%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU221+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n013.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 1.32s 1.74s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 13 unt; 0 def)
% Number of atoms : 278 ( 68 equ)
% Maximal formula atoms : 130 ( 7 avg)
% Number of connectives : 410 ( 169 ~; 185 |; 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(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/sandbox/benchmark/theBenchmark.p',d8_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(t62_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_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(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/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(c_0_5,plain,
! [X57,X58,X59] :
( ( ~ one_to_one(X57)
| ~ in(X58,relation_dom(X57))
| ~ in(X59,relation_dom(X57))
| apply(X57,X58) != apply(X57,X59)
| X58 = X59
| ~ relation(X57)
| ~ function(X57) )
& ( in(esk1_1(X57),relation_dom(X57))
| one_to_one(X57)
| ~ relation(X57)
| ~ function(X57) )
& ( in(esk2_1(X57),relation_dom(X57))
| one_to_one(X57)
| ~ relation(X57)
| ~ function(X57) )
& ( apply(X57,esk1_1(X57)) = apply(X57,esk2_1(X57))
| one_to_one(X57)
| ~ relation(X57)
| ~ function(X57) )
& ( esk1_1(X57) != esk2_1(X57)
| one_to_one(X57)
| ~ relation(X57)
| ~ function(X57) ) ),
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])])])])]) ).
fof(c_0_6,plain,
! [X62] :
( ( relation(function_inverse(X62))
| ~ relation(X62)
| ~ function(X62) )
& ( function(function_inverse(X62))
| ~ relation(X62)
| ~ function(X62) ) ),
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]) ).
cnf(c_0_8,plain,
( in(esk2_1(X1),relation_dom(X1))
| one_to_one(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_6]) ).
cnf(c_0_10,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( relation(esk16_0)
& function(esk16_0)
& one_to_one(esk16_0)
& ~ one_to_one(function_inverse(esk16_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_12,plain,
! [X89,X90,X91,X92,X93,X94] :
( ( relation_dom(X90) = relation_rng(X89)
| X90 != function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( in(X92,relation_dom(X89))
| ~ in(X91,relation_rng(X89))
| X92 != apply(X90,X91)
| X90 != function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( X91 = apply(X89,X92)
| ~ in(X91,relation_rng(X89))
| X92 != apply(X90,X91)
| X90 != function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( in(X93,relation_rng(X89))
| ~ in(X94,relation_dom(X89))
| X93 != apply(X89,X94)
| X90 != function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( X94 = apply(X90,X93)
| ~ in(X94,relation_dom(X89))
| X93 != apply(X89,X94)
| X90 != function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( in(esk15_2(X89,X90),relation_dom(X89))
| in(esk12_2(X89,X90),relation_rng(X89))
| relation_dom(X90) != relation_rng(X89)
| X90 = function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( esk14_2(X89,X90) = apply(X89,esk15_2(X89,X90))
| in(esk12_2(X89,X90),relation_rng(X89))
| relation_dom(X90) != relation_rng(X89)
| X90 = function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( ~ in(esk14_2(X89,X90),relation_rng(X89))
| esk15_2(X89,X90) != apply(X90,esk14_2(X89,X90))
| in(esk12_2(X89,X90),relation_rng(X89))
| relation_dom(X90) != relation_rng(X89)
| X90 = function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( in(esk15_2(X89,X90),relation_dom(X89))
| esk13_2(X89,X90) = apply(X90,esk12_2(X89,X90))
| relation_dom(X90) != relation_rng(X89)
| X90 = function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( esk14_2(X89,X90) = apply(X89,esk15_2(X89,X90))
| esk13_2(X89,X90) = apply(X90,esk12_2(X89,X90))
| relation_dom(X90) != relation_rng(X89)
| X90 = function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( ~ in(esk14_2(X89,X90),relation_rng(X89))
| esk15_2(X89,X90) != apply(X90,esk14_2(X89,X90))
| esk13_2(X89,X90) = apply(X90,esk12_2(X89,X90))
| relation_dom(X90) != relation_rng(X89)
| X90 = function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( in(esk15_2(X89,X90),relation_dom(X89))
| ~ in(esk13_2(X89,X90),relation_dom(X89))
| esk12_2(X89,X90) != apply(X89,esk13_2(X89,X90))
| relation_dom(X90) != relation_rng(X89)
| X90 = function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( esk14_2(X89,X90) = apply(X89,esk15_2(X89,X90))
| ~ in(esk13_2(X89,X90),relation_dom(X89))
| esk12_2(X89,X90) != apply(X89,esk13_2(X89,X90))
| relation_dom(X90) != relation_rng(X89)
| X90 = function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) )
& ( ~ in(esk14_2(X89,X90),relation_rng(X89))
| esk15_2(X89,X90) != apply(X90,esk14_2(X89,X90))
| ~ in(esk13_2(X89,X90),relation_dom(X89))
| esk12_2(X89,X90) != apply(X89,esk13_2(X89,X90))
| relation_dom(X90) != relation_rng(X89)
| X90 = function_inverse(X89)
| ~ relation(X90)
| ~ function(X90)
| ~ one_to_one(X89)
| ~ relation(X89)
| ~ function(X89) ) ),
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])])])])])]) ).
cnf(c_0_13,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_5]) ).
cnf(c_0_14,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_8,c_0_9]),c_0_10]) ).
cnf(c_0_15,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
function(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
~ one_to_one(function_inverse(esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,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_12]) ).
cnf(c_0_19,plain,
( in(esk1_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_20,plain,
! [X99,X100] :
( ( X99 = apply(X100,apply(function_inverse(X100),X99))
| ~ one_to_one(X100)
| ~ in(X99,relation_rng(X100))
| ~ relation(X100)
| ~ function(X100) )
& ( X99 = apply(relation_composition(function_inverse(X100),X100),X99)
| ~ one_to_one(X100)
| ~ in(X99,relation_rng(X100))
| ~ relation(X100)
| ~ function(X100) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t57_funct_1])])]) ).
cnf(c_0_21,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_13,c_0_9]),c_0_10]) ).
cnf(c_0_22,negated_conjecture,
in(esk2_1(function_inverse(esk16_0)),relation_dom(function_inverse(esk16_0))),
inference(sr,[status(thm)],[inference(cn,[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_23,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_18]),c_0_10]),c_0_9]) ).
cnf(c_0_24,negated_conjecture,
one_to_one(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,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_19,c_0_9]),c_0_10]) ).
cnf(c_0_26,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_20]) ).
cnf(c_0_27,negated_conjecture,
apply(function_inverse(esk16_0),esk2_1(function_inverse(esk16_0))) = apply(function_inverse(esk16_0),esk1_1(function_inverse(esk16_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_15]),c_0_16])]),c_0_17]) ).
cnf(c_0_28,negated_conjecture,
in(esk2_1(function_inverse(esk16_0)),relation_rng(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_15]),c_0_16])]) ).
cnf(c_0_29,negated_conjecture,
in(esk1_1(function_inverse(esk16_0)),relation_dom(function_inverse(esk16_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_15]),c_0_16])]),c_0_17]) ).
cnf(c_0_30,negated_conjecture,
apply(esk16_0,apply(function_inverse(esk16_0),esk1_1(function_inverse(esk16_0)))) = esk2_1(function_inverse(esk16_0)),
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_16]),c_0_28])]) ).
cnf(c_0_31,negated_conjecture,
in(esk1_1(function_inverse(esk16_0)),relation_rng(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_23]),c_0_24]),c_0_15]),c_0_16])]) ).
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_5]) ).
cnf(c_0_33,negated_conjecture,
esk2_1(function_inverse(esk16_0)) = esk1_1(function_inverse(esk16_0)),
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_30]),c_0_24]),c_0_15]),c_0_16]),c_0_31])]) ).
cnf(c_0_34,negated_conjecture,
( ~ relation(function_inverse(esk16_0))
| ~ function(function_inverse(esk16_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_17]) ).
cnf(c_0_35,negated_conjecture,
~ relation(function_inverse(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_10]),c_0_15]),c_0_16])]) ).
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_9]),c_0_15]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU221+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.14/0.32 % Computer : n013.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:49:11 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.32/1.74 % Version : CSE_E---1.7
% 1.32/1.74 % Problem : theBenchmark.p
% 1.32/1.74 % SZS status Theorem for theBenchmark.p
% 1.32/1.74 % SZS output start CNFRefutation
% See solution above
% 1.32/1.74 % Total time : 1.370s
%------------------------------------------------------------------------------