%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU221+3 : 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 : n019.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 05:11:08 PM UTC 2026
% Result : Theorem 1.90s 1.90s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 14 unt; 0 def)
% Number of atoms : 277 ( 70 equ)
% Maximal formula atoms : 130 ( 7 avg)
% Number of connectives : 407 ( 167 ~; 184 |; 40 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 24 !; 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(t62_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
fof(d8_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(t57_funct_1,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
fof(c_0_5,plain,
! [X115,X116,X117,X118,X119,X120] :
( ( relation_dom(X116) = relation_rng(X115)
| X116 != function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( in(X118,relation_dom(X115))
| ~ in(X117,relation_rng(X115))
| X118 != apply(X116,X117)
| X116 != function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( X117 = apply(X115,X118)
| ~ in(X117,relation_rng(X115))
| X118 != apply(X116,X117)
| X116 != function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( in(X119,relation_rng(X115))
| ~ in(X120,relation_dom(X115))
| X119 != apply(X115,X120)
| X116 != function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( X120 = apply(X116,X119)
| ~ in(X120,relation_dom(X115))
| X119 != apply(X115,X120)
| X116 != function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( in(esk17_2(X115,X116),relation_dom(X115))
| in(esk14_2(X115,X116),relation_rng(X115))
| relation_dom(X116) != relation_rng(X115)
| X116 = function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( esk16_2(X115,X116) = apply(X115,esk17_2(X115,X116))
| in(esk14_2(X115,X116),relation_rng(X115))
| relation_dom(X116) != relation_rng(X115)
| X116 = function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( ~ in(esk16_2(X115,X116),relation_rng(X115))
| esk17_2(X115,X116) != apply(X116,esk16_2(X115,X116))
| in(esk14_2(X115,X116),relation_rng(X115))
| relation_dom(X116) != relation_rng(X115)
| X116 = function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( in(esk17_2(X115,X116),relation_dom(X115))
| esk15_2(X115,X116) = apply(X116,esk14_2(X115,X116))
| relation_dom(X116) != relation_rng(X115)
| X116 = function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( esk16_2(X115,X116) = apply(X115,esk17_2(X115,X116))
| esk15_2(X115,X116) = apply(X116,esk14_2(X115,X116))
| relation_dom(X116) != relation_rng(X115)
| X116 = function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( ~ in(esk16_2(X115,X116),relation_rng(X115))
| esk17_2(X115,X116) != apply(X116,esk16_2(X115,X116))
| esk15_2(X115,X116) = apply(X116,esk14_2(X115,X116))
| relation_dom(X116) != relation_rng(X115)
| X116 = function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( in(esk17_2(X115,X116),relation_dom(X115))
| ~ in(esk15_2(X115,X116),relation_dom(X115))
| esk14_2(X115,X116) != apply(X115,esk15_2(X115,X116))
| relation_dom(X116) != relation_rng(X115)
| X116 = function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( esk16_2(X115,X116) = apply(X115,esk17_2(X115,X116))
| ~ in(esk15_2(X115,X116),relation_dom(X115))
| esk14_2(X115,X116) != apply(X115,esk15_2(X115,X116))
| relation_dom(X116) != relation_rng(X115)
| X116 = function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) )
& ( ~ in(esk16_2(X115,X116),relation_rng(X115))
| esk17_2(X115,X116) != apply(X116,esk16_2(X115,X116))
| ~ in(esk15_2(X115,X116),relation_dom(X115))
| esk14_2(X115,X116) != apply(X115,esk15_2(X115,X116))
| relation_dom(X116) != relation_rng(X115)
| X116 = function_inverse(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| ~ relation(X115)
| ~ function(X115) ) ),
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_6,plain,
! [X77] :
( ( relation(function_inverse(X77))
| ~ relation(X77)
| ~ function(X77) )
& ( function(function_inverse(X77))
| ~ relation(X77)
| ~ function(X77) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
inference(assume_negation,[status(cth)],[t62_funct_1]) ).
fof(c_0_8,plain,
! [X72,X73,X74] :
( ( ~ one_to_one(X72)
| ~ in(X73,relation_dom(X72))
| ~ in(X74,relation_dom(X72))
| apply(X72,X73) != apply(X72,X74)
| X73 = X74
| ~ relation(X72)
| ~ function(X72) )
& ( in(esk1_1(X72),relation_dom(X72))
| one_to_one(X72)
| ~ relation(X72)
| ~ function(X72) )
& ( in(esk2_1(X72),relation_dom(X72))
| one_to_one(X72)
| ~ relation(X72)
| ~ function(X72) )
& ( apply(X72,esk1_1(X72)) = apply(X72,esk2_1(X72))
| one_to_one(X72)
| ~ relation(X72)
| ~ function(X72) )
& ( esk1_1(X72) != esk2_1(X72)
| one_to_one(X72)
| ~ relation(X72)
| ~ function(X72) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).
cnf(c_0_9,plain,
( relation_dom(X1) = relation_rng(X2)
| X1 != function_inverse(X2)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,negated_conjecture,
( relation(esk18_0)
& function(esk18_0)
& one_to_one(esk18_0)
& ~ one_to_one(function_inverse(esk18_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_13,plain,
( in(esk2_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( relation_dom(function_inverse(X1)) = relation_rng(X1)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_9]),c_0_10]),c_0_11]) ).
cnf(c_0_15,negated_conjecture,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
one_to_one(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
function(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( in(esk1_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_19,plain,
! [X125,X126] :
( ( X125 = apply(X126,apply(function_inverse(X126),X125))
| ~ one_to_one(X126)
| ~ in(X125,relation_rng(X126))
| ~ relation(X126)
| ~ function(X126) )
& ( X125 = apply(relation_composition(function_inverse(X126),X126),X125)
| ~ one_to_one(X126)
| ~ in(X125,relation_rng(X126))
| ~ relation(X126)
| ~ function(X126) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t57_funct_1])])]) ).
cnf(c_0_20,plain,
( one_to_one(function_inverse(X1))
| in(esk2_1(function_inverse(X1)),relation_dom(function_inverse(X1)))
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_10]) ).
cnf(c_0_21,negated_conjecture,
relation_dom(function_inverse(esk18_0)) = relation_rng(esk18_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,
~ one_to_one(function_inverse(esk18_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
( apply(X1,esk1_1(X1)) = apply(X1,esk2_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,plain,
( one_to_one(function_inverse(X1))
| in(esk1_1(function_inverse(X1)),relation_dom(function_inverse(X1)))
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_11]),c_0_10]) ).
cnf(c_0_25,plain,
( X1 = apply(X2,apply(function_inverse(X2),X1))
| ~ one_to_one(X2)
| ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
in(esk2_1(function_inverse(esk18_0)),relation_rng(esk18_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_15]),c_0_21]),c_0_17])]),c_0_22]) ).
cnf(c_0_27,plain,
( apply(function_inverse(X1),esk2_1(function_inverse(X1))) = apply(function_inverse(X1),esk1_1(function_inverse(X1)))
| one_to_one(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_11]),c_0_10]) ).
cnf(c_0_28,negated_conjecture,
in(esk1_1(function_inverse(esk18_0)),relation_rng(esk18_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_15]),c_0_21]),c_0_17])]),c_0_22]) ).
cnf(c_0_29,negated_conjecture,
apply(esk18_0,apply(function_inverse(esk18_0),esk2_1(function_inverse(esk18_0)))) = esk2_1(function_inverse(esk18_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_16]),c_0_15]),c_0_17])]) ).
cnf(c_0_30,negated_conjecture,
apply(function_inverse(esk18_0),esk2_1(function_inverse(esk18_0))) = apply(function_inverse(esk18_0),esk1_1(function_inverse(esk18_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_15]),c_0_17])]),c_0_22]) ).
cnf(c_0_31,negated_conjecture,
apply(esk18_0,apply(function_inverse(esk18_0),esk1_1(function_inverse(esk18_0)))) = esk1_1(function_inverse(esk18_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_28]),c_0_16]),c_0_15]),c_0_17])]) ).
cnf(c_0_32,plain,
( one_to_one(X1)
| esk1_1(X1) != esk2_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_33,negated_conjecture,
esk2_1(function_inverse(esk18_0)) = esk1_1(function_inverse(esk18_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
function(function_inverse(esk18_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_15]),c_0_17])]) ).
cnf(c_0_35,negated_conjecture,
~ relation(function_inverse(esk18_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),c_0_22]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_11]),c_0_15]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU221+3 : 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
% 0.15/0.32 % Computer : n019.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 02:49:29 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.90/1.90 % Version : CSE_E---1.7
% 1.90/1.90 % Problem : theBenchmark.p
% 1.90/1.90 % SZS status Theorem for theBenchmark.p
% 1.90/1.90 % SZS output start CNFRefutation
% See solution above
% 1.90/1.90 % Total time : 1.369s
%------------------------------------------------------------------------------