34.59 (step @p78 :rule instantiate :premises (@p19) :args ((@list @t53 @t76))) % 34.00/34.59 (step @p79 :rule cnf_equiv_pos1 :args (@t85)) % 34.00/34.59 (step @p80 :rule reordering :premises (@p79) :args ((or @t80 @t84 (not @t85)))) % 34.00/34.59 (step @p81 :rule instantiate :premises (@p5) :args ((@list @t76 @t53 @t54))) % 34.00/34.59 (step @p82 :rule cnf_equiv_pos1 :args (@t89)) % 34.00/34.59 (step @p83 :rule reordering :premises (@p82) :args ((or (not @t84) @t88 (not @t89)))) % 34.00/34.59 (step @p84 :rule instantiate :premises (@p45) :args (@t90)) % 34.00/34.59 (step @p85 :rule cnf_equiv_pos2 :args (@t93)) % 34.00/34.59 (step @p86 :rule reordering :premises (@p85) :args ((or @t92 @t95 @t94))) % 34.00/34.59 (step @p87 :rule bool-impl-elim :args (@t5 @t12)) % 34.00/34.59 (step @p88 :rule cong :premises (@p87) :args (@t30)) % 34.00/34.59 (step @p89 :rule refl :args (@t31)) % 34.00/34.59 (step @p90 :rule refl :args (@t32)) % 34.00/34.59 (step @p91 :rule nary_cong :premises (@p90 @p89 @p88) :args (@t33)) % 34.00/34.59 (step @p92 :rule refl :args (@t34)) % 34.00/34.59 (step @p93 :rule cong :premises (@p92 @p91) :args (@t35)) % 34.00/34.59 (step @p94 :rule cong :premises (@p93) :args (@t37)) % 34.00/34.59 (step @p95 :rule eq_resolve :premises (@p12 @p94)) % 34.00/34.59 (step @p96 :rule instantiate :premises (@p95) :args (@t96)) % 34.00/34.59 (step @p97 :rule bool-impl-elim :args (@t34 @t50)) % 34.00/34.59 (step @p98 :rule cong :premises (@p97) :args (@t51)) % 34.00/34.59 (step @p99 :rule cong :premises (@p98) :args (@t52)) % 34.00/34.59 (step @p100 :rule eq_resolve :premises (@p21 @p99)) % 34.00/34.59 (step @p101 :rule skolemize :premises (@p100)) % 34.00/34.59 (step @p102 :rule bool-double-not-elim :args (@t97)) % 34.00/34.59 (step @p103 :rule refl :args (@t100)) % 34.00/34.59 (step @p104 :rule nary_cong :premises (@p103 @p102) :args ((or @t100 (not @t99)))) % 34.00/34.59 (step @p105 :rule cnf_or_neg :args (@t100 0)) % 34.00/34.59 (step @p106 :rule eq_resolve :premises (@p105 @p104)) % 34.00/34.59 (step @p107 :rule reordering :premises (@p106) :args ((or @t97 @t100))) % 34.00/34.59 (step @p108 :rule chain_m_resolution :premises (@p107 @p101) :args (@t97 @t101 @t102)) % 34.00/34.59 (step @p109 :rule cnf_equiv_pos1 :args (@t105)) % 34.00/34.59 (step @p110 :rule reordering :premises (@p109) :args ((or @t99 @t104 (not @t105)))) % 34.00/34.59 (step @p111 :rule chain_m_resolution :premises (@p110 @p108 @p96) :args (@t104 @t106 (@list @t97 @t105))) % 34.00/34.59 (step @p112 :rule cnf_and_pos :args (@t104 2)) % 34.00/34.59 (step @p113 :rule reordering :premises (@p112) :args ((or @t103 (not @t104)))) % 34.00/34.59 (step @p114 :rule chain_m_resolution :premises (@p113 @p111) :args (@t103 @t107 (@list @t104))) % 34.00/34.59 (step @p115 :rule instantiate :premises (@p114) :args ((@list @t76))) % 34.00/34.59 (step @p116 :rule cnf_or_pos :args (@t109)) % 34.00/34.59 (step @p117 :rule reordering :premises (@p116) :args ((or @t92 @t108 (not @t109)))) % 34.00/34.59 (step @p118 :rule refl :args (@t115)) % 34.00/34.59 (step @p119 :rule bool-double-not-elim :args (@t91)) % 34.00/34.59 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((or (not @t95) @t115))) % 34.00/34.59 (assume-push @p267 @t95) % 34.00/34.59 (step @p122 :rule skolemize :premises (@p267)) % 34.00/34.59 (step-pop @p268 :rule scope :premises (@p122)) % 34.00/34.59 (step @p123 :rule process_scope :premises (@p268) :args (@t115)) % 34.00/34.59 (step @p125 :rule implies_elim :premises (@p123)) % 34.00/34.59 (step @p126 :rule eq_resolve :premises (@p125 @p120)) % 34.00/34.59 (step @p127 :rule cnf_or_pos :args (@t88)) % 34.00/34.59 (step @p128 :rule reordering :premises (@p127) :args ((or @t87 @t86 @t116))) % 34.00/34.59 (step @p129 :rule bool-double-not-elim :args (@t112)) % 34.00/34.59 (step @p130 :rule refl :args (@t114)) % 34.00/34.59 (step @p131 :rule nary_cong :premises (@p130 @p129) :args ((or @t114 (not @t113)))) % 34.00/34.59 (step @p132 :rule cnf_or_neg :args (@t114 0)) % 34.00/34.59 (step @p133 :rule eq_resolve :premises (@p132 @p131)) % 34.00/34.59 (step @p134 :rule reordering :premises (@p133) :args ((or @t112 @t114))) % 34.00/34.59 (step @p135 :rule cnf_or_neg :args (@t114 1)) % 34.00/34.59 (step @p136 :rule instantiate :premises (@p27) :args (@t90)) % 34.00/34.59 (step @p137 :rule cnf_equiv_pos1 :args (@t118)) % 34.00/34.59 (step @p138 :rule reordering :premises (@p137) :args ((or (not @t86) @t117 (not @t118)))) % 34.00/34.59 (step @p139 :rule refl :args (@t119)) % 34.00/34.59 (step @p140 :rule bool-double-not-elim :args (@t111)) % 34.00/34.59 (step @p141 :rule refl :args (@t113)) % 34.00/34.59 (step @p142 :rule nary_cong :premises (@p141 @p140 @p139) :args ((or @t113 (not @t120) @t119))) % 34.00/34.59 (assume-push @p269 @t120) % 34.00/34.59 (assume-push @p270 @t117) % 34.00/34.59 (assume-push @p271 @t112) % 34.00/34.59 (step @p146 :rule evaluate :args ((= true false))) % 34.00/34.59 (step @p147 :rule false_intro :premises (@p269)) % 34.00/34.59 (step @p148 :rule symm :premises (@p270)) % 34.00/34.59 (step @p149 :rule refl :args (@t110)) % 34.00/34.59 (step @p150 :rule cong :premises (@p149 @p148) :args (@t112)) % 34.00/34.59 (step @p151 :rule true_intro :premises (@p271)) % 34.00/34.59 (step @p152 :rule symm :premises (@p151)) % 34.00/34.59 (step @p153 :rule trans :premises (@p152 @p150 @p147)) % 34.00/34.59 (step @p154 false :rule eq_resolve :premises (@p153 @p146)) % 34.00/34.59 (step-pop @p272 :rule scope :premises (@p154)) % 34.00/34.59 (step-pop @p273 :rule scope :premises (@p272)) % 34.00/34.59 (step-pop @p274 :rule scope :premises (@p273)) % 34.00/34.59 (step @p155 :rule process_scope :premises (@p274) :args (false)) % 34.00/34.59 (assume-push @p275 @t112) % 34.00/34.59 (assume-push @p276 @t120) % 34.00/34.59 (assume-push @p277 @t117) % 34.00/34.59 (step @p162 :rule and_intro :premises (@p276 @p277 @p275)) % 34.00/34.59 (step-pop @p278 :rule scope :premises (@p162)) % 34.00/34.59 (step-pop @p279 :rule scope :premises (@p278)) % 34.00/34.59 (step-pop @p280 :rule scope :premises (@p279)) % 34.00/34.59 (step @p163 :rule process_scope :premises (@p280) :args (@t121)) % 34.00/34.59 (step @p167 :rule implies_elim :premises (@p163)) % 34.00/34.59 (step @p168 :rule resolution :premises (@p167 @p155) :args (true @t121)) % 34.00/34.59 (step @p169 :rule not_and :premises (@p168)) % 34.00/34.59 (step @p170 :rule eq_resolve :premises (@p169 @p142)) % 34.00/34.59 (step @p171 :rule chain_m_resolution :premises (@p170 @p138 @p136 @p135 @p134 @p128 @p126 @p117 @p115 @p86 @p84) :args ((or @t92 @t116) (@list false false true false false true true false true false) (@list @t117 @t118 @t111 @t112 @t86 @t114 @t87 @t109 @t91 @t93))) % 34.00/34.59 (step @p172 :rule cnf_equiv_pos1 :args (@t93)) % 34.00/34.59 (step @p173 :rule reordering :premises (@p172) :args ((or (not @t92) @t91 @t94))) % 34.00/34.59 (step @p174 :rule cnf_or_pos :args (@t122)) % 34.00/34.59 (step @p175 :rule reordering :premises (@p174) :args ((or @t69 @t78 (not @t122)))) % 34.00/34.59 (assume-push @p281 @t91) % 34.00/34.59 (step @p177 :rule instantiate :premises (@p281) :args ((@list @t67))) % 34.00/34.59 (step-pop @p282 :rule scope :premises (@p177)) % 34.00/34.59 (step @p178 :rule process_scope :premises (@p282) :args (@t122)) % 34.00/34.59 (step @p180 :rule implies_elim :premises (@p178)) % 34.00/34.59 (step @p181 :rule chain_m_resolution :premises (@p180 @p175 @p173 @p84 @p171 @p83 @p81 @p80 @p78 @p77 @p72 @p66 @p57 @p55 @p54 @p53) :args (@t71 (@list true false false false false false false false false false true true false true false) (@list @t122 @t91 @t93 @t92 @t88 @t89 @t84 @t85 @t77 @t79 @t81 @t73 @t75 @t69 @t68))) % 34.00/34.59 (step @p182 :rule refl :args (@t123)) % 34.00/34.59 (step @p183 :rule bool-double-not-elim :args (@t66)) % 34.00/34.59 (step @p184 :rule nary_cong :premises (@p183 @p182) :args ((or (not @t124) @t123))) % 34.00/34.59 (assume-push @p283 @t124) % 34.00/34.59 (step @p186 :rule skolemize :premises (@p283)) % 34.00/34.59 (step-pop @p284 :rule scope :premises (@p186)) % 34.00/34.59 (step @p187 :rule process_scope :premises (@p284) :args (@t123)) % 34.00/34.59 (step @p189 :rule implies_elim :premises (@p187)) % 34.00/34.59 (step @p190 :rule eq_resolve :premises (@p189 @p184)) % 34.00/34.59 (step @p191 :rule chain_m_resolution :premises (@p190 @p181) :args (@t66 @t107 (@list @t71))) % 34.00/34.59 (step @p192 :rule cnf_equiv_pos2 :args (@t126)) % 34.00/34.59 (step @p193 :rule reordering :premises (@p192) :args ((or @t125 @t124 (not @t126)))) % 34.00/34.59 (step @p194 :rule chain_m_resolution :premises (@p193 @p191 @p47) :args (@t125 @t106 (@list @t66 @t126))) % 34.00/34.59 (step @p195 :rule instantiate :premises (@p2) :args (@t65)) % 34.00/34.59 (step @p196 :rule cnf_or_neg :args (@t100 1)) % 34.00/34.59 (step @p197 :rule chain_m_resolution :premises (@p196 @p101) :args ((not @t98) @t101 @t102)) % 34.00/34.59 (step @p198 :rule cnf_equiv_pos2 :args (@t129)) % 34.00/34.59 (step @p199 :rule reordering :premises (@p198) :args ((or @t98 @t130 (not @t129)))) % 34.00/34.59 (step @p200 :rule chain_m_resolution :premises (@p199 @p197 @p195) :args (@t130 @t131 (@list @t98 @t129))) % 34.00/34.59 (step @p201 :rule cnf_and_neg :args (@t128)) % 34.00/34.59 (step @p202 :rule chain_m_resolution :premises (@p201 @p200 @p194) :args ((not @t127) @t131 (@list @t128 @t125))) % 34.00/34.59 (step @p203 :rule cnf_equiv_pos2 :args (@t132)) % 34.00/34.59 (step @p204 :rule reordering :premises (@p203) :args ((or @t127 @t133 (not @t132)))) % 34.00/34.59 (step @p205 :rule chain_m_resolution :premises (@p204 @p202 @p46) :args (@t133 @t131 (@list @t127 @t132))) % 34.00/34.59 (step @p206 :rule refl :args (@t138)) % 34.00/34.59 (step @p207 :rule bool-double-not-elim :args (@t63)) % 34.00/34.60 (step @p208 :rule nary_cong :premises (@p207 @p206) :args ((or (not @t133) @t138))) % 34.00/34.60 (assume-push @p285 @t133) % 34.00/34.60 (step @p210 :rule skolemize :premises (@p285)) % 34.00/34.60 (step-pop @p286 :rule scope :premises (@p210)) % 34.00/34.60 (step @p211 :rule process_scope :premises (@p286) :args (@t138)) % 34.00/34.60 (step @p213 :rule implies_elim :premises (@p211)) % 34.00/34.60 (step @p214 :rule eq_resolve :premises (@p213 @p208)) % 34.00/34.60 (step @p215 :rule chain_m_resolution :premises (@p214 @p205) :args (@t138 @t101 (@list @t63))) % 34.00/34.60 (step @p216 :rule cnf_or_neg :args (@t137 1)) % 34.00/34.60 (step @p217 :rule chain_m_resolution :premises (@p216 @p215) :args ((not @t134) @t101 @t139)) % 34.00/34.60 (step @p218 :rule bool-double-not-elim :args (@t140)) % 34.00/34.60 (step @p219 :rule refl :args (@t134)) % 34.00/34.60 (step @p220 :rule refl :args (@t143)) % 34.00/34.60 (step @p221 :rule nary_cong :premises (@p220 @p219 @p218) :args ((or @t143 @t134 (not @t141)))) % 34.00/34.60 (step @p222 :rule cnf_equiv_pos2 :args (@t142)) % 34.00/34.60 (step @p223 :rule eq_resolve :premises (@p222 @p221)) % 34.00/34.60 (step @p224 :rule reordering :premises (@p223) :args ((or @t134 @t140 @t143))) % 34.00/34.60 (step @p225 :rule chain_m_resolution :premises (@p224 @p217 @p39) :args (@t140 @t131 (@list @t134 @t142))) % 34.00/34.60 (assume-push @p287 @t140) % 34.00/34.60 (step @p227 :rule instantiate :premises (@p287) :args (@t96)) % 34.00/34.60 (step-pop @p288 :rule scope :premises (@p227)) % 34.00/34.60 (step @p228 :rule process_scope :premises (@p288) :args (@t146)) % 34.00/34.60 (step @p230 :rule implies_elim :premises (@p228)) % 34.00/34.60 (step @p231 :rule chain_m_resolution :premises (@p230 @p225) :args (@t146 @t107 (@list @t140))) % 34.00/34.60 (step @p232 :rule bool-double-not-elim :args (@t135)) % 34.00/34.60 (step @p233 :rule refl :args (@t137)) % 34.00/34.60 (step @p234 :rule nary_cong :premises (@p233 @p232) :args ((or @t137 (not @t136)))) % 34.00/34.60 (step @p235 :rule cnf_or_neg :args (@t137 0)) % 34.00/34.60 (step @p236 :rule eq_resolve :premises (@p235 @p234)) % 34.00/34.60 (step @p237 :rule reordering :premises (@p236) :args ((or @t135 @t137))) % 34.00/34.60 (step @p238 :rule chain_m_resolution :premises (@p237 @p215) :args (@t135 @t101 @t139)) % 34.00/34.60 (step @p239 :rule cnf_or_pos :args (@t146)) % 34.00/34.60 (step @p240 :rule reordering :premises (@p239) :args ((or @t136 @t145 (not @t146)))) % 34.00/34.60 (step @p241 :rule chain_m_resolution :premises (@p240 @p238 @p231) :args (@t145 @t106 (@list @t135 @t146))) % 34.00/34.60 (step @p242 :rule cnf_equiv_pos2 :args (@t148)) % 34.00/34.60 (step @p243 :rule reordering :premises (@p242) :args ((or @t144 @t149 (not @t148)))) % 34.00/34.60 (step @p244 :rule chain_m_resolution :premises (@p243 @p241 @p29) :args (@t149 @t131 (@list @t144 @t148))) % 34.00/34.60 (step @p245 :rule cnf_equiv_pos2 :args (@t152)) % 34.00/34.60 (step @p246 :rule reordering :premises (@p245) :args ((or @t147 @t153 (not @t152)))) % 34.00/34.60 (step @p247 :rule chain_m_resolution :premises (@p246 @p244 @p28) :args (@t153 @t131 (@list @t147 @t152))) % 34.00/34.60 (step @p248 :rule cnf_or_neg :args (@t151 1)) % 34.00/34.60 (step @p249 :rule reordering :premises (@p248) :args ((or @t154 @t151))) % 34.00/34.60 (step @p250 :rule chain_m_resolution :premises (@p249 @p247) :args (@t154 @t101 (@list @t151))) % 34.00/34.60 (step @p251 :rule bool-eq-true :args (@t150)) % 34.00/34.60 (step @p252 :rule eq-refl :args (@t53)) % 34.00/34.60 (step @p253 :rule refl :args (@t150)) % 34.00/34.60 (step @p254 :rule cong :premises (@p253 @p252) :args (@t155)) % 34.00/34.60 (step @p255 :rule trans :premises (@p254 @p251)) % 34.00/34.60 (step @p256 :rule refl :args (@t156)) % 34.00/34.60 (step @p257 :rule cong :premises (@p256 @p255) :args ((=> @t156 @t155))) % 34.00/34.60 (assume-push @p289 @t156) % 34.00/34.60 (step @p259 :rule instantiate :premises (@p27) :args (@t55)) % 34.00/34.60 (step-pop @p290 :rule scope :premises (@p259)) % 34.00/34.60 (step @p260 :rule process_scope :premises (@p290) :args (@t155)) % 34.00/34.60 (step @p262 :rule eq_resolve :premises (@p260 @p257)) % 34.00/34.60 (step @p263 :rule implies_elim :premises (@p262)) % 34.00/34.60 (step @p264 false :rule chain_m_resolution :premises (@p263 @p250 @p27) :args (false @t131 (@list @t150 @t156))) % 34.00/34.60 ) % 34.00/34.60 % SZS output end Proof % 34.00/34.60 % cvc5 exiting %------------------------------------------------------------------------------