%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP209_3 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:54:33 PM UTC 2026
% Result : Theorem 0.14s 0.60s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
a: $tType ).
tff(decl_sort2,type,
fun_a_fun_a_a: $tType ).
tff(decl_sort3,type,
fun_a_a: $tType ).
tff(decl_24,type,
aa_a_fun_a_a: ( a * fun_a_fun_a_a ) > fun_a_a ).
tff(decl_25,type,
aa_a_a: ( a * fun_a_a ) > a ).
tff(decl_26,type,
a2: a ).
tff(decl_27,type,
b: a ).
tff(decl_28,type,
c: a ).
tff(decl_29,type,
f: fun_a_fun_a_a ).
tff(conj_0,conjecture,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(fact_3_right__assoc,axiom,
! [X1: a,X2: a,X3: a] : ( aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,X1),X2)),X3) = aa_a_a(aa_a_fun_a_a(f,X1),aa_a_a(aa_a_fun_a_a(f,X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_right__assoc) ).
tff(fact_1_commute,axiom,
! [X1: a,X2: a] : ( aa_a_a(aa_a_fun_a_a(f,X1),X2) = aa_a_a(aa_a_fun_a_a(f,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_commute) ).
tff(c_0_3,negated_conjecture,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_4,negated_conjecture,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
tff(c_0_5,negated_conjecture,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
inference(fof_nnf,[status(thm)],[c_0_4]) ).
tff(c_0_6,plain,
! [X49: a,X50: a,X51: a] : ( aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,X49),X50)),X51) = aa_a_a(aa_a_fun_a_a(f,X49),aa_a_a(aa_a_fun_a_a(f,X50),X51)) ),
inference(variable_rename,[status(thm)],[fact_3_right__assoc]) ).
tff(c_0_7,plain,
! [X44: a,X45: a] : ( aa_a_a(aa_a_fun_a_a(f,X44),X45) = aa_a_a(aa_a_fun_a_a(f,X45),X44) ),
inference(variable_rename,[status(thm)],[fact_1_commute]) ).
tcf(c_0_8,negated_conjecture,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
tcf(c_0_9,plain,
! [X1: a,X2: a,X3: a] : aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,X1),X2)),X3) = aa_a_a(aa_a_fun_a_a(f,X1),aa_a_a(aa_a_fun_a_a(f,X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
tcf(c_0_10,plain,
! [X2: a,X1: a] : aa_a_a(aa_a_fun_a_a(f,X1),X2) = aa_a_a(aa_a_fun_a_a(f,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP209_3 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.53 % Computer : n018.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Sun Sep 20 22:09:44 UTC 2026
% 0.09/0.53 % CPUTime :
% 0.09/0.53 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.58 Running first-order theorem proving
% 0.14/0.58 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.14/0.60 % Version: 3.5.1
% 0.14/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.60 % Starting sh5l with 300s (1) cores
% 0.14/0.60 % new_bool_3 with pid 290825 completed with status 0
% 0.14/0.60 % Result found by new_bool_3
% 0.14/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.60 % Search class: FHUSS-FFMF21-MFFFFFNN
% 0.14/0.60 % partial match(1): FHUSM-FFMF21-MFFFFFNN
% 0.14/0.60 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.60 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.60 % SubtermCWHack with pid 290833 completed with status 0
% 0.14/0.60 % Result found by SubtermCWHack
% 0.14/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.60 % Search class: FHUSS-FFMF21-MFFFFFNN
% 0.14/0.60 % partial match(1): FHUSM-FFMF21-MFFFFFNN
% 0.14/0.60 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.60 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.60 % Preprocessing time : 0.001 s
% 0.14/0.60
% 0.14/0.60 % Proof found!
% 0.14/0.60 % SZS status Theorem
% 0.14/0.60 % SZS output start CNFRefutation
% See solution above
% 0.14/0.60 % Parsed axioms : 21
% 0.14/0.60 % Removed by relevancy pruning/SinE : 10
% 0.14/0.60 % Initial clauses : 13
% 0.14/0.60 % Removed in clause preprocessing : 0
% 0.14/0.60 % Initial clauses in saturation : 13
% 0.14/0.60 % Processed clauses : 7
% 0.14/0.60 % ...of these trivial : 0
% 0.14/0.60 % ...subsumed : 1
% 0.14/0.60 % ...remaining for further processing : 5
% 0.14/0.60 % Other redundant clauses eliminated : 0
% 0.14/0.60 % Clauses deleted for lack of memory : 0
% 0.14/0.60 % Backward-subsumed : 0
% 0.14/0.60 % Backward-rewritten : 0
% 0.14/0.60 % Generated clauses : 35
% 0.14/0.60 % ...of the previous two non-redundant : 34
% 0.14/0.60 % ...aggressively subsumed : 0
% 0.14/0.60 % Contextual simplify-reflections : 0
% 0.14/0.60 % Paramodulations : 35
% 0.14/0.60 % Factorizations : 0
% 0.14/0.60 % NegExts : 0
% 0.14/0.60 % Equation resolutions : 0
% 0.14/0.60 % Disequality decompositions : 0
% 0.14/0.60 % Total rewrite steps : 32
% 0.14/0.60 % ...of those cached : 20
% 0.14/0.60 % Propositional unsat checks : 0
% 0.14/0.60 % Propositional check models : 0
% 0.14/0.60 % Propositional check unsatisfiable : 0
% 0.14/0.60 % Propositional clauses : 0
% 0.14/0.60 % Propositional clauses after purity: 0
% 0.14/0.60 % Propositional unsat core size : 0
% 0.14/0.60 % Propositional preprocessing time : 0.000
% 0.14/0.60 % Propositional encoding time : 0.000
% 0.14/0.60 % Propositional solver time : 0.000
% 0.14/0.60 % Success case prop preproc time : 0.000
% 0.14/0.60 % Success case prop encoding time : 0.000
% 0.14/0.60 % Success case prop solver time : 0.000
% 0.14/0.60 % Current number of processed clauses : 5
% 0.14/0.60 % Positive orientable unit clauses : 2
% 0.14/0.60 % Positive unorientable unit clauses: 2
% 0.14/0.60 % Negative unit clauses : 0
% 0.14/0.60 % Non-unit-clauses : 1
% 0.14/0.60 % Current number of unprocessed clauses: 40
% 0.14/0.60 % ...number of literals in the above : 48
% 0.14/0.60 % Current number of archived formulas : 0
% 0.14/0.60 % Current number of archived clauses : 0
% 0.14/0.60 % Clause-clause subsumption calls (NU) : 1
% 0.14/0.60 % Rec. Clause-clause subsumption calls : 1
% 0.14/0.60 % Non-unit clause-clause subsumptions : 1
% 0.14/0.60 % Unit Clause-clause subsumption calls : 0
% 0.14/0.60 % Rewrite failures with RHS unbound : 0
% 0.14/0.60 % BW rewrite match attempts : 0
% 0.14/0.60 % BW rewrite match successes : 0
% 0.14/0.60 % Condensation attempts : 0
% 0.14/0.60 % Condensation successes : 0
% 0.14/0.60 % Termbank termtop insertions : 1982
% 0.14/0.60 % Search garbage collected termcells : 200
% 0.14/0.60
% 0.14/0.60 % -------------------------------------------------
% 0.14/0.60 % User time : 0.005 s
% 0.14/0.60 % System time : 0.001 s
% 0.14/0.60 % Total time : 0.006 s
% 0.14/0.60 % Maximum resident set size: 3652 pages
% 0.14/0.60
% 0.14/0.60 % -------------------------------------------------
% 0.14/0.60 % User time : 0.007 s
% 0.14/0.60 % System time : 0.005 s
% 0.14/0.60 % Total time : 0.013 s
% 0.14/0.60 % Maximum resident set size: 4608 pages
% 0.14/0.60 % E exiting
%------------------------------------------------------------------------------