%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ITP005+5 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %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 : Tue May 5 04:31:26 PM UTC 2026
% Result : Theorem 10.00s 7.01s
% Output : CNFRefutation 10.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 9 unt; 0 def)
% Number of atoms : 54 ( 15 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 54 ( 21 ~; 16 |; 3 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 30 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_thm_2Eset__relation_2Erel__to__reln__inv,conjecture,
! [X9] :
( ne(X9)
=> ! [X11] :
( ne(X11)
=> ! [X178] :
( mem(X178,arr(X9,arr(X11,bool)))
=> ap(c_2Eset__relation_2Ereln__to__rel(X9,X11),ap(c_2Eset__relation_2Erel__to__reln(X9,X11),X178)) = X178 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eset__relation_2Erel__to__reln__inv) ).
fof(conj_thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY,axiom,
! [X9] :
( ne(X9)
=> ! [X11] :
( ne(X11)
=> c_2Eset__relation_2Erel__to__reln(X9,X11) = c_2Epair_2EUNCURRY(X9,X11,bool) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY) ).
fof(conj_thm_2Eset__relation_2Ereln__to__rel__IS__CURRY,axiom,
! [X9] :
( ne(X9)
=> ! [X11] :
( ne(X11)
=> c_2Eset__relation_2Ereln__to__rel(X9,X11) = c_2Epair_2ECURRY(X9,X11,bool) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eset__relation_2Ereln__to__rel__IS__CURRY) ).
fof(conj_thm_2Epair_2ECURRY__UNCURRY__THM,axiom,
! [X9] :
( ne(X9)
=> ! [X11] :
( ne(X11)
=> ! [X59] :
( ne(X59)
=> ! [X19] :
( mem(X19,arr(X9,arr(X11,X59)))
=> ap(c_2Epair_2ECURRY(X9,X11,X59),ap(c_2Epair_2EUNCURRY(X9,X11,X59),X19)) = X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP014+5.ax',conj_thm_2Epair_2ECURRY__UNCURRY__THM) ).
fof(bool_ne,axiom,
ne(bool),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',bool_ne) ).
fof(c_0_5,negated_conjecture,
~ ! [X9] :
( ne(X9)
=> ! [X11] :
( ne(X11)
=> ! [X178] :
( mem(X178,arr(X9,arr(X11,bool)))
=> ap(c_2Eset__relation_2Ereln__to__rel(X9,X11),ap(c_2Eset__relation_2Erel__to__reln(X9,X11),X178)) = X178 ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Eset__relation_2Erel__to__reln__inv]) ).
fof(c_0_6,negated_conjecture,
( ne(esk1_0)
& ne(esk2_0)
& mem(esk3_0,arr(esk1_0,arr(esk2_0,bool)))
& ap(c_2Eset__relation_2Ereln__to__rel(esk1_0,esk2_0),ap(c_2Eset__relation_2Erel__to__reln(esk1_0,esk2_0),esk3_0)) != esk3_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_7,plain,
! [X2258,X2259] :
( ~ ne(X2258)
| ~ ne(X2259)
| c_2Eset__relation_2Erel__to__reln(X2258,X2259) = c_2Epair_2EUNCURRY(X2258,X2259,bool) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY])])]) ).
cnf(c_0_8,negated_conjecture,
ap(c_2Eset__relation_2Ereln__to__rel(esk1_0,esk2_0),ap(c_2Eset__relation_2Erel__to__reln(esk1_0,esk2_0),esk3_0)) != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( c_2Eset__relation_2Erel__to__reln(X1,X2) = c_2Epair_2EUNCURRY(X1,X2,bool)
| ~ ne(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
ne(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
ne(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,plain,
! [X2267,X2268] :
( ~ ne(X2267)
| ~ ne(X2268)
| c_2Eset__relation_2Ereln__to__rel(X2267,X2268) = c_2Epair_2ECURRY(X2267,X2268,bool) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Eset__relation_2Ereln__to__rel__IS__CURRY])])]) ).
cnf(c_0_13,negated_conjecture,
ap(c_2Eset__relation_2Ereln__to__rel(esk1_0,esk2_0),ap(c_2Epair_2EUNCURRY(esk1_0,esk2_0,bool),esk3_0)) != esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11])]) ).
cnf(c_0_14,plain,
( c_2Eset__relation_2Ereln__to__rel(X1,X2) = c_2Epair_2ECURRY(X1,X2,bool)
| ~ ne(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X2931,X2932,X2933,X2934] :
( ~ ne(X2931)
| ~ ne(X2932)
| ~ ne(X2933)
| ~ mem(X2934,arr(X2931,arr(X2932,X2933)))
| ap(c_2Epair_2ECURRY(X2931,X2932,X2933),ap(c_2Epair_2EUNCURRY(X2931,X2932,X2933),X2934)) = X2934 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Epair_2ECURRY__UNCURRY__THM])])]) ).
cnf(c_0_16,negated_conjecture,
ap(c_2Epair_2ECURRY(esk1_0,esk2_0,bool),ap(c_2Epair_2EUNCURRY(esk1_0,esk2_0,bool),esk3_0)) != esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_10]),c_0_11])]) ).
cnf(c_0_17,plain,
( ap(c_2Epair_2ECURRY(X1,X2,X3),ap(c_2Epair_2EUNCURRY(X1,X2,X3),X4)) = X4
| ~ ne(X1)
| ~ ne(X2)
| ~ ne(X3)
| ~ mem(X4,arr(X1,arr(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
mem(esk3_0,arr(esk1_0,arr(esk2_0,bool))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,plain,
ne(bool),
inference(split_conjunct,[status(thm)],[bool_ne]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_10]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP005+5 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n028.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 19:36:46 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 10.00/7.01 % Version : CSE_E---1.7
% 10.00/7.01 % Problem : theBenchmark.p
% 10.00/7.01 % SZS status Theorem for theBenchmark.p
% 10.00/7.01 % SZS output start CNFRefutation
% See solution above
% 10.13/7.04 % Total time : 5.393s
%------------------------------------------------------------------------------