%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU056+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n006.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 : Thu Aug 31 16:29:10 EDT 2023

% Result   : Theorem 0.17s 0.52s
% Output   : Proof 0.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SEU056+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12  % Command    : do_cvc5 %s %d
% 0.11/0.33  % Computer : n006.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Wed Aug 23 18:26:08 EDT 2023
% 0.11/0.33  % CPUTime    : 
% 0.17/0.46  %----Proving TF0_NAR, FOF, or CNF
% 0.17/0.52  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.XWqCLxRA4K/cvc5---1.0.5_21175.p...
% 0.17/0.52  ------- get file name : TPTP file name is SEU056+1
% 0.17/0.52  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_21175.smt2...
% 0.17/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.17/0.52  % SZS status Theorem for SEU056+1
% 0.17/0.52  % SZS output start Proof for SEU056+1
% 0.17/0.52  (
% 0.17/0.52  (let ((_let_1 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_image A tptp.empty_set) tptp.empty_set))))) (let ((_let_2 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (and (tptp.disjoint A B) (tptp.one_to_one C)) (tptp.disjoint (tptp.relation_image C A) (tptp.relation_image C B)))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.one_to_one C) (= (tptp.relation_image C (tptp.set_intersection2 A B)) (tptp.set_intersection2 (tptp.relation_image C A) (tptp.relation_image C B)))))))) (let ((_let_4 (tptp.relation tptp.empty_set))) (let ((_let_5 (tptp.empty tptp.empty_set))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))))) (let ((_let_7 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_8 (= tptp.empty_set _let_7))) (let ((_let_9 (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_10 (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_11 (tptp.set_intersection2 _let_10 _let_9))) (let ((_let_12 (= tptp.empty_set _let_11))) (let ((_let_13 (= tptp.empty_set (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 tptp.empty_set)))) (let ((_let_14 (= _let_11 (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_7)))) (let ((_let_15 (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_16 (= _let_15 _let_8))) (let ((_let_17 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= tptp.empty_set (tptp.set_intersection2 A B)))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (_let_17))) (let ((_let_20 ((tptp.disjoint A B)))) (let ((_let_21 (tptp.disjoint _let_10 _let_9))) (let ((_let_22 (tptp.one_to_one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_23 (not _let_22))) (let ((_let_24 (not _let_15))) (let ((_let_25 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26 _let_24 _let_23 _let_21))) (let ((_let_30 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation C)) (not (tptp.function C)) (not (tptp.disjoint A B)) (not (tptp.one_to_one C)) (tptp.disjoint (tptp.relation_image C A) (tptp.relation_image C B)))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (or))) (let ((_let_34 (not _let_30))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_32) :args (_let_34))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_30))) (REFL :args (_let_31)) :args _let_33)) _let_32 :args (_let_31 true _let_30)))) (let ((_let_36 (REFL :args (_let_29)))) (let ((_let_37 (= _let_21 _let_12))) (let ((_let_38 (not _let_12))) (let ((_let_39 (or _let_28 _let_13))) (let ((_let_40 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (= tptp.empty_set (tptp.relation_image A tptp.empty_set)))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_33)) :args ((or _let_27 _let_29))) _let_35 :args (_let_27 true _let_29)))) (let ((_let_43 (or _let_28 _let_26 _let_23 _let_14))) (let ((_let_44 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation C)) (not (tptp.function C)) (not (tptp.one_to_one C)) (= (tptp.relation_image C (tptp.set_intersection2 A B)) (tptp.set_intersection2 (tptp.relation_image C A) (tptp.relation_image C B))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (not _let_14))) (let ((_let_47 (not _let_13))) (let ((_let_48 (not _let_8))) (let ((_let_49 (_let_46))) (let ((_let_50 (ASSUME :args (_let_14)))) (let ((_let_51 (ASSUME :args (_let_38)))) (let ((_let_52 (ASSUME :args (_let_13)))) (let ((_let_53 (ASSUME :args (_let_8)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_52 _let_53 _let_51) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (SYMM _let_53) :args (APPLY_UF tptp.relation_image)) (SYMM _let_52)) (REFL :args (_let_11)) :args (=)) (FALSE_INTRO _let_51)) :args ((= _let_14 false)))) :args (_let_13 _let_8 _let_38))) _let_50) :args (_let_8 _let_13 _let_38 _let_14)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_49))) (TRUE_INTRO _let_50))) :args (_let_46 _let_14)) :args ((not (and _let_8 _let_13 _let_38 _let_14)) SB_LITERAL))) (CONG (REFL :args (_let_48)) (REFL :args (_let_47)) (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_12))) (REFL :args _let_49) :args _let_33)) :args ((or _let_12 _let_48 _let_47 _let_46))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_28 _let_26 _let_23 _let_14 (not _let_43)))) _let_42 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_33)) :args ((or _let_25 _let_29))) _let_35 :args (_let_25 true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 3)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_33)) :args ((or _let_22 _let_29))) _let_35 :args (_let_22 true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING ((tptp.relation_image C (tptp.set_intersection2 A B))))) :args (_let_44)))) _let_45 :args (_let_43 false _let_44)) :args (_let_14 false _let_27 false _let_25 false _let_22 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_28 _let_13 (not _let_39)))) _let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_13 false _let_27 false _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_37)) :args ((or _let_21 _let_38 (not _let_37)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 4)) _let_35 :args ((not _let_21) true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (_let_10 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_20)) :args _let_19)) _let_18 :args (_let_37 false _let_17)) :args (_let_38 true _let_21 false _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_16)) :args ((or _let_24 _let_8 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 2)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_15))) :args _let_33)) :args ((or _let_15 _let_29))) _let_35 :args (_let_15 true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_20)) :args _let_19)) _let_18 :args (_let_16 false _let_17)) :args (_let_8 false _let_15 false _let_16)) :args (false false _let_14 false _let_13 true _let_12 false _let_8)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) _let_6 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (and _let_5 _let_4 (tptp.relation_empty_yielding tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_intersection2 A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_5 (and _let_5 _let_4) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))) _let_3 _let_2 _let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.17/0.52  )
% 0.17/0.52  % SZS output end Proof for SEU056+1
% 0.17/0.52  % cvc5---1.0.5 exiting
% 0.17/0.52  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------