%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU031+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:23:42 PM UTC 2026
% Result : Theorem 3.85s 1.07s
% Output : CNFRefutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 141 ( 44 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 183 ( 71 ~; 68 |; 29 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l72_funct_1,axiom,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ! [X4] :
( ( function(X4)
& relation(X4) )
=> ( ( relation_composition(X3,X4) = identity_relation(X1)
& relation_composition(X2,X3) = identity_relation(relation_dom(X4))
& relation_rng(X2) = X1 )
=> X4 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l72_funct_1) ).
fof(t64_funct_1,conjecture,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_composition(X2,X1) = identity_relation(relation_rng(X1))
& relation_rng(X2) = relation_dom(X1)
& one_to_one(X1) )
=> X2 = function_inverse(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_1) ).
fof(t55_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ( one_to_one(X1)
=> ( relation_dom(X1) = relation_rng(function_inverse(X1))
& relation_rng(X1) = relation_dom(function_inverse(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ( function(function_inverse(X1))
& relation(function_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(t61_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ( one_to_one(X1)
=> ( relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1))
& relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).
fof(c_0_5,plain,
! [X28,X29,X30,X31] :
( X31 = X29
| relation_composition(X30,X31) != identity_relation(X28)
| relation_composition(X29,X30) != identity_relation(relation_dom(X31))
| relation_rng(X29) != X28
| ~ function(X31)
| ~ relation(X31)
| ~ function(X30)
| ~ relation(X30)
| ~ function(X29)
| ~ relation(X29) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l72_funct_1])])])]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_composition(X2,X1) = identity_relation(relation_rng(X1))
& relation_rng(X2) = relation_dom(X1)
& one_to_one(X1) )
=> X2 = function_inverse(X1) ) ) ),
inference(assume_negation,[status(cth)],[t64_funct_1]) ).
cnf(c_0_7,plain,
( relation_composition(X2,X3) != identity_relation(X4)
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| relation_rng(X1) != X4
| ~ function(X3)
| ~ relation(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X54] :
( ( ~ function(X54)
| ~ relation(X54)
| ~ one_to_one(X54)
| relation_dom(X54) = relation_rng(function_inverse(X54)) )
& ( ~ function(X54)
| ~ relation(X54)
| ~ one_to_one(X54)
| relation_rng(X54) = relation_dom(function_inverse(X54)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])])]) ).
fof(c_0_9,plain,
! [X10] :
( ( ~ function(X10)
| ~ relation(X10)
| function(function_inverse(X10)) )
& ( ~ function(X10)
| ~ relation(X10)
| relation(function_inverse(X10)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])])]) ).
fof(c_0_10,plain,
! [X58] :
( ( ~ function(X58)
| ~ relation(X58)
| ~ one_to_one(X58)
| relation_composition(function_inverse(X58),X58) = identity_relation(relation_rng(X58)) )
& ( ~ function(X58)
| ~ relation(X58)
| ~ one_to_one(X58)
| relation_composition(X58,function_inverse(X58)) = identity_relation(relation_dom(X58)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t61_funct_1])])])]) ).
fof(c_0_11,negated_conjecture,
( esk13_0 != function_inverse(esk12_0)
& relation_composition(esk13_0,esk12_0) = identity_relation(relation_rng(esk12_0))
& relation_rng(esk13_0) = relation_dom(esk12_0)
& one_to_one(esk12_0)
& function(esk13_0)
& relation(esk13_0)
& function(esk12_0)
& relation(esk12_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_12,plain,
( ~ function(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| relation_composition(X3,X2) != identity_relation(relation_rng(X1))
| relation_composition(X1,X3) != identity_relation(relation_dom(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| relation_rng(X1) = relation_dom(function_inverse(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ function(X1)
| ~ relation(X1)
| function(function_inverse(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ function(X1)
| ~ relation(X1)
| relation(function_inverse(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
relation_rng(esk13_0) = relation_dom(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
one_to_one(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
function(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
( ~ function(X2)
| ~ function(X1)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X3)
| ~ one_to_one(X2)
| relation_composition(X1,X3) != identity_relation(relation_rng(X2))
| relation_composition(X3,function_inverse(X2)) != identity_relation(relation_rng(X1))
| X1 = function_inverse(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).
cnf(c_0_22,negated_conjecture,
identity_relation(relation_rng(esk13_0)) = relation_composition(esk12_0,function_inverse(esk12_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_23,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,negated_conjecture,
( ~ function(X1)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ one_to_one(X1)
| relation_composition(esk13_0,X2) != identity_relation(relation_rng(X1))
| relation_composition(X2,function_inverse(X1)) != relation_composition(esk12_0,function_inverse(esk12_0))
| function_inverse(X1) = esk13_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_26,negated_conjecture,
relation_composition(esk13_0,esk12_0) = identity_relation(relation_rng(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,negated_conjecture,
esk13_0 != function_inverse(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_25]),c_0_26]),c_0_18]),c_0_19]),c_0_20])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU031+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n020.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 05:48:18 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.85/1.07 % Version: 3.5.1
% 3.85/1.07 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.85/1.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.85/1.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.85/1.07 % Starting new_bool_3 with 300s (1) cores
% 3.85/1.07 % Starting new_bool_1 with 300s (1) cores
% 3.85/1.07 % Starting sh5l with 300s (1) cores
% 3.85/1.07 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2135214 completed with status 0
% 3.85/1.07 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.85/1.07 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.85/1.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.85/1.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.85/1.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.85/1.07 % No SInE strategy applied
% 3.85/1.07 % Search class: FGHSM-FFMM21-SFFFFFNN
% 3.85/1.07 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.85/1.07 % Starting SubtermCWHack with 136s (1) cores
% 3.85/1.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.85/1.07 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 3.85/1.07 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 3.85/1.07 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 3.85/1.07 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with pid 2135223 completed with status 0
% 3.85/1.07 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y
% 3.85/1.07 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.85/1.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.85/1.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.85/1.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.85/1.07 % No SInE strategy applied
% 3.85/1.07 % Search class: FGHSM-FFMM21-SFFFFFNN
% 3.85/1.07 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.85/1.07 % Starting SubtermCWHack with 136s (1) cores
% 3.85/1.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.85/1.07 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 3.85/1.07 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 3.85/1.07 % Preprocessing time : 0.004 s
% 3.85/1.07
% 3.85/1.07 % Proof found!
% 3.85/1.07 % SZS status Theorem
% 3.85/1.07 % SZS output start CNFRefutation
% See solution above
% 3.85/1.07 % Parsed axioms : 43
% 3.85/1.07 % Removed by relevancy pruning/SinE : 0
% 3.85/1.07 % Initial clauses : 75
% 3.85/1.07 % Removed in clause preprocessing : 2
% 3.85/1.07 % Initial clauses in saturation : 73
% 3.85/1.07 % Processed clauses : 1187
% 3.85/1.07 % ...of these trivial : 6
% 3.85/1.07 % ...subsumed : 698
% 3.85/1.07 % ...remaining for further processing : 483
% 3.85/1.07 % Other redundant clauses eliminated : 0
% 3.85/1.07 % Clauses deleted for lack of memory : 0
% 3.85/1.07 % Backward-subsumed : 177
% 3.85/1.07 % Backward-rewritten : 26
% 3.85/1.07 % Generated clauses : 8474
% 3.85/1.07 % ...of the previous two non-redundant : 7708
% 3.85/1.07 % ...aggressively subsumed : 0
% 3.85/1.07 % Contextual simplify-reflections : 139
% 3.85/1.07 % Paramodulations : 8463
% 3.85/1.07 % Factorizations : 0
% 3.85/1.07 % NegExts : 0
% 3.85/1.07 % Equation resolutions : 11
% 3.85/1.07 % Disequality decompositions : 0
% 3.85/1.07 % Total rewrite steps : 3496
% 3.85/1.07 % ...of those cached : 3445
% 3.85/1.07 % Propositional unsat checks : 0
% 3.85/1.07 % Propositional check models : 0
% 3.85/1.07 % Propositional check unsatisfiable : 0
% 3.85/1.07 % Propositional clauses : 0
% 3.85/1.07 % Propositional clauses after purity: 0
% 3.85/1.07 % Propositional unsat core size : 0
% 3.85/1.07 % Propositional preprocessing time : 0.000
% 3.85/1.07 % Propositional encoding time : 0.000
% 3.85/1.07 % Propositional solver time : 0.000
% 3.85/1.07 % Success case prop preproc time : 0.000
% 3.85/1.07 % Success case prop encoding time : 0.000
% 3.85/1.07 % Success case prop solver time : 0.000
% 3.85/1.07 % Current number of processed clauses : 280
% 3.85/1.07 % Positive orientable unit clauses : 37
% 3.85/1.07 % Positive unorientable unit clauses: 0
% 3.85/1.07 % Negative unit clauses : 8
% 3.85/1.07 % Non-unit-clauses : 235
% 3.85/1.07 % Current number of unprocessed clauses: 5789
% 3.85/1.07 % ...number of literals in the above : 45026
% 3.85/1.07 % Current number of archived formulas : 0
% 3.85/1.07 % Current number of archived clauses : 203
% 3.85/1.07 % Clause-clause subsumption calls (NU) : 35178
% 3.85/1.07 % Rec. Clause-clause subsumption calls : 14795
% 3.85/1.07 % Non-unit clause-clause subsumptions : 702
% 3.85/1.07 % Unit Clause-clause subsumption calls : 702
% 3.85/1.07 % Rewrite failures with RHS unbound : 0
% 3.85/1.07 % BW rewrite match attempts : 7
% 3.85/1.07 % BW rewrite match successes : 7
% 3.85/1.07 % Condensation attempts : 0
% 3.85/1.07 % Condensation successes : 0
% 3.85/1.07 % Termbank termtop insertions : 144388
% 3.85/1.07 % Search garbage collected termcells : 651
% 3.85/1.07
% 3.85/1.07 % -------------------------------------------------
% 3.85/1.07 % User time : 0.431 s
% 3.85/1.07 % System time : 0.016 s
% 3.85/1.07 % Total time : 0.447 s
% 3.85/1.07 % Maximum resident set size: 3668 pages
% 3.85/1.07
% 3.85/1.07 % -------------------------------------------------
% 3.85/1.07 % User time : 2.403 s
% 3.85/1.07 % System time : 0.094 s
% 3.85/1.07 % Total time : 2.498 s
% 3.85/1.07 % Maximum resident set size: 4864 pages
% 3.85/1.07 % E exiting
%------------------------------------------------------------------------------