%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET679+3 : TPTP v9.2.1. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n023.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:48:25 AM UTC 2026 % Result : Theorem 31.33s 31.57s % Output : Proof 31.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET679+3 : TPTP v9.2.1. Released v2.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n023.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 16:08:28 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 31.33/31.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 31.33/31.57 --- Run --no-e-matching --full-saturate-quant at 6... % 31.33/31.57 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 31.33/31.57 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 31.33/31.57 % SZS status Theorem % 31.33/31.57 % SZS output start Proof % 31.33/31.57 ( % 31.33/31.57 (declare-sort $$unsorted 0) % 31.33/31.57 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 31.33/31.57 (declare-const tptp.identity_relation_of (-> $$unsorted $$unsorted)) % 31.33/31.57 (declare-const tptp.member_type (-> $$unsorted $$unsorted)) % 31.33/31.57 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 31.33/31.57 (declare-const tptp.not_equal (-> $$unsorted $$unsorted Bool)) % 31.33/31.57 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 31.33/31.57 (declare-const tptp.binary_relation_type $$unsorted) % 31.33/31.57 (declare-const tptp.set_type $$unsorted) % 31.33/31.57 (declare-const tptp.type (-> $$unsorted $$unsorted Bool)) % 31.33/31.57 (declare-const tptp.relation_like (-> $$unsorted Bool)) % 31.33/31.57 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 31.33/31.57 (declare-const tptp.ilf_type (-> $$unsorted $$unsorted Bool)) % 31.33/31.57 (declare-const tptp.empty (-> $$unsorted Bool)) % 31.33/31.57 (declare-const tptp.empty_set $$unsorted) % 31.33/31.57 (declare-const tptp.subset_type (-> $$unsorted $$unsorted)) % 31.33/31.57 (define @t1 () (@var "B" $$unsorted)) % 31.33/31.57 (define @t2 () (tptp.identity_relation_of @t1)) % 31.33/31.57 (define @t3 () (@var "C" $$unsorted)) % 31.33/31.57 (define @t4 () (tptp.member @t3 @t1)) % 31.33/31.57 (define @t5 () (= @t4 (tptp.member (tptp.ordered_pair @t3 @t3) @t2))) % 31.33/31.57 (define @t6 () (tptp.ilf_type @t3 tptp.set_type)) % 31.33/31.57 (define @t7 () (@list @t3)) % 31.33/31.57 (define @t8 () (forall @t7 (=> @t6 @t5))) % 31.33/31.57 (define @t9 () (tptp.ilf_type @t1 tptp.set_type)) % 31.33/31.57 (define @t10 () (=> @t9 @t8)) % 31.33/31.57 (define @t11 () (@list @t1)) % 31.33/31.57 (define @t12 () (forall @t11 @t10)) % 31.33/31.57 (define @t13 () (not (tptp.member @t1 tptp.empty_set))) % 31.33/31.57 (define @t14 () (forall @t11 (=> @t9 @t13))) % 31.33/31.57 (define @t15 () (@var "D" $$unsorted)) % 31.33/31.57 (define @t16 () (tptp.ilf_type @t15 tptp.set_type)) % 31.33/31.57 (define @t17 () (@list @t15)) % 31.33/31.57 (define @t18 () (tptp.member @t15 @t3)) % 31.33/31.57 (define @t19 () (tptp.member @t15 @t1)) % 31.33/31.57 (define @t20 () (= @t1 @t3)) % 31.33/31.57 (define @t21 () (= (tptp.not_equal @t1 @t3) (not @t20))) % 31.33/31.57 (define @t22 () (forall @t7 (=> @t6 @t21))) % 31.33/31.57 (define @t23 () (=> @t9 @t22)) % 31.33/31.57 (define @t24 () (forall @t11 @t23)) % 31.33/31.57 (define @t25 () (not @t4)) % 31.33/31.57 (define @t26 () (forall @t7 (=> @t6 @t25))) % 31.33/31.57 (define @t27 () (tptp.empty @t1)) % 31.33/31.57 (define @t28 () (= @t27 @t26)) % 31.33/31.57 (define @t29 () (=> @t9 @t28)) % 31.33/31.57 (define @t30 () (forall @t11 @t29)) % 31.33/31.57 (define @t31 () (tptp.ilf_type (tptp.ordered_pair @t1 @t3) tptp.set_type)) % 31.33/31.57 (define @t32 () (forall @t7 (=> @t6 @t31))) % 31.33/31.57 (define @t33 () (=> @t9 @t32)) % 31.33/31.57 (define @t34 () (forall @t11 @t33)) % 31.33/31.57 (define @t35 () (tptp.relation_like @t1)) % 31.33/31.57 (define @t36 () (tptp.ilf_type @t1 tptp.binary_relation_type)) % 31.33/31.57 (define @t37 () (@var "E" $$unsorted)) % 31.33/31.57 (define @t38 () (tptp.cross_product @t1 @t3)) % 31.33/31.57 (define @t39 () (tptp.power_set @t1)) % 31.33/31.57 (define @t40 () (tptp.ilf_type @t3 (tptp.subset_type @t1))) % 31.33/31.57 (define @t41 () (not @t27)) % 31.33/31.57 (define @t42 () (and @t41 @t9)) % 31.33/31.57 (define @t43 () (tptp.not_equal @t2 tptp.empty_set)) % 31.33/31.57 (define @t44 () (forall @t11 (=> @t42 @t43))) % 31.33/31.57 (define @t45 () (not @t44)) % 31.33/31.57 (define @t46 () (not @t9)) % 31.33/31.57 (define @t47 () (or @t27 @t46 @t43)) % 31.33/31.57 (define @t48 () (@quantifiers_skolemize (forall @t11 @t47) 0)) % 31.33/31.57 (define @t49 () (not @t6)) % 31.33/31.57 (define @t50 () (forall @t7 (or @t49 (not (tptp.member @t3 @t48))))) % 31.33/31.57 (define @t51 () (@quantifiers_skolemize @t50 0)) % 31.33/31.57 (define @t52 () (tptp.ordered_pair @t51 @t51)) % 31.33/31.57 (define @t53 () (@var "BOUND_VARIABLE_7726" $$unsorted)) % 31.33/31.57 (define @t54 () (tptp.ilf_type (tptp.ordered_pair @t1 @t53) tptp.set_type)) % 31.33/31.57 (define @t55 () (not (tptp.ilf_type @t53 tptp.set_type))) % 31.33/31.57 (define @t56 () (or @t55 @t54)) % 31.33/31.57 (define @t57 () (or @t46 @t56)) % 31.33/31.57 (define @t58 () (forall (@list @t1 @t53) @t57)) % 31.33/31.57 (define @t59 () (@list @t53)) % 31.33/31.57 (define @t60 () (forall @t59 @t57)) % 31.33/31.57 (define @t61 () (forall @t59 @t56)) % 31.33/31.57 (define @t62 () (@list @t3)) % 31.33/31.57 (define @t63 () (or @t46 @t61)) % 31.33/31.57 (define @t64 () (forall @t7 (or @t49 @t31))) % 31.33/31.57 (define @t65 () (= @t27 (forall @t7 (or @t49 @t25)))) % 31.33/31.57 (define @t66 () (tptp.ilf_type @t48 tptp.set_type)) % 31.33/31.57 (define @t67 () (tptp.identity_relation_of @t48)) % 31.33/31.57 (define @t68 () (tptp.not_equal @t67 tptp.empty_set)) % 31.33/31.57 (define @t69 () (not @t66)) % 31.33/31.57 (define @t70 () (tptp.empty @t48)) % 31.33/31.57 (define @t71 () (or @t70 @t69 @t68)) % 31.33/31.57 (define @t72 () (@list true)) % 31.33/31.57 (define @t73 () (@list @t71)) % 31.33/31.57 (define @t74 () (= @t70 @t50)) % 31.33/31.57 (define @t75 () (or @t69 @t74)) % 31.33/31.57 (define @t76 () (@list false false)) % 31.33/31.57 (define @t77 () (not @t50)) % 31.33/31.57 (define @t78 () (@list true false)) % 31.33/31.57 (define @t79 () (tptp.ilf_type @t51 tptp.set_type)) % 31.33/31.57 (define @t80 () (tptp.member @t51 @t48)) % 31.33/31.57 (define @t81 () (not @t80)) % 31.33/31.57 (define @t82 () (not @t79)) % 31.33/31.57 (define @t83 () (or @t82 @t81)) % 31.33/31.57 (define @t84 () (@list @t83)) % 31.33/31.57 (define @t85 () (tptp.ilf_type @t52 tptp.set_type)) % 31.33/31.57 (define @t86 () (or @t82 @t82 @t85)) % 31.33/31.57 (define @t87 () (not (tptp.member @t52 tptp.empty_set))) % 31.33/31.57 (define @t88 () (not @t85)) % 31.33/31.57 (define @t89 () (or @t88 @t87)) % 31.33/31.57 (define @t90 () (@var "BOUND_VARIABLE_7697" $$unsorted)) % 31.33/31.57 (define @t91 () (= (tptp.not_equal @t1 @t90) (not (= @t1 @t90)))) % 31.33/31.57 (define @t92 () (not (tptp.ilf_type @t90 tptp.set_type))) % 31.33/31.57 (define @t93 () (or @t46 @t92 @t91)) % 31.33/31.57 (define @t94 () (or @t92 @t91)) % 31.33/31.57 (define @t95 () (or @t46 @t94)) % 31.33/31.57 (define @t96 () (@list @t1 @t90)) % 31.33/31.57 (define @t97 () (forall @t96 @t95)) % 31.33/31.57 (define @t98 () (@list @t90)) % 31.33/31.57 (define @t99 () (forall @t98 @t95)) % 31.33/31.57 (define @t100 () (forall @t98 @t94)) % 31.33/31.57 (define @t101 () (or @t46 @t100)) % 31.33/31.57 (define @t102 () (forall @t7 (or @t49 @t21))) % 31.33/31.57 (define @t103 () (not (= @t67 tptp.empty_set))) % 31.33/31.57 (define @t104 () (= @t68 @t103)) % 31.33/31.57 (define @t105 () (tptp.ilf_type tptp.empty_set tptp.set_type)) % 31.33/31.57 (define @t106 () (not @t105)) % 31.33/31.57 (define @t107 () (tptp.ilf_type @t67 tptp.set_type)) % 31.33/31.57 (define @t108 () (not @t107)) % 31.33/31.57 (define @t109 () (or @t108 @t106 @t104)) % 31.33/31.57 (define @t110 () (forall @t96 @t93)) % 31.33/31.57 (define @t111 () (= tptp.empty_set @t67)) % 31.33/31.57 (define @t112 () (not @t111)) % 31.33/31.57 (define @t113 () (= @t68 @t112)) % 31.33/31.57 (define @t114 () (or @t108 @t106 @t113)) % 31.33/31.57 (define @t115 () (@list false false false)) % 31.33/31.57 (define @t116 () (not @t113)) % 31.33/31.57 (define @t117 () (tptp.member @t52 @t67)) % 31.33/31.57 (define @t118 () (@var "BOUND_VARIABLE_7595" $$unsorted)) % 31.33/31.57 (define @t119 () (= (tptp.member @t118 @t1) (tptp.member (tptp.ordered_pair @t118 @t118) @t2))) % 31.33/31.57 (define @t120 () (not (tptp.ilf_type @t118 tptp.set_type))) % 31.33/31.57 (define @t121 () (or @t120 @t119)) % 31.33/31.57 (define @t122 () (or @t46 @t121)) % 31.33/31.57 (define @t123 () (forall (@list @t1 @t118) @t122)) % 31.33/31.57 (define @t124 () (@list @t118)) % 31.33/31.57 (define @t125 () (forall @t124 @t122)) % 31.33/31.57 (define @t126 () (forall @t124 @t121)) % 31.33/31.57 (define @t127 () (or @t46 @t126)) % 31.33/31.57 (define @t128 () (forall @t7 (or @t49 @t5))) % 31.33/31.57 (define @t129 () (= @t80 @t117)) % 31.33/31.57 (define @t130 () (or @t69 @t82 @t129)) % 31.33/31.57 (assume @p1 @t12) % 31.33/31.57 (assume @p2 @t14) % 31.33/31.57 (assume @p3 (tptp.empty tptp.empty_set)) % 31.33/31.57 (assume @p4 (tptp.type tptp.empty_set tptp.set_type)) % 31.33/31.57 (assume @p5 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (forall @t17 (=> @t16 (= (tptp.member (tptp.ordered_pair @t3 @t15) @t2) (and @t4 (= @t3 @t15)))))))))) % 31.33/31.57 (assume @p6 (forall @t11 (=> @t9 (tptp.ilf_type @t2 tptp.binary_relation_type)))) % 31.33/31.57 (assume @p7 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (= @t20 (forall @t17 (=> @t16 (= @t19 @t18))))))))) % 31.33/31.57 (assume @p8 @t24) % 31.33/31.57 (assume @p9 @t30) % 31.33/31.57 (assume @p10 @t34) % 31.33/31.57 (assume @p11 (forall @t11 (=> @t9 (= @t36 (and @t35 @t9))))) % 31.33/31.57 (assume @p12 (exists @t11 @t36)) % 31.33/31.57 (assume @p13 (forall @t11 (=> @t9 (= @t35 (forall @t7 (=> @t6 (=> @t4 (exists @t17 (and @t16 (exists (@list @t37) (and (tptp.ilf_type @t37 tptp.set_type) (= @t3 (tptp.ordered_pair @t15 @t37))))))))))))) % 31.33/31.57 (assume @p14 (forall @t11 (=> (and @t27 @t9) @t35))) % 31.33/31.57 (assume @p15 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (forall @t17 (=> (tptp.ilf_type @t15 (tptp.subset_type @t38)) (tptp.relation_like @t15)))))))) % 31.33/31.57 (assume @p16 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (tptp.ilf_type @t38 tptp.set_type)))))) % 31.33/31.57 (assume @p17 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (= @t40 (tptp.ilf_type @t3 (tptp.member_type @t39)))))))) % 31.33/31.57 (assume @p18 (forall @t11 (=> @t9 (exists @t7 @t40)))) % 31.33/31.57 (assume @p19 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (= (tptp.member @t1 (tptp.power_set @t3)) (forall @t17 (=> @t16 (=> @t19 @t18))))))))) % 31.33/31.57 (assume @p20 (forall @t11 (=> @t9 (and (not (tptp.empty @t39)) (tptp.ilf_type @t39 tptp.set_type))))) % 31.33/31.57 (assume @p21 (forall @t11 (=> @t9 (forall @t7 (=> (and (not (tptp.empty @t3)) @t6) (= (tptp.ilf_type @t1 (tptp.member_type @t3)) (tptp.member @t1 @t3))))))) % 31.33/31.57 (assume @p22 (forall @t11 (=> @t42 (exists @t7 (tptp.ilf_type @t3 (tptp.member_type @t1)))))) % 31.33/31.57 (assume @p23 (forall @t11 @t9)) % 31.33/31.57 (assume @p24 @t45) % 31.33/31.57 (assume @p25 true) % 31.33/31.57 (step @p26 :rule evaluate :args ((= true false))) % 31.33/31.57 (step @p27 :rule bool-impl-elim :args (@t9 @t13)) % 31.33/31.57 (step @p28 :rule cong :premises (@p27) :args (@t14)) % 31.33/31.57 (step @p29 :rule eq_resolve :premises (@p2 @p28)) % 31.33/31.57 (step @p30 :rule instantiate :premises (@p29) :args ((@list @t52))) % 31.33/31.57 (step @p31 :rule aci_norm :args ((= @t57 (or @t46 @t55 @t54)))) % 31.33/31.57 (step @p32 :rule cong :premises (@p31) :args (@t58)) % 31.33/31.57 (step @p33 :rule quant-merge-prenex :args ((= (forall @t11 @t60) @t58))) % 31.33/31.57 (step @p34 :rule alpha_equiv :args (@t61 (@list @t53) @t62)) % 31.33/31.57 (step @p35 :rule refl :args (@t46)) % 31.33/31.57 (step @p36 :rule nary_cong :premises (@p35 @p34) :args (@t63)) % 31.33/31.57 (step @p37 :rule quant-miniscope-or :args ((= @t60 @t63))) % 31.33/31.57 (step @p38 :rule trans :premises (@p37 @p36)) % 31.33/31.57 (step @p39 :rule symm :premises (@p38)) % 31.33/31.57 (step @p40 :rule cong :premises (@p39) :args ((forall @t11 (or @t46 @t64)))) % 31.33/31.57 (step @p41 :rule trans :premises (@p40 @p33)) % 31.33/31.57 (step @p42 :rule trans :premises (@p41 @p32)) % 31.33/31.57 (step @p43 :rule bool-impl-elim :args (@t9 @t64)) % 31.33/31.57 (step @p44 :rule cong :premises (@p43) :args ((forall @t11 (=> @t9 @t64)))) % 31.33/31.57 (step @p45 :rule trans :premises (@p44 @p42)) % 31.33/31.57 (step @p46 :rule bool-impl-elim :args (@t6 @t31)) % 31.33/31.57 (step @p47 :rule cong :premises (@p46) :args (@t32)) % 31.33/31.57 (step @p48 :rule refl :args (@t9)) % 31.33/31.57 (step @p49 :rule cong :premises (@p48 @p47) :args (@t33)) % 31.33/31.57 (step @p50 :rule cong :premises (@p49) :args (@t34)) % 31.33/31.57 (step @p51 :rule trans :premises (@p50 @p45)) % 31.33/31.57 (step @p52 :rule eq_resolve :premises (@p10 @p51)) % 31.33/31.57 (step @p53 :rule instantiate :premises (@p52) :args ((@list @t51 @t51))) % 31.33/31.57 (step @p54 :rule bool-impl-elim :args (@t9 @t65)) % 31.33/31.57 (step @p55 :rule cong :premises (@p54) :args ((forall @t11 (=> @t9 @t65)))) % 31.33/31.57 (step @p56 :rule bool-impl-elim :args (@t6 @t25)) % 31.33/31.57 (step @p57 :rule cong :premises (@p56) :args (@t26)) % 31.33/31.57 (step @p58 :rule refl :args (@t27)) % 31.33/31.57 (step @p59 :rule cong :premises (@p58 @p57) :args (@t28)) % 31.33/31.57 (step @p60 :rule cong :premises (@p48 @p59) :args (@t29)) % 31.33/31.57 (step @p61 :rule cong :premises (@p60) :args (@t30)) % 31.33/31.57 (step @p62 :rule trans :premises (@p61 @p55)) % 31.33/31.57 (step @p63 :rule eq_resolve :premises (@p9 @p62)) % 31.33/31.57 (step @p64 :rule instantiate :premises (@p63) :args ((@list @t48))) % 31.33/31.57 (step @p65 :rule aci_norm :args ((= (or (or @t27 @t46) @t43) @t47))) % 31.33/31.57 (step @p66 :rule refl :args (@t43)) % 31.33/31.57 (step @p67 :rule bool-double-not-elim :args (@t27)) % 31.33/31.57 (step @p68 :rule nary_cong :premises (@p67 @p35) :args ((or (not @t41) @t46))) % 31.33/31.57 (step @p69 :rule bool-and-de-morgan :args (@t41 @t9 true)) % 31.33/31.57 (step @p70 :rule trans :premises (@p69 @p68)) % 31.33/31.57 (step @p71 :rule nary_cong :premises (@p70 @p66) :args ((or (not @t42) @t43))) % 31.33/31.57 (step @p72 :rule trans :premises (@p71 @p65)) % 31.33/31.57 (step @p73 :rule bool-impl-elim :args (@t42 @t43)) % 31.33/31.57 (step @p74 :rule trans :premises (@p73 @p72)) % 31.33/31.57 (step @p75 :rule cong :premises (@p74) :args (@t44)) % 31.33/31.57 (step @p76 :rule cong :premises (@p75) :args (@t45)) % 31.33/31.57 (step @p77 :rule eq_resolve :premises (@p24 @p76)) % 31.33/31.57 (step @p78 :rule skolemize :premises (@p77)) % 31.33/31.57 (step @p79 :rule bool-double-not-elim :args (@t66)) % 31.33/31.57 (step @p80 :rule refl :args (@t71)) % 31.33/31.57 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or @t71 (not @t69)))) % 31.33/31.57 (step @p82 :rule cnf_or_neg :args (@t71 1)) % 31.33/31.57 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 31.33/31.57 (step @p84 :rule reordering :premises (@p83) :args ((or @t66 @t71))) % 31.33/31.57 (step @p85 :rule chain_m_resolution :premises (@p84 @p78) :args (@t66 @t72 @t73)) % 31.33/31.57 (step @p86 :rule cnf_or_pos :args (@t75)) % 31.33/31.57 (step @p87 :rule reordering :premises (@p86) :args ((or @t69 @t74 (not @t75)))) % 31.33/31.57 (step @p88 :rule chain_m_resolution :premises (@p87 @p85 @p64) :args (@t74 @t76 (@list @t66 @t75))) % 31.33/31.57 (step @p89 :rule cnf_or_neg :args (@t71 0)) % 31.33/31.57 (step @p90 :rule chain_m_resolution :premises (@p89 @p78) :args ((not @t70) @t72 @t73)) % 31.33/31.57 (step @p91 :rule cnf_equiv_pos2 :args (@t74)) % 31.33/31.57 (step @p92 :rule reordering :premises (@p91) :args ((or @t70 @t77 (not @t74)))) % 31.33/31.57 (step @p93 :rule chain_m_resolution :premises (@p92 @p90 @p88) :args (@t77 @t78 (@list @t70 @t74))) % 31.33/31.57 (step @p94 :rule skolemize :premises (@p93)) % 31.33/31.57 (step @p95 :rule bool-double-not-elim :args (@t79)) % 31.33/31.57 (step @p96 :rule refl :args (@t83)) % 31.33/31.57 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or @t83 (not @t82)))) % 31.33/31.57 (step @p98 :rule cnf_or_neg :args (@t83 0)) % 31.33/31.57 (step @p99 :rule eq_resolve :premises (@p98 @p97)) % 31.33/31.57 (step @p100 :rule reordering :premises (@p99) :args ((or @t79 @t83))) % 31.33/31.57 (step @p101 :rule chain_m_resolution :premises (@p100 @p94) :args (@t79 @t72 @t84)) % 31.33/31.57 (step @p102 :rule cnf_or_pos :args (@t86)) % 31.33/31.57 (step @p103 :rule factoring :premises (@p102)) % 31.33/31.57 (step @p104 :rule reordering :premises (@p103) :args ((or @t82 @t85 (not @t86)))) % 31.33/31.57 (step @p105 :rule chain_m_resolution :premises (@p104 @p101 @p53) :args (@t85 @t76 (@list @t79 @t86))) % 31.33/31.57 (step @p106 :rule cnf_or_pos :args (@t89)) % 31.33/31.57 (step @p107 :rule reordering :premises (@p106) :args ((or @t88 @t87 (not @t89)))) % 31.33/31.57 (step @p108 :rule chain_m_resolution :premises (@p107 @p105 @p30) :args (@t87 @t76 (@list @t85 @t89))) % 31.33/31.57 (step @p109 :rule false_intro :premises (@p108)) % 31.33/31.57 (step @p110 :rule aci_norm :args ((= @t95 @t93))) % 31.33/31.57 (step @p111 :rule cong :premises (@p110) :args (@t97)) % 31.33/31.57 (step @p112 :rule quant-merge-prenex :args ((= (forall @t11 @t99) @t97))) % 31.33/31.57 (step @p113 :rule alpha_equiv :args (@t100 (@list @t90) @t62)) % 31.33/31.57 (step @p114 :rule nary_cong :premises (@p35 @p113) :args (@t101)) % 31.33/31.57 (step @p115 :rule quant-miniscope-or :args ((= @t99 @t101))) % 31.33/31.57 (step @p116 :rule trans :premises (@p115 @p114)) % 31.33/31.57 (step @p117 :rule symm :premises (@p116)) % 31.33/31.57 (step @p118 :rule cong :premises (@p117) :args ((forall @t11 (or @t46 @t102)))) % 31.33/31.57 (step @p119 :rule trans :premises (@p118 @p112)) % 31.33/31.57 (step @p120 :rule trans :premises (@p119 @p111)) % 31.33/31.57 (step @p121 :rule bool-impl-elim :args (@t9 @t102)) % 31.33/31.57 (step @p122 :rule cong :premises (@p121) :args ((forall @t11 (=> @t9 @t102)))) % 31.33/31.57 (step @p123 :rule trans :premises (@p122 @p120)) % 31.33/31.57 (step @p124 :rule bool-impl-elim :args (@t6 @t21)) % 31.33/31.57 (step @p125 :rule cong :premises (@p124) :args (@t22)) % 31.33/31.57 (step @p126 :rule cong :premises (@p48 @p125) :args (@t23)) % 31.33/31.57 (step @p127 :rule cong :premises (@p126) :args (@t24)) % 31.33/31.57 (step @p128 :rule trans :premises (@p127 @p123)) % 31.33/31.57 (step @p129 :rule eq_resolve :premises (@p8 @p128)) % 31.33/31.57 (step @p130 :rule eq-symm :args (@t67 tptp.empty_set)) % 31.33/31.57 (step @p131 :rule cong :premises (@p130) :args (@t103)) % 31.33/31.57 (step @p132 :rule refl :args (@t68)) % 31.33/31.57 (step @p133 :rule cong :premises (@p132 @p131) :args (@t104)) % 31.33/31.57 (step @p134 :rule refl :args (@t106)) % 31.33/31.57 (step @p135 :rule refl :args (@t108)) % 31.33/31.57 (step @p136 :rule nary_cong :premises (@p135 @p134 @p133) :args (@t109)) % 31.33/31.57 (step @p137 :rule refl :args (@t110)) % 31.33/31.57 (step @p138 :rule cong :premises (@p137 @p136) :args ((=> @t110 @t109))) % 31.33/31.57 (assume-push @p200 @t110) % 31.33/31.57 (step @p140 :rule instantiate :premises (@p129) :args ((@list @t67 tptp.empty_set))) % 31.33/31.57 (step-pop @p201 :rule scope :premises (@p140)) % 31.33/31.57 (step @p141 :rule process_scope :premises (@p201) :args (@t109)) % 31.33/31.57 (step @p143 :rule eq_resolve :premises (@p141 @p138)) % 31.33/31.57 (step @p144 :rule implies_elim :premises (@p143)) % 31.33/31.57 (step @p145 :rule chain_m_resolution :premises (@p144 @p129) :args (@t114 (@list false) (@list @t110))) % 31.33/31.57 (step @p146 :rule instantiate :premises (@p23) :args ((@list tptp.empty_set))) % 31.33/31.57 (step @p147 :rule instantiate :premises (@p23) :args ((@list @t67))) % 31.33/31.57 (step @p148 :rule cnf_or_pos :args (@t114)) % 31.33/31.57 (step @p149 :rule reordering :premises (@p148) :args ((or @t108 @t106 @t113 (not @t114)))) % 31.33/31.57 (step @p150 :rule chain_m_resolution :premises (@p149 @p147 @p146 @p145) :args (@t113 @t115 (@list @t107 @t105 @t114))) % 31.33/31.57 (step @p151 :rule cnf_or_neg :args (@t71 2)) % 31.33/31.57 (step @p152 :rule chain_m_resolution :premises (@p151 @p78) :args ((not @t68) @t72 @t73)) % 31.33/31.57 (step @p153 :rule bool-double-not-elim :args (@t111)) % 31.33/31.57 (step @p154 :rule refl :args (@t116)) % 31.33/31.57 (step @p155 :rule nary_cong :premises (@p154 @p132 @p153) :args ((or @t116 @t68 (not @t112)))) % 31.33/31.57 (step @p156 :rule cnf_equiv_pos2 :args (@t113)) % 31.33/31.57 (step @p157 :rule eq_resolve :premises (@p156 @p155)) % 31.33/31.57 (step @p158 :rule reordering :premises (@p157) :args ((or @t68 @t111 @t116))) % 31.33/31.57 (step @p159 :rule chain_m_resolution :premises (@p158 @p152 @p150) :args (@t111 @t78 (@list @t68 @t113))) % 31.33/31.57 (step @p160 :rule symm :premises (@p159)) % 31.33/31.57 (step @p161 :rule refl :args (@t52)) % 31.33/31.57 (step @p162 :rule cong :premises (@p161 @p160) :args (@t117)) % 31.33/31.57 (step @p163 :rule aci_norm :args ((= @t122 (or @t46 @t120 @t119)))) % 31.33/31.57 (step @p164 :rule cong :premises (@p163) :args (@t123)) % 31.33/31.57 (step @p165 :rule quant-merge-prenex :args ((= (forall @t11 @t125) @t123))) % 31.33/31.57 (step @p166 :rule alpha_equiv :args (@t126 (@list @t118) @t62)) % 31.33/31.57 (step @p167 :rule nary_cong :premises (@p35 @p166) :args (@t127)) % 31.33/31.57 (step @p168 :rule quant-miniscope-or :args ((= @t125 @t127))) % 31.33/31.57 (step @p169 :rule trans :premises (@p168 @p167)) % 31.33/31.57 (step @p170 :rule symm :premises (@p169)) % 31.33/31.57 (step @p171 :rule cong :premises (@p170) :args ((forall @t11 (or @t46 @t128)))) % 31.33/31.57 (step @p172 :rule trans :premises (@p171 @p165)) % 31.33/31.57 (step @p173 :rule trans :premises (@p172 @p164)) % 31.33/31.57 (step @p174 :rule bool-impl-elim :args (@t9 @t128)) % 31.33/31.57 (step @p175 :rule cong :premises (@p174) :args ((forall @t11 (=> @t9 @t128)))) % 31.33/31.57 (step @p176 :rule trans :premises (@p175 @p173)) % 31.33/31.57 (step @p177 :rule bool-impl-elim :args (@t6 @t5)) % 31.33/31.57 (step @p178 :rule cong :premises (@p177) :args (@t8)) % 31.33/31.57 (step @p179 :rule cong :premises (@p48 @p178) :args (@t10)) % 31.33/31.57 (step @p180 :rule cong :premises (@p179) :args (@t12)) % 31.33/31.57 (step @p181 :rule trans :premises (@p180 @p176)) % 31.33/31.57 (step @p182 :rule eq_resolve :premises (@p1 @p181)) % 31.33/31.57 (step @p183 :rule instantiate :premises (@p182) :args ((@list @t48 @t51))) % 31.33/31.57 (step @p184 :rule cnf_or_pos :args (@t130)) % 31.33/31.57 (step @p185 :rule reordering :premises (@p184) :args ((or @t69 @t82 @t129 (not @t130)))) % 31.33/31.57 (step @p186 :rule chain_m_resolution :premises (@p185 @p85 @p101 @p183) :args (@t129 @t115 (@list @t66 @t79 @t130))) % 31.33/31.57 (step @p187 :rule bool-double-not-elim :args (@t80)) % 31.33/31.57 (step @p188 :rule nary_cong :premises (@p96 @p187) :args ((or @t83 (not @t81)))) % 31.33/31.57 (step @p189 :rule cnf_or_neg :args (@t83 1)) % 31.33/31.57 (step @p190 :rule eq_resolve :premises (@p189 @p188)) % 31.33/31.57 (step @p191 :rule reordering :premises (@p190) :args ((or @t80 @t83))) % 31.33/31.57 (step @p192 :rule chain_m_resolution :premises (@p191 @p94) :args (@t80 @t72 @t84)) % 31.33/31.57 (step @p193 :rule cnf_equiv_pos1 :args (@t129)) % 31.33/31.57 (step @p194 :rule reordering :premises (@p193) :args ((or @t81 @t117 (not @t129)))) % 31.33/31.57 (step @p195 :rule chain_m_resolution :premises (@p194 @p192 @p186) :args (@t117 @t76 (@list @t80 @t129))) % 31.33/31.57 (step @p196 :rule true_intro :premises (@p195)) % 31.33/31.57 (step @p197 :rule symm :premises (@p196)) % 31.33/31.57 (step @p198 :rule trans :premises (@p197 @p162 @p109)) % 31.33/31.57 (step @p199 false :rule eq_resolve :premises (@p198 @p26)) % 31.33/31.57 ) % 31.33/31.57 % SZS output end Proof % 31.33/31.57 % cvc5 exiting %------------------------------------------------------------------------------