%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n028.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 01:53:30 EDT 2023

% Result   : Theorem 0.22s 0.70s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem    : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.16  % Command    : do_cvc5 %s %d
% 0.16/0.37  % Computer : n028.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Mon Aug 28 02:49:39 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.22/0.53  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.70  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.5Qr7ihefre/cvc5---1.0.5_22935.p...
% 0.22/0.70  ------- get file name : TPTP file name is HAL003+3
% 0.22/0.70  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22935.smt2...
% 0.22/0.70  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.70  % SZS status Theorem for HAL003+3
% 0.22/0.70  % SZS output start Proof for HAL003+3
% 0.22/0.70  (
% 0.22/0.70  (let ((_let_1 (tptp.surjection tptp.g))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((E $$unsorted)) (=> (tptp.element E tptp.e) (exists ((B1 $$unsorted) (B2 $$unsorted)) (and (tptp.element B1 tptp.b) (tptp.element B2 tptp.b) (= (tptp.apply tptp.g (tptp.subtract tptp.b B1 B2)) E))))))) (let ((_let_4 (tptp.morphism tptp.g tptp.b tptp.e))) (let ((_let_5 (forall ((Dom $$unsorted) (El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom)) (tptp.element (tptp.subtract Dom El1 El2) Dom))))) (let ((_let_6 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.morphism Morphism Dom Cod) (forall ((ElCod $$unsorted)) (=> (tptp.element ElCod Cod) (exists ((ElDom $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism ElDom) ElCod)))))) (tptp.surjection Morphism))))) (let ((_let_7 (tptp.subtract tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_8 (tptp.apply tptp.g _let_7))) (let ((_let_9 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_8))) (let ((_let_10 (not _let_9))) (let ((_let_11 (tptp.element _let_7 tptp.b))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_10))) (let ((_let_14 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 tptp.b))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 tptp.b))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_15 _let_10))) (let ((_let_19 (forall ((B1 $$unsorted) (B2 $$unsorted)) (or (not (tptp.element B1 tptp.b)) (not (tptp.element B2 tptp.b)) (not (= (tptp.apply tptp.g (tptp.subtract tptp.b B1 B2)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (not _let_19))) (let ((_let_22 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.e))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21))) (let ((_let_25 (forall ((E $$unsorted)) (or (not (tptp.element E tptp.e)) (not (forall ((B1 $$unsorted) (B2 $$unsorted)) (or (not (tptp.element B1 tptp.b)) (not (tptp.element B2 tptp.b)) (not (= E (tptp.apply tptp.g (tptp.subtract tptp.b B1 B2))))))))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom tptp.b)) (not (= (tptp.apply tptp.g ElDom) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_23 _let_28))) (let ((_let_30 (forall ((ElCod $$unsorted)) (or (not (tptp.element ElCod tptp.e)) (not (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom tptp.b)) (not (= ElCod (tptp.apply tptp.g ElDom)))))))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (not _let_30))) (let ((_let_33 (not _let_4))) (let ((_let_34 (or _let_33 _let_32 _let_1))) (let ((_let_35 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (or (not (tptp.morphism Morphism Dom Cod)) (not (forall ((ElCod $$unsorted)) (or (not (tptp.element ElCod Cod)) (not (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom Dom)) (not (= ElCod (tptp.apply Morphism ElDom))))))))) (tptp.surjection Morphism))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (or))) (let ((_let_38 (_let_32))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_38)) :args _let_38) (REWRITE :args ((=> _let_32 (not (or _let_23 (not (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom tptp.b)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.apply tptp.g ElDom))))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_30))) (REFL :args (_let_31)) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_1 _let_33 _let_32 (not _let_34)))) (ASSUME :args (_let_2)) (ASSUME :args (_let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.g tptp.b tptp.e QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.morphism Morphism Dom Cod) false))))) :args (_let_35))) _let_36 :args (_let_34 false _let_35)) :args (_let_32 true _let_1 false _let_4 false _let_34)) :args (_let_31 true _let_30)))) (let ((_let_40 (REFL :args (_let_29)))) (let ((_let_41 (_let_21))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_41)) :args _let_41) (REWRITE :args ((=> _let_21 (not (or _let_17 _let_15 (not (= _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_19))) (REFL :args (_let_20)) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_21 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_37)) :args ((or _let_22 _let_29))) _let_39 :args (_let_22 true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.element E tptp.e) false))))) :args (_let_25)))) _let_26 :args (_let_24 false _let_25)) :args (_let_21 false _let_22 false _let_24)) :args (_let_20 true _let_19)))) (let ((_let_43 (REFL :args (_let_18)))) (let ((_let_44 (_let_27))) (let ((_let_45 (or _let_17 _let_15 _let_11))) (let ((_let_46 (forall ((Dom $$unsorted) (El1 $$unsorted) (El2 $$unsorted)) (or (not (tptp.element El1 Dom)) (not (tptp.element El2 Dom)) (tptp.element (tptp.subtract Dom El1 El2) Dom))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_13)) :args ((or _let_10 _let_12 (not _let_13)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_17 _let_15 _let_11 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 0)) (CONG _let_43 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_37)) :args ((or _let_16 _let_18))) _let_42 :args (_let_16 true _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 1)) (CONG _let_43 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_37)) :args ((or _let_14 _let_18))) _let_42 :args (_let_14 true _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subtract Dom El1 El2)))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_11 false _let_16 false _let_14 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_44) :args (_let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.apply tptp.g ElDom)))) :args _let_44))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_37)) :args ((or _let_27 _let_29))) _let_39 :args (_let_27 true _let_29)) :args (_let_13 false _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 2)) (CONG _let_43 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_37)) :args ((or _let_9 _let_18))) _let_42 :args (_let_9 true _let_18)) :args (false false _let_11 false _let_13 false _let_9)) :args ((forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (tptp.morphism Morphism Dom Cod) (and (forall ((El $$unsorted)) (=> (tptp.element El Dom) (tptp.element (tptp.apply Morphism El) Cod))) (= (tptp.apply Morphism (tptp.zero Dom)) (tptp.zero Cod))))) (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.injection Morphism) (tptp.morphism Morphism Dom Cod)) (forall ((El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom) (= (tptp.apply Morphism El1) (tptp.apply Morphism El2))) (= El1 El2))))) (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.morphism Morphism Dom Cod) (forall ((El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom) (= (tptp.apply Morphism El1) (tptp.apply Morphism El2))) (= El1 El2)))) (tptp.injection Morphism))) (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.surjection Morphism) (tptp.morphism Morphism Dom Cod)) (forall ((ElCod $$unsorted)) (=> (tptp.element ElCod Cod) (exists ((ElDom $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism ElDom) ElCod))))))) _let_6 (forall ((Morphism1 $$unsorted) (Morphism2 $$unsorted) (Dom $$unsorted) (CodDom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.exact Morphism1 Morphism2) (tptp.morphism Morphism1 Dom CodDom) (tptp.morphism Morphism2 CodDom Cod)) (forall ((ElCodDom $$unsorted)) (= (and (tptp.element ElCodDom CodDom) (= (tptp.apply Morphism2 ElCodDom) (tptp.zero Cod))) (exists ((ElDom $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism1 ElDom) ElCodDom))))))) (forall ((Morphism1 $$unsorted) (Morphism2 $$unsorted) (Dom $$unsorted) (CodDom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.morphism Morphism1 Dom CodDom) (tptp.morphism Morphism2 CodDom Cod) (forall ((ElCodDom $$unsorted)) (= (and (tptp.element ElCodDom CodDom) (= (tptp.apply Morphism2 ElCodDom) (tptp.zero Cod))) (exists ((ElDom $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism1 ElDom) ElCodDom)))))) (tptp.exact Morphism1 Morphism2))) (forall ((M1 $$unsorted) (M2 $$unsorted) (M3 $$unsorted) (M4 $$unsorted) (Dom $$unsorted) (DomCod1 $$unsorted) (DomCod2 $$unsorted) (Cod $$unsorted)) (=> (and (tptp.commute M1 M2 M3 M4) (tptp.morphism M1 Dom DomCod1) (tptp.morphism M2 DomCod1 Cod) (tptp.morphism M3 Dom DomCod2) (tptp.morphism M4 DomCod2 Cod)) (forall ((ElDom $$unsorted)) (=> (tptp.element ElDom Dom) (= (tptp.apply M2 (tptp.apply M1 ElDom)) (tptp.apply M4 (tptp.apply M3 ElDom))))))) (forall ((M1 $$unsorted) (M2 $$unsorted) (M3 $$unsorted) (M4 $$unsorted) (Dom $$unsorted) (DomCod1 $$unsorted) (DomCod2 $$unsorted) (Cod $$unsorted)) (=> (and (tptp.morphism M1 Dom DomCod1) (tptp.morphism M2 DomCod1 Cod) (tptp.morphism M3 Dom DomCod2) (tptp.morphism M4 DomCod2 Cod) (forall ((ElDom $$unsorted)) (=> (tptp.element ElDom Dom) (= (tptp.apply M2 (tptp.apply M1 ElDom)) (tptp.apply M4 (tptp.apply M3 ElDom)))))) (tptp.commute M1 M2 M3 M4))) _let_5 (forall ((Dom $$unsorted) (El $$unsorted)) (=> (tptp.element El Dom) (= (tptp.subtract Dom El El) (tptp.zero Dom)))) (forall ((Dom $$unsorted) (El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom)) (= (tptp.subtract Dom El1 (tptp.subtract Dom El1 El2)) El2))) (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (tptp.morphism Morphism Dom Cod) (forall ((El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom)) (= (tptp.apply Morphism (tptp.subtract Dom El1 El2)) (tptp.subtract Cod (tptp.apply Morphism El1) (tptp.apply Morphism El2))))))) (tptp.morphism tptp.alpha tptp.a tptp.b) (tptp.morphism tptp.beta tptp.b tptp.c) (tptp.morphism tptp.gamma tptp.d tptp.e) (tptp.morphism tptp.delta tptp.e tptp.r) (tptp.morphism tptp.f tptp.a tptp.d) _let_4 (tptp.morphism tptp.h tptp.c tptp.r) (tptp.injection tptp.alpha) (tptp.injection tptp.gamma) (tptp.surjection tptp.beta) (tptp.surjection tptp.delta) (tptp.exact tptp.alpha tptp.beta) (tptp.exact tptp.gammma tptp.delta) (tptp.commute tptp.alpha tptp.g tptp.f tptp.gamma) (tptp.commute tptp.beta tptp.h tptp.g tptp.delta) (tptp.surjection tptp.f) (tptp.surjection tptp.h) (forall ((E $$unsorted)) (=> (tptp.element E tptp.e) (exists ((R $$unsorted) (B1 $$unsorted)) (and (tptp.element R tptp.r) (= (tptp.apply tptp.delta E) R) (tptp.element B1 tptp.b) (= (tptp.apply tptp.h (tptp.apply tptp.beta B1)) R) (= (tptp.apply tptp.delta (tptp.apply tptp.g B1)) R))))) (forall ((E $$unsorted)) (=> (tptp.element E tptp.e) (exists ((B1 $$unsorted) (E1 $$unsorted) (A $$unsorted)) (and (tptp.element B1 tptp.b) (tptp.element E1 tptp.e) (= (tptp.subtract tptp.e (tptp.apply tptp.g B1) E) E1) (tptp.element A tptp.a) (= (tptp.apply tptp.gamma (tptp.apply tptp.f A)) E1) (= (tptp.apply tptp.g (tptp.apply tptp.alpha A)) E1))))) _let_3 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.70  )
% 0.22/0.70  % SZS output end Proof for HAL003+3
% 0.22/0.70  % cvc5---1.0.5 exiting
% 0.22/0.71  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------