%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU178+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n009.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 08:50:51 AM UTC 2026 % Result : Theorem 33.89s 34.08s % Output : Proof 33.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU178+1 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n009.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 16:33:29 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 33.89/34.08 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 33.89/34.08 --- Run --no-e-matching --full-saturate-quant at 6... % 33.89/34.08 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 33.89/34.08 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 33.89/34.08 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 33.89/34.08 % SZS status Theorem % 33.89/34.08 % SZS output start Proof % 33.89/34.08 ( % 33.89/34.08 (declare-sort $$unsorted 0) % 33.89/34.08 (declare-const tptp.empty (-> $$unsorted Bool)) % 33.89/34.08 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 33.89/34.08 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 33.89/34.08 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 33.89/34.08 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 33.89/34.08 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 33.89/34.08 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 33.89/34.08 (declare-const tptp.relation (-> $$unsorted Bool)) % 33.89/34.08 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 33.89/34.08 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 33.89/34.08 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 33.89/34.08 (declare-const tptp.empty_set $$unsorted) % 33.89/34.08 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 33.89/34.08 (define @t1 () (@var "A" $$unsorted)) % 33.89/34.08 (define @t2 () (@var "B" $$unsorted)) % 33.89/34.08 (define @t3 () (tptp.in @t2 @t1)) % 33.89/34.08 (define @t4 () (tptp.in @t1 @t2)) % 33.89/34.08 (define @t5 () (@list @t1 @t2)) % 33.89/34.08 (define @t6 () (tptp.unordered_pair @t1 @t2)) % 33.89/34.08 (define @t7 () (@var "D" $$unsorted)) % 33.89/34.08 (define @t8 () (@var "C" $$unsorted)) % 33.89/34.08 (define @t9 () (tptp.ordered_pair @t8 @t7)) % 33.89/34.08 (define @t10 () (@list @t8 @t7)) % 33.89/34.08 (define @t11 () (forall @t10 (not (= @t2 @t9)))) % 33.89/34.08 (define @t12 () (@list @t2)) % 33.89/34.08 (define @t13 () (forall @t12 (not (and @t3 @t11)))) % 33.89/34.08 (define @t14 () (tptp.relation @t1)) % 33.89/34.08 (define @t15 () (= @t14 @t13)) % 33.89/34.08 (define @t16 () (@list @t1)) % 33.89/34.08 (define @t17 () (forall @t16 @t15)) % 33.89/34.08 (define @t18 () (tptp.in @t8 @t2)) % 33.89/34.08 (define @t19 () (tptp.in @t8 @t1)) % 33.89/34.08 (define @t20 () (@list @t8)) % 33.89/34.08 (define @t21 () (forall @t20 (=> @t19 @t18))) % 33.89/34.08 (define @t22 () (tptp.subset @t1 @t2)) % 33.89/34.08 (define @t23 () (= @t22 @t21)) % 33.89/34.08 (define @t24 () (forall @t5 @t23)) % 33.89/34.08 (define @t25 () (tptp.in @t9 @t1)) % 33.89/34.08 (define @t26 () (@list @t7)) % 33.89/34.08 (define @t27 () (exists @t26 @t25)) % 33.89/34.08 (define @t28 () (= @t18 @t27)) % 33.89/34.08 (define @t29 () (forall @t20 @t28)) % 33.89/34.08 (define @t30 () (tptp.relation_dom @t1)) % 33.89/34.08 (define @t31 () (= @t2 @t30)) % 33.89/34.08 (define @t32 () (= @t31 @t29)) % 33.89/34.08 (define @t33 () (forall @t12 @t32)) % 33.89/34.08 (define @t34 () (=> @t14 @t33)) % 33.89/34.08 (define @t35 () (forall @t16 @t34)) % 33.89/34.08 (define @t36 () (tptp.ordered_pair @t7 @t8)) % 33.89/34.08 (define @t37 () (tptp.in @t36 @t1)) % 33.89/34.08 (define @t38 () (exists @t26 @t37)) % 33.89/34.08 (define @t39 () (= @t18 @t38)) % 33.89/34.08 (define @t40 () (forall @t20 @t39)) % 33.89/34.08 (define @t41 () (tptp.relation_rng @t1)) % 33.89/34.08 (define @t42 () (= @t2 @t41)) % 33.89/34.08 (define @t43 () (= @t42 @t40)) % 33.89/34.08 (define @t44 () (forall @t12 @t43)) % 33.89/34.08 (define @t45 () (=> @t14 @t44)) % 33.89/34.08 (define @t46 () (forall @t16 @t45)) % 33.89/34.08 (define @t47 () (tptp.singleton @t1)) % 33.89/34.08 (define @t48 () (tptp.ordered_pair @t1 @t2)) % 33.89/34.08 (define @t49 () (tptp.powerset @t1)) % 33.89/34.08 (define @t50 () (tptp.empty @t2)) % 33.89/34.08 (define @t51 () (not @t50)) % 33.89/34.08 (define @t52 () (tptp.empty @t1)) % 33.89/34.08 (define @t53 () (not @t52)) % 33.89/34.08 (define @t54 () (tptp.element @t2 @t49)) % 33.89/34.08 (define @t55 () (tptp.element @t1 @t2)) % 33.89/34.08 (define @t56 () (tptp.subset @t1 (tptp.cartesian_product2 @t30 @t41))) % 33.89/34.08 (define @t57 () (forall @t16 (=> @t14 @t56))) % 33.89/34.08 (define @t58 () (not @t57)) % 33.89/34.08 (define @t59 () (tptp.element @t2 (tptp.powerset @t8))) % 33.89/34.08 (define @t60 () (@list @t1 @t2 @t8)) % 33.89/34.08 (define @t61 () (@var "BOUND_VARIABLE_7628" $$unsorted)) % 33.89/34.08 (define @t62 () (tptp.in @t8 @t61)) % 33.89/34.08 (define @t63 () (not (forall @t26 (not @t37)))) % 33.89/34.08 (define @t64 () (forall @t20 (= @t62 @t63))) % 33.89/34.08 (define @t65 () (= (= @t61 @t41) @t64)) % 33.89/34.08 (define @t66 () (not @t14)) % 33.89/34.08 (define @t67 () (or @t66 @t65)) % 33.89/34.08 (define @t68 () (@list @t1 @t61)) % 33.89/34.08 (define @t69 () (forall @t68 @t67)) % 33.89/34.08 (define @t70 () (@list @t61)) % 33.89/34.08 (define @t71 () (forall @t70 @t67)) % 33.89/34.08 (define @t72 () (forall @t70 @t65)) % 33.89/34.08 (define @t73 () (@list @t2)) % 33.89/34.08 (define @t74 () (or @t66 @t72)) % 33.89/34.08 (define @t75 () (forall @t12 (= @t42 (forall @t20 (= @t18 @t63))))) % 33.89/34.08 (define @t76 () (@quantifiers_skolemize (forall @t16 (or @t66 @t56)) 0)) % 33.89/34.08 (define @t77 () (tptp.relation_rng @t76)) % 33.89/34.08 (define @t78 () (forall @t20 (= (not (forall @t26 (not (tptp.in @t36 @t76)))) (tptp.in @t8 @t77)))) % 33.89/34.08 (define @t79 () (= (= @t77 @t77) @t78)) % 33.89/34.08 (define @t80 () (tptp.relation @t76)) % 33.89/34.08 (define @t81 () (not @t80)) % 33.89/34.08 (define @t82 () (or @t81 @t79)) % 33.89/34.08 (define @t83 () (forall @t68 (or @t66 (= (= @t41 @t61) (forall @t20 (= @t63 @t62)))))) % 33.89/34.08 (define @t84 () (or @t81 @t78)) % 33.89/34.08 (define @t85 () (@list false)) % 33.89/34.08 (define @t86 () (tptp.relation_dom @t76)) % 33.89/34.08 (define @t87 () (tptp.cartesian_product2 @t86 @t77)) % 33.89/34.08 (define @t88 () (tptp.subset @t76 @t87)) % 33.89/34.08 (define @t89 () (or @t81 @t88)) % 33.89/34.08 (define @t90 () (@list true)) % 33.89/34.08 (define @t91 () (@list @t89)) % 33.89/34.08 (define @t92 () (@list false false)) % 33.89/34.08 (define @t93 () (forall @t12 (or (not (tptp.in @t2 @t76)) (not @t11)))) % 33.89/34.08 (define @t94 () (= @t80 @t93)) % 33.89/34.08 (define @t95 () (forall @t20 (or (not (tptp.in @t8 @t76)) (tptp.in @t8 @t87)))) % 33.89/34.08 (define @t96 () (@quantifiers_skolemize @t95 0)) % 33.89/34.08 (define @t97 () (not (= @t96 @t9))) % 33.89/34.08 (define @t98 () (forall @t10 @t97)) % 33.89/34.08 (define @t99 () (not @t98)) % 33.89/34.08 (define @t100 () (tptp.in @t96 @t76)) % 33.89/34.08 (define @t101 () (not @t100)) % 33.89/34.08 (define @t102 () (or @t101 @t99)) % 33.89/34.08 (define @t103 () (forall @t10 (not (= @t9 @t96)))) % 33.89/34.08 (define @t104 () (not @t103)) % 33.89/34.08 (define @t105 () (or @t101 @t104)) % 33.89/34.08 (define @t106 () (= @t88 @t95)) % 33.89/34.08 (define @t107 () (not @t95)) % 33.89/34.08 (define @t108 () (@list true false)) % 33.89/34.08 (define @t109 () (tptp.in @t96 @t87)) % 33.89/34.08 (define @t110 () (or @t101 @t109)) % 33.89/34.08 (define @t111 () (@list @t110)) % 33.89/34.08 (define @t112 () (@quantifiers_skolemize @t103 1)) % 33.89/34.08 (define @t113 () (@quantifiers_skolemize @t103 0)) % 33.89/34.08 (define @t114 () (tptp.ordered_pair @t113 @t112)) % 33.89/34.08 (define @t115 () (= @t96 @t114)) % 33.89/34.08 (define @t116 () (= @t114 @t96)) % 33.89/34.08 (define @t117 () (not (not @t116))) % 33.89/34.08 (define @t118 () (tptp.in @t114 @t76)) % 33.89/34.08 (define @t119 () (not @t115)) % 33.89/34.08 (define @t120 () (not @t118)) % 33.89/34.08 (define @t121 () (and @t120 @t115 @t100)) % 33.89/34.08 (define @t122 () (forall @t26 (not (tptp.in (tptp.ordered_pair @t7 @t112) @t76)))) % 33.89/34.08 (define @t123 () (@list @t113)) % 33.89/34.08 (define @t124 () (not @t122)) % 33.89/34.08 (define @t125 () (@list @t118)) % 33.89/34.08 (define @t126 () (@var "BOUND_VARIABLE_7600" $$unsorted)) % 33.89/34.08 (define @t127 () (tptp.in @t8 @t126)) % 33.89/34.08 (define @t128 () (not (forall @t26 (not @t25)))) % 33.89/34.08 (define @t129 () (forall @t20 (= @t127 @t128))) % 33.89/34.08 (define @t130 () (= (= @t126 @t30) @t129)) % 33.89/34.08 (define @t131 () (or @t66 @t130)) % 33.89/34.08 (define @t132 () (@list @t1 @t126)) % 33.89/34.08 (define @t133 () (forall @t132 @t131)) % 33.89/34.08 (define @t134 () (@list @t126)) % 33.89/34.08 (define @t135 () (forall @t134 @t131)) % 33.89/34.08 (define @t136 () (forall @t134 @t130)) % 33.89/34.08 (define @t137 () (or @t66 @t136)) % 33.89/34.08 (define @t138 () (forall @t12 (= @t31 (forall @t20 (= @t18 @t128))))) % 33.89/34.08 (define @t139 () (forall @t20 (= (not (forall @t26 (not (tptp.in @t9 @t76)))) (tptp.in @t8 @t86)))) % 33.89/34.08 (define @t140 () (= (= @t86 @t86) @t139)) % 33.89/34.08 (define @t141 () (or @t81 @t140)) % 33.89/34.08 (define @t142 () (forall @t132 (or @t66 (= (= @t30 @t126) (forall @t20 (= @t128 @t127)))))) % 33.89/34.08 (define @t143 () (or @t81 @t139)) % 33.89/34.08 (define @t144 () (forall @t26 (not (tptp.in (tptp.ordered_pair @t113 @t7) @t76)))) % 33.89/34.08 (define @t145 () (not @t144)) % 33.89/34.08 (define @t146 () (tptp.in @t113 @t86)) % 33.89/34.08 (define @t147 () (= @t145 @t146)) % 33.89/34.08 (define @t148 () (= @t146 @t145)) % 33.89/34.08 (define @t149 () (@list @t112)) % 33.89/34.08 (define @t150 () (not @t148)) % 33.89/34.08 (define @t151 () (tptp.in @t114 @t87)) % 33.89/34.08 (define @t152 () (tptp.in @t112 @t77)) % 33.89/34.08 (define @t153 () (and @t146 @t152)) % 33.89/34.08 (define @t154 () (= @t151 @t153)) % 33.89/34.08 (define @t155 () (not @t153)) % 33.89/34.08 (define @t156 () (= @t152 @t124)) % 33.89/34.08 (define @t157 () (not @t156)) % 33.89/34.08 (define @t158 () (= @t124 @t152)) % 33.89/34.08 (assume @p1 (forall @t5 (=> @t4 (not @t3)))) % 33.89/34.08 (assume @p2 (forall @t5 (= @t6 (tptp.unordered_pair @t2 @t1)))) % 33.89/34.08 (assume @p3 @t17) % 33.89/34.08 (assume @p4 @t24) % 33.89/34.08 (assume @p5 @t35) % 33.89/34.08 (assume @p6 @t46) % 33.89/34.08 (assume @p7 (forall @t5 (= @t48 (tptp.unordered_pair @t6 @t47)))) % 33.89/34.08 (assume @p8 true) % 33.89/34.08 (assume @p9 (forall @t16 (exists @t12 (tptp.element @t2 @t1)))) % 33.89/34.08 (assume @p10 (forall @t16 (not (tptp.empty @t49)))) % 33.89/34.08 (assume @p11 (tptp.empty tptp.empty_set)) % 33.89/34.08 (assume @p12 (forall @t5 (not (tptp.empty @t48)))) % 33.89/34.08 (assume @p13 (forall @t16 (not (tptp.empty @t47)))) % 33.89/34.08 (assume @p14 (forall @t5 (not (tptp.empty @t6)))) % 33.89/34.08 (assume @p15 (forall @t5 (=> (and @t53 @t51) (not (tptp.empty (tptp.cartesian_product2 @t1 @t2)))))) % 33.89/34.08 (assume @p16 (exists @t16 (and @t52 @t14))) % 33.89/34.08 (assume @p17 (forall @t16 (=> @t53 (exists @t12 (and @t54 @t51))))) % 33.89/34.08 (assume @p18 (exists @t16 @t52)) % 33.89/34.08 (assume @p19 (forall @t16 (exists @t12 (and @t54 @t50)))) % 33.89/34.08 (assume @p20 (exists @t16 @t53)) % 33.89/34.08 (assume @p21 (forall @t5 (tptp.subset @t1 @t1))) % 33.89/34.08 (assume @p22 (forall (@list @t1 @t2 @t8 @t7) (= (tptp.in @t48 (tptp.cartesian_product2 @t8 @t7)) (and (tptp.in @t1 @t8) (tptp.in @t2 @t7))))) % 33.89/34.08 (assume @p23 (forall @t5 (=> @t4 @t55))) % 33.89/34.08 (assume @p24 @t58) % 33.89/34.08 (assume @p25 (forall @t5 (=> @t55 (or @t50 @t4)))) % 33.89/34.08 (assume @p26 (forall @t5 (= (tptp.element @t1 (tptp.powerset @t2)) @t22))) % 33.89/34.08 (assume @p27 (forall @t60 (=> (and @t4 @t59) (tptp.element @t1 @t8)))) % 33.89/34.08 (assume @p28 (forall @t60 (not (and @t4 @t59 (tptp.empty @t8))))) % 33.89/34.08 (assume @p29 (forall @t16 (=> @t52 (= @t1 tptp.empty_set)))) % 33.89/34.08 (assume @p30 (forall @t5 (not (and @t4 @t50)))) % 33.89/34.08 (assume @p31 (forall @t5 (not (and @t52 (not (= @t1 @t2)) @t50)))) % 33.89/34.08 (step @p32 :rule eq-symm :args (@t62 @t63)) % 33.89/34.08 (step @p33 :rule cong :premises (@p32) :args (@t64)) % 33.89/34.08 (step @p34 :rule eq-symm :args (@t61 @t41)) % 33.89/34.08 (step @p35 :rule cong :premises (@p34 @p33) :args (@t65)) % 33.89/34.08 (step @p36 :rule refl :args (@t66)) % 33.89/34.08 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t67)) % 33.89/34.08 (step @p38 :rule cong :premises (@p37) :args (@t69)) % 33.89/34.08 (step @p39 :rule quant-merge-prenex :args ((= (forall @t16 @t71) @t69))) % 33.89/34.08 (step @p40 :rule alpha_equiv :args (@t72 (@list @t61) @t73)) % 33.89/34.08 (step @p41 :rule refl :args (@t66)) % 33.89/34.08 (step @p42 :rule nary_cong :premises (@p41 @p40) :args (@t74)) % 33.89/34.08 (step @p43 :rule quant-miniscope-or :args ((= @t71 @t74))) % 33.89/34.08 (step @p44 :rule trans :premises (@p43 @p42)) % 33.89/34.08 (step @p45 :rule symm :premises (@p44)) % 33.89/34.08 (step @p46 :rule cong :premises (@p45) :args ((forall @t16 (or @t66 @t75)))) % 33.89/34.08 (step @p47 :rule trans :premises (@p46 @p39)) % 33.89/34.08 (step @p48 :rule trans :premises (@p47 @p38)) % 33.89/34.08 (step @p49 :rule bool-impl-elim :args (@t14 @t75)) % 33.89/34.08 (step @p50 :rule cong :premises (@p49) :args ((forall @t16 (=> @t14 @t75)))) % 33.89/34.08 (step @p51 :rule trans :premises (@p50 @p48)) % 33.89/34.08 (step @p52 :rule exists-elim :args ((= @t38 @t63))) % 33.89/34.08 (step @p53 :rule refl :args (@t18)) % 33.89/34.08 (step @p54 :rule cong :premises (@p53 @p52) :args (@t39)) % 33.89/34.08 (step @p55 :rule cong :premises (@p54) :args (@t40)) % 33.89/34.08 (step @p56 :rule refl :args (@t42)) % 33.89/34.08 (step @p57 :rule cong :premises (@p56 @p55) :args (@t43)) % 33.89/34.08 (step @p58 :rule cong :premises (@p57) :args (@t44)) % 33.89/34.08 (step @p59 :rule refl :args (@t14)) % 33.89/34.08 (step @p60 :rule cong :premises (@p59 @p58) :args (@t45)) % 33.89/34.08 (step @p61 :rule cong :premises (@p60) :args (@t46)) % 33.89/34.08 (step @p62 :rule trans :premises (@p61 @p51)) % 33.89/34.08 (step @p63 :rule eq_resolve :premises (@p6 @p62)) % 33.89/34.08 (step @p64 :rule bool-eq-true :args (@t78)) % 33.89/34.08 (step @p65 :rule eq-symm :args (true @t78)) % 33.89/34.08 (step @p66 :rule trans :premises (@p65 @p64)) % 33.89/34.08 (step @p67 :rule refl :args (@t78)) % 33.89/34.08 (step @p68 :rule eq-refl :args (@t77)) % 33.89/34.08 (step @p69 :rule cong :premises (@p68 @p67) :args (@t79)) % 33.89/34.08 (step @p70 :rule trans :premises (@p69 @p66)) % 33.89/34.08 (step @p71 :rule refl :args (@t81)) % 33.89/34.08 (step @p72 :rule nary_cong :premises (@p71 @p70) :args (@t82)) % 33.89/34.08 (step @p73 :rule refl :args (@t83)) % 33.89/34.08 (step @p74 :rule cong :premises (@p73 @p72) :args ((=> @t83 @t82))) % 33.89/34.08 (assume-push @p300 @t83) % 33.89/34.08 (step @p76 :rule instantiate :premises (@p63) :args ((@list @t76 @t77))) % 33.89/34.08 (step-pop @p301 :rule scope :premises (@p76)) % 33.89/34.08 (step @p77 :rule process_scope :premises (@p301) :args (@t82)) % 33.89/34.08 (step @p79 :rule eq_resolve :premises (@p77 @p74)) % 33.89/34.08 (step @p80 :rule implies_elim :premises (@p79)) % 33.89/34.08 (step @p81 :rule chain_m_resolution :premises (@p80 @p63) :args (@t84 @t85 (@list @t83))) % 33.89/34.08 (step @p82 :rule bool-impl-elim :args (@t14 @t56)) % 33.89/34.08 (step @p83 :rule cong :premises (@p82) :args (@t57)) % 33.89/34.08 (step @p84 :rule cong :premises (@p83) :args (@t58)) % 33.89/34.08 (step @p85 :rule eq_resolve :premises (@p24 @p84)) % 33.89/34.08 (step @p86 :rule skolemize :premises (@p85)) % 33.89/34.08 (step @p87 :rule bool-double-not-elim :args (@t80)) % 33.89/34.08 (step @p88 :rule refl :args (@t89)) % 33.89/34.08 (step @p89 :rule nary_cong :premises (@p88 @p87) :args ((or @t89 (not @t81)))) % 33.89/34.08 (step @p90 :rule cnf_or_neg :args (@t89 0)) % 33.89/34.08 (step @p91 :rule eq_resolve :premises (@p90 @p89)) % 33.89/34.08 (step @p92 :rule reordering :premises (@p91) :args ((or @t80 @t89))) % 33.89/34.08 (step @p93 :rule chain_m_resolution :premises (@p92 @p86) :args (@t80 @t90 @t91)) % 33.89/34.08 (step @p94 :rule cnf_or_pos :args (@t84)) % 33.89/34.08 (step @p95 :rule reordering :premises (@p94) :args ((or @t81 @t78 (not @t84)))) % 33.89/34.08 (step @p96 :rule chain_m_resolution :premises (@p95 @p93 @p81) :args (@t78 @t92 (@list @t80 @t84))) % 33.89/34.08 (step @p97 :rule bool-and-de-morgan :args (@t3 @t11 true)) % 33.89/34.08 (step @p98 :rule cong :premises (@p97) :args (@t13)) % 33.89/34.08 (step @p99 :rule cong :premises (@p59 @p98) :args (@t15)) % 33.89/34.08 (step @p100 :rule cong :premises (@p99) :args (@t17)) % 33.89/34.08 (step @p101 :rule eq_resolve :premises (@p3 @p100)) % 33.89/34.08 (step @p102 :rule instantiate :premises (@p101) :args ((@list @t76))) % 33.89/34.08 (step @p103 :rule cnf_equiv_pos1 :args (@t94)) % 33.89/34.08 (step @p104 :rule reordering :premises (@p103) :args ((or @t81 @t93 (not @t94)))) % 33.89/34.08 (step @p105 :rule chain_m_resolution :premises (@p104 @p93 @p102) :args (@t93 @t92 (@list @t80 @t94))) % 33.89/34.08 (step @p106 :rule eq-symm :args (@t96 @t9)) % 33.89/34.08 (step @p107 :rule cong :premises (@p106) :args (@t97)) % 33.89/34.08 (step @p108 :rule cong :premises (@p107) :args (@t98)) % 33.89/34.09 (step @p109 :rule cong :premises (@p108) :args (@t99)) % 33.89/34.09 (step @p110 :rule refl :args (@t101)) % 33.89/34.09 (step @p111 :rule nary_cong :premises (@p110 @p109) :args (@t102)) % 33.89/34.09 (step @p112 :rule refl :args (@t93)) % 33.89/34.09 (step @p113 :rule cong :premises (@p112 @p111) :args ((=> @t93 @t102))) % 33.89/34.09 (assume-push @p302 @t93) % 33.89/34.09 (step @p115 :rule instantiate :premises (@p105) :args ((@list @t96))) % 33.89/34.09 (step-pop @p303 :rule scope :premises (@p115)) % 33.89/34.09 (step @p116 :rule process_scope :premises (@p303) :args (@t102)) % 33.89/34.09 (step @p118 :rule eq_resolve :premises (@p116 @p113)) % 33.89/34.09 (step @p119 :rule implies_elim :premises (@p118)) % 33.89/34.09 (step @p120 :rule chain_m_resolution :premises (@p119 @p105) :args (@t105 @t85 (@list @t93))) % 33.89/34.09 (step @p121 :rule bool-impl-elim :args (@t19 @t18)) % 33.89/34.09 (step @p122 :rule cong :premises (@p121) :args (@t21)) % 33.89/34.09 (step @p123 :rule refl :args (@t22)) % 33.89/34.09 (step @p124 :rule cong :premises (@p123 @p122) :args (@t23)) % 33.89/34.09 (step @p125 :rule cong :premises (@p124) :args (@t24)) % 33.89/34.09 (step @p126 :rule eq_resolve :premises (@p4 @p125)) % 33.89/34.09 (step @p127 :rule instantiate :premises (@p126) :args ((@list @t76 @t87))) % 33.89/34.09 (step @p128 :rule cnf_or_neg :args (@t89 1)) % 33.89/34.09 (step @p129 :rule chain_m_resolution :premises (@p128 @p86) :args ((not @t88) @t90 @t91)) % 33.89/34.09 (step @p130 :rule cnf_equiv_pos2 :args (@t106)) % 33.89/34.09 (step @p131 :rule reordering :premises (@p130) :args ((or @t88 @t107 (not @t106)))) % 33.89/34.09 (step @p132 :rule chain_m_resolution :premises (@p131 @p129 @p127) :args (@t107 @t108 (@list @t88 @t106))) % 33.89/34.09 (step @p133 :rule skolemize :premises (@p132)) % 33.89/34.09 (step @p134 :rule bool-double-not-elim :args (@t100)) % 33.89/34.09 (step @p135 :rule refl :args (@t110)) % 33.89/34.09 (step @p136 :rule nary_cong :premises (@p135 @p134) :args ((or @t110 (not @t101)))) % 33.89/34.09 (step @p137 :rule cnf_or_neg :args (@t110 0)) % 33.89/34.09 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 33.89/34.09 (step @p139 :rule reordering :premises (@p138) :args ((or @t100 @t110))) % 33.89/34.09 (step @p140 :rule chain_m_resolution :premises (@p139 @p133) :args (@t100 @t90 @t111)) % 33.89/34.09 (step @p141 :rule cnf_or_pos :args (@t105)) % 33.89/34.09 (step @p142 :rule reordering :premises (@p141) :args ((or @t101 @t104 (not @t105)))) % 33.89/34.09 (step @p143 :rule chain_m_resolution :premises (@p142 @p140 @p120) :args (@t104 @t92 (@list @t100 @t105))) % 33.89/34.09 (step @p144 :rule refl :args (@t115)) % 33.89/34.09 (step @p145 :rule bool-double-not-elim :args (@t103)) % 33.89/34.09 (step @p146 :rule nary_cong :premises (@p145 @p144) :args ((or (not @t104) @t115))) % 33.89/34.09 (step @p147 :rule eq-symm :args (@t114 @t96)) % 33.89/34.09 (step @p148 :rule bool-double-not-elim :args (@t116)) % 33.89/34.09 (step @p149 :rule trans :premises (@p148 @p147)) % 33.89/34.09 (step @p150 :rule refl :args (@t104)) % 33.89/34.09 (step @p151 :rule cong :premises (@p150 @p149) :args ((=> @t104 @t117))) % 33.89/34.09 (assume-push @p304 @t104) % 33.89/34.09 (step @p153 :rule skolemize :premises (@p143)) % 33.89/34.09 (step-pop @p305 :rule scope :premises (@p153)) % 33.89/34.09 (step @p154 :rule process_scope :premises (@p305) :args (@t117)) % 33.89/34.09 (step @p156 :rule eq_resolve :premises (@p154 @p151)) % 33.89/34.09 (step @p157 :rule implies_elim :premises (@p156)) % 33.89/34.09 (step @p158 :rule eq_resolve :premises (@p157 @p146)) % 33.89/34.09 (step @p159 :rule chain_m_resolution :premises (@p158 @p143) :args (@t115 @t90 (@list @t103))) % 33.89/34.09 (step @p160 :rule bool-double-not-elim :args (@t118)) % 33.89/34.09 (step @p161 :rule refl :args (@t119)) % 33.89/34.09 (step @p162 :rule nary_cong :premises (@p110 @p161 @p160) :args ((or @t101 @t119 (not @t120)))) % 33.89/34.09 (assume-push @p306 @t120) % 33.89/34.09 (assume-push @p307 @t115) % 33.89/34.09 (assume-push @p308 @t100) % 33.89/34.09 (step @p166 :rule evaluate :args ((= true false))) % 33.89/34.09 (step @p167 :rule false_intro :premises (@p306)) % 33.89/34.09 (step @p168 :rule refl :args (@t76)) % 33.89/34.09 (step @p169 :rule cong :premises (@p159 @p168) :args (@t100)) % 33.89/34.09 (step @p170 :rule true_intro :premises (@p140)) % 33.89/34.09 (step @p171 :rule symm :premises (@p170)) % 33.89/34.09 (step @p172 :rule trans :premises (@p171 @p169 @p167)) % 33.89/34.09 (step @p173 false :rule eq_resolve :premises (@p172 @p166)) % 33.89/34.09 (step-pop @p309 :rule scope :premises (@p173)) % 33.89/34.09 (step-pop @p310 :rule scope :premises (@p309)) % 33.89/34.09 (step-pop @p311 :rule scope :premises (@p310)) % 33.89/34.09 (step @p174 :rule process_scope :premises (@p311) :args (false)) % 33.89/34.09 (assume-push @p312 @t100) % 33.89/34.09 (assume-push @p313 @t115) % 33.89/34.09 (assume-push @p314 @t120) % 33.89/34.09 (step @p181 :rule and_intro :premises (@p314 @p159 @p140)) % 33.89/34.09 (step-pop @p315 :rule scope :premises (@p181)) % 33.89/34.09 (step-pop @p316 :rule scope :premises (@p315)) % 33.89/34.09 (step-pop @p317 :rule scope :premises (@p316)) % 33.89/34.09 (step @p182 :rule process_scope :premises (@p317) :args (@t121)) % 33.89/34.09 (step @p186 :rule implies_elim :premises (@p182)) % 33.89/34.09 (step @p187 :rule resolution :premises (@p186 @p174) :args (true @t121)) % 33.89/34.09 (step @p188 :rule not_and :premises (@p187)) % 33.89/34.09 (step @p189 :rule eq_resolve :premises (@p188 @p162)) % 33.89/34.09 (step @p190 :rule chain_m_resolution :premises (@p189 @p140 @p159) :args (@t118 @t92 (@list @t100 @t115))) % 33.89/34.09 (assume-push @p318 @t122) % 33.89/34.09 (step @p192 :rule instantiate :premises (@p318) :args (@t123)) % 33.89/34.09 (step-pop @p319 :rule scope :premises (@p192)) % 33.89/34.09 (step @p193 :rule process_scope :premises (@p319) :args (@t120)) % 33.89/34.09 (step @p195 :rule implies_elim :premises (@p193)) % 33.89/34.09 (step @p196 :rule reordering :premises (@p195) :args ((or @t120 @t124))) % 33.89/34.09 (step @p197 :rule chain_m_resolution :premises (@p196 @p190) :args (@t124 @t85 @t125)) % 33.89/34.09 (step @p198 :rule eq-symm :args (@t127 @t128)) % 33.89/34.09 (step @p199 :rule cong :premises (@p198) :args (@t129)) % 33.89/34.09 (step @p200 :rule eq-symm :args (@t126 @t30)) % 33.89/34.09 (step @p201 :rule cong :premises (@p200 @p199) :args (@t130)) % 33.89/34.09 (step @p202 :rule nary_cong :premises (@p36 @p201) :args (@t131)) % 33.89/34.09 (step @p203 :rule cong :premises (@p202) :args (@t133)) % 33.89/34.09 (step @p204 :rule quant-merge-prenex :args ((= (forall @t16 @t135) @t133))) % 33.89/34.09 (step @p205 :rule alpha_equiv :args (@t136 (@list @t126) @t73)) % 33.89/34.09 (step @p206 :rule nary_cong :premises (@p41 @p205) :args (@t137)) % 33.89/34.09 (step @p207 :rule quant-miniscope-or :args ((= @t135 @t137))) % 33.89/34.09 (step @p208 :rule trans :premises (@p207 @p206)) % 33.89/34.09 (step @p209 :rule symm :premises (@p208)) % 33.89/34.09 (step @p210 :rule cong :premises (@p209) :args ((forall @t16 (or @t66 @t138)))) % 33.89/34.09 (step @p211 :rule trans :premises (@p210 @p204)) % 33.89/34.09 (step @p212 :rule trans :premises (@p211 @p203)) % 33.89/34.09 (step @p213 :rule bool-impl-elim :args (@t14 @t138)) % 33.89/34.09 (step @p214 :rule cong :premises (@p213) :args ((forall @t16 (=> @t14 @t138)))) % 33.89/34.09 (step @p215 :rule trans :premises (@p214 @p212)) % 33.89/34.09 (step @p216 :rule exists-elim :args ((= @t27 @t128))) % 33.89/34.09 (step @p217 :rule cong :premises (@p53 @p216) :args (@t28)) % 33.89/34.09 (step @p218 :rule cong :premises (@p217) :args (@t29)) % 33.89/34.09 (step @p219 :rule refl :args (@t31)) % 33.89/34.09 (step @p220 :rule cong :premises (@p219 @p218) :args (@t32)) % 33.89/34.09 (step @p221 :rule cong :premises (@p220) :args (@t33)) % 33.89/34.09 (step @p222 :rule cong :premises (@p59 @p221) :args (@t34)) % 33.89/34.09 (step @p223 :rule cong :premises (@p222) :args (@t35)) % 33.89/34.09 (step @p224 :rule trans :premises (@p223 @p215)) % 33.89/34.09 (step @p225 :rule eq_resolve :premises (@p5 @p224)) % 33.89/34.09 (step @p226 :rule bool-eq-true :args (@t139)) % 33.89/34.09 (step @p227 :rule eq-symm :args (true @t139)) % 33.89/34.09 (step @p228 :rule trans :premises (@p227 @p226)) % 33.89/34.09 (step @p229 :rule refl :args (@t139)) % 33.89/34.09 (step @p230 :rule eq-refl :args (@t86)) % 33.89/34.09 (step @p231 :rule cong :premises (@p230 @p229) :args (@t140)) % 33.89/34.09 (step @p232 :rule trans :premises (@p231 @p228)) % 33.89/34.09 (step @p233 :rule nary_cong :premises (@p71 @p232) :args (@t141)) % 33.89/34.09 (step @p234 :rule refl :args (@t142)) % 33.89/34.09 (step @p235 :rule cong :premises (@p234 @p233) :args ((=> @t142 @t141))) % 33.89/34.09 (assume-push @p320 @t142) % 33.89/34.09 (step @p237 :rule instantiate :premises (@p225) :args ((@list @t76 @t86))) % 33.89/34.09 (step-pop @p321 :rule scope :premises (@p237)) % 33.89/34.09 (step @p238 :rule process_scope :premises (@p321) :args (@t141)) % 33.89/34.09 (step @p240 :rule eq_resolve :premises (@p238 @p235)) % 33.89/34.09 (step @p241 :rule implies_elim :premises (@p240)) % 33.89/34.09 (step @p242 :rule chain_m_resolution :premises (@p241 @p225) :args (@t143 @t85 (@list @t142))) % 33.89/34.09 (step @p243 :rule cnf_or_pos :args (@t143)) % 33.89/34.09 (step @p244 :rule reordering :premises (@p243) :args ((or @t81 @t139 (not @t143)))) % 33.89/34.09 (step @p245 :rule chain_m_resolution :premises (@p244 @p93 @p242) :args (@t139 @t92 (@list @t80 @t143))) % 33.89/34.09 (step @p246 :rule eq-symm :args (@t145 @t146)) % 33.89/34.09 (step @p247 :rule cong :premises (@p229 @p246) :args ((=> @t139 @t147))) % 33.89/34.09 (assume-push @p322 @t139) % 33.89/34.09 (step @p249 :rule instantiate :premises (@p245) :args (@t123)) % 33.89/34.09 (step-pop @p323 :rule scope :premises (@p249)) % 33.89/34.09 (step @p250 :rule process_scope :premises (@p323) :args (@t147)) % 33.89/34.09 (step @p252 :rule eq_resolve :premises (@p250 @p247)) % 33.89/34.09 (step @p253 :rule implies_elim :premises (@p252)) % 33.89/34.09 (step @p254 :rule chain_m_resolution :premises (@p253 @p245) :args (@t148 @t85 (@list @t139))) % 33.89/34.09 (assume-push @p324 @t144) % 33.89/34.09 (step @p256 :rule instantiate :premises (@p324) :args (@t149)) % 33.89/34.09 (step-pop @p325 :rule scope :premises (@p256)) % 33.89/34.09 (step @p257 :rule process_scope :premises (@p325) :args (@t120)) % 33.89/34.09 (step @p259 :rule implies_elim :premises (@p257)) % 33.89/34.09 (step @p260 :rule chain_m_resolution :premises (@p259 @p190) :args (@t145 @t85 @t125)) % 33.89/34.09 (step @p261 :rule bool-double-not-elim :args (@t144)) % 33.89/34.09 (step @p262 :rule refl :args (@t146)) % 33.89/34.09 (step @p263 :rule refl :args (@t150)) % 33.89/34.09 (step @p264 :rule nary_cong :premises (@p263 @p262 @p261) :args ((or @t150 @t146 (not @t145)))) % 33.89/34.09 (step @p265 :rule cnf_equiv_pos2 :args (@t148)) % 33.89/34.09 (step @p266 :rule eq_resolve :premises (@p265 @p264)) % 33.89/34.09 (step @p267 :rule reordering :premises (@p266) :args ((or @t146 @t144 @t150))) % 33.89/34.09 (step @p268 :rule chain_m_resolution :premises (@p267 @p260 @p254) :args (@t146 @t108 (@list @t144 @t148))) % 33.89/34.09 (step @p269 :rule instantiate :premises (@p22) :args ((@list @t113 @t112 @t86 @t77))) % 33.89/34.09 (step @p270 :rule cnf_or_neg :args (@t110 1)) % 33.89/34.09 (step @p271 :rule chain_m_resolution :premises (@p270 @p133) :args ((not @t109) @t90 @t111)) % 33.89/34.09 (step @p272 :rule false_intro :premises (@p271)) % 33.89/34.09 (step @p273 :rule refl :args (@t87)) % 33.89/34.09 (step @p274 :rule symm :premises (@p159)) % 33.89/34.09 (step @p275 :rule cong :premises (@p274 @p273) :args (@t151)) % 33.89/34.09 (step @p276 :rule trans :premises (@p275 @p272)) % 33.89/34.09 (step @p277 :rule false_elim :premises (@p276)) % 33.89/34.09 (step @p278 :rule cnf_equiv_pos2 :args (@t154)) % 33.89/34.09 (step @p279 :rule reordering :premises (@p278) :args ((or @t151 @t155 (not @t154)))) % 33.89/34.09 (step @p280 :rule chain_m_resolution :premises (@p279 @p277 @p269) :args (@t155 @t108 (@list @t151 @t154))) % 33.89/34.09 (step @p281 :rule cnf_and_neg :args (@t153)) % 33.89/34.09 (step @p282 :rule chain_m_resolution :premises (@p281 @p280 @p268) :args ((not @t152) @t108 (@list @t153 @t146))) % 33.89/34.09 (step @p283 :rule bool-double-not-elim :args (@t122)) % 33.89/34.09 (step @p284 :rule refl :args (@t152)) % 33.89/34.09 (step @p285 :rule refl :args (@t157)) % 33.89/34.09 (step @p286 :rule nary_cong :premises (@p285 @p284 @p283) :args ((or @t157 @t152 (not @t124)))) % 33.89/34.09 (step @p287 :rule cnf_equiv_pos2 :args (@t156)) % 33.89/34.09 (step @p288 :rule eq_resolve :premises (@p287 @p286)) % 33.89/34.09 (step @p289 :rule reordering :premises (@p288) :args ((or @t152 @t122 @t157))) % 33.89/34.09 (step @p290 :rule chain_m_resolution :premises (@p289 @p282 @p197) :args (@t157 (@list true true) (@list @t152 @t122))) % 33.89/34.09 (step @p291 :rule eq-symm :args (@t124 @t152)) % 33.89/34.09 (step @p292 :rule cong :premises (@p67 @p291) :args ((=> @t78 @t158))) % 33.89/34.09 (assume-push @p326 @t78) % 33.89/34.09 (step @p294 :rule instantiate :premises (@p96) :args (@t149)) % 33.89/34.09 (step-pop @p327 :rule scope :premises (@p294)) % 33.89/34.09 (step @p295 :rule process_scope :premises (@p327) :args (@t158)) % 33.89/34.09 (step @p297 :rule eq_resolve :premises (@p295 @p292)) % 33.89/34.09 (step @p298 :rule implies_elim :premises (@p297)) % 33.89/34.09 (step @p299 false :rule chain_m_resolution :premises (@p298 @p290 @p96) :args (false @t108 (@list @t156 @t78))) % 33.89/34.09 ) % 33.89/34.09 % SZS output end Proof % 33.89/34.09 % cvc5 exiting %------------------------------------------------------------------------------