%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU075+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 : n008.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 05:10:35 PM UTC 2026
% Result : Theorem 226.52s 76.57s
% Output : CNFRefutation 226.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 183 ( 62 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 237 ( 90 ~; 94 |; 35 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 58 ( 0 sgn 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t156_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ! [X4] :
( ( relation(X4)
& function(X4) )
=> ( ( X1 = relation_rng(X2)
& relation_dom(X3) = X1
& relation_dom(X4) = X1
& relation_composition(X2,X3) = relation_composition(X2,X4) )
=> X3 = X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_funct_1) ).
fof(t23_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(t9_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_dom(X1) = relation_dom(X2)
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
fof(c_0_4,plain,
! [X75,X76,X77,X79,X80,X81,X83] :
( ( in(esk1_3(X75,X76,X77),relation_dom(X75))
| ~ in(X77,X76)
| X76 != relation_rng(X75)
| ~ relation(X75)
| ~ function(X75) )
& ( X77 = apply(X75,esk1_3(X75,X76,X77))
| ~ in(X77,X76)
| X76 != relation_rng(X75)
| ~ relation(X75)
| ~ function(X75) )
& ( ~ in(X80,relation_dom(X75))
| X79 != apply(X75,X80)
| in(X79,X76)
| X76 != relation_rng(X75)
| ~ relation(X75)
| ~ function(X75) )
& ( ~ in(esk2_2(X75,X81),X81)
| ~ in(X83,relation_dom(X75))
| esk2_2(X75,X81) != apply(X75,X83)
| X81 = relation_rng(X75)
| ~ relation(X75)
| ~ function(X75) )
& ( in(esk3_2(X75,X81),relation_dom(X75))
| in(esk2_2(X75,X81),X81)
| X81 = relation_rng(X75)
| ~ relation(X75)
| ~ function(X75) )
& ( esk2_2(X75,X81) = apply(X75,esk3_2(X75,X81))
| in(esk2_2(X75,X81),X81)
| X81 = relation_rng(X75)
| ~ relation(X75)
| ~ function(X75) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_funct_1])])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ! [X4] :
( ( relation(X4)
& function(X4) )
=> ( ( X1 = relation_rng(X2)
& relation_dom(X3) = X1
& relation_dom(X4) = X1
& relation_composition(X2,X3) = relation_composition(X2,X4) )
=> X3 = X4 ) ) ) ),
inference(assume_negation,[status(cth)],[t156_funct_1]) ).
cnf(c_0_6,plain,
( X1 = apply(X2,esk1_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,negated_conjecture,
( relation(esk16_0)
& function(esk16_0)
& relation(esk17_0)
& function(esk17_0)
& relation(esk18_0)
& function(esk18_0)
& esk15_0 = relation_rng(esk16_0)
& relation_dom(esk17_0) = esk15_0
& relation_dom(esk18_0) = esk15_0
& relation_composition(esk16_0,esk17_0) = relation_composition(esk16_0,esk18_0)
& esk17_0 != esk18_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_8,plain,
( in(esk1_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_9,plain,
! [X119,X120,X121] :
( ~ relation(X120)
| ~ function(X120)
| ~ relation(X121)
| ~ function(X121)
| ~ in(X119,relation_dom(X120))
| apply(relation_composition(X120,X121),X119) = apply(X121,apply(X120,X119)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
cnf(c_0_10,plain,
( apply(X1,esk1_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
esk15_0 = relation_rng(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
function(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( in(esk1_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
( apply(esk16_0,esk1_3(esk16_0,esk15_0,X1)) = X1
| ~ in(X1,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_17,negated_conjecture,
( in(esk1_3(esk16_0,esk15_0,X1),relation_dom(esk16_0))
| ~ in(X1,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_18,plain,
( apply(relation_composition(X1,X2),esk1_3(X1,relation_rng(X1),X3)) = apply(X2,X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1)
| ~ in(X3,relation_rng(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_10]),c_0_14]) ).
cnf(c_0_19,negated_conjecture,
relation_composition(esk16_0,esk17_0) = relation_composition(esk16_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
function(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_22,plain,
! [X137,X138] :
( ( in(esk19_2(X137,X138),relation_dom(X137))
| relation_dom(X137) != relation_dom(X138)
| X137 = X138
| ~ relation(X138)
| ~ function(X138)
| ~ relation(X137)
| ~ function(X137) )
& ( apply(X137,esk19_2(X137,X138)) != apply(X138,esk19_2(X137,X138))
| relation_dom(X137) != relation_dom(X138)
| X137 = X138
| ~ relation(X138)
| ~ function(X138)
| ~ relation(X137)
| ~ function(X137) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_funct_1])])])])]) ).
cnf(c_0_23,negated_conjecture,
( apply(relation_composition(esk16_0,X1),esk1_3(esk16_0,esk15_0,X2)) = apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,esk15_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_12]),c_0_13])]),c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( apply(relation_composition(esk16_0,esk17_0),esk1_3(esk16_0,esk15_0,X1)) = apply(esk18_0,X1)
| ~ in(X1,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_11]),c_0_20]),c_0_12]),c_0_21]),c_0_13]),c_0_11])]) ).
cnf(c_0_25,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,plain,
( in(esk19_2(X1,X2),relation_dom(X1))
| X1 = X2
| relation_dom(X1) != relation_dom(X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
relation_dom(esk18_0) = esk15_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_29,plain,
( X1 = X2
| apply(X1,esk19_2(X1,X2)) != apply(X2,esk19_2(X1,X2))
| relation_dom(X1) != relation_dom(X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
( apply(esk18_0,X1) = apply(esk17_0,X1)
| ~ in(X1,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_31,negated_conjecture,
( esk18_0 = X1
| in(esk19_2(esk18_0,X1),esk15_0)
| esk15_0 != relation_dom(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20]),c_0_21])]) ).
cnf(c_0_32,negated_conjecture,
( esk18_0 = X1
| apply(esk17_0,esk19_2(esk18_0,X1)) != apply(X1,esk19_2(esk18_0,X1))
| esk15_0 != relation_dom(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_28]),c_0_20]),c_0_21])]),c_0_31]) ).
cnf(c_0_33,negated_conjecture,
relation_dom(esk17_0) = esk15_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_34,negated_conjecture,
esk17_0 != esk18_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_32]),c_0_33]),c_0_25]),c_0_26])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU075+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
% 0.14/0.33 % Computer : n008.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:43:28 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 226.52/76.57 % Version : CSE_E---1.7
% 226.52/76.57 % Problem : theBenchmark.p
% 226.52/76.57 % SZS status Theorem for theBenchmark.p
% 226.52/76.57 % SZS output start CNFRefutation
% See solution above
% 226.93/76.98 % Total time : 60.274s
%------------------------------------------------------------------------------