%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU220+3 : 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 : n003.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 05:11:07 PM UTC 2026
% Result : Theorem 26.84s 18.18s
% Output : CNFRefutation 26.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 248 ( 73 equ)
% Maximal formula atoms : 130 ( 8 avg)
% Number of connectives : 375 ( 156 ~; 164 |; 39 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t57_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(t54_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = function_inverse(X1)
<=> ( relation_dom(X2) = relation_rng(X1)
& ! [X3,X4] :
( ( ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) )
=> ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) )
=> ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',t55_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(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t57_funct_1]) ).
fof(c_0_6,plain,
! [X113,X114,X115,X116,X117,X118] :
( ( relation_dom(X114) = relation_rng(X113)
| X114 != function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( in(X116,relation_dom(X113))
| ~ in(X115,relation_rng(X113))
| X116 != apply(X114,X115)
| X114 != function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( X115 = apply(X113,X116)
| ~ in(X115,relation_rng(X113))
| X116 != apply(X114,X115)
| X114 != function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( in(X117,relation_rng(X113))
| ~ in(X118,relation_dom(X113))
| X117 != apply(X113,X118)
| X114 != function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( X118 = apply(X114,X117)
| ~ in(X118,relation_dom(X113))
| X117 != apply(X113,X118)
| X114 != function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( in(esk15_2(X113,X114),relation_dom(X113))
| in(esk12_2(X113,X114),relation_rng(X113))
| relation_dom(X114) != relation_rng(X113)
| X114 = function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( esk14_2(X113,X114) = apply(X113,esk15_2(X113,X114))
| in(esk12_2(X113,X114),relation_rng(X113))
| relation_dom(X114) != relation_rng(X113)
| X114 = function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( ~ in(esk14_2(X113,X114),relation_rng(X113))
| esk15_2(X113,X114) != apply(X114,esk14_2(X113,X114))
| in(esk12_2(X113,X114),relation_rng(X113))
| relation_dom(X114) != relation_rng(X113)
| X114 = function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( in(esk15_2(X113,X114),relation_dom(X113))
| esk13_2(X113,X114) = apply(X114,esk12_2(X113,X114))
| relation_dom(X114) != relation_rng(X113)
| X114 = function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( esk14_2(X113,X114) = apply(X113,esk15_2(X113,X114))
| esk13_2(X113,X114) = apply(X114,esk12_2(X113,X114))
| relation_dom(X114) != relation_rng(X113)
| X114 = function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( ~ in(esk14_2(X113,X114),relation_rng(X113))
| esk15_2(X113,X114) != apply(X114,esk14_2(X113,X114))
| esk13_2(X113,X114) = apply(X114,esk12_2(X113,X114))
| relation_dom(X114) != relation_rng(X113)
| X114 = function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( in(esk15_2(X113,X114),relation_dom(X113))
| ~ in(esk13_2(X113,X114),relation_dom(X113))
| esk12_2(X113,X114) != apply(X113,esk13_2(X113,X114))
| relation_dom(X114) != relation_rng(X113)
| X114 = function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( esk14_2(X113,X114) = apply(X113,esk15_2(X113,X114))
| ~ in(esk13_2(X113,X114),relation_dom(X113))
| esk12_2(X113,X114) != apply(X113,esk13_2(X113,X114))
| relation_dom(X114) != relation_rng(X113)
| X114 = function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( ~ in(esk14_2(X113,X114),relation_rng(X113))
| esk15_2(X113,X114) != apply(X114,esk14_2(X113,X114))
| ~ in(esk13_2(X113,X114),relation_dom(X113))
| esk12_2(X113,X114) != apply(X113,esk13_2(X113,X114))
| relation_dom(X114) != relation_rng(X113)
| X114 = function_inverse(X113)
| ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) ) ),
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)],[t54_funct_1])])])])])]) ).
fof(c_0_7,plain,
! [X72] :
( ( relation(function_inverse(X72))
| ~ relation(X72)
| ~ function(X72) )
& ( function(function_inverse(X72))
| ~ relation(X72)
| ~ function(X72) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(c_0_8,plain,
! [X123] :
( ( relation_rng(X123) = relation_dom(function_inverse(X123))
| ~ one_to_one(X123)
| ~ relation(X123)
| ~ function(X123) )
& ( relation_dom(X123) = relation_rng(function_inverse(X123))
| ~ one_to_one(X123)
| ~ relation(X123)
| ~ function(X123) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).
fof(c_0_9,negated_conjecture,
( relation(esk17_0)
& function(esk17_0)
& one_to_one(esk17_0)
& in(esk16_0,relation_rng(esk17_0))
& ( esk16_0 != apply(esk17_0,apply(function_inverse(esk17_0),esk16_0))
| esk16_0 != apply(relation_composition(function_inverse(esk17_0),esk17_0),esk16_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_10,plain,
( X1 = apply(X2,X3)
| ~ in(X1,relation_rng(X2))
| X3 != apply(X4,X1)
| X4 != function_inverse(X2)
| ~ relation(X4)
| ~ function(X4)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,plain,
! [X103,X104,X105] :
( ~ relation(X104)
| ~ function(X104)
| ~ relation(X105)
| ~ function(X105)
| ~ in(X103,relation_dom(X104))
| apply(relation_composition(X104,X105),X103) = apply(X105,apply(X104,X103)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
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_8]) ).
cnf(c_0_15,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
one_to_one(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
( apply(X1,apply(function_inverse(X1),X2)) = X2
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]),c_0_11]),c_0_12]) ).
cnf(c_0_19,negated_conjecture,
in(esk16_0,relation_rng(esk17_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,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_13]) ).
cnf(c_0_21,negated_conjecture,
relation_dom(function_inverse(esk17_0)) = relation_rng(esk17_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_22,negated_conjecture,
function(function_inverse(esk17_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_15]),c_0_17])]) ).
cnf(c_0_23,negated_conjecture,
( esk16_0 != apply(esk17_0,apply(function_inverse(esk17_0),esk16_0))
| esk16_0 != apply(relation_composition(function_inverse(esk17_0),esk17_0),esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,negated_conjecture,
apply(esk17_0,apply(function_inverse(esk17_0),esk16_0)) = esk16_0,
inference(cn,[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_16]),c_0_15]),c_0_17])]) ).
cnf(c_0_25,negated_conjecture,
( apply(relation_composition(function_inverse(esk17_0),X1),X2) = apply(X1,apply(function_inverse(esk17_0),X2))
| ~ relation(function_inverse(esk17_0))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(esk17_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
apply(relation_composition(function_inverse(esk17_0),esk17_0),esk16_0) != esk16_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_27,negated_conjecture,
( apply(relation_composition(function_inverse(esk17_0),X1),X2) = apply(X1,apply(function_inverse(esk17_0),X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(esk17_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_12]),c_0_15]),c_0_17])]) ).
cnf(c_0_28,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_26,c_0_27]),c_0_24]),c_0_15]),c_0_17]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU220+3 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n003.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:49:26 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 26.84/18.18 % Version : CSE_E---1.7
% 26.84/18.18 % Problem : theBenchmark.p
% 26.84/18.18 % SZS status Theorem for theBenchmark.p
% 26.84/18.18 % SZS output start CNFRefutation
% See solution above
% 26.92/18.30 % Total time : 13.403s
%------------------------------------------------------------------------------