%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU026+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.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 05:10:31 PM UTC 2026
% Result : Theorem 10.92s 7.96s
% Output : CNFRefutation 11.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 100 ( 28 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 114 ( 46 ~; 42 |; 13 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 29 ( 1 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t59_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_dom(relation_composition(function_inverse(X1),X1)) = relation_rng(X1)
& relation_rng(relation_composition(function_inverse(X1),X1)) = relation_rng(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_1) ).
fof(t55_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(t46_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
fof(dt_k2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(t47_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_dom(X1),relation_rng(X2))
=> relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_dom(relation_composition(function_inverse(X1),X1)) = relation_rng(X1)
& relation_rng(relation_composition(function_inverse(X1),X1)) = relation_rng(X1) ) ) ),
inference(assume_negation,[status(cth)],[t59_funct_1]) ).
fof(c_0_7,plain,
! [X109] :
( ( relation_rng(X109) = relation_dom(function_inverse(X109))
| ~ one_to_one(X109)
| ~ relation(X109)
| ~ function(X109) )
& ( relation_dom(X109) = relation_rng(function_inverse(X109))
| ~ one_to_one(X109)
| ~ relation(X109)
| ~ function(X109) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).
fof(c_0_8,negated_conjecture,
( relation(esk12_0)
& function(esk12_0)
& one_to_one(esk12_0)
& ( relation_dom(relation_composition(function_inverse(esk12_0),esk12_0)) != relation_rng(esk12_0)
| relation_rng(relation_composition(function_inverse(esk12_0),esk12_0)) != relation_rng(esk12_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X102,X103] :
( ~ relation(X102)
| ~ relation(X103)
| ~ subset(relation_rng(X102),relation_dom(X103))
| relation_dom(relation_composition(X102,X103)) = relation_dom(X102) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_relat_1])])]) ).
cnf(c_0_10,plain,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
one_to_one(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
function(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(relation_rng(X1),relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
relation_rng(function_inverse(esk12_0)) = relation_dom(esk12_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,
relation_dom(function_inverse(esk12_0)) = relation_rng(esk12_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])]) ).
fof(c_0_18,plain,
! [X67] :
( ( relation(function_inverse(X67))
| ~ relation(X67)
| ~ function(X67) )
& ( function(function_inverse(X67))
| ~ relation(X67)
| ~ function(X67) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(c_0_19,plain,
! [X104,X105] :
( ~ relation(X104)
| ~ relation(X105)
| ~ subset(relation_dom(X104),relation_rng(X105))
| relation_rng(relation_composition(X105,X104)) = relation_rng(X104) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_relat_1])])]) ).
cnf(c_0_20,negated_conjecture,
( relation_dom(relation_composition(function_inverse(esk12_0),X1)) = relation_rng(esk12_0)
| ~ subset(relation_dom(esk12_0),relation_dom(X1))
| ~ relation(function_inverse(esk12_0))
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X95] : subset(X95,X95),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_23,plain,
( relation_rng(relation_composition(X2,X1)) = relation_rng(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(relation_dom(X1),relation_rng(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( relation_dom(relation_composition(function_inverse(esk12_0),X1)) = relation_rng(esk12_0)
| ~ subset(relation_dom(esk12_0),relation_dom(X1))
| ~ relation(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_11]),c_0_13])]) ).
cnf(c_0_25,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( relation_rng(relation_composition(function_inverse(esk12_0),X1)) = relation_rng(X1)
| ~ subset(relation_dom(X1),relation_dom(esk12_0))
| ~ relation(function_inverse(esk12_0))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_27,negated_conjecture,
( relation_dom(relation_composition(function_inverse(esk12_0),esk12_0)) != relation_rng(esk12_0)
| relation_rng(relation_composition(function_inverse(esk12_0),esk12_0)) != relation_rng(esk12_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,negated_conjecture,
relation_dom(relation_composition(function_inverse(esk12_0),esk12_0)) = relation_rng(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_11])]) ).
cnf(c_0_29,negated_conjecture,
( relation_rng(relation_composition(function_inverse(esk12_0),X1)) = relation_rng(X1)
| ~ subset(relation_dom(X1),relation_dom(esk12_0))
| ~ relation(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_11]),c_0_13])]) ).
cnf(c_0_30,negated_conjecture,
relation_rng(relation_composition(function_inverse(esk12_0),esk12_0)) != relation_rng(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_11])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU026+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n017.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:40:13 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 10.92/7.96 % Version : CSE_E---1.7
% 10.92/7.96 % Problem : theBenchmark.p
% 10.92/7.96 % SZS status Theorem for theBenchmark.p
% 10.92/7.96 % SZS output start CNFRefutation
% See solution above
% 11.04/8.03 % Total time : 5.371s
%------------------------------------------------------------------------------