%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU023+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 : n001.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 1.65s 1.85s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 225 ( 66 equ)
% Maximal formula atoms : 130 ( 9 avg)
% Number of connectives : 343 ( 143 ~; 150 |; 36 &)
% ( 1 <=>; 13 =>; 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 : 34 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t56_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_dom(X2)) )
=> ( X1 = apply(function_inverse(X2),apply(X2,X1))
& X1 = apply(relation_composition(X2,function_inverse(X2)),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_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_4,plain,
! [X112,X113,X114,X115,X116,X117] :
( ( relation_dom(X113) = relation_rng(X112)
| X113 != function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( in(X115,relation_dom(X112))
| ~ in(X114,relation_rng(X112))
| X115 != apply(X113,X114)
| X113 != function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( X114 = apply(X112,X115)
| ~ in(X114,relation_rng(X112))
| X115 != apply(X113,X114)
| X113 != function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( in(X116,relation_rng(X112))
| ~ in(X117,relation_dom(X112))
| X116 != apply(X112,X117)
| X113 != function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( X117 = apply(X113,X116)
| ~ in(X117,relation_dom(X112))
| X116 != apply(X112,X117)
| X113 != function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( in(esk15_2(X112,X113),relation_dom(X112))
| in(esk12_2(X112,X113),relation_rng(X112))
| relation_dom(X113) != relation_rng(X112)
| X113 = function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( esk14_2(X112,X113) = apply(X112,esk15_2(X112,X113))
| in(esk12_2(X112,X113),relation_rng(X112))
| relation_dom(X113) != relation_rng(X112)
| X113 = function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( ~ in(esk14_2(X112,X113),relation_rng(X112))
| esk15_2(X112,X113) != apply(X113,esk14_2(X112,X113))
| in(esk12_2(X112,X113),relation_rng(X112))
| relation_dom(X113) != relation_rng(X112)
| X113 = function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( in(esk15_2(X112,X113),relation_dom(X112))
| esk13_2(X112,X113) = apply(X113,esk12_2(X112,X113))
| relation_dom(X113) != relation_rng(X112)
| X113 = function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( esk14_2(X112,X113) = apply(X112,esk15_2(X112,X113))
| esk13_2(X112,X113) = apply(X113,esk12_2(X112,X113))
| relation_dom(X113) != relation_rng(X112)
| X113 = function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( ~ in(esk14_2(X112,X113),relation_rng(X112))
| esk15_2(X112,X113) != apply(X113,esk14_2(X112,X113))
| esk13_2(X112,X113) = apply(X113,esk12_2(X112,X113))
| relation_dom(X113) != relation_rng(X112)
| X113 = function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( in(esk15_2(X112,X113),relation_dom(X112))
| ~ in(esk13_2(X112,X113),relation_dom(X112))
| esk12_2(X112,X113) != apply(X112,esk13_2(X112,X113))
| relation_dom(X113) != relation_rng(X112)
| X113 = function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( esk14_2(X112,X113) = apply(X112,esk15_2(X112,X113))
| ~ in(esk13_2(X112,X113),relation_dom(X112))
| esk12_2(X112,X113) != apply(X112,esk13_2(X112,X113))
| relation_dom(X113) != relation_rng(X112)
| X113 = function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) )
& ( ~ in(esk14_2(X112,X113),relation_rng(X112))
| esk15_2(X112,X113) != apply(X113,esk14_2(X112,X113))
| ~ in(esk13_2(X112,X113),relation_dom(X112))
| esk12_2(X112,X113) != apply(X112,esk13_2(X112,X113))
| relation_dom(X113) != relation_rng(X112)
| X113 = function_inverse(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ one_to_one(X112)
| ~ relation(X112)
| ~ function(X112) ) ),
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_5,plain,
! [X71] :
( ( relation(function_inverse(X71))
| ~ relation(X71)
| ~ function(X71) )
& ( function(function_inverse(X71))
| ~ relation(X71)
| ~ function(X71) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_dom(X2)) )
=> ( X1 = apply(function_inverse(X2),apply(X2,X1))
& X1 = apply(relation_composition(X2,function_inverse(X2)),X1) ) ) ),
inference(assume_negation,[status(cth)],[t56_funct_1]) ).
cnf(c_0_7,plain,
( X1 = apply(X2,X3)
| ~ in(X1,relation_dom(X4))
| X3 != apply(X4,X1)
| X2 != function_inverse(X4)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,negated_conjecture,
( relation(esk17_0)
& function(esk17_0)
& one_to_one(esk17_0)
& in(esk16_0,relation_dom(esk17_0))
& ( esk16_0 != apply(function_inverse(esk17_0),apply(esk17_0,esk16_0))
| esk16_0 != apply(relation_composition(esk17_0,function_inverse(esk17_0)),esk16_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_11,plain,
( apply(function_inverse(X1),apply(X1,X2)) = X2
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_7])]),c_0_8]),c_0_9]) ).
cnf(c_0_12,negated_conjecture,
in(esk16_0,relation_dom(esk17_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
one_to_one(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X102,X103,X104] :
( ~ relation(X103)
| ~ function(X103)
| ~ relation(X104)
| ~ function(X104)
| ~ in(X102,relation_dom(X103))
| apply(relation_composition(X103,X104),X102) = apply(X104,apply(X103,X102)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
cnf(c_0_17,negated_conjecture,
( esk16_0 != apply(function_inverse(esk17_0),apply(esk17_0,esk16_0))
| esk16_0 != apply(relation_composition(esk17_0,function_inverse(esk17_0)),esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
apply(function_inverse(esk17_0),apply(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_11,c_0_12]),c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_19,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_16]) ).
cnf(c_0_20,negated_conjecture,
apply(relation_composition(esk17_0,function_inverse(esk17_0)),esk16_0) != esk16_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_21,negated_conjecture,
( apply(relation_composition(esk17_0,X1),esk16_0) = apply(X1,apply(esk17_0,esk16_0))
| ~ relation(X1)
| ~ function(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_12]),c_0_14]),c_0_15])]) ).
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_8,c_0_14]),c_0_15])]) ).
cnf(c_0_23,negated_conjecture,
~ relation(function_inverse(esk17_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18]),c_0_22])]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_9]),c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU023+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
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 02:42:19 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.65/1.85 % Version : CSE_E---1.7
% 1.65/1.85 % Problem : theBenchmark.p
% 1.65/1.85 % SZS status Theorem for theBenchmark.p
% 1.65/1.85 % SZS output start CNFRefutation
% See solution above
% 1.65/1.85 % Total time : 1.373s
%------------------------------------------------------------------------------