%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET103+1 : TPTP v9.2.1. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n026.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 08:47:24 AM UTC 2026 % Result : Theorem 1.32s 1.55s % Output : Proof 1.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET103+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n026.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 14:56:10 EDT 2026 % 0.18/0.35 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 1.32/1.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.32/1.55 % SZS status Theorem % 1.32/1.55 % SZS output start Proof % 1.32/1.55 ( % 1.32/1.55 (declare-sort $$unsorted 0) % 1.32/1.55 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 1.32/1.55 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.element_relation $$unsorted) % 1.32/1.55 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.universal_class $$unsorted) % 1.32/1.55 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.inductive (-> $$unsorted Bool)) % 1.32/1.55 (declare-const tptp.function (-> $$unsorted Bool)) % 1.32/1.55 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 1.32/1.55 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 1.32/1.55 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.null_class $$unsorted) % 1.32/1.55 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.successor_relation $$unsorted) % 1.32/1.55 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 1.32/1.55 (declare-const tptp.identity_relation $$unsorted) % 1.32/1.55 (define @t1 () (@var "Y" $$unsorted)) % 1.32/1.55 (define @t2 () (@var "U" $$unsorted)) % 1.32/1.55 (define @t3 () (tptp.member @t2 @t1)) % 1.32/1.55 (define @t4 () (@var "X" $$unsorted)) % 1.32/1.55 (define @t5 () (tptp.member @t2 @t4)) % 1.32/1.55 (define @t6 () (@list @t2)) % 1.32/1.55 (define @t7 () (tptp.subclass @t4 @t1)) % 1.32/1.55 (define @t8 () (@list @t4 @t1)) % 1.32/1.55 (define @t9 () (@list @t4)) % 1.32/1.55 (define @t10 () (or (= @t2 @t4) (= @t2 @t1))) % 1.32/1.55 (define @t11 () (tptp.member @t2 tptp.universal_class)) % 1.32/1.55 (define @t12 () (and @t11 @t10)) % 1.32/1.55 (define @t13 () (tptp.unordered_pair @t4 @t1)) % 1.32/1.55 (define @t14 () (tptp.member @t2 @t13)) % 1.32/1.55 (define @t15 () (= @t14 @t12)) % 1.32/1.55 (define @t16 () (@list @t2 @t4 @t1)) % 1.32/1.55 (define @t17 () (forall @t16 @t15)) % 1.32/1.55 (define @t18 () (tptp.singleton @t4)) % 1.32/1.55 (define @t19 () (tptp.singleton @t1)) % 1.32/1.55 (define @t20 () (tptp.ordered_pair @t4 @t1)) % 1.32/1.55 (define @t21 () (@var "V" $$unsorted)) % 1.32/1.55 (define @t22 () (tptp.cross_product @t4 @t1)) % 1.32/1.55 (define @t23 () (tptp.ordered_pair @t2 @t21)) % 1.32/1.55 (define @t24 () (tptp.member @t1 tptp.universal_class)) % 1.32/1.55 (define @t25 () (tptp.member @t4 tptp.universal_class)) % 1.32/1.55 (define @t26 () (@var "Z" $$unsorted)) % 1.32/1.55 (define @t27 () (@list @t4 @t1 @t26)) % 1.32/1.55 (define @t28 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 1.32/1.55 (define @t29 () (tptp.member @t26 @t1)) % 1.32/1.55 (define @t30 () (tptp.member @t26 @t4)) % 1.32/1.55 (define @t31 () (tptp.member @t26 tptp.universal_class)) % 1.32/1.55 (define @t32 () (@list @t4 @t26)) % 1.32/1.55 (define @t33 () (@var "XR" $$unsorted)) % 1.32/1.55 (define @t34 () (@var "W" $$unsorted)) % 1.32/1.55 (define @t35 () (tptp.cross_product @t28 tptp.universal_class)) % 1.32/1.55 (define @t36 () (tptp.ordered_pair @t23 @t34)) % 1.32/1.55 (define @t37 () (tptp.member @t36 @t35)) % 1.32/1.55 (define @t38 () (tptp.rotate @t4)) % 1.32/1.55 (define @t39 () (tptp.flip @t4)) % 1.32/1.55 (define @t40 () (tptp.successor @t4)) % 1.32/1.55 (define @t41 () (@list @t1)) % 1.32/1.55 (define @t42 () (@list @t26)) % 1.32/1.55 (define @t43 () (tptp.inductive @t4)) % 1.32/1.55 (define @t44 () (tptp.sum_class @t4)) % 1.32/1.55 (define @t45 () (@list @t2 @t4)) % 1.32/1.55 (define @t46 () (@var "YR" $$unsorted)) % 1.32/1.55 (define @t47 () (tptp.compose @t46 @t33)) % 1.32/1.55 (define @t48 () (@var "XF" $$unsorted)) % 1.32/1.55 (define @t49 () (tptp.function @t48)) % 1.32/1.55 (define @t50 () (@list @t48)) % 1.32/1.55 (define @t51 () (tptp.apply @t48 @t1)) % 1.32/1.55 (define @t52 () (tptp.member @t51 @t1)) % 1.32/1.55 (define @t53 () (= @t1 tptp.null_class)) % 1.32/1.55 (define @t54 () (or @t53 @t52)) % 1.32/1.55 (define @t55 () (forall @t41 (=> @t24 @t54))) % 1.32/1.55 (define @t56 () (and @t49 @t55)) % 1.32/1.55 (define @t57 () (exists @t50 @t56)) % 1.32/1.55 (define @t58 () (tptp.unordered_pair @t18 (tptp.unordered_pair @t4 tptp.null_class))) % 1.32/1.55 (define @t59 () (or (= @t58 @t20) @t24)) % 1.32/1.55 (define @t60 () (forall @t8 @t59)) % 1.32/1.55 (define @t61 () (not @t60)) % 1.32/1.55 (define @t62 () (forall @t8 (or (= @t20 @t58) @t24))) % 1.32/1.55 (define @t63 () (@quantifiers_skolemize @t62 1)) % 1.32/1.55 (define @t64 () (tptp.member @t63 tptp.universal_class)) % 1.32/1.55 (define @t65 () (@quantifiers_skolemize @t62 0)) % 1.32/1.55 (define @t66 () (tptp.singleton @t65)) % 1.32/1.55 (define @t67 () (tptp.ordered_pair @t65 @t63)) % 1.32/1.55 (define @t68 () (= @t67 (tptp.unordered_pair @t66 (tptp.unordered_pair @t65 tptp.null_class)))) % 1.32/1.55 (define @t69 () (or @t68 @t64)) % 1.32/1.55 (define @t70 () (@list true)) % 1.32/1.55 (define @t71 () (@list @t69)) % 1.32/1.55 (define @t72 () (not @t24)) % 1.32/1.55 (define @t73 () (or @t72 @t53 @t52)) % 1.32/1.55 (define @t74 () (forall @t41 @t73)) % 1.32/1.55 (define @t75 () (and @t49 @t74)) % 1.32/1.55 (define @t76 () (forall @t50 (not @t75))) % 1.32/1.55 (define @t77 () (not @t76)) % 1.32/1.55 (define @t78 () (@quantifiers_skolemize (forall @t50 (or (not @t49) (not @t74))) 0)) % 1.32/1.55 (define @t79 () (forall @t41 (or @t72 @t53 (tptp.member (tptp.apply @t78 @t1) @t1)))) % 1.32/1.55 (define @t80 () (not @t79)) % 1.32/1.55 (define @t81 () (or (not (tptp.function @t78)) @t80)) % 1.32/1.55 (define @t82 () (tptp.unordered_pair @t63 @t63)) % 1.32/1.55 (define @t83 () (tptp.apply @t78 @t82)) % 1.32/1.55 (define @t84 () (tptp.member @t83 @t82)) % 1.32/1.55 (define @t85 () (tptp.member @t82 tptp.universal_class)) % 1.32/1.55 (define @t86 () (not @t85)) % 1.32/1.55 (define @t87 () (or @t86 (= @t82 tptp.null_class) @t84)) % 1.32/1.55 (define @t88 () (= tptp.null_class @t82)) % 1.32/1.55 (define @t89 () (or @t86 @t88 @t84)) % 1.32/1.55 (define @t90 () (@list false)) % 1.32/1.55 (define @t91 () (= @t63 @t83)) % 1.32/1.55 (define @t92 () (or @t91 @t91)) % 1.32/1.55 (define @t93 () (tptp.member @t83 tptp.universal_class)) % 1.32/1.55 (define @t94 () (and @t93 @t92)) % 1.32/1.55 (define @t95 () (= @t84 @t94)) % 1.32/1.55 (define @t96 () (forall @t16 (= @t14 (and @t11 (or (= @t4 @t2) (= @t1 @t2)))))) % 1.32/1.55 (define @t97 () (and @t93 @t91)) % 1.32/1.55 (define @t98 () (= @t84 @t97)) % 1.32/1.55 (define @t99 () (not @t97)) % 1.32/1.55 (define @t100 () (not @t64)) % 1.32/1.55 (define @t101 () (not @t91)) % 1.32/1.55 (define @t102 () (not @t93)) % 1.32/1.55 (define @t103 () (and @t100 @t91 @t93)) % 1.32/1.55 (define @t104 () (not @t84)) % 1.32/1.55 (define @t105 () (tptp.singleton @t63)) % 1.32/1.55 (define @t106 () (tptp.unordered_pair @t65 @t105)) % 1.32/1.55 (define @t107 () (tptp.unordered_pair @t66 @t106)) % 1.32/1.55 (define @t108 () (= @t67 @t107)) % 1.32/1.55 (define @t109 () (= @t105 @t82)) % 1.32/1.55 (define @t110 () (and @t108 @t109 @t88)) % 1.32/1.55 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 1.32/1.55 (assume @p2 (forall @t9 (tptp.subclass @t4 tptp.universal_class))) % 1.32/1.55 (assume @p3 (forall @t8 (= (= @t4 @t1) (and @t7 (tptp.subclass @t1 @t4))))) % 1.32/1.55 (assume @p4 @t17) % 1.32/1.55 (assume @p5 (forall @t8 (tptp.member @t13 tptp.universal_class))) % 1.32/1.55 (assume @p6 (forall @t9 (= @t18 (tptp.unordered_pair @t4 @t4)))) % 1.32/1.55 (assume @p7 (forall @t8 (= @t20 (tptp.unordered_pair @t18 (tptp.unordered_pair @t4 @t19))))) % 1.32/1.55 (assume @p8 (forall (@list @t2 @t21 @t4 @t1) (= (tptp.member @t23 @t22) (and @t5 (tptp.member @t21 @t1))))) % 1.32/1.55 (assume @p9 (forall @t8 (=> (and @t25 @t24) (and (= (tptp.first @t20) @t4) (= (tptp.second @t20) @t1))))) % 1.32/1.55 (assume @p10 (forall @t27 (=> (tptp.member @t26 @t22) (= @t26 (tptp.ordered_pair (tptp.first @t26) (tptp.second @t26)))))) % 1.32/1.55 (assume @p11 (forall @t8 (= (tptp.member @t20 tptp.element_relation) (and @t24 (tptp.member @t4 @t1))))) % 1.32/1.55 (assume @p12 (tptp.subclass tptp.element_relation @t28)) % 1.32/1.55 (assume @p13 (forall @t27 (= (tptp.member @t26 (tptp.intersection @t4 @t1)) (and @t30 @t29)))) % 1.32/1.55 (assume @p14 (forall @t32 (= (tptp.member @t26 (tptp.complement @t4)) (and @t31 (not @t30))))) % 1.32/1.55 (assume @p15 (forall (@list @t4 @t33 @t1) (= (tptp.restrict @t33 @t4 @t1) (tptp.intersection @t33 @t22)))) % 1.32/1.55 (assume @p16 (forall @t9 (not (tptp.member @t4 tptp.null_class)))) % 1.32/1.55 (assume @p17 (forall @t32 (= (tptp.member @t26 (tptp.domain_of @t4)) (and @t31 (not (= (tptp.restrict @t4 (tptp.singleton @t26) tptp.universal_class) tptp.null_class)))))) % 1.32/1.55 (assume @p18 (forall (@list @t4 @t2 @t21 @t34) (= (tptp.member @t36 @t38) (and @t37 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t34) @t2) @t4))))) % 1.32/1.55 (assume @p19 (forall @t9 (tptp.subclass @t38 @t35))) % 1.32/1.55 (assume @p20 (forall (@list @t2 @t21 @t34 @t4) (= (tptp.member @t36 @t39) (and @t37 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t2) @t34) @t4))))) % 1.32/1.55 (assume @p21 (forall @t9 (tptp.subclass @t39 @t35))) % 1.32/1.55 (assume @p22 (forall @t27 (= (tptp.member @t26 (tptp.union @t4 @t1)) (or @t30 @t29)))) % 1.32/1.55 (assume @p23 (forall @t9 (= @t40 (tptp.union @t4 @t18)))) % 1.32/1.55 (assume @p24 (tptp.subclass tptp.successor_relation @t28)) % 1.32/1.55 (assume @p25 (forall @t8 (= (tptp.member @t20 tptp.successor_relation) (and @t25 @t24 (= @t40 @t1))))) % 1.32/1.55 (assume @p26 (forall @t41 (= (tptp.inverse @t1) (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class)))))) % 1.32/1.55 (assume @p27 (forall @t42 (= (tptp.range_of @t26) (tptp.domain_of (tptp.inverse @t26))))) % 1.32/1.55 (assume @p28 (forall (@list @t4 @t33) (= (tptp.image @t33 @t4) (tptp.range_of (tptp.restrict @t33 @t4 tptp.universal_class))))) % 1.32/1.55 (assume @p29 (forall @t9 (= @t43 (and (tptp.member tptp.null_class @t4) (tptp.subclass (tptp.image tptp.successor_relation @t4) @t4))))) % 1.32/1.55 (assume @p30 (exists @t9 (and @t25 @t43 (forall @t41 (=> (tptp.inductive @t1) @t7))))) % 1.32/1.55 (assume @p31 (forall @t45 (= (tptp.member @t2 @t44) (exists @t41 (and @t3 (tptp.member @t1 @t4)))))) % 1.32/1.55 (assume @p32 (forall @t9 (=> @t25 (tptp.member @t44 tptp.universal_class)))) % 1.32/1.55 (assume @p33 (forall @t45 (= (tptp.member @t2 (tptp.power_class @t4)) (and @t11 (tptp.subclass @t2 @t4))))) % 1.32/1.55 (assume @p34 (forall @t6 (=> @t11 (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 1.32/1.55 (assume @p35 (forall (@list @t33 @t46) (tptp.subclass @t47 @t28))) % 1.32/1.55 (assume @p36 (forall (@list @t33 @t46 @t2 @t21) (= (tptp.member @t23 @t47) (and @t11 (tptp.member @t21 (tptp.image @t46 (tptp.image @t33 (tptp.singleton @t2)))))))) % 1.32/1.55 (assume @p37 (forall @t42 (= (tptp.member @t26 tptp.identity_relation) (exists @t9 (and @t25 (= @t26 (tptp.ordered_pair @t4 @t4))))))) % 1.32/1.55 (assume @p38 (forall @t50 (= @t49 (and (tptp.subclass @t48 @t28) (tptp.subclass (tptp.compose @t48 (tptp.inverse @t48)) tptp.identity_relation))))) % 1.32/1.55 (assume @p39 (forall (@list @t4 @t48) (=> (and @t25 @t49) (tptp.member (tptp.image @t48 @t4) tptp.universal_class)))) % 1.32/1.55 (assume @p40 (forall @t8 (= (tptp.disjoint @t4 @t1) (forall @t6 (not (and @t5 @t3)))))) % 1.32/1.55 (assume @p41 (forall @t9 (=> (not (= @t4 tptp.null_class)) (exists @t6 (and @t11 @t5 (tptp.disjoint @t2 @t4)))))) % 1.32/1.55 (assume @p42 (forall (@list @t48 @t1) (= @t51 (tptp.sum_class (tptp.image @t48 @t19))))) % 1.32/1.55 (assume @p43 @t57) % 1.32/1.55 (assume @p44 @t61) % 1.32/1.55 (assume @p45 true) % 1.32/1.55 (step @p46 :rule refl :args (@t24)) % 1.32/1.55 (step @p47 :rule eq-symm :args (@t58 @t20)) % 1.32/1.55 (step @p48 :rule nary_cong :premises (@p47 @p46) :args (@t59)) % 1.32/1.55 (step @p49 :rule cong :premises (@p48) :args (@t60)) % 1.32/1.55 (step @p50 :rule cong :premises (@p49) :args (@t61)) % 1.32/1.55 (step @p51 :rule eq_resolve :premises (@p44 @p50)) % 1.32/1.55 (step @p52 :rule skolemize :premises (@p51)) % 1.32/1.55 (step @p53 :rule cnf_or_neg :args (@t69 0)) % 1.32/1.55 (step @p54 :rule chain_m_resolution :premises (@p53 @p52) :args ((not @t68) @t70 @t71)) % 1.32/1.55 (step @p55 :rule instantiate :premises (@p7) :args ((@list @t65 @t63))) % 1.32/1.55 (step @p56 :rule instantiate :premises (@p6) :args ((@list @t63))) % 1.32/1.55 (step @p57 :rule bool-and-de-morgan :args (@t49 @t74 true)) % 1.32/1.55 (step @p58 :rule cong :premises (@p57) :args (@t76)) % 1.32/1.55 (step @p59 :rule cong :premises (@p58) :args (@t77)) % 1.32/1.55 (step @p60 :rule exists-elim :args ((= (exists @t50 @t75) @t77))) % 1.32/1.55 (step @p61 :rule trans :premises (@p60 @p59)) % 1.32/1.55 (step @p62 :rule aci_norm :args ((= (or @t72 @t54) @t73))) % 1.32/1.55 (step @p63 :rule bool-impl-elim :args (@t24 @t54)) % 1.32/1.55 (step @p64 :rule trans :premises (@p63 @p62)) % 1.32/1.55 (step @p65 :rule cong :premises (@p64) :args (@t55)) % 1.32/1.55 (step @p66 :rule refl :args (@t49)) % 1.32/1.55 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t56)) % 1.32/1.55 (step @p68 :rule cong :premises (@p67) :args (@t57)) % 1.32/1.55 (step @p69 :rule trans :premises (@p68 @p61)) % 1.32/1.55 (step @p70 :rule eq_resolve :premises (@p43 @p69)) % 1.32/1.55 (step @p71 :rule skolemize :premises (@p70)) % 1.32/1.55 (step @p72 :rule bool-double-not-elim :args (@t79)) % 1.32/1.55 (step @p73 :rule refl :args (@t81)) % 1.32/1.55 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t81 (not @t80)))) % 1.32/1.55 (step @p75 :rule cnf_or_neg :args (@t81 1)) % 1.32/1.55 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 1.32/1.55 (step @p77 :rule reordering :premises (@p76) :args ((or @t79 @t81))) % 1.32/1.55 (step @p78 :rule chain_m_resolution :premises (@p77 @p71) :args (@t79 @t70 (@list @t81))) % 1.32/1.55 (step @p79 :rule refl :args (@t84)) % 1.32/1.55 (step @p80 :rule eq-symm :args (@t82 tptp.null_class)) % 1.32/1.55 (step @p81 :rule refl :args (@t86)) % 1.32/1.55 (step @p82 :rule nary_cong :premises (@p81 @p80 @p79) :args (@t87)) % 1.32/1.55 (step @p83 :rule refl :args (@t79)) % 1.32/1.55 (step @p84 :rule cong :premises (@p83 @p82) :args ((=> @t79 @t87))) % 1.32/1.55 (assume-push @p188 @t79) % 1.32/1.55 (step @p86 :rule instantiate :premises (@p78) :args ((@list @t82))) % 1.32/1.55 (step-pop @p189 :rule scope :premises (@p86)) % 1.32/1.55 (step @p87 :rule process_scope :premises (@p189) :args (@t87)) % 1.32/1.55 (step @p89 :rule eq_resolve :premises (@p87 @p84)) % 1.32/1.55 (step @p90 :rule implies_elim :premises (@p89)) % 1.32/1.55 (step @p91 :rule chain_m_resolution :premises (@p90 @p78) :args (@t89 @t90 (@list @t79))) % 1.32/1.55 (step @p92 :rule eq-symm :args (@t2 @t1)) % 1.32/1.55 (step @p93 :rule eq-symm :args (@t2 @t4)) % 1.32/1.55 (step @p94 :rule nary_cong :premises (@p93 @p92) :args (@t10)) % 1.32/1.55 (step @p95 :rule refl :args (@t11)) % 1.32/1.55 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t12)) % 1.32/1.55 (step @p97 :rule refl :args (@t14)) % 1.32/1.55 (step @p98 :rule cong :premises (@p97 @p96) :args (@t15)) % 1.32/1.55 (step @p99 :rule cong :premises (@p98) :args (@t17)) % 1.32/1.55 (step @p100 :rule eq_resolve :premises (@p4 @p99)) % 1.32/1.55 (step @p101 :rule aci_norm :args ((= @t92 @t91))) % 1.32/1.55 (step @p102 :rule refl :args (@t93)) % 1.32/1.55 (step @p103 :rule nary_cong :premises (@p102 @p101) :args (@t94)) % 1.32/1.55 (step @p104 :rule cong :premises (@p79 @p103) :args (@t95)) % 1.32/1.55 (step @p105 :rule refl :args (@t96)) % 1.32/1.55 (step @p106 :rule cong :premises (@p105 @p104) :args ((=> @t96 @t95))) % 1.32/1.55 (assume-push @p190 @t96) % 1.32/1.55 (step @p108 :rule instantiate :premises (@p100) :args ((@list @t83 @t63 @t63))) % 1.32/1.55 (step-pop @p191 :rule scope :premises (@p108)) % 1.32/1.55 (step @p109 :rule process_scope :premises (@p191) :args (@t95)) % 1.32/1.55 (step @p111 :rule eq_resolve :premises (@p109 @p106)) % 1.32/1.55 (step @p112 :rule implies_elim :premises (@p111)) % 1.32/1.55 (step @p113 :rule chain_m_resolution :premises (@p112 @p100) :args (@t98 @t90 (@list @t96))) % 1.32/1.55 (step @p114 :rule cnf_and_pos :args (@t97 0)) % 1.32/1.55 (step @p115 :rule reordering :premises (@p114) :args ((or @t93 @t99))) % 1.32/1.55 (step @p116 :rule cnf_and_pos :args (@t97 1)) % 1.32/1.55 (step @p117 :rule reordering :premises (@p116) :args ((or @t91 @t99))) % 1.32/1.55 (step @p118 :rule cnf_or_neg :args (@t69 1)) % 1.32/1.55 (step @p119 :rule chain_m_resolution :premises (@p118 @p52) :args (@t100 @t70 @t71)) % 1.32/1.55 (step @p120 :rule refl :args (@t101)) % 1.32/1.55 (step @p121 :rule refl :args (@t102)) % 1.32/1.55 (step @p122 :rule bool-double-not-elim :args (@t64)) % 1.32/1.55 (step @p123 :rule nary_cong :premises (@p122 @p121 @p120) :args ((or (not @t100) @t102 @t101))) % 1.32/1.55 (assume-push @p192 @t100) % 1.32/1.55 (assume-push @p193 @t91) % 1.32/1.55 (assume-push @p194 @t93) % 1.32/1.55 (step @p127 :rule evaluate :args ((= true false))) % 1.32/1.55 (step @p128 :rule false_intro :premises (@p119)) % 1.32/1.55 (step @p129 :rule refl :args (tptp.universal_class)) % 1.32/1.55 (step @p130 :rule symm :premises (@p193)) % 1.32/1.55 (step @p131 :rule cong :premises (@p130 @p129) :args (@t93)) % 1.32/1.55 (step @p132 :rule true_intro :premises (@p194)) % 1.32/1.55 (step @p133 :rule symm :premises (@p132)) % 1.32/1.55 (step @p134 :rule trans :premises (@p133 @p131 @p128)) % 1.32/1.55 (step @p135 false :rule eq_resolve :premises (@p134 @p127)) % 1.32/1.55 (step-pop @p195 :rule scope :premises (@p135)) % 1.32/1.55 (step-pop @p196 :rule scope :premises (@p195)) % 1.32/1.55 (step-pop @p197 :rule scope :premises (@p196)) % 1.32/1.55 (step @p136 :rule process_scope :premises (@p197) :args (false)) % 1.32/1.55 (assume-push @p198 @t100) % 1.32/1.55 (assume-push @p199 @t93) % 1.32/1.55 (assume-push @p200 @t91) % 1.32/1.55 (step @p143 :rule and_intro :premises (@p119 @p200 @p199)) % 1.32/1.55 (step-pop @p201 :rule scope :premises (@p143)) % 1.32/1.55 (step-pop @p202 :rule scope :premises (@p201)) % 1.32/1.55 (step-pop @p203 :rule scope :premises (@p202)) % 1.32/1.55 (step @p144 :rule process_scope :premises (@p203) :args (@t103)) % 1.32/1.55 (step @p148 :rule implies_elim :premises (@p144)) % 1.32/1.55 (step @p149 :rule resolution :premises (@p148 @p136) :args (true @t103)) % 1.32/1.55 (step @p150 :rule not_and :premises (@p149)) % 1.32/1.55 (step @p151 :rule eq_resolve :premises (@p150 @p123)) % 1.32/1.55 (step @p152 :rule chain_m_resolution :premises (@p151 @p119 @p117 @p115) :args (@t99 (@list true false false) (@list @t64 @t91 @t93))) % 1.32/1.56 (step @p153 :rule cnf_equiv_pos1 :args (@t98)) % 1.32/1.56 (step @p154 :rule reordering :premises (@p153) :args ((or @t104 @t97 (not @t98)))) % 1.32/1.56 (step @p155 :rule chain_m_resolution :premises (@p154 @p152 @p113) :args (@t104 (@list true false) (@list @t97 @t98))) % 1.32/1.56 (step @p156 :rule instantiate :premises (@p5) :args ((@list @t63 @t63))) % 1.32/1.56 (step @p157 :rule cnf_or_pos :args (@t89)) % 1.32/1.56 (step @p158 :rule reordering :premises (@p157) :args ((or @t86 @t84 @t88 (not @t89)))) % 1.32/1.56 (step @p159 :rule chain_m_resolution :premises (@p158 @p156 @p155 @p91) :args (@t88 (@list false true false) (@list @t85 @t84 @t89))) % 1.32/1.56 (assume-push @p204 @t108) % 1.32/1.56 (assume-push @p205 @t109) % 1.32/1.56 (assume-push @p206 @t88) % 1.32/1.56 (assume-push @p207 @t88) % 1.32/1.56 (assume-push @p208 @t109) % 1.32/1.56 (assume-push @p209 @t108) % 1.32/1.56 (step @p166 :rule symm :premises (@p206)) % 1.32/1.56 (step @p167 :rule trans :premises (@p56 @p166)) % 1.32/1.56 (step @p168 :rule refl :args (@t65)) % 1.32/1.56 (step @p169 :rule cong :premises (@p168 @p167) :args (@t106)) % 1.32/1.56 (step @p170 :rule refl :args (@t66)) % 1.32/1.56 (step @p171 :rule cong :premises (@p170 @p169) :args (@t107)) % 1.32/1.56 (step @p172 :rule trans :premises (@p55 @p171)) % 1.32/1.56 (step-pop @p210 :rule scope :premises (@p172)) % 1.32/1.56 (step-pop @p211 :rule scope :premises (@p210)) % 1.32/1.56 (step-pop @p212 :rule scope :premises (@p211)) % 1.32/1.56 (step @p173 :rule process_scope :premises (@p212) :args (@t68)) % 1.32/1.56 (step @p177 :rule and_intro :premises (@p206 @p56 @p55)) % 1.32/1.56 (step @p178 :rule modus_ponens :premises (@p177 @p173)) % 1.32/1.56 (step-pop @p213 :rule scope :premises (@p178)) % 1.32/1.56 (step-pop @p214 :rule scope :premises (@p213)) % 1.32/1.56 (step-pop @p215 :rule scope :premises (@p214)) % 1.32/1.56 (step @p179 :rule process_scope :premises (@p215) :args (@t68)) % 1.32/1.56 (step @p183 :rule implies_elim :premises (@p179)) % 1.32/1.56 (step @p184 :rule cnf_and_neg :args (@t110)) % 1.32/1.56 (step @p185 :rule resolution :premises (@p184 @p183) :args (true @t110)) % 1.32/1.56 (step @p186 :rule reordering :premises (@p185) :args ((or @t68 (not @t108) (not @t109) (not @t88)))) % 1.32/1.56 (step @p187 false :rule chain_m_resolution :premises (@p186 @p159 @p56 @p55 @p54) :args (false (@list false false false true) (@list @t88 @t109 @t108 @t68))) % 1.32/1.56 ) % 1.32/1.56 % SZS output end Proof % 1.32/1.56 % cvc5 exiting %------------------------------------------------------------------------------