%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU143+2 : 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 : n005.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 08:50:42 AM UTC 2026 % Result : Theorem 1.21s 1.42s % Output : Proof 1.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU143+2 : 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 % 0.17/0.34 % Computer : n005.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 16:31:48 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 1.21/1.42 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.21/1.42 % SZS status Theorem % 1.21/1.42 % SZS output start Proof % 1.21/1.42 ( % 1.21/1.42 (declare-sort $$unsorted 0) % 1.21/1.42 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 1.21/1.42 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 1.21/1.42 (declare-const tptp.empty_set $$unsorted) % 1.21/1.42 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 1.21/1.42 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 1.21/1.42 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 1.21/1.42 (declare-const tptp.empty (-> $$unsorted Bool)) % 1.21/1.42 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.21/1.42 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 1.21/1.42 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 1.21/1.42 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 1.21/1.42 (define @t1 () (@var "A" $$unsorted)) % 1.21/1.42 (define @t2 () (@var "B" $$unsorted)) % 1.21/1.42 (define @t3 () (not (tptp.in @t2 @t1))) % 1.21/1.42 (define @t4 () (tptp.in @t1 @t2)) % 1.21/1.42 (define @t5 () (@list @t1 @t2)) % 1.21/1.42 (define @t6 () (tptp.proper_subset @t2 @t1)) % 1.21/1.42 (define @t7 () (tptp.proper_subset @t1 @t2)) % 1.21/1.42 (define @t8 () (tptp.unordered_pair @t1 @t2)) % 1.21/1.42 (define @t9 () (tptp.set_union2 @t2 @t1)) % 1.21/1.42 (define @t10 () (tptp.set_union2 @t1 @t2)) % 1.21/1.42 (define @t11 () (tptp.set_intersection2 @t1 @t2)) % 1.21/1.42 (define @t12 () (tptp.subset @t1 @t2)) % 1.21/1.42 (define @t13 () (= @t1 @t2)) % 1.21/1.42 (define @t14 () (@var "C" $$unsorted)) % 1.21/1.42 (define @t15 () (tptp.in @t14 @t2)) % 1.21/1.42 (define @t16 () (= @t15 (= @t14 @t1))) % 1.21/1.42 (define @t17 () (@list @t14)) % 1.21/1.42 (define @t18 () (forall @t17 @t16)) % 1.21/1.42 (define @t19 () (tptp.singleton @t1)) % 1.21/1.42 (define @t20 () (= @t2 @t19)) % 1.21/1.42 (define @t21 () (= @t20 @t18)) % 1.21/1.42 (define @t22 () (forall @t5 @t21)) % 1.21/1.42 (define @t23 () (= @t1 tptp.empty_set)) % 1.21/1.42 (define @t24 () (@list @t1)) % 1.21/1.42 (define @t25 () (@var "D" $$unsorted)) % 1.21/1.42 (define @t26 () (tptp.in @t25 @t14)) % 1.21/1.42 (define @t27 () (@list @t25)) % 1.21/1.42 (define @t28 () (@list @t1 @t2 @t14)) % 1.21/1.42 (define @t29 () (tptp.in @t25 @t2)) % 1.21/1.42 (define @t30 () (tptp.in @t25 @t1)) % 1.21/1.42 (define @t31 () (tptp.in @t14 @t1)) % 1.21/1.42 (define @t32 () (forall @t27 (= @t26 (and @t30 @t29)))) % 1.21/1.42 (define @t33 () (= (= @t14 @t11) @t32)) % 1.21/1.42 (define @t34 () (forall @t28 @t33)) % 1.21/1.42 (define @t35 () (tptp.set_difference @t1 @t2)) % 1.21/1.42 (define @t36 () (tptp.disjoint @t1 @t2)) % 1.21/1.42 (define @t37 () (forall @t5 (= @t36 (= @t11 tptp.empty_set)))) % 1.21/1.42 (define @t38 () (not @t13)) % 1.21/1.42 (define @t39 () (tptp.empty @t1)) % 1.21/1.42 (define @t40 () (not @t39)) % 1.21/1.42 (define @t41 () (tptp.set_intersection2 @t1 @t1)) % 1.21/1.42 (define @t42 () (forall @t5 (= @t41 @t1))) % 1.21/1.42 (define @t43 () (forall @t24 (not (= @t19 tptp.empty_set)))) % 1.21/1.42 (define @t44 () (not @t43)) % 1.21/1.42 (define @t45 () (tptp.set_intersection2 @t2 @t14)) % 1.21/1.42 (define @t46 () (tptp.subset @t1 @t14)) % 1.21/1.42 (define @t47 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 1.21/1.42 (define @t48 () (and @t31 @t15)) % 1.21/1.42 (define @t49 () (exists @t17 @t48)) % 1.21/1.42 (define @t50 () (and @t49 @t36)) % 1.21/1.42 (define @t51 () (not @t50)) % 1.21/1.42 (define @t52 () (forall @t17 (not @t48))) % 1.21/1.42 (define @t53 () (not @t36)) % 1.21/1.42 (define @t54 () (and @t53 @t52)) % 1.21/1.42 (define @t55 () (not @t54)) % 1.21/1.42 (define @t56 () (and @t55 @t51)) % 1.21/1.42 (define @t57 () (forall @t5 @t56)) % 1.21/1.42 (define @t58 () (tptp.set_difference @t1 @t35)) % 1.21/1.42 (define @t59 () (forall @t5 (= @t58 @t11))) % 1.21/1.42 (define @t60 () (tptp.in @t14 @t11)) % 1.21/1.42 (define @t61 () (tptp.empty @t2)) % 1.21/1.42 (define @t62 () (@var "BOUND_VARIABLE_7822" $$unsorted)) % 1.21/1.42 (define @t63 () (@var "BOUND_VARIABLE_7836" $$unsorted)) % 1.21/1.42 (define @t64 () (not (tptp.in @t63 @t62))) % 1.21/1.42 (define @t65 () (@var "BOUND_VARIABLE_7820" $$unsorted)) % 1.21/1.42 (define @t66 () (not (tptp.in @t63 @t65))) % 1.21/1.42 (define @t67 () (not (tptp.disjoint @t65 @t62))) % 1.21/1.42 (define @t68 () (or @t67 @t66 @t64)) % 1.21/1.42 (define @t69 () (or @t66 @t64)) % 1.21/1.42 (define @t70 () (or @t69 @t67)) % 1.21/1.42 (define @t71 () (@list @t65 @t62 @t63)) % 1.21/1.42 (define @t72 () (forall @t71 @t70)) % 1.21/1.42 (define @t73 () (@list @t63)) % 1.21/1.42 (define @t74 () (forall @t73 @t70)) % 1.21/1.42 (define @t75 () (@list @t65 @t62)) % 1.21/1.42 (define @t76 () (forall @t73 @t69)) % 1.21/1.42 (define @t77 () (or @t76 @t67)) % 1.21/1.42 (define @t78 () (forall @t75 (or (forall @t17 (or (not (tptp.in @t14 @t65)) (not (tptp.in @t14 @t62)))) @t67))) % 1.21/1.42 (define @t79 () (@var "BOUND_VARIABLE_7807" $$unsorted)) % 1.21/1.42 (define @t80 () (@var "BOUND_VARIABLE_7805" $$unsorted)) % 1.21/1.42 (define @t81 () (forall (@list @t80 @t79) (or (tptp.disjoint @t80 @t79) (not (forall @t17 (or (not (tptp.in @t14 @t80)) (not (tptp.in @t14 @t79)))))))) % 1.21/1.42 (define @t82 () (forall @t17 (or (not @t31) (not @t15)))) % 1.21/1.42 (define @t83 () (or @t82 @t53)) % 1.21/1.42 (define @t84 () (forall @t5 @t83)) % 1.21/1.42 (define @t85 () (@list @t1 @t2)) % 1.21/1.42 (define @t86 () (not @t82)) % 1.21/1.42 (define @t87 () (or @t36 @t86)) % 1.21/1.42 (define @t88 () (forall @t5 @t87)) % 1.21/1.42 (define @t89 () (and @t88 @t84)) % 1.21/1.42 (define @t90 () (and (not (and @t53 @t82)) (not (and @t86 @t36)))) % 1.21/1.42 (define @t91 () (not @t52)) % 1.21/1.42 (define @t92 () (@quantifiers_skolemize @t43 0)) % 1.21/1.42 (define @t93 () (tptp.in @t14 tptp.empty_set)) % 1.21/1.42 (define @t94 () (= @t93 (= @t92 @t14))) % 1.21/1.42 (define @t95 () (forall @t17 @t94)) % 1.21/1.42 (define @t96 () (tptp.singleton @t92)) % 1.21/1.42 (define @t97 () (= tptp.empty_set @t96)) % 1.21/1.42 (define @t98 () (= @t97 @t95)) % 1.21/1.42 (define @t99 () (forall @t5 (= @t20 (forall @t17 (= @t15 (= @t1 @t14)))))) % 1.21/1.42 (define @t100 () (forall @t17 (= @t93 (= @t14 @t92)))) % 1.21/1.42 (define @t101 () (= @t97 @t100)) % 1.21/1.42 (define @t102 () (@list false)) % 1.21/1.42 (define @t103 () (= @t96 tptp.empty_set)) % 1.21/1.42 (define @t104 () (not (not @t103))) % 1.21/1.42 (define @t105 () (@list false false)) % 1.21/1.42 (define @t106 () (tptp.set_difference @t92 (tptp.set_difference @t92 @t92))) % 1.21/1.42 (define @t107 () (tptp.in @t106 tptp.empty_set)) % 1.21/1.42 (define @t108 () (= @t106 @t92)) % 1.21/1.42 (define @t109 () (= @t107 @t108)) % 1.21/1.42 (define @t110 () (= @t92 @t106)) % 1.21/1.42 (define @t111 () (= @t110 @t107)) % 1.21/1.42 (define @t112 () (= @t1 @t41)) % 1.21/1.42 (define @t113 () (tptp.disjoint tptp.empty_set tptp.empty_set)) % 1.21/1.42 (define @t114 () (tptp.set_intersection2 tptp.empty_set tptp.empty_set)) % 1.21/1.42 (define @t115 () (= @t114 tptp.empty_set)) % 1.21/1.42 (define @t116 () (= @t113 @t115)) % 1.21/1.42 (define @t117 () (= tptp.empty_set @t114)) % 1.21/1.42 (define @t118 () (= @t117 @t113)) % 1.21/1.42 (define @t119 () (= @t11 @t14)) % 1.21/1.42 (define @t120 () (tptp.in @t25 tptp.empty_set)) % 1.21/1.42 (define @t121 () (and @t120 @t120)) % 1.21/1.42 (define @t122 () (= @t120 @t121)) % 1.21/1.42 (define @t123 () (forall @t27 @t122)) % 1.21/1.42 (define @t124 () (= @t123 @t115)) % 1.21/1.42 (define @t125 () (forall @t28 (= @t32 @t119))) % 1.21/1.42 (define @t126 () (not @t107)) % 1.21/1.42 (define @t127 () (not @t113)) % 1.21/1.42 (define @t128 () (or @t127 @t126 @t126)) % 1.21/1.42 (define @t129 () (not @t128)) % 1.21/1.42 (define @t130 () (forall @t71 @t68)) % 1.21/1.42 (assume @p1 (forall @t5 (=> @t4 @t3))) % 1.21/1.42 (assume @p2 (forall @t5 (=> @t7 (not @t6)))) % 1.21/1.42 (assume @p3 (forall @t5 (= @t8 (tptp.unordered_pair @t2 @t1)))) % 1.21/1.42 (assume @p4 (forall @t5 (= @t10 @t9))) % 1.21/1.42 (assume @p5 (forall @t5 (= @t11 (tptp.set_intersection2 @t2 @t1)))) % 1.21/1.42 (assume @p6 (forall @t5 (= @t13 (and @t12 (tptp.subset @t2 @t1))))) % 1.21/1.42 (assume @p7 @t22) % 1.21/1.42 (assume @p8 (forall @t24 (= @t23 (forall (@list @t2) @t3)))) % 1.21/1.42 (assume @p9 (forall @t28 (= (= @t14 @t8) (forall @t27 (= @t26 (or (= @t25 @t1) (= @t25 @t2))))))) % 1.21/1.42 (assume @p10 (forall @t28 (= (= @t14 @t10) (forall @t27 (= @t26 (or @t30 @t29)))))) % 1.21/1.42 (assume @p11 (forall @t5 (= @t12 (forall @t17 (=> @t31 @t15))))) % 1.21/1.42 (assume @p12 @t34) % 1.21/1.42 (assume @p13 (forall @t28 (= (= @t14 @t35) (forall @t27 (= @t26 (and @t30 (not @t29))))))) % 1.21/1.42 (assume @p14 @t37) % 1.21/1.42 (assume @p15 (forall @t5 (= @t7 (and @t12 @t38)))) % 1.21/1.42 (assume @p16 true) % 1.21/1.42 (assume @p17 (tptp.empty tptp.empty_set)) % 1.21/1.42 (assume @p18 (forall @t5 (=> @t40 (not (tptp.empty @t10))))) % 1.21/1.42 (assume @p19 (forall @t5 (=> @t40 (not (tptp.empty @t9))))) % 1.21/1.42 (assume @p20 (forall @t5 (= (tptp.set_union2 @t1 @t1) @t1))) % 1.21/1.42 (assume @p21 @t42) % 1.21/1.42 (assume @p22 (forall @t5 (not (tptp.proper_subset @t1 @t1)))) % 1.21/1.42 (assume @p23 @t44) % 1.21/1.42 (assume @p24 (forall @t5 (= (= @t35 tptp.empty_set) @t12))) % 1.21/1.42 (assume @p25 (exists @t24 @t39)) % 1.21/1.42 (assume @p26 (exists @t24 @t40)) % 1.21/1.42 (assume @p27 (forall @t5 (tptp.subset @t1 @t1))) % 1.21/1.42 (assume @p28 (forall @t5 (=> @t36 (tptp.disjoint @t2 @t1)))) % 1.21/1.42 (assume @p29 (forall @t5 (=> @t12 (= @t10 @t2)))) % 1.21/1.42 (assume @p30 (forall @t5 (tptp.subset @t11 @t1))) % 1.21/1.42 (assume @p31 (forall @t28 (=> (and @t12 @t46) (tptp.subset @t1 @t45)))) % 1.21/1.42 (assume @p32 (forall @t24 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 1.21/1.42 (assume @p33 (forall @t28 (=> (and @t12 (tptp.subset @t2 @t14)) @t46))) % 1.21/1.42 (assume @p34 (forall @t28 (=> @t12 (tptp.subset (tptp.set_intersection2 @t1 @t14) @t45)))) % 1.21/1.42 (assume @p35 (forall @t5 (=> @t12 (= @t11 @t1)))) % 1.21/1.42 (assume @p36 (forall @t24 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 1.21/1.42 (assume @p37 (forall @t5 (=> (forall @t17 (= @t31 @t15)) @t13))) % 1.21/1.42 (assume @p38 (forall @t24 (tptp.subset tptp.empty_set @t1))) % 1.21/1.42 (assume @p39 (forall @t28 (=> @t12 (tptp.subset (tptp.set_difference @t1 @t14) (tptp.set_difference @t2 @t14))))) % 1.21/1.42 (assume @p40 (forall @t5 (tptp.subset @t35 @t1))) % 1.21/1.42 (assume @p41 (forall @t5 (= @t47 @t10))) % 1.21/1.42 (assume @p42 (forall @t24 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 1.21/1.42 (assume @p43 @t57) % 1.21/1.42 (assume @p44 (forall @t24 (=> (tptp.subset @t1 tptp.empty_set) @t23))) % 1.21/1.42 (assume @p45 (forall @t5 (= (tptp.set_difference @t10 @t2) @t35))) % 1.21/1.42 (assume @p46 (forall @t5 (=> @t12 (= @t2 @t47)))) % 1.21/1.42 (assume @p47 @t59) % 1.21/1.42 (assume @p48 (forall @t24 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 1.21/1.42 (assume @p49 (forall @t5 (and (not (and @t53 (forall @t17 (not @t60)))) (not (and (exists @t17 @t60) @t36))))) % 1.21/1.42 (assume @p50 (forall @t5 (not (and @t12 @t6)))) % 1.21/1.42 (assume @p51 (forall @t28 (=> (and @t12 (tptp.disjoint @t2 @t14)) (tptp.disjoint @t1 @t14)))) % 1.21/1.42 (assume @p52 (forall @t24 (= (tptp.unordered_pair @t1 @t1) @t19))) % 1.21/1.42 (assume @p53 (forall @t24 (=> @t39 @t23))) % 1.21/1.42 (assume @p54 (forall @t5 (not (and @t4 @t61)))) % 1.21/1.42 (assume @p55 (forall @t5 (tptp.subset @t1 @t10))) % 1.21/1.42 (assume @p56 (forall @t5 (= @t36 (= @t35 @t1)))) % 1.21/1.42 (assume @p57 (forall @t5 (not (and @t39 @t38 @t61)))) % 1.21/1.42 (assume @p58 (forall @t28 (=> (and @t12 (tptp.subset @t14 @t2)) (tptp.subset (tptp.set_union2 @t1 @t14) @t2)))) % 1.21/1.42 (step @p59 :rule aci_norm :args ((= @t70 @t68))) % 1.21/1.42 (step @p60 :rule cong :premises (@p59) :args (@t72)) % 1.21/1.42 (step @p61 :rule quant-merge-prenex :args ((= (forall @t75 @t74) @t72))) % 1.21/1.42 (step @p62 :rule refl :args (@t67)) % 1.21/1.42 (step @p63 :rule alpha_equiv :args (@t76 (@list @t63) (@list @t14))) % 1.21/1.42 (step @p64 :rule nary_cong :premises (@p63 @p62) :args (@t77)) % 1.21/1.42 (step @p65 :rule quant-miniscope-or :args ((= @t74 @t77))) % 1.21/1.42 (step @p66 :rule trans :premises (@p65 @p64)) % 1.21/1.42 (step @p67 :rule symm :premises (@p66)) % 1.21/1.42 (step @p68 :rule cong :premises (@p67) :args (@t78)) % 1.21/1.42 (step @p69 :rule trans :premises (@p68 @p61)) % 1.21/1.42 (step @p70 :rule trans :premises (@p69 @p60)) % 1.21/1.42 (step @p71 :rule refl :args (@t81)) % 1.21/1.42 (step @p72 :rule nary_cong :premises (@p71 @p70) :args ((and @t81 @t78))) % 1.21/1.42 (step @p73 :rule alpha_equiv :args (@t84 @t85 (@list @t65 @t62))) % 1.21/1.42 (step @p74 :rule alpha_equiv :args (@t88 @t85 (@list @t80 @t79))) % 1.21/1.42 (step @p75 :rule nary_cong :premises (@p74 @p73) :args (@t89)) % 1.21/1.42 (step @p76 :rule quant-miniscope-and :args ((= (forall @t5 (and @t87 @t83)) @t89))) % 1.21/1.42 (step @p77 :rule trans :premises (@p76 @p75)) % 1.21/1.42 (step @p78 :rule trans :premises (@p77 @p72)) % 1.21/1.42 (step @p79 :rule refl :args (@t53)) % 1.21/1.42 (step @p80 :rule bool-double-not-elim :args (@t82)) % 1.21/1.42 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or (not @t86) @t53))) % 1.21/1.42 (step @p82 :rule bool-and-de-morgan :args (@t86 @t36 true)) % 1.21/1.42 (step @p83 :rule trans :premises (@p82 @p81)) % 1.21/1.42 (step @p84 :rule refl :args (@t86)) % 1.21/1.42 (step @p85 :rule bool-double-not-elim :args (@t36)) % 1.21/1.42 (step @p86 :rule nary_cong :premises (@p85 @p84) :args ((or (not @t53) @t86))) % 1.21/1.42 (step @p87 :rule bool-and-de-morgan :args (@t53 @t82 true)) % 1.21/1.42 (step @p88 :rule trans :premises (@p87 @p86)) % 1.21/1.42 (step @p89 :rule nary_cong :premises (@p88 @p83) :args (@t90)) % 1.21/1.42 (step @p90 :rule cong :premises (@p89) :args ((forall @t5 @t90))) % 1.21/1.42 (step @p91 :rule trans :premises (@p90 @p78)) % 1.21/1.42 (step @p92 :rule refl :args (@t36)) % 1.21/1.42 (step @p93 :rule bool-and-de-morgan :args (@t31 @t15 true)) % 1.21/1.42 (step @p94 :rule cong :premises (@p93) :args (@t52)) % 1.21/1.42 (step @p95 :rule cong :premises (@p94) :args (@t91)) % 1.21/1.42 (step @p96 :rule exists-elim :args ((= @t49 @t91))) % 1.21/1.42 (step @p97 :rule trans :premises (@p96 @p95)) % 1.21/1.42 (step @p98 :rule nary_cong :premises (@p97 @p92) :args (@t50)) % 1.21/1.42 (step @p99 :rule cong :premises (@p98) :args (@t51)) % 1.21/1.42 (step @p100 :rule refl :args (@t53)) % 1.21/1.42 (step @p101 :rule nary_cong :premises (@p100 @p94) :args (@t54)) % 1.21/1.42 (step @p102 :rule cong :premises (@p101) :args (@t55)) % 1.21/1.42 (step @p103 :rule nary_cong :premises (@p102 @p99) :args (@t56)) % 1.21/1.42 (step @p104 :rule cong :premises (@p103) :args (@t57)) % 1.21/1.42 (step @p105 :rule trans :premises (@p104 @p91)) % 1.21/1.42 (step @p106 :rule eq_resolve :premises (@p43 @p105)) % 1.21/1.42 (step @p107 :rule and_elim :premises (@p106) :args (1)) % 1.21/1.42 (step @p108 :rule eq-symm :args (@t14 @t1)) % 1.21/1.42 (step @p109 :rule refl :args (@t15)) % 1.21/1.42 (step @p110 :rule cong :premises (@p109 @p108) :args (@t16)) % 1.21/1.42 (step @p111 :rule cong :premises (@p110) :args (@t18)) % 1.21/1.42 (step @p112 :rule refl :args (@t20)) % 1.21/1.42 (step @p113 :rule cong :premises (@p112 @p111) :args (@t21)) % 1.21/1.42 (step @p114 :rule cong :premises (@p113) :args (@t22)) % 1.21/1.42 (step @p115 :rule eq_resolve :premises (@p7 @p114)) % 1.21/1.42 (step @p116 :rule eq-symm :args (@t92 @t14)) % 1.21/1.42 (step @p117 :rule refl :args (@t93)) % 1.21/1.42 (step @p118 :rule cong :premises (@p117 @p116) :args (@t94)) % 1.21/1.42 (step @p119 :rule cong :premises (@p118) :args (@t95)) % 1.21/1.42 (step @p120 :rule refl :args (@t97)) % 1.21/1.42 (step @p121 :rule cong :premises (@p120 @p119) :args (@t98)) % 1.21/1.42 (step @p122 :rule refl :args (@t99)) % 1.21/1.42 (step @p123 :rule cong :premises (@p122 @p121) :args ((=> @t99 @t98))) % 1.21/1.42 (assume-push @p233 @t99) % 1.21/1.42 (step @p125 :rule instantiate :premises (@p115) :args ((@list @t92 tptp.empty_set))) % 1.21/1.42 (step-pop @p234 :rule scope :premises (@p125)) % 1.21/1.42 (step @p126 :rule process_scope :premises (@p234) :args (@t98)) % 1.21/1.42 (step @p128 :rule eq_resolve :premises (@p126 @p123)) % 1.21/1.42 (step @p129 :rule implies_elim :premises (@p128)) % 1.21/1.42 (step @p130 :rule chain_m_resolution :premises (@p129 @p115) :args (@t101 @t102 (@list @t99))) % 1.21/1.42 (step @p131 :rule bool-double-not-elim :args (@t43)) % 1.21/1.42 (step @p132 :rule nary_cong :premises (@p131 @p120) :args ((or (not @t44) @t97))) % 1.21/1.42 (step @p133 :rule eq-symm :args (@t96 tptp.empty_set)) % 1.21/1.42 (step @p134 :rule bool-double-not-elim :args (@t103)) % 1.21/1.42 (step @p135 :rule trans :premises (@p134 @p133)) % 1.21/1.42 (step @p136 :rule refl :args (@t44)) % 1.21/1.42 (step @p137 :rule cong :premises (@p136 @p135) :args ((=> @t44 @t104))) % 1.21/1.42 (assume-push @p235 @t44) % 1.21/1.42 (step @p139 :rule skolemize :premises (@p23)) % 1.21/1.42 (step-pop @p236 :rule scope :premises (@p139)) % 1.21/1.42 (step @p140 :rule process_scope :premises (@p236) :args (@t104)) % 1.21/1.42 (step @p142 :rule eq_resolve :premises (@p140 @p137)) % 1.21/1.42 (step @p143 :rule implies_elim :premises (@p142)) % 1.21/1.42 (step @p144 :rule eq_resolve :premises (@p143 @p132)) % 1.21/1.42 (step @p145 :rule chain_m_resolution :premises (@p144 @p23) :args (@t97 (@list true) (@list @t43))) % 1.21/1.42 (step @p146 :rule cnf_equiv_pos1 :args (@t101)) % 1.21/1.42 (step @p147 :rule reordering :premises (@p146) :args ((or (not @t97) @t100 (not @t101)))) % 1.21/1.42 (step @p148 :rule chain_m_resolution :premises (@p147 @p145 @p130) :args (@t100 @t105 (@list @t97 @t101))) % 1.21/1.42 (step @p149 :rule refl :args (@t107)) % 1.21/1.42 (step @p150 :rule eq-symm :args (@t106 @t92)) % 1.21/1.42 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t108 @t107))) % 1.21/1.42 (step @p152 :rule eq-symm :args (@t107 @t108)) % 1.21/1.42 (step @p153 :rule trans :premises (@p152 @p151)) % 1.21/1.42 (step @p154 :rule refl :args (@t100)) % 1.21/1.42 (step @p155 :rule cong :premises (@p154 @p153) :args ((=> @t100 @t109))) % 1.21/1.42 (assume-push @p237 @t100) % 1.21/1.42 (step @p157 :rule instantiate :premises (@p148) :args ((@list @t106))) % 1.21/1.42 (step-pop @p238 :rule scope :premises (@p157)) % 1.21/1.42 (step @p158 :rule process_scope :premises (@p238) :args (@t109)) % 1.21/1.42 (step @p160 :rule eq_resolve :premises (@p158 @p155)) % 1.21/1.42 (step @p161 :rule implies_elim :premises (@p160)) % 1.21/1.42 (step @p162 :rule chain_m_resolution :premises (@p161 @p148) :args (@t111 @t102 (@list @t100))) % 1.21/1.42 (step @p163 :rule eq-symm :args (@t58 @t11)) % 1.21/1.42 (step @p164 :rule cong :premises (@p163) :args (@t59)) % 1.21/1.42 (step @p165 :rule eq_resolve :premises (@p47 @p164)) % 1.21/1.42 (step @p166 :rule instantiate :premises (@p165) :args ((@list @t92 @t92))) % 1.21/1.42 (step @p167 :rule quant-unused-vars :args ((= (forall @t5 @t112) (forall @t24 @t112)))) % 1.21/1.42 (step @p168 :rule eq-symm :args (@t41 @t1)) % 1.21/1.42 (step @p169 :rule cong :premises (@p168) :args (@t42)) % 1.21/1.42 (step @p170 :rule trans :premises (@p169 @p167)) % 1.21/1.42 (step @p171 :rule eq_resolve :premises (@p21 @p170)) % 1.21/1.42 (step @p172 :rule instantiate :premises (@p171) :args ((@list @t92))) % 1.21/1.42 (step @p173 :rule trans :premises (@p172 @p166)) % 1.21/1.42 (step @p174 :rule cnf_equiv_pos1 :args (@t111)) % 1.21/1.42 (step @p175 :rule reordering :premises (@p174) :args ((or (not @t110) @t107 (not @t111)))) % 1.21/1.42 (step @p176 :rule chain_m_resolution :premises (@p175 @p173 @p162) :args (@t107 @t105 (@list @t110 @t111))) % 1.21/1.42 (step @p177 :rule refl :args (@t113)) % 1.21/1.42 (step @p178 :rule eq-symm :args (@t114 tptp.empty_set)) % 1.21/1.42 (step @p179 :rule cong :premises (@p178 @p177) :args ((= @t115 @t113))) % 1.21/1.43 (step @p180 :rule eq-symm :args (@t113 @t115)) % 1.21/1.43 (step @p181 :rule trans :premises (@p180 @p179)) % 1.21/1.43 (step @p182 :rule refl :args (@t37)) % 1.21/1.43 (step @p183 :rule cong :premises (@p182 @p181) :args ((=> @t37 @t116))) % 1.21/1.43 (assume-push @p239 @t37) % 1.21/1.43 (step @p185 :rule instantiate :premises (@p14) :args ((@list tptp.empty_set tptp.empty_set))) % 1.21/1.43 (step-pop @p240 :rule scope :premises (@p185)) % 1.21/1.43 (step @p186 :rule process_scope :premises (@p240) :args (@t116)) % 1.21/1.43 (step @p188 :rule eq_resolve :premises (@p186 @p183)) % 1.21/1.43 (step @p189 :rule implies_elim :premises (@p188)) % 1.21/1.43 (step @p190 :rule chain_m_resolution :premises (@p189 @p14) :args (@t118 @t102 (@list @t37))) % 1.21/1.43 (step @p191 :rule eq-symm :args (@t119 @t32)) % 1.21/1.43 (step @p192 :rule refl :args (@t32)) % 1.21/1.43 (step @p193 :rule eq-symm :args (@t14 @t11)) % 1.21/1.43 (step @p194 :rule cong :premises (@p193 @p192) :args (@t33)) % 1.21/1.43 (step @p195 :rule trans :premises (@p194 @p191)) % 1.21/1.43 (step @p196 :rule cong :premises (@p195) :args (@t34)) % 1.21/1.43 (step @p197 :rule eq_resolve :premises (@p12 @p196)) % 1.21/1.43 (step @p198 :rule bool-eq-true :args (@t117)) % 1.21/1.43 (step @p199 :rule eq-symm :args (true @t117)) % 1.21/1.43 (step @p200 :rule trans :premises (@p199 @p198)) % 1.21/1.43 (step @p201 :rule quant-unused-vars :args ((= (forall @t27 true) true))) % 1.21/1.43 (step @p202 :rule eq-refl :args (@t120)) % 1.21/1.43 (step @p203 :rule aci_norm :args ((= @t121 @t120))) % 1.21/1.43 (step @p204 :rule refl :args (@t120)) % 1.21/1.43 (step @p205 :rule cong :premises (@p204 @p203) :args (@t122)) % 1.21/1.43 (step @p206 :rule trans :premises (@p205 @p202)) % 1.21/1.43 (step @p207 :rule cong :premises (@p206) :args (@t123)) % 1.21/1.43 (step @p208 :rule trans :premises (@p207 @p201)) % 1.21/1.43 (step @p209 :rule cong :premises (@p208 @p178) :args (@t124)) % 1.21/1.43 (step @p210 :rule trans :premises (@p209 @p200)) % 1.21/1.43 (step @p211 :rule refl :args (@t125)) % 1.21/1.43 (step @p212 :rule cong :premises (@p211 @p210) :args ((=> @t125 @t124))) % 1.21/1.43 (assume-push @p241 @t125) % 1.21/1.43 (step @p214 :rule instantiate :premises (@p197) :args ((@list tptp.empty_set tptp.empty_set tptp.empty_set))) % 1.21/1.43 (step-pop @p242 :rule scope :premises (@p214)) % 1.21/1.43 (step @p215 :rule process_scope :premises (@p242) :args (@t124)) % 1.21/1.43 (step @p217 :rule eq_resolve :premises (@p215 @p212)) % 1.21/1.43 (step @p218 :rule implies_elim :premises (@p217)) % 1.21/1.43 (step @p219 :rule chain_m_resolution :premises (@p218 @p197) :args (@t117 @t102 (@list @t125))) % 1.21/1.43 (step @p220 :rule cnf_equiv_pos1 :args (@t118)) % 1.21/1.43 (step @p221 :rule reordering :premises (@p220) :args ((or @t113 (not @t117) (not @t118)))) % 1.21/1.43 (step @p222 :rule chain_m_resolution :premises (@p221 @p219 @p190) :args (@t113 @t105 (@list @t117 @t118))) % 1.21/1.43 (step @p223 :rule cnf_or_pos :args (@t128)) % 1.21/1.43 (step @p224 :rule factoring :premises (@p223)) % 1.21/1.43 (step @p225 :rule reordering :premises (@p224) :args ((or @t127 @t126 @t129))) % 1.21/1.43 (step @p226 :rule chain_m_resolution :premises (@p225 @p222 @p176) :args (@t129 @t105 (@list @t113 @t107))) % 1.21/1.43 (assume-push @p243 @t130) % 1.21/1.43 (step @p228 :rule instantiate :premises (@p107) :args ((@list tptp.empty_set tptp.empty_set @t106))) % 1.21/1.43 (step-pop @p244 :rule scope :premises (@p228)) % 1.21/1.43 (step @p229 :rule process_scope :premises (@p244) :args (@t128)) % 1.21/1.43 (step @p231 :rule implies_elim :premises (@p229)) % 1.21/1.43 (step @p232 false :rule chain_m_resolution :premises (@p231 @p226 @p107) :args (false (@list true false) (@list @t128 @t130))) % 1.21/1.43 ) % 1.21/1.43 % SZS output end Proof % 1.21/1.43 % cvc5 exiting %------------------------------------------------------------------------------