%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU120+2 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n003.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 08:50:36 AM UTC 2026 % Result : Theorem 0.38s 0.61s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU120+2 : TPTP v9.2.1. Released v3.3.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.33 % Computer : n003.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue Jun 2 16:30:29 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.61 % SZS status Theorem % 0.38/0.61 % SZS output start Proof % 0.38/0.61 ( % 0.38/0.61 (declare-sort $$unsorted 0) % 0.38/0.61 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.empty_set $$unsorted) % 0.38/0.61 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (define @t1 () (@var "A" $$unsorted)) % 0.38/0.61 (define @t2 () (@var "B" $$unsorted)) % 0.38/0.61 (define @t3 () (not (tptp.in @t2 @t1))) % 0.38/0.61 (define @t4 () (@list @t1 @t2)) % 0.38/0.61 (define @t5 () (tptp.set_intersection2 @t1 @t2)) % 0.38/0.61 (define @t6 () (@list @t1)) % 0.38/0.61 (define @t7 () (@var "D" $$unsorted)) % 0.38/0.61 (define @t8 () (@var "C" $$unsorted)) % 0.38/0.61 (define @t9 () (tptp.disjoint @t1 @t2)) % 0.38/0.61 (define @t10 () (forall @t4 (= @t9 (= @t5 tptp.empty_set)))) % 0.38/0.61 (define @t11 () (tptp.set_intersection2 @t1 @t1)) % 0.38/0.61 (define @t12 () (forall @t4 (= @t11 @t1))) % 0.38/0.61 (define @t13 () (tptp.empty @t1)) % 0.38/0.61 (define @t14 () (tptp.in @t8 @t2)) % 0.38/0.61 (define @t15 () (tptp.in @t8 @t1)) % 0.38/0.61 (define @t16 () (and @t15 @t14)) % 0.38/0.61 (define @t17 () (@list @t8)) % 0.38/0.61 (define @t18 () (exists @t17 @t16)) % 0.38/0.61 (define @t19 () (and @t18 @t9)) % 0.38/0.61 (define @t20 () (not @t19)) % 0.38/0.61 (define @t21 () (forall @t17 (not @t16))) % 0.38/0.61 (define @t22 () (not @t9)) % 0.38/0.61 (define @t23 () (and @t22 @t21)) % 0.38/0.61 (define @t24 () (not @t23)) % 0.38/0.61 (define @t25 () (and @t24 @t20)) % 0.38/0.61 (define @t26 () (forall @t4 @t25)) % 0.38/0.61 (define @t27 () (tptp.in @t8 @t5)) % 0.38/0.61 (define @t28 () (exists @t17 @t27)) % 0.38/0.61 (define @t29 () (and @t28 @t9)) % 0.38/0.61 (define @t30 () (not @t29)) % 0.38/0.61 (define @t31 () (forall @t17 (not @t27))) % 0.38/0.61 (define @t32 () (not (and @t22 @t31))) % 0.38/0.61 (define @t33 () (and @t32 @t30)) % 0.38/0.61 (define @t34 () (forall @t4 @t33)) % 0.38/0.61 (define @t35 () (not @t34)) % 0.38/0.61 (define @t36 () (= @t1 @t11)) % 0.38/0.61 (define @t37 () (@var "BOUND_VARIABLE_7596" $$unsorted)) % 0.38/0.61 (define @t38 () (@var "BOUND_VARIABLE_7594" $$unsorted)) % 0.38/0.61 (define @t39 () (not (tptp.disjoint @t38 @t37))) % 0.38/0.61 (define @t40 () (tptp.set_intersection2 @t38 @t37)) % 0.38/0.61 (define @t41 () (@var "BOUND_VARIABLE_7608" $$unsorted)) % 0.38/0.61 (define @t42 () (not (tptp.in @t41 @t40))) % 0.38/0.61 (define @t43 () (or @t42 @t39)) % 0.38/0.61 (define @t44 () (forall (@list @t38 @t37 @t41) @t43)) % 0.38/0.61 (define @t45 () (@quantifiers_skolemize @t44 1)) % 0.38/0.61 (define @t46 () (@quantifiers_skolemize @t44 0)) % 0.38/0.61 (define @t47 () (tptp.set_intersection2 @t46 @t45)) % 0.38/0.61 (define @t48 () (tptp.disjoint @t46 @t45)) % 0.38/0.61 (define @t49 () (= @t48 (= @t47 tptp.empty_set))) % 0.38/0.61 (define @t50 () (= tptp.empty_set @t47)) % 0.38/0.61 (define @t51 () (= @t48 @t50)) % 0.38/0.61 (define @t52 () (@list false)) % 0.38/0.61 (define @t53 () (@list @t10)) % 0.38/0.61 (define @t54 () (@var "BOUND_VARIABLE_7583" $$unsorted)) % 0.38/0.61 (define @t55 () (@var "BOUND_VARIABLE_7581" $$unsorted)) % 0.38/0.61 (define @t56 () (forall (@list @t55 @t54) (or (tptp.disjoint @t55 @t54) (not (forall @t17 (not (tptp.in @t8 (tptp.set_intersection2 @t55 @t54)))))))) % 0.38/0.61 (define @t57 () (@quantifiers_skolemize @t56 1)) % 0.38/0.61 (define @t58 () (@quantifiers_skolemize @t56 0)) % 0.38/0.61 (define @t59 () (tptp.set_intersection2 @t58 @t57)) % 0.38/0.61 (define @t60 () (not (tptp.in @t8 @t59))) % 0.38/0.61 (define @t61 () (forall @t17 @t60)) % 0.38/0.61 (define @t62 () (not @t61)) % 0.38/0.61 (define @t63 () (tptp.disjoint @t58 @t57)) % 0.38/0.61 (define @t64 () (or @t63 @t62)) % 0.38/0.61 (define @t65 () (= @t63 (= @t59 tptp.empty_set))) % 0.38/0.61 (define @t66 () (= tptp.empty_set @t59)) % 0.38/0.61 (define @t67 () (= @t63 @t66)) % 0.38/0.61 (define @t68 () (not @t66)) % 0.38/0.61 (define @t69 () (@var "BOUND_VARIABLE_7544" $$unsorted)) % 0.38/0.61 (define @t70 () (@var "BOUND_VARIABLE_7558" $$unsorted)) % 0.38/0.61 (define @t71 () (not (tptp.in @t70 @t69))) % 0.38/0.61 (define @t72 () (@var "BOUND_VARIABLE_7542" $$unsorted)) % 0.38/0.61 (define @t73 () (not (tptp.in @t70 @t72))) % 0.38/0.61 (define @t74 () (not (tptp.disjoint @t72 @t69))) % 0.38/0.61 (define @t75 () (or @t73 @t71)) % 0.38/0.61 (define @t76 () (or @t75 @t74)) % 0.38/0.61 (define @t77 () (forall (@list @t72 @t69 @t70) @t76)) % 0.38/0.61 (define @t78 () (@list @t70)) % 0.38/0.61 (define @t79 () (forall @t78 @t76)) % 0.38/0.61 (define @t80 () (@list @t72 @t69)) % 0.38/0.61 (define @t81 () (forall @t78 @t75)) % 0.38/0.61 (define @t82 () (@list @t8)) % 0.38/0.61 (define @t83 () (or @t81 @t74)) % 0.38/0.61 (define @t84 () (forall @t80 (or (forall @t17 (or (not (tptp.in @t8 @t72)) (not (tptp.in @t8 @t69)))) @t74))) % 0.38/0.61 (define @t85 () (@var "BOUND_VARIABLE_7529" $$unsorted)) % 0.38/0.61 (define @t86 () (@var "BOUND_VARIABLE_7527" $$unsorted)) % 0.38/0.61 (define @t87 () (forall (@list @t86 @t85) (or (tptp.disjoint @t86 @t85) (not (forall @t17 (or (not (tptp.in @t8 @t86)) (not (tptp.in @t8 @t85)))))))) % 0.38/0.61 (define @t88 () (forall @t17 (or (not @t15) (not @t14)))) % 0.38/0.61 (define @t89 () (or @t88 @t22)) % 0.38/0.61 (define @t90 () (forall @t4 @t89)) % 0.38/0.61 (define @t91 () (@list @t1 @t2)) % 0.38/0.61 (define @t92 () (not @t88)) % 0.38/0.61 (define @t93 () (or @t9 @t92)) % 0.38/0.61 (define @t94 () (forall @t4 @t93)) % 0.38/0.61 (define @t95 () (and @t94 @t90)) % 0.38/0.61 (define @t96 () (not @t22)) % 0.38/0.61 (define @t97 () (and (not (and @t22 @t88)) (not (and @t92 @t9)))) % 0.38/0.61 (define @t98 () (not @t21)) % 0.38/0.61 (define @t99 () (or @t60 @t60)) % 0.38/0.61 (define @t100 () (forall @t17 @t99)) % 0.38/0.61 (define @t101 () (not @t100)) % 0.38/0.61 (define @t102 () (tptp.disjoint @t59 @t59)) % 0.38/0.61 (define @t103 () (or @t102 @t101)) % 0.38/0.61 (define @t104 () (@list @t59 @t59)) % 0.38/0.61 (define @t105 () (or @t102 @t62)) % 0.38/0.61 (define @t106 () (tptp.set_intersection2 @t59 @t59)) % 0.38/0.61 (define @t107 () (= @t102 (= @t106 tptp.empty_set))) % 0.38/0.61 (define @t108 () (= tptp.empty_set @t106)) % 0.38/0.61 (define @t109 () (= @t102 @t108)) % 0.38/0.61 (define @t110 () (not @t108)) % 0.38/0.61 (define @t111 () (= @t59 @t106)) % 0.38/0.61 (define @t112 () (not @t111)) % 0.38/0.61 (define @t113 () (and @t68 @t111)) % 0.38/0.61 (define @t114 () (not @t64)) % 0.38/0.61 (define @t115 () (not @t56)) % 0.38/0.61 (define @t116 () (@list @t41)) % 0.38/0.61 (define @t117 () (forall @t116 @t43)) % 0.38/0.61 (define @t118 () (@list @t38 @t37)) % 0.38/0.61 (define @t119 () (forall @t116 @t42)) % 0.38/0.61 (define @t120 () (or @t119 @t39)) % 0.38/0.61 (define @t121 () (forall @t118 (or (forall @t17 (not (tptp.in @t8 @t40))) @t39))) % 0.38/0.61 (define @t122 () (or @t31 @t22)) % 0.38/0.61 (define @t123 () (forall @t4 @t122)) % 0.38/0.61 (define @t124 () (not @t31)) % 0.38/0.61 (define @t125 () (or @t9 @t124)) % 0.38/0.61 (define @t126 () (forall @t4 @t125)) % 0.38/0.61 (define @t127 () (and @t126 @t123)) % 0.38/0.61 (define @t128 () (and @t32 (not (and @t124 @t9)))) % 0.38/0.61 (define @t129 () (not @t44)) % 0.38/0.61 (define @t130 () (not @t48)) % 0.38/0.61 (define @t131 () (@quantifiers_skolemize @t44 2)) % 0.38/0.61 (define @t132 () (tptp.in @t131 @t47)) % 0.38/0.61 (define @t133 () (not @t132)) % 0.38/0.61 (define @t134 () (or @t133 @t130)) % 0.38/0.61 (define @t135 () (not @t134)) % 0.38/0.61 (define @t136 () (@list true)) % 0.38/0.61 (define @t137 () (@list @t134)) % 0.38/0.61 (define @t138 () (@list false false)) % 0.38/0.61 (define @t139 () (tptp.set_intersection2 @t47 @t47)) % 0.38/0.61 (define @t140 () (tptp.disjoint @t47 @t47)) % 0.38/0.61 (define @t141 () (= @t140 (= @t139 tptp.empty_set))) % 0.38/0.61 (define @t142 () (= tptp.empty_set @t139)) % 0.38/0.61 (define @t143 () (= @t140 @t142)) % 0.38/0.61 (define @t144 () (not @t140)) % 0.38/0.61 (define @t145 () (or @t144 @t133 @t133)) % 0.38/0.61 (define @t146 () (not @t142)) % 0.38/0.61 (define @t147 () (= @t47 @t139)) % 0.38/0.61 (define @t148 () (and @t50 @t147)) % 0.38/0.61 (assume @p1 (forall @t4 (=> (tptp.in @t1 @t2) @t3))) % 0.38/0.61 (assume @p2 (forall @t4 (= @t5 (tptp.set_intersection2 @t2 @t1)))) % 0.38/0.61 (assume @p3 (forall @t6 (= (= @t1 tptp.empty_set) (forall (@list @t2) @t3)))) % 0.38/0.61 (assume @p4 (forall (@list @t1 @t2 @t8) (= (= @t8 @t5) (forall (@list @t7) (= (tptp.in @t7 @t8) (and (tptp.in @t7 @t1) (tptp.in @t7 @t2))))))) % 0.38/0.61 (assume @p5 @t10) % 0.38/0.61 (assume @p6 true) % 0.38/0.61 (assume @p7 (tptp.empty tptp.empty_set)) % 0.38/0.61 (assume @p8 @t12) % 0.38/0.61 (assume @p9 (exists @t6 @t13)) % 0.38/0.61 (assume @p10 (exists @t6 (not @t13))) % 0.38/0.61 (assume @p11 (forall @t4 (=> @t9 (tptp.disjoint @t2 @t1)))) % 0.38/0.61 (assume @p12 @t26) % 0.38/0.61 (assume @p13 @t35) % 0.38/0.61 (step @p14 :rule quant-unused-vars :args ((= (forall @t4 @t36) (forall @t6 @t36)))) % 0.38/0.61 (step @p15 :rule eq-symm :args (@t11 @t1)) % 0.38/0.61 (step @p16 :rule cong :premises (@p15) :args (@t12)) % 0.38/0.61 (step @p17 :rule trans :premises (@p16 @p14)) % 0.38/0.61 (step @p18 :rule eq_resolve :premises (@p8 @p17)) % 0.38/0.61 (step @p19 :rule instantiate :premises (@p18) :args ((@list @t47))) % 0.38/0.61 (step @p20 :rule eq-symm :args (@t47 tptp.empty_set)) % 0.38/0.61 (step @p21 :rule refl :args (@t48)) % 0.38/0.61 (step @p22 :rule cong :premises (@p21 @p20) :args (@t49)) % 0.38/0.61 (step @p23 :rule refl :args (@t10)) % 0.38/0.61 (step @p24 :rule cong :premises (@p23 @p22) :args ((=> @t10 @t49))) % 0.38/0.61 (assume-push @p270 @t10) % 0.38/0.61 (step @p26 :rule instantiate :premises (@p5) :args ((@list @t46 @t45))) % 0.38/0.61 (step-pop @p271 :rule scope :premises (@p26)) % 0.38/0.61 (step @p27 :rule process_scope :premises (@p271) :args (@t49)) % 0.38/0.61 (step @p29 :rule eq_resolve :premises (@p27 @p24)) % 0.38/0.61 (step @p30 :rule implies_elim :premises (@p29)) % 0.38/0.61 (step @p31 :rule chain_m_resolution :premises (@p30 @p5) :args (@t51 @t52 @t53)) % 0.38/0.61 (step @p32 :rule cnf_or_neg :args (@t64 0)) % 0.38/0.61 (step @p33 :rule bool-double-not-elim :args (@t61)) % 0.38/0.61 (step @p34 :rule refl :args (@t64)) % 0.38/0.61 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or @t64 (not @t62)))) % 0.38/0.61 (step @p36 :rule cnf_or_neg :args (@t64 1)) % 0.38/0.61 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 0.38/0.61 (step @p38 :rule reordering :premises (@p37) :args ((or @t61 @t64))) % 0.38/0.61 (step @p39 :rule eq-symm :args (@t59 tptp.empty_set)) % 0.38/0.61 (step @p40 :rule refl :args (@t63)) % 0.38/0.61 (step @p41 :rule cong :premises (@p40 @p39) :args (@t65)) % 0.38/0.61 (step @p42 :rule cong :premises (@p23 @p41) :args ((=> @t10 @t65))) % 0.38/0.61 (assume-push @p272 @t10) % 0.38/0.61 (step @p44 :rule instantiate :premises (@p5) :args ((@list @t58 @t57))) % 0.38/0.61 (step-pop @p273 :rule scope :premises (@p44)) % 0.38/0.61 (step @p45 :rule process_scope :premises (@p273) :args (@t65)) % 0.38/0.61 (step @p47 :rule eq_resolve :premises (@p45 @p42)) % 0.38/0.61 (step @p48 :rule implies_elim :premises (@p47)) % 0.38/0.61 (step @p49 :rule chain_m_resolution :premises (@p48 @p5) :args (@t67 @t52 @t53)) % 0.38/0.61 (step @p50 :rule cnf_equiv_pos2 :args (@t67)) % 0.38/0.61 (step @p51 :rule reordering :premises (@p50) :args ((or @t63 @t68 (not @t67)))) % 0.38/0.61 (step @p52 :rule aci_norm :args ((= @t76 (or @t74 @t73 @t71)))) % 0.38/0.61 (step @p53 :rule cong :premises (@p52) :args (@t77)) % 0.38/0.61 (step @p54 :rule quant-merge-prenex :args ((= (forall @t80 @t79) @t77))) % 0.38/0.61 (step @p55 :rule refl :args (@t74)) % 0.38/0.61 (step @p56 :rule alpha_equiv :args (@t81 (@list @t70) @t82)) % 0.38/0.61 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t83)) % 0.38/0.61 (step @p58 :rule quant-miniscope-or :args ((= @t79 @t83))) % 0.38/0.61 (step @p59 :rule trans :premises (@p58 @p57)) % 0.38/0.61 (step @p60 :rule symm :premises (@p59)) % 0.38/0.61 (step @p61 :rule cong :premises (@p60) :args (@t84)) % 0.38/0.61 (step @p62 :rule trans :premises (@p61 @p54)) % 0.38/0.61 (step @p63 :rule trans :premises (@p62 @p53)) % 0.38/0.61 (step @p64 :rule refl :args (@t87)) % 0.38/0.61 (step @p65 :rule nary_cong :premises (@p64 @p63) :args ((and @t87 @t84))) % 0.38/0.61 (step @p66 :rule alpha_equiv :args (@t90 @t91 (@list @t72 @t69))) % 0.38/0.61 (step @p67 :rule alpha_equiv :args (@t94 @t91 (@list @t86 @t85))) % 0.38/0.61 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t95)) % 0.38/0.61 (step @p69 :rule quant-miniscope-and :args ((= (forall @t4 (and @t93 @t89)) @t95))) % 0.38/0.61 (step @p70 :rule trans :premises (@p69 @p68)) % 0.38/0.61 (step @p71 :rule trans :premises (@p70 @p65)) % 0.38/0.61 (step @p72 :rule refl :args (@t22)) % 0.38/0.61 (step @p73 :rule bool-double-not-elim :args (@t88)) % 0.38/0.61 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or (not @t92) @t22))) % 0.38/0.61 (step @p75 :rule bool-and-de-morgan :args (@t92 @t9 true)) % 0.38/0.61 (step @p76 :rule trans :premises (@p75 @p74)) % 0.38/0.61 (step @p77 :rule refl :args (@t92)) % 0.38/0.61 (step @p78 :rule bool-double-not-elim :args (@t9)) % 0.38/0.61 (step @p79 :rule nary_cong :premises (@p78 @p77) :args ((or @t96 @t92))) % 0.38/0.61 (step @p80 :rule bool-and-de-morgan :args (@t22 @t88 true)) % 0.38/0.61 (step @p81 :rule trans :premises (@p80 @p79)) % 0.38/0.61 (step @p82 :rule nary_cong :premises (@p81 @p76) :args (@t97)) % 0.38/0.61 (step @p83 :rule cong :premises (@p82) :args ((forall @t4 @t97))) % 0.38/0.61 (step @p84 :rule trans :premises (@p83 @p71)) % 0.38/0.61 (step @p85 :rule refl :args (@t9)) % 0.38/0.61 (step @p86 :rule bool-and-de-morgan :args (@t15 @t14 true)) % 0.38/0.61 (step @p87 :rule cong :premises (@p86) :args (@t21)) % 0.38/0.61 (step @p88 :rule cong :premises (@p87) :args (@t98)) % 0.38/0.61 (step @p89 :rule exists-elim :args ((= @t18 @t98))) % 0.38/0.61 (step @p90 :rule trans :premises (@p89 @p88)) % 0.38/0.61 (step @p91 :rule nary_cong :premises (@p90 @p85) :args (@t19)) % 0.38/0.61 (step @p92 :rule cong :premises (@p91) :args (@t20)) % 0.38/0.61 (step @p93 :rule refl :args (@t22)) % 0.38/0.61 (step @p94 :rule nary_cong :premises (@p93 @p87) :args (@t23)) % 0.38/0.61 (step @p95 :rule cong :premises (@p94) :args (@t24)) % 0.38/0.61 (step @p96 :rule nary_cong :premises (@p95 @p92) :args (@t25)) % 0.38/0.61 (step @p97 :rule cong :premises (@p96) :args (@t26)) % 0.38/0.61 (step @p98 :rule trans :premises (@p97 @p84)) % 0.38/0.61 (step @p99 :rule eq_resolve :premises (@p12 @p98)) % 0.38/0.61 (step @p100 :rule and_elim :premises (@p99) :args (0)) % 0.38/0.61 (step @p101 :rule aci_norm :args ((= @t99 @t60))) % 0.38/0.61 (step @p102 :rule cong :premises (@p101) :args (@t100)) % 0.38/0.61 (step @p103 :rule cong :premises (@p102) :args (@t101)) % 0.38/0.61 (step @p104 :rule refl :args (@t102)) % 0.38/0.61 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t103)) % 0.38/0.61 (step @p106 :rule cong :premises (@p64 @p105) :args ((=> @t87 @t103))) % 0.38/0.61 (assume-push @p274 @t87) % 0.38/0.61 (step @p108 :rule instantiate :premises (@p100) :args (@t104)) % 0.38/0.61 (step-pop @p275 :rule scope :premises (@p108)) % 0.38/0.61 (step @p109 :rule process_scope :premises (@p275) :args (@t103)) % 0.38/0.61 (step @p111 :rule eq_resolve :premises (@p109 @p106)) % 0.38/0.61 (step @p112 :rule implies_elim :premises (@p111)) % 0.38/0.61 (step @p113 :rule chain_m_resolution :premises (@p112 @p100) :args (@t105 @t52 (@list @t87))) % 0.38/0.61 (step @p114 :rule cnf_or_pos :args (@t105)) % 0.38/0.61 (step @p115 :rule reordering :premises (@p114) :args ((or @t62 @t102 (not @t105)))) % 0.38/0.61 (step @p116 :rule eq-symm :args (@t106 tptp.empty_set)) % 0.38/0.61 (step @p117 :rule cong :premises (@p104 @p116) :args (@t107)) % 0.38/0.61 (step @p118 :rule cong :premises (@p23 @p117) :args ((=> @t10 @t107))) % 0.38/0.61 (assume-push @p276 @t10) % 0.38/0.61 (step @p120 :rule instantiate :premises (@p5) :args (@t104)) % 0.38/0.61 (step-pop @p277 :rule scope :premises (@p120)) % 0.38/0.61 (step @p121 :rule process_scope :premises (@p277) :args (@t107)) % 0.38/0.61 (step @p123 :rule eq_resolve :premises (@p121 @p118)) % 0.38/0.61 (step @p124 :rule implies_elim :premises (@p123)) % 0.38/0.61 (step @p125 :rule chain_m_resolution :premises (@p124 @p5) :args (@t109 @t52 @t53)) % 0.38/0.61 (step @p126 :rule cnf_equiv_pos1 :args (@t109)) % 0.38/0.61 (step @p127 :rule reordering :premises (@p126) :args ((or (not @t102) @t108 (not @t109)))) % 0.38/0.61 (step @p128 :rule instantiate :premises (@p18) :args ((@list @t59))) % 0.38/0.61 (step @p129 :rule refl :args (@t110)) % 0.38/0.61 (step @p130 :rule refl :args (@t112)) % 0.38/0.61 (step @p131 :rule bool-double-not-elim :args (@t66)) % 0.38/0.61 (step @p132 :rule nary_cong :premises (@p131 @p130 @p129) :args ((or (not @t68) @t112 @t110))) % 0.38/0.61 (assume-push @p278 @t68) % 0.38/0.61 (assume-push @p279 @t111) % 0.38/0.61 (assume-push @p280 @t68) % 0.38/0.61 (assume-push @p281 @t111) % 0.38/0.61 (step @p137 :rule false_intro :premises (@p278)) % 0.38/0.61 (step @p138 :rule symm :premises (@p128)) % 0.38/0.61 (step @p139 :rule refl :args (tptp.empty_set)) % 0.38/0.61 (step @p140 :rule cong :premises (@p139 @p138) :args (@t108)) % 0.38/0.61 (step @p141 :rule trans :premises (@p140 @p137)) % 0.38/0.61 (step @p142 :rule false_elim :premises (@p141)) % 0.38/0.61 (step-pop @p282 :rule scope :premises (@p142)) % 0.38/0.61 (step-pop @p283 :rule scope :premises (@p282)) % 0.38/0.61 (step @p143 :rule process_scope :premises (@p283) :args (@t110)) % 0.38/0.61 (step @p146 :rule and_intro :premises (@p278 @p128)) % 0.38/0.61 (step @p147 :rule modus_ponens :premises (@p146 @p143)) % 0.38/0.61 (step-pop @p284 :rule scope :premises (@p147)) % 0.38/0.61 (step-pop @p285 :rule scope :premises (@p284)) % 0.38/0.61 (step @p148 :rule process_scope :premises (@p285) :args (@t110)) % 0.38/0.61 (step @p151 :rule implies_elim :premises (@p148)) % 0.38/0.61 (step @p152 :rule cnf_and_neg :args (@t113)) % 0.38/0.61 (step @p153 :rule resolution :premises (@p152 @p151) :args (true @t113)) % 0.38/0.61 (step @p154 :rule eq_resolve :premises (@p153 @p132)) % 0.38/0.61 (step @p155 :rule reordering :premises (@p154) :args ((or @t66 @t110 @t112))) % 0.38/0.61 (step @p156 :rule chain_m_resolution :premises (@p155 @p128 @p127 @p125 @p115 @p113 @p51 @p49 @p38 @p32) :args (@t64 (@list false false false false false true false false true) (@list @t111 @t108 @t109 @t102 @t105 @t66 @t67 @t61 @t63))) % 0.38/0.61 (step @p157 :rule refl :args (@t114)) % 0.38/0.61 (step @p158 :rule bool-double-not-elim :args (@t56)) % 0.38/0.61 (step @p159 :rule nary_cong :premises (@p158 @p157) :args ((or (not @t115) @t114))) % 0.38/0.61 (assume-push @p286 @t115) % 0.38/0.61 (step @p161 :rule skolemize :premises (@p286)) % 0.38/0.61 (step-pop @p287 :rule scope :premises (@p161)) % 0.38/0.61 (step @p162 :rule process_scope :premises (@p287) :args (@t114)) % 0.38/0.61 (step @p164 :rule implies_elim :premises (@p162)) % 0.38/0.61 (step @p165 :rule eq_resolve :premises (@p164 @p159)) % 0.38/0.61 (step @p166 :rule chain_m_resolution :premises (@p165 @p156) :args (@t56 @t52 (@list @t64))) % 0.38/0.61 (step @p167 :rule quant-merge-prenex :args ((= (forall @t118 @t117) @t44))) % 0.38/0.61 (step @p168 :rule refl :args (@t39)) % 0.38/0.61 (step @p169 :rule alpha_equiv :args (@t119 (@list @t41) @t82)) % 0.38/0.61 (step @p170 :rule nary_cong :premises (@p169 @p168) :args (@t120)) % 0.38/0.61 (step @p171 :rule quant-miniscope-or :args ((= @t117 @t120))) % 0.38/0.61 (step @p172 :rule trans :premises (@p171 @p170)) % 0.38/0.61 (step @p173 :rule symm :premises (@p172)) % 0.38/0.61 (step @p174 :rule cong :premises (@p173) :args (@t121)) % 0.38/0.61 (step @p175 :rule trans :premises (@p174 @p167)) % 0.38/0.61 (step @p176 :rule refl :args (@t56)) % 0.38/0.61 (step @p177 :rule nary_cong :premises (@p176 @p175) :args ((and @t56 @t121))) % 0.38/0.61 (step @p178 :rule alpha_equiv :args (@t123 @t91 (@list @t38 @t37))) % 0.38/0.61 (step @p179 :rule alpha_equiv :args (@t126 @t91 (@list @t55 @t54))) % 0.38/0.61 (step @p180 :rule nary_cong :premises (@p179 @p178) :args (@t127)) % 0.38/0.61 (step @p181 :rule quant-miniscope-and :args ((= (forall @t4 (and @t125 @t122)) @t127))) % 0.38/0.61 (step @p182 :rule trans :premises (@p181 @p180)) % 0.38/0.61 (step @p183 :rule trans :premises (@p182 @p177)) % 0.38/0.61 (step @p184 :rule bool-double-not-elim :args (@t31)) % 0.38/0.61 (step @p185 :rule nary_cong :premises (@p184 @p72) :args ((or (not @t124) @t22))) % 0.38/0.61 (step @p186 :rule bool-and-de-morgan :args (@t124 @t9 true)) % 0.38/0.61 (step @p187 :rule trans :premises (@p186 @p185)) % 0.38/0.61 (step @p188 :rule refl :args (@t124)) % 0.38/0.61 (step @p189 :rule nary_cong :premises (@p78 @p188) :args ((or @t96 @t124))) % 0.38/0.61 (step @p190 :rule bool-and-de-morgan :args (@t22 @t31 true)) % 0.38/0.61 (step @p191 :rule trans :premises (@p190 @p189)) % 0.38/0.61 (step @p192 :rule nary_cong :premises (@p191 @p187) :args (@t128)) % 0.38/0.61 (step @p193 :rule cong :premises (@p192) :args ((forall @t4 @t128))) % 0.38/0.61 (step @p194 :rule trans :premises (@p193 @p183)) % 0.38/0.61 (step @p195 :rule exists-elim :args ((= @t28 @t124))) % 0.38/0.61 (step @p196 :rule nary_cong :premises (@p195 @p85) :args (@t29)) % 0.38/0.61 (step @p197 :rule cong :premises (@p196) :args (@t30)) % 0.38/0.61 (step @p198 :rule refl :args (@t32)) % 0.38/0.61 (step @p199 :rule nary_cong :premises (@p198 @p197) :args (@t33)) % 0.38/0.61 (step @p200 :rule cong :premises (@p199) :args (@t34)) % 0.38/0.61 (step @p201 :rule trans :premises (@p200 @p194)) % 0.38/0.61 (step @p202 :rule cong :premises (@p201) :args (@t35)) % 0.38/0.61 (step @p203 :rule eq_resolve :premises (@p13 @p202)) % 0.38/0.61 (step @p204 :rule not_and :premises (@p203)) % 0.38/0.61 (step @p205 :rule chain_m_resolution :premises (@p204 @p166) :args (@t129 @t52 (@list @t56))) % 0.38/0.61 (step @p206 :rule refl :args (@t135)) % 0.38/0.61 (step @p207 :rule bool-double-not-elim :args (@t44)) % 0.38/0.61 (step @p208 :rule nary_cong :premises (@p207 @p206) :args ((or (not @t129) @t135))) % 0.38/0.61 (assume-push @p288 @t129) % 0.38/0.61 (step @p210 :rule skolemize :premises (@p288)) % 0.38/0.61 (step-pop @p289 :rule scope :premises (@p210)) % 0.38/0.61 (step @p211 :rule process_scope :premises (@p289) :args (@t135)) % 0.38/0.61 (step @p213 :rule implies_elim :premises (@p211)) % 0.38/0.61 (step @p214 :rule eq_resolve :premises (@p213 @p208)) % 0.38/0.61 (step @p215 :rule chain_m_resolution :premises (@p214 @p205) :args (@t135 @t136 (@list @t44))) % 0.38/0.61 (step @p216 :rule bool-double-not-elim :args (@t48)) % 0.38/0.61 (step @p217 :rule refl :args (@t134)) % 0.38/0.61 (step @p218 :rule nary_cong :premises (@p217 @p216) :args ((or @t134 (not @t130)))) % 0.38/0.61 (step @p219 :rule cnf_or_neg :args (@t134 1)) % 0.38/0.61 (step @p220 :rule eq_resolve :premises (@p219 @p218)) % 0.38/0.61 (step @p221 :rule reordering :premises (@p220) :args ((or @t48 @t134))) % 0.38/0.61 (step @p222 :rule chain_m_resolution :premises (@p221 @p215) :args (@t48 @t136 @t137)) % 0.38/0.61 (step @p223 :rule cnf_equiv_pos1 :args (@t51)) % 0.38/0.61 (step @p224 :rule reordering :premises (@p223) :args ((or @t130 @t50 (not @t51)))) % 0.38/0.61 (step @p225 :rule chain_m_resolution :premises (@p224 @p222 @p31) :args (@t50 @t138 (@list @t48 @t51))) % 0.38/0.61 (step @p226 :rule eq-symm :args (@t139 tptp.empty_set)) % 0.38/0.61 (step @p227 :rule refl :args (@t140)) % 0.38/0.61 (step @p228 :rule cong :premises (@p227 @p226) :args (@t141)) % 0.38/0.61 (step @p229 :rule cong :premises (@p23 @p228) :args ((=> @t10 @t141))) % 0.38/0.61 (assume-push @p290 @t10) % 0.38/0.61 (step @p231 :rule instantiate :premises (@p5) :args ((@list @t47 @t47))) % 0.38/0.61 (step-pop @p291 :rule scope :premises (@p231)) % 0.38/0.61 (step @p232 :rule process_scope :premises (@p291) :args (@t141)) % 0.38/0.61 (step @p234 :rule eq_resolve :premises (@p232 @p229)) % 0.38/0.61 (step @p235 :rule implies_elim :premises (@p234)) % 0.38/0.61 (step @p236 :rule chain_m_resolution :premises (@p235 @p5) :args (@t143 @t52 @t53)) % 0.38/0.61 (step @p237 :rule and_elim :premises (@p99) :args (1)) % 0.38/0.61 (step @p238 :rule instantiate :premises (@p237) :args ((@list @t47 @t47 @t131))) % 0.38/0.61 (step @p239 :rule bool-double-not-elim :args (@t132)) % 0.38/0.61 (step @p240 :rule nary_cong :premises (@p217 @p239) :args ((or @t134 (not @t133)))) % 0.38/0.61 (step @p241 :rule cnf_or_neg :args (@t134 0)) % 0.38/0.61 (step @p242 :rule eq_resolve :premises (@p241 @p240)) % 0.38/0.61 (step @p243 :rule reordering :premises (@p242) :args ((or @t132 @t134))) % 0.38/0.61 (step @p244 :rule chain_m_resolution :premises (@p243 @p215) :args (@t132 @t136 @t137)) % 0.38/0.61 (step @p245 :rule cnf_or_pos :args (@t145)) % 0.38/0.61 (step @p246 :rule factoring :premises (@p245)) % 0.38/0.61 (step @p247 :rule reordering :premises (@p246) :args ((or @t133 @t144 (not @t145)))) % 0.38/0.61 (step @p248 :rule chain_m_resolution :premises (@p247 @p244 @p238) :args (@t144 @t138 (@list @t132 @t145))) % 0.38/0.61 (step @p249 :rule cnf_equiv_pos2 :args (@t143)) % 0.38/0.61 (step @p250 :rule reordering :premises (@p249) :args ((or @t140 @t146 (not @t143)))) % 0.38/0.61 (step @p251 :rule chain_m_resolution :premises (@p250 @p248 @p236) :args (@t146 (@list true false) (@list @t140 @t143))) % 0.38/0.61 (assume-push @p292 @t50) % 0.38/0.61 (assume-push @p293 @t147) % 0.38/0.61 (assume-push @p294 @t147) % 0.38/0.61 (assume-push @p295 @t50) % 0.38/0.61 (step @p256 :rule trans :premises (@p292 @p19)) % 0.38/0.61 (step-pop @p296 :rule scope :premises (@p256)) % 0.38/0.61 (step-pop @p297 :rule scope :premises (@p296)) % 0.38/0.61 (step @p257 :rule process_scope :premises (@p297) :args (@t142)) % 0.38/0.61 (step @p260 :rule and_intro :premises (@p19 @p292)) % 0.38/0.61 (step @p261 :rule modus_ponens :premises (@p260 @p257)) % 0.38/0.61 (step-pop @p298 :rule scope :premises (@p261)) % 0.38/0.61 (step-pop @p299 :rule scope :premises (@p298)) % 0.38/0.61 (step @p262 :rule process_scope :premises (@p299) :args (@t142)) % 0.38/0.61 (step @p265 :rule implies_elim :premises (@p262)) % 0.38/0.61 (step @p266 :rule cnf_and_neg :args (@t148)) % 0.38/0.61 (step @p267 :rule resolution :premises (@p266 @p265) :args (true @t148)) % 0.38/0.61 (step @p268 :rule reordering :premises (@p267) :args ((or (not @t50) @t142 (not @t147)))) % 0.38/0.61 (step @p269 false :rule chain_m_resolution :premises (@p268 @p251 @p225 @p19) :args (false (@list true false false) (@list @t142 @t50 @t147))) % 0.38/0.61 ) % 0.38/0.61 % SZS output end Proof % 0.38/0.61 % cvc5 exiting %------------------------------------------------------------------------------