%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU034+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 : n013.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 0.14s 0.78s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 17 unt; 0 def)
% Number of atoms : 101 ( 34 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 109 ( 44 ~; 41 |; 16 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 36 ( 3 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t52_funct_1,axiom,
! [X1] : one_to_one(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
fof(t71_relat_1,axiom,
! [X1] :
( relation_rng(identity_relation(X1)) = X1
& relation_dom(identity_relation(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( function(identity_relation(X1))
& relation(identity_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_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(t44_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_composition(X1,X2) = X1
& relation_rng(X1) = relation_dom(X2) )
=> X2 = identity_relation(relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_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(t67_funct_1,conjecture,
! [X1] : function_inverse(identity_relation(X1)) = identity_relation(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_1) ).
fof(c_0_9,plain,
! [X56] :
( ( ~ function(X56)
| ~ relation(X56)
| ~ one_to_one(X56)
| relation_composition(function_inverse(X56),X56) = identity_relation(relation_rng(X56)) )
& ( ~ function(X56)
| ~ relation(X56)
| ~ one_to_one(X56)
| relation_composition(X56,function_inverse(X56)) = identity_relation(relation_dom(X56)) ) ),
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_10,plain,
! [X51] : one_to_one(identity_relation(X51)),
inference(variable_rename,[status(thm)],[t52_funct_1]) ).
fof(c_0_11,plain,
! [X59] :
( relation_rng(identity_relation(X59)) = X59
& relation_dom(identity_relation(X59)) = X59 ),
inference(variable_rename,[status(thm)],[t71_relat_1]) ).
fof(c_0_12,plain,
! [X12] : relation(identity_relation(X12)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_13,plain,
! [X20] :
( function(identity_relation(X20))
& relation(identity_relation(X20)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(c_0_14,plain,
! [X52] :
( ( ~ function(X52)
| ~ relation(X52)
| ~ one_to_one(X52)
| relation_dom(X52) = relation_rng(function_inverse(X52)) )
& ( ~ function(X52)
| ~ relation(X52)
| ~ one_to_one(X52)
| relation_rng(X52) = relation_dom(function_inverse(X52)) ) ),
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_15,plain,
! [X46,X47] :
( X47 = identity_relation(relation_dom(X47))
| relation_composition(X46,X47) != X46
| relation_rng(X46) != relation_dom(X47)
| ~ function(X47)
| ~ relation(X47)
| ~ function(X46)
| ~ relation(X46) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t44_funct_1])])])]) ).
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_9]) ).
cnf(c_0_17,plain,
one_to_one(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| relation_rng(X1) = relation_dom(function_inverse(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
relation_rng(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,plain,
( relation_composition(X1,X2) != X1
| relation_rng(X1) != relation_dom(X2)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| X2 = identity_relation(relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
relation_composition(identity_relation(X1),function_inverse(identity_relation(X1))) = identity_relation(X1),
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_25,plain,
relation_dom(function_inverse(identity_relation(X1))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_22]),c_0_17]),c_0_20])]) ).
fof(c_0_26,plain,
! [X9] :
( ( ~ function(X9)
| ~ relation(X9)
| function(function_inverse(X9)) )
& ( ~ function(X9)
| ~ relation(X9)
| relation(function_inverse(X9)) ) ),
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_27,negated_conjecture,
~ ! [X1] : function_inverse(identity_relation(X1)) = identity_relation(X1),
inference(assume_negation,[status(cth)],[t67_funct_1]) ).
cnf(c_0_28,plain,
( ~ function(function_inverse(identity_relation(X1)))
| ~ relation(function_inverse(identity_relation(X1)))
| function_inverse(identity_relation(X1)) = identity_relation(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_22]),c_0_25]),c_0_19]),c_0_20])]) ).
cnf(c_0_29,plain,
( ~ function(X1)
| ~ relation(X1)
| relation(function_inverse(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_30,negated_conjecture,
function_inverse(identity_relation(esk12_0)) != identity_relation(esk12_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
cnf(c_0_31,plain,
( ~ function(function_inverse(identity_relation(X1)))
| function_inverse(identity_relation(X1)) = identity_relation(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_19]),c_0_20])]) ).
cnf(c_0_32,plain,
( ~ function(X1)
| ~ relation(X1)
| function(function_inverse(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
function_inverse(identity_relation(esk12_0)) != identity_relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
function_inverse(identity_relation(X1)) = identity_relation(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_19]),c_0_20])]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU034+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.55 % Computer : n013.cluster.edu
% 0.10/0.55 % Model : x86_64 x86_64
% 0.10/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.55 % Memory : 8046.5625MB
% 0.10/0.55 % OS : Linux 6.8.0-71-generic
% 0.10/0.55 % CPULimit : 300
% 0.10/0.55 % WCLimit : 300
% 0.10/0.55 % DateTime : Mon Sep 21 05:46:37 UTC 2026
% 0.10/0.55 % CPUTime :
% 0.10/0.55 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.59 Running first-order theorem proving
% 0.14/0.59 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
% 0.14/0.78 % Version: 3.5.1
% 0.14/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.78 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.78 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.78 % Starting sh5l with 300s (1) cores
% 0.14/0.78 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 59599 completed with status 0
% 0.14/0.78 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.78 % No SInE strategy applied
% 0.14/0.78 % Search class: FGHSM-FFMM21-SFFFFFNN
% 0.14/0.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.78 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.78 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.78 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.14/0.78 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 0.14/0.78 % G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with pid 59607 completed with status 0
% 0.14/0.78 % Result found by G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN
% 0.14/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.78 % No SInE strategy applied
% 0.14/0.78 % Search class: FGHSM-FFMM21-SFFFFFNN
% 0.14/0.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.78 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.78 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.78 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.14/0.78 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 0.14/0.78 % Preprocessing time : 0.001 s
% 0.14/0.78 % Presaturation interreduction done
% 0.14/0.78
% 0.14/0.78 % Proof found!
% 0.14/0.78 % SZS status Theorem
% 0.14/0.78 % SZS output start CNFRefutation
% See solution above
% 0.14/0.78 % Parsed axioms : 45
% 0.14/0.78 % Removed by relevancy pruning/SinE : 0
% 0.14/0.78 % Initial clauses : 71
% 0.14/0.78 % Removed in clause preprocessing : 2
% 0.14/0.78 % Initial clauses in saturation : 69
% 0.14/0.78 % Processed clauses : 1532
% 0.14/0.78 % ...of these trivial : 5
% 0.14/0.78 % ...subsumed : 711
% 0.14/0.78 % ...remaining for further processing : 816
% 0.14/0.78 % Other redundant clauses eliminated : 0
% 0.14/0.78 % Clauses deleted for lack of memory : 0
% 0.14/0.78 % Backward-subsumed : 14
% 0.14/0.78 % Backward-rewritten : 213
% 0.14/0.78 % Generated clauses : 13693
% 0.14/0.78 % ...of the previous two non-redundant : 8223
% 0.14/0.78 % ...aggressively subsumed : 0
% 0.14/0.78 % Contextual simplify-reflections : 32
% 0.14/0.78 % Paramodulations : 13693
% 0.14/0.78 % Factorizations : 0
% 0.14/0.78 % NegExts : 0
% 0.14/0.78 % Equation resolutions : 0
% 0.14/0.78 % Disequality decompositions : 0
% 0.14/0.78 % Total rewrite steps : 32987
% 0.14/0.78 % ...of those cached : 32452
% 0.14/0.78 % Propositional unsat checks : 0
% 0.14/0.78 % Propositional check models : 0
% 0.14/0.78 % Propositional check unsatisfiable : 0
% 0.14/0.78 % Propositional clauses : 0
% 0.14/0.78 % Propositional clauses after purity: 0
% 0.14/0.78 % Propositional unsat core size : 0
% 0.14/0.78 % Propositional preprocessing time : 0.000
% 0.14/0.78 % Propositional encoding time : 0.000
% 0.14/0.78 % Propositional solver time : 0.000
% 0.14/0.78 % Success case prop preproc time : 0.000
% 0.14/0.78 % Success case prop encoding time : 0.000
% 0.14/0.78 % Success case prop solver time : 0.000
% 0.14/0.78 % Current number of processed clauses : 525
% 0.14/0.78 % Positive orientable unit clauses : 47
% 0.14/0.78 % Positive unorientable unit clauses: 0
% 0.14/0.78 % Negative unit clauses : 5
% 0.14/0.78 % Non-unit-clauses : 473
% 0.14/0.78 % Current number of unprocessed clauses: 6585
% 0.14/0.78 % ...number of literals in the above : 17007
% 0.14/0.78 % Current number of archived formulas : 0
% 0.14/0.78 % Current number of archived clauses : 291
% 0.14/0.78 % Clause-clause subsumption calls (NU) : 73866
% 0.14/0.78 % Rec. Clause-clause subsumption calls : 68948
% 0.14/0.78 % Non-unit clause-clause subsumptions : 721
% 0.14/0.78 % Unit Clause-clause subsumption calls : 773
% 0.14/0.78 % Rewrite failures with RHS unbound : 0
% 0.14/0.78 % BW rewrite match attempts : 114
% 0.14/0.78 % BW rewrite match successes : 111
% 0.14/0.78 % Condensation attempts : 0
% 0.14/0.78 % Condensation successes : 0
% 0.14/0.78 % Termbank termtop insertions : 214327
% 0.14/0.78 % Search garbage collected termcells : 543
% 0.14/0.78
% 0.14/0.78 % -------------------------------------------------
% 0.14/0.78 % User time : 0.146 s
% 0.14/0.78 % System time : 0.010 s
% 0.14/0.78 % Total time : 0.156 s
% 0.14/0.78 % Maximum resident set size: 3664 pages
% 0.14/0.78
% 0.14/0.78 % -------------------------------------------------
% 0.14/0.78 % User time : 0.765 s
% 0.14/0.78 % System time : 0.044 s
% 0.14/0.78 % Total time : 0.808 s
% 0.14/0.78 % Maximum resident set size: 4608 pages
% 0.14/0.78 % E exiting
%------------------------------------------------------------------------------