%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU019+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n029.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 05:10:30 PM UTC 2026
% Result : Theorem 1.80s 1.88s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 107 ( 29 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 127 ( 49 ~; 58 |; 14 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 38 ( 3 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t34_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(d8_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(t52_funct_1,conjecture,
! [X1] : one_to_one(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
fof(c_0_5,plain,
! [X82,X83,X84] :
( ( relation_dom(X83) = X82
| X83 != identity_relation(X82)
| ~ relation(X83)
| ~ function(X83) )
& ( ~ in(X84,X82)
| apply(X83,X84) = X84
| X83 != identity_relation(X82)
| ~ relation(X83)
| ~ function(X83) )
& ( in(esk12_2(X82,X83),X82)
| relation_dom(X83) != X82
| X83 = identity_relation(X82)
| ~ relation(X83)
| ~ function(X83) )
& ( apply(X83,esk12_2(X82,X83)) != esk12_2(X82,X83)
| relation_dom(X83) != X82
| X83 = identity_relation(X82)
| ~ relation(X83)
| ~ function(X83) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
fof(c_0_6,plain,
! [X60] : relation(identity_relation(X60)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_7,plain,
! [X64] :
( relation(identity_relation(X64))
& function(identity_relation(X64)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(c_0_8,plain,
! [X55,X56,X57] :
( ( ~ one_to_one(X55)
| ~ in(X56,relation_dom(X55))
| ~ in(X57,relation_dom(X55))
| apply(X55,X56) != apply(X55,X57)
| X56 = X57
| ~ relation(X55)
| ~ function(X55) )
& ( in(esk1_1(X55),relation_dom(X55))
| one_to_one(X55)
| ~ relation(X55)
| ~ function(X55) )
& ( in(esk2_1(X55),relation_dom(X55))
| one_to_one(X55)
| ~ relation(X55)
| ~ function(X55) )
& ( apply(X55,esk1_1(X55)) = apply(X55,esk2_1(X55))
| one_to_one(X55)
| ~ relation(X55)
| ~ function(X55) )
& ( esk1_1(X55) != esk2_1(X55)
| one_to_one(X55)
| ~ relation(X55)
| ~ function(X55) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).
cnf(c_0_9,plain,
( relation_dom(X1) = X2
| X1 != identity_relation(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( apply(X3,X1) = X1
| ~ in(X1,X2)
| X3 != identity_relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
( apply(X1,esk1_1(X1)) = apply(X1,esk2_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( in(esk2_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
relation_dom(identity_relation(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_9]),c_0_10]),c_0_11])]) ).
cnf(c_0_16,plain,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_10]),c_0_11])]) ).
cnf(c_0_17,plain,
( apply(identity_relation(X1),esk2_1(identity_relation(X1))) = apply(identity_relation(X1),esk1_1(identity_relation(X1)))
| one_to_one(identity_relation(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_10]),c_0_11])]) ).
cnf(c_0_18,plain,
( one_to_one(identity_relation(X1))
| in(esk2_1(identity_relation(X1)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_15]),c_0_11])]) ).
cnf(c_0_19,plain,
( in(esk1_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] : one_to_one(identity_relation(X1)),
inference(assume_negation,[status(cth)],[t52_funct_1]) ).
cnf(c_0_21,plain,
( apply(identity_relation(X1),esk1_1(identity_relation(X1))) = esk2_1(identity_relation(X1))
| one_to_one(identity_relation(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_22,plain,
( one_to_one(identity_relation(X1))
| in(esk1_1(identity_relation(X1)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_10]),c_0_15]),c_0_11])]) ).
fof(c_0_23,negated_conjecture,
~ one_to_one(identity_relation(esk13_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_24,plain,
( one_to_one(X1)
| esk1_1(X1) != esk2_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,plain,
( esk2_1(identity_relation(X1)) = esk1_1(identity_relation(X1))
| one_to_one(identity_relation(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_21]),c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ one_to_one(identity_relation(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
one_to_one(identity_relation(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_10]),c_0_11])]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU019+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:41:59 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.80/1.88 % Version : CSE_E---1.7
% 1.80/1.88 % Problem : theBenchmark.p
% 1.80/1.88 % SZS status Theorem for theBenchmark.p
% 1.80/1.88 % SZS output start CNFRefutation
% See solution above
% 1.80/1.89 % Total time : 1.369s
%------------------------------------------------------------------------------