%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET676+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 : 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 08:48:25 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET676+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 % 0.15/0.34 % Computer : n005.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 16:08:03 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (declare-const tptp.relation_like (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.member_type (-> $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.identity_relation_of_type (-> $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.subset_type (-> $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.set_type $$unsorted) % 0.37/0.58 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.ilf_type (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.relation_type (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (define @t1 () (@var "C" $$unsorted)) % 0.37/0.58 (define @t2 () (@var "B" $$unsorted)) % 0.37/0.58 (define @t3 () (tptp.relation_type @t2 @t1)) % 0.37/0.58 (define @t4 () (tptp.cross_product @t2 @t1)) % 0.37/0.58 (define @t5 () (tptp.ilf_type @t4 @t3)) % 0.37/0.58 (define @t6 () (tptp.ilf_type @t1 tptp.set_type)) % 0.37/0.58 (define @t7 () (@list @t1)) % 0.37/0.58 (define @t8 () (forall @t7 (=> @t6 @t5))) % 0.37/0.58 (define @t9 () (tptp.ilf_type @t2 tptp.set_type)) % 0.37/0.58 (define @t10 () (=> @t9 @t8)) % 0.37/0.58 (define @t11 () (@list @t2)) % 0.37/0.58 (define @t12 () (forall @t11 @t10)) % 0.37/0.58 (define @t13 () (@var "F" $$unsorted)) % 0.37/0.58 (define @t14 () (@var "E" $$unsorted)) % 0.37/0.58 (define @t15 () (@var "D" $$unsorted)) % 0.37/0.58 (define @t16 () (tptp.ilf_type @t14 tptp.set_type)) % 0.37/0.58 (define @t17 () (@list @t14)) % 0.37/0.58 (define @t18 () (tptp.ilf_type @t15 tptp.set_type)) % 0.37/0.58 (define @t19 () (@list @t15)) % 0.37/0.58 (define @t20 () (tptp.ilf_type @t4 tptp.set_type)) % 0.37/0.58 (define @t21 () (forall @t7 (=> @t6 @t20))) % 0.37/0.58 (define @t22 () (=> @t9 @t21)) % 0.37/0.58 (define @t23 () (forall @t11 @t22)) % 0.37/0.58 (define @t24 () (tptp.relation_type @t2 @t2)) % 0.37/0.58 (define @t25 () (tptp.identity_relation_of_type @t2)) % 0.37/0.58 (define @t26 () (tptp.ilf_type @t1 @t25)) % 0.37/0.58 (define @t27 () (= @t26 (tptp.ilf_type @t1 @t24))) % 0.37/0.58 (define @t28 () (forall @t7 (=> @t6 @t27))) % 0.37/0.58 (define @t29 () (=> @t9 @t28)) % 0.37/0.58 (define @t30 () (forall @t11 @t29)) % 0.37/0.58 (define @t31 () (tptp.subset_type @t4)) % 0.37/0.58 (define @t32 () (tptp.ilf_type @t15 @t31)) % 0.37/0.58 (define @t33 () (tptp.power_set @t2)) % 0.37/0.58 (define @t34 () (tptp.ilf_type @t1 (tptp.subset_type @t2))) % 0.37/0.58 (define @t35 () (tptp.empty @t2)) % 0.37/0.58 (define @t36 () (tptp.member @t1 @t2)) % 0.37/0.58 (define @t37 () (tptp.relation_like @t2)) % 0.37/0.58 (define @t38 () (tptp.ilf_type (tptp.cross_product @t2 @t2) @t25)) % 0.37/0.58 (define @t39 () (forall @t11 (=> @t9 @t38))) % 0.37/0.58 (define @t40 () (not @t39)) % 0.37/0.58 (define @t41 () (not @t9)) % 0.37/0.58 (define @t42 () (@quantifiers_skolemize (forall @t11 (or @t41 @t38)) 0)) % 0.37/0.58 (define @t43 () (tptp.ilf_type @t42 tptp.set_type)) % 0.37/0.58 (define @t44 () (tptp.cross_product @t42 @t42)) % 0.37/0.58 (define @t45 () (tptp.ilf_type @t44 (tptp.identity_relation_of_type @t42))) % 0.37/0.58 (define @t46 () (not @t43)) % 0.37/0.58 (define @t47 () (or @t46 @t45)) % 0.37/0.58 (define @t48 () (@list true)) % 0.37/0.58 (define @t49 () (@list @t47)) % 0.37/0.58 (define @t50 () (@var "BOUND_VARIABLE_7738" $$unsorted)) % 0.37/0.58 (define @t51 () (= (tptp.ilf_type @t50 @t25) (tptp.ilf_type @t50 @t24))) % 0.37/0.58 (define @t52 () (not (tptp.ilf_type @t50 tptp.set_type))) % 0.37/0.58 (define @t53 () (or @t52 @t51)) % 0.37/0.58 (define @t54 () (or @t41 @t53)) % 0.37/0.58 (define @t55 () (forall (@list @t2 @t50) @t54)) % 0.37/0.58 (define @t56 () (@list @t50)) % 0.37/0.58 (define @t57 () (forall @t56 @t54)) % 0.37/0.58 (define @t58 () (forall @t56 @t53)) % 0.37/0.58 (define @t59 () (@list @t1)) % 0.37/0.58 (define @t60 () (or @t41 @t58)) % 0.37/0.58 (define @t61 () (not @t6)) % 0.37/0.58 (define @t62 () (forall @t7 (or @t61 @t27))) % 0.37/0.58 (define @t63 () (@var "BOUND_VARIABLE_7719" $$unsorted)) % 0.37/0.58 (define @t64 () (tptp.ilf_type (tptp.cross_product @t2 @t63) tptp.set_type)) % 0.37/0.58 (define @t65 () (not (tptp.ilf_type @t63 tptp.set_type))) % 0.37/0.58 (define @t66 () (or @t65 @t64)) % 0.37/0.58 (define @t67 () (or @t41 @t66)) % 0.37/0.58 (define @t68 () (forall (@list @t2 @t63) @t67)) % 0.37/0.58 (define @t69 () (@list @t63)) % 0.37/0.58 (define @t70 () (forall @t69 @t67)) % 0.37/0.58 (define @t71 () (forall @t69 @t66)) % 0.37/0.58 (define @t72 () (or @t41 @t71)) % 0.37/0.58 (define @t73 () (forall @t7 (or @t61 @t20))) % 0.37/0.58 (define @t74 () (@list @t42 @t42)) % 0.37/0.58 (define @t75 () (tptp.ilf_type @t44 tptp.set_type)) % 0.37/0.58 (define @t76 () (or @t46 @t46 @t75)) % 0.37/0.58 (define @t77 () (@list false false)) % 0.37/0.58 (define @t78 () (@var "BOUND_VARIABLE_7599" $$unsorted)) % 0.37/0.58 (define @t79 () (tptp.ilf_type (tptp.cross_product @t2 @t78) (tptp.relation_type @t2 @t78))) % 0.37/0.58 (define @t80 () (not (tptp.ilf_type @t78 tptp.set_type))) % 0.37/0.58 (define @t81 () (or @t80 @t79)) % 0.37/0.58 (define @t82 () (or @t41 @t81)) % 0.37/0.58 (define @t83 () (forall (@list @t2 @t78) @t82)) % 0.37/0.58 (define @t84 () (@list @t78)) % 0.37/0.58 (define @t85 () (forall @t84 @t82)) % 0.37/0.58 (define @t86 () (forall @t84 @t81)) % 0.37/0.58 (define @t87 () (or @t41 @t86)) % 0.37/0.58 (define @t88 () (forall @t7 (or @t61 @t5))) % 0.37/0.58 (define @t89 () (tptp.ilf_type @t44 (tptp.relation_type @t42 @t42))) % 0.37/0.58 (define @t90 () (or @t46 @t46 @t89)) % 0.37/0.58 (define @t91 () (= @t45 @t89)) % 0.37/0.58 (define @t92 () (not @t91)) % 0.37/0.58 (define @t93 () (not @t75)) % 0.37/0.58 (define @t94 () (or @t46 @t93 @t91)) % 0.37/0.58 (assume @p1 @t12) % 0.37/0.58 (assume @p2 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (forall @t19 (=> @t18 (= (tptp.member @t15 @t4) (exists @t17 (and @t16 (exists (@list @t13) (and (tptp.ilf_type @t13 tptp.set_type) (tptp.member @t14 @t2) (tptp.member @t13 @t1) (= @t15 (tptp.ordered_pair @t14 @t13)))))))))))))) % 0.37/0.58 (assume @p3 @t23) % 0.37/0.58 (assume @p4 @t30) % 0.37/0.58 (assume @p5 (forall @t11 (=> @t9 (exists @t7 @t26)))) % 0.37/0.58 (assume @p6 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (tptp.ilf_type (tptp.ordered_pair @t2 @t1) tptp.set_type)))))) % 0.37/0.58 (assume @p7 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (and (forall @t19 (=> @t32 (tptp.ilf_type @t15 @t3))) (forall @t17 (=> (tptp.ilf_type @t14 @t3) (tptp.ilf_type @t14 @t31))))))))) % 0.37/0.58 (assume @p8 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (exists @t19 (tptp.ilf_type @t15 (tptp.relation_type @t1 @t2)))))))) % 0.37/0.58 (assume @p9 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (= @t34 (tptp.ilf_type @t1 (tptp.member_type @t33)))))))) % 0.37/0.58 (assume @p10 (forall @t11 (=> @t9 (exists @t7 @t34)))) % 0.37/0.58 (assume @p11 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (= (tptp.member @t2 (tptp.power_set @t1)) (forall @t19 (=> @t18 (=> (tptp.member @t15 @t2) (tptp.member @t15 @t1)))))))))) % 0.37/0.58 (assume @p12 (forall @t11 (=> @t9 (and (not (tptp.empty @t33)) (tptp.ilf_type @t33 tptp.set_type))))) % 0.37/0.58 (assume @p13 (forall @t11 (=> @t9 (forall @t7 (=> (and (not (tptp.empty @t1)) @t6) (= (tptp.ilf_type @t2 (tptp.member_type @t1)) (tptp.member @t2 @t1))))))) % 0.37/0.58 (assume @p14 (forall @t11 (=> (and (not @t35) @t9) (exists @t7 (tptp.ilf_type @t1 (tptp.member_type @t2)))))) % 0.37/0.58 (assume @p15 (forall @t11 (=> @t9 (= @t35 (forall @t7 (=> @t6 (not @t36))))))) % 0.37/0.58 (assume @p16 (forall @t11 (=> @t9 (= @t37 (forall @t7 (=> @t6 (=> @t36 (exists @t19 (and @t18 (exists @t17 (and @t16 (= @t1 (tptp.ordered_pair @t15 @t14))))))))))))) % 0.37/0.58 (assume @p17 (forall @t11 (=> (and @t35 @t9) @t37))) % 0.37/0.58 (assume @p18 (forall @t11 (=> @t9 (forall @t7 (=> @t6 (forall @t19 (=> @t32 (tptp.relation_like @t15)))))))) % 0.37/0.58 (assume @p19 (forall @t11 @t9)) % 0.37/0.58 (assume @p20 @t40) % 0.37/0.58 (assume @p21 true) % 0.37/0.58 (step @p22 :rule bool-impl-elim :args (@t9 @t38)) % 0.37/0.58 (step @p23 :rule cong :premises (@p22) :args (@t39)) % 0.37/0.58 (step @p24 :rule cong :premises (@p23) :args (@t40)) % 0.37/0.58 (step @p25 :rule eq_resolve :premises (@p20 @p24)) % 0.37/0.58 (step @p26 :rule skolemize :premises (@p25)) % 0.37/0.58 (step @p27 :rule bool-double-not-elim :args (@t43)) % 0.37/0.58 (step @p28 :rule refl :args (@t47)) % 0.37/0.58 (step @p29 :rule nary_cong :premises (@p28 @p27) :args ((or @t47 (not @t46)))) % 0.37/0.58 (step @p30 :rule cnf_or_neg :args (@t47 0)) % 0.37/0.58 (step @p31 :rule eq_resolve :premises (@p30 @p29)) % 0.37/0.58 (step @p32 :rule reordering :premises (@p31) :args ((or @t43 @t47))) % 0.37/0.58 (step @p33 :rule chain_m_resolution :premises (@p32 @p26) :args (@t43 @t48 @t49)) % 0.37/0.58 (step @p34 :rule aci_norm :args ((= @t54 (or @t41 @t52 @t51)))) % 0.37/0.58 (step @p35 :rule cong :premises (@p34) :args (@t55)) % 0.37/0.58 (step @p36 :rule quant-merge-prenex :args ((= (forall @t11 @t57) @t55))) % 0.37/0.58 (step @p37 :rule alpha_equiv :args (@t58 (@list @t50) @t59)) % 0.37/0.58 (step @p38 :rule refl :args (@t41)) % 0.37/0.58 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t60)) % 0.37/0.58 (step @p40 :rule quant-miniscope-or :args ((= @t57 @t60))) % 0.37/0.58 (step @p41 :rule trans :premises (@p40 @p39)) % 0.37/0.58 (step @p42 :rule symm :premises (@p41)) % 0.37/0.58 (step @p43 :rule cong :premises (@p42) :args ((forall @t11 (or @t41 @t62)))) % 0.37/0.58 (step @p44 :rule trans :premises (@p43 @p36)) % 0.37/0.58 (step @p45 :rule trans :premises (@p44 @p35)) % 0.37/0.58 (step @p46 :rule bool-impl-elim :args (@t9 @t62)) % 0.37/0.58 (step @p47 :rule cong :premises (@p46) :args ((forall @t11 (=> @t9 @t62)))) % 0.37/0.58 (step @p48 :rule trans :premises (@p47 @p45)) % 0.37/0.58 (step @p49 :rule bool-impl-elim :args (@t6 @t27)) % 0.37/0.58 (step @p50 :rule cong :premises (@p49) :args (@t28)) % 0.37/0.58 (step @p51 :rule refl :args (@t9)) % 0.37/0.58 (step @p52 :rule cong :premises (@p51 @p50) :args (@t29)) % 0.37/0.58 (step @p53 :rule cong :premises (@p52) :args (@t30)) % 0.37/0.58 (step @p54 :rule trans :premises (@p53 @p48)) % 0.37/0.58 (step @p55 :rule eq_resolve :premises (@p4 @p54)) % 0.37/0.58 (step @p56 :rule instantiate :premises (@p55) :args ((@list @t42 @t44))) % 0.37/0.58 (step @p57 :rule aci_norm :args ((= @t67 (or @t41 @t65 @t64)))) % 0.37/0.58 (step @p58 :rule cong :premises (@p57) :args (@t68)) % 0.37/0.58 (step @p59 :rule quant-merge-prenex :args ((= (forall @t11 @t70) @t68))) % 0.37/0.58 (step @p60 :rule alpha_equiv :args (@t71 (@list @t63) @t59)) % 0.37/0.58 (step @p61 :rule nary_cong :premises (@p38 @p60) :args (@t72)) % 0.37/0.58 (step @p62 :rule quant-miniscope-or :args ((= @t70 @t72))) % 0.37/0.58 (step @p63 :rule trans :premises (@p62 @p61)) % 0.37/0.58 (step @p64 :rule symm :premises (@p63)) % 0.37/0.58 (step @p65 :rule cong :premises (@p64) :args ((forall @t11 (or @t41 @t73)))) % 0.37/0.58 (step @p66 :rule trans :premises (@p65 @p59)) % 0.37/0.58 (step @p67 :rule trans :premises (@p66 @p58)) % 0.37/0.58 (step @p68 :rule bool-impl-elim :args (@t9 @t73)) % 0.37/0.58 (step @p69 :rule cong :premises (@p68) :args ((forall @t11 (=> @t9 @t73)))) % 0.37/0.58 (step @p70 :rule trans :premises (@p69 @p67)) % 0.37/0.58 (step @p71 :rule bool-impl-elim :args (@t6 @t20)) % 0.37/0.58 (step @p72 :rule cong :premises (@p71) :args (@t21)) % 0.37/0.58 (step @p73 :rule cong :premises (@p51 @p72) :args (@t22)) % 0.37/0.58 (step @p74 :rule cong :premises (@p73) :args (@t23)) % 0.37/0.58 (step @p75 :rule trans :premises (@p74 @p70)) % 0.37/0.58 (step @p76 :rule eq_resolve :premises (@p3 @p75)) % 0.37/0.58 (step @p77 :rule instantiate :premises (@p76) :args (@t74)) % 0.37/0.58 (step @p78 :rule cnf_or_pos :args (@t76)) % 0.37/0.58 (step @p79 :rule factoring :premises (@p78)) % 0.37/0.58 (step @p80 :rule reordering :premises (@p79) :args ((or @t46 @t75 (not @t76)))) % 0.37/0.58 (step @p81 :rule chain_m_resolution :premises (@p80 @p33 @p77) :args (@t75 @t77 (@list @t43 @t76))) % 0.37/0.58 (step @p82 :rule aci_norm :args ((= @t82 (or @t41 @t80 @t79)))) % 0.37/0.58 (step @p83 :rule cong :premises (@p82) :args (@t83)) % 0.37/0.58 (step @p84 :rule quant-merge-prenex :args ((= (forall @t11 @t85) @t83))) % 0.37/0.58 (step @p85 :rule alpha_equiv :args (@t86 (@list @t78) @t59)) % 0.37/0.58 (step @p86 :rule nary_cong :premises (@p38 @p85) :args (@t87)) % 0.37/0.58 (step @p87 :rule quant-miniscope-or :args ((= @t85 @t87))) % 0.37/0.58 (step @p88 :rule trans :premises (@p87 @p86)) % 0.37/0.58 (step @p89 :rule symm :premises (@p88)) % 0.37/0.58 (step @p90 :rule cong :premises (@p89) :args ((forall @t11 (or @t41 @t88)))) % 0.37/0.58 (step @p91 :rule trans :premises (@p90 @p84)) % 0.37/0.58 (step @p92 :rule trans :premises (@p91 @p83)) % 0.37/0.58 (step @p93 :rule bool-impl-elim :args (@t9 @t88)) % 0.37/0.58 (step @p94 :rule cong :premises (@p93) :args ((forall @t11 (=> @t9 @t88)))) % 0.37/0.58 (step @p95 :rule trans :premises (@p94 @p92)) % 0.37/0.58 (step @p96 :rule bool-impl-elim :args (@t6 @t5)) % 0.37/0.58 (step @p97 :rule cong :premises (@p96) :args (@t8)) % 0.37/0.58 (step @p98 :rule cong :premises (@p51 @p97) :args (@t10)) % 0.37/0.58 (step @p99 :rule cong :premises (@p98) :args (@t12)) % 0.37/0.58 (step @p100 :rule trans :premises (@p99 @p95)) % 0.37/0.58 (step @p101 :rule eq_resolve :premises (@p1 @p100)) % 0.37/0.58 (step @p102 :rule instantiate :premises (@p101) :args (@t74)) % 0.37/0.58 (step @p103 :rule cnf_or_pos :args (@t90)) % 0.37/0.58 (step @p104 :rule factoring :premises (@p103)) % 0.37/0.58 (step @p105 :rule reordering :premises (@p104) :args ((or @t46 @t89 (not @t90)))) % 0.37/0.58 (step @p106 :rule chain_m_resolution :premises (@p105 @p33 @p102) :args (@t89 @t77 (@list @t43 @t90))) % 0.37/0.58 (step @p107 :rule cnf_or_neg :args (@t47 1)) % 0.37/0.58 (step @p108 :rule chain_m_resolution :premises (@p107 @p26) :args ((not @t45) @t48 @t49)) % 0.37/0.58 (step @p109 :rule cnf_equiv_pos2 :args (@t91)) % 0.37/0.58 (step @p110 :rule reordering :premises (@p109) :args ((or @t45 (not @t89) @t92))) % 0.37/0.58 (step @p111 :rule chain_m_resolution :premises (@p110 @p108 @p106) :args (@t92 (@list true false) (@list @t45 @t89))) % 0.37/0.58 (step @p112 :rule cnf_or_pos :args (@t94)) % 0.37/0.58 (step @p113 :rule reordering :premises (@p112) :args ((or @t46 @t93 @t91 (not @t94)))) % 0.37/0.58 (step @p114 false :rule chain_m_resolution :premises (@p113 @p111 @p81 @p56 @p33) :args (false (@list true false false false) (@list @t91 @t75 @t94 @t43))) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------