%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU034+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 : n025.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 60.44s 36.14s
% Output : CNFRefutation 60.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 17 unt; 0 def)
% Number of atoms : 110 ( 37 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 125 ( 52 ~; 49 |; 16 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 37 ( 3 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t44_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_rng(X1) = relation_dom(X2)
& relation_composition(X1,X2) = X1 )
=> X2 = identity_relation(relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_1) ).
fof(t61_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1))
& relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_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(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(t71_relat_1,axiom,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
fof(t52_funct_1,axiom,
! [X1] : one_to_one(identity_relation(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(t67_funct_1,conjecture,
! [X1] : function_inverse(identity_relation(X1)) = identity_relation(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_funct_1) ).
fof(c_0_9,plain,
! [X107,X108] :
( ~ relation(X107)
| ~ function(X107)
| ~ relation(X108)
| ~ function(X108)
| relation_rng(X107) != relation_dom(X108)
| relation_composition(X107,X108) != X107
| X108 = identity_relation(relation_dom(X108)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t44_funct_1])])]) ).
fof(c_0_10,plain,
! [X117] :
( ( relation_composition(X117,function_inverse(X117)) = identity_relation(relation_dom(X117))
| ~ one_to_one(X117)
| ~ relation(X117)
| ~ function(X117) )
& ( relation_composition(function_inverse(X117),X117) = identity_relation(relation_rng(X117))
| ~ one_to_one(X117)
| ~ relation(X117)
| ~ function(X117) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t61_funct_1])])]) ).
fof(c_0_11,plain,
! [X70] :
( ( relation(function_inverse(X70))
| ~ relation(X70)
| ~ function(X70) )
& ( function(function_inverse(X70))
| ~ relation(X70)
| ~ function(X70) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(c_0_12,plain,
! [X113] :
( ( relation_rng(X113) = relation_dom(function_inverse(X113))
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( relation_dom(X113) = relation_rng(function_inverse(X113))
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).
fof(c_0_13,plain,
! [X120] :
( relation_dom(identity_relation(X120)) = X120
& relation_rng(identity_relation(X120)) = X120 ),
inference(variable_rename,[status(thm)],[t71_relat_1]) ).
cnf(c_0_14,plain,
( X2 = identity_relation(relation_dom(X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| relation_rng(X1) != relation_dom(X2)
| relation_composition(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
relation_rng(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( identity_relation(relation_dom(function_inverse(X1))) = function_inverse(X1)
| identity_relation(relation_dom(X1)) != X1
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]),c_0_18]) ).
fof(c_0_21,plain,
! [X112] : one_to_one(identity_relation(X112)),
inference(variable_rename,[status(thm)],[t52_funct_1]) ).
fof(c_0_22,plain,
! [X73] : relation(identity_relation(X73)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_23,plain,
! [X81] :
( relation(identity_relation(X81))
& function(identity_relation(X81)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
cnf(c_0_24,plain,
( relation_rng(function_inverse(X1)) = relation_dom(function_inverse(X1))
| identity_relation(relation_dom(X1)) != X1
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,plain,
one_to_one(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_29,negated_conjecture,
~ ! [X1] : function_inverse(identity_relation(X1)) = identity_relation(X1),
inference(assume_negation,[status(cth)],[t67_funct_1]) ).
cnf(c_0_30,plain,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_31,plain,
relation_rng(function_inverse(identity_relation(X1))) = relation_dom(function_inverse(identity_relation(X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28])]) ).
fof(c_0_32,negated_conjecture,
function_inverse(identity_relation(esk12_0)) != identity_relation(esk12_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
cnf(c_0_33,plain,
relation_dom(function_inverse(identity_relation(X1))) = X1,
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_30,c_0_31]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_34,negated_conjecture,
function_inverse(identity_relation(esk12_0)) != identity_relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,plain,
function_inverse(identity_relation(X1)) = identity_relation(X1),
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_20,c_0_33]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU034+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
% 0.16/0.33 % Computer : n025.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 02:44:28 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 60.44/36.14 % Version : CSE_E---1.7
% 60.44/36.14 % Problem : theBenchmark.p
% 60.44/36.14 % SZS status Theorem for theBenchmark.p
% 60.44/36.14 % SZS output start CNFRefutation
% See solution above
% 60.72/36.42 % Total time : 25.417s
%------------------------------------------------------------------------------