%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL081-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:09:33 PM UTC 2026
% Result : Unsatisfiable 0.15s 1.25s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 18 ( 14 unt; 0 nHn; 8 RR)
% Number of literals : 22 ( 21 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(extensionality2,axiom,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',extensionality2) ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',abstraction) ).
cnf(k_definition,axiom,
apply(k(X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',k_definition) ).
cnf(prove_TRC2c,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC2c) ).
cnf(c_0_4,plain,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[extensionality2]) ).
cnf(c_0_5,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
abstraction ).
cnf(c_0_6,axiom,
apply(k(X1),X2) = X1,
k_definition ).
cnf(c_0_7,plain,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
c_0_4 ).
cnf(c_0_8,plain,
apply(apply(apply(apply(abstraction,abstraction),X1),X2),X3) = apply(X2,apply(apply(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_5]),c_0_6]) ).
cnf(c_0_9,plain,
( apply(X2,n(k(X1),X2)) != X1
| k(X1) = X2 ),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_10,plain,
apply(apply(apply(apply(abstraction,abstraction),X1),k(X2)),X3) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_11,plain,
apply(apply(apply(abstraction,X1),k(X2)),X3) = apply(apply(X1,k(X3)),X2),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_12,plain,
apply(apply(apply(abstraction,abstraction),X1),k(X2)) = k(X2),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10])]) ).
cnf(c_0_13,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
inference(fof_simplification,[status(thm)],[prove_TRC2c]) ).
cnf(c_0_14,plain,
apply(apply(abstraction,k(k(X1))),X2) = k(X1),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
c_0_13 ).
cnf(c_0_16,plain,
apply(abstraction,k(k(X1))) = k(k(X1)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_14])]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.63 % Problem : COL081-1 : TPTP v9.3.1. Released v1.2.0.
% 0.01/0.65 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/1.12 % Computer : n010.cluster.edu
% 0.11/1.12 % Model : x86_64 x86_64
% 0.11/1.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/1.12 % Memory : 8046.5625MB
% 0.11/1.12 % OS : Linux 6.8.0-71-generic
% 0.11/1.12 % CPULimit : 300
% 0.11/1.12 % WCLimit : 300
% 0.11/1.12 % DateTime : Mon Sep 21 14:09:58 UTC 2026
% 0.11/1.13 % CPUTime :
% 0.15/1.13 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/1.17 Running first-order theorem proving
% 0.15/1.17 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
% 0.15/1.25 % Version: 3.5.1
% 0.15/1.25 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/1.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/1.25 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/1.25 % Starting new_bool_3 with 300s (1) cores
% 0.15/1.25 % Starting new_bool_1 with 300s (1) cores
% 0.15/1.25 % Starting sh5l with 300s (1) cores
% 0.15/1.25 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1062335 completed with status 0
% 0.15/1.25 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.15/1.25 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/1.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/1.25 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/1.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/1.25 % No SInE strategy applied
% 0.15/1.25 % Search class: FGUPM-FFSF21-MFFFFFNN
% 0.15/1.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/1.25 % Starting SubtermCWHack with 136s (1) cores
% 0.15/1.25 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.15/1.25 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 136s (1) cores
% 0.15/1.25 % Starting new_bool_3 with 136s (1) cores
% 0.15/1.25 % Starting new_bool_1 with 136s (1) cores
% 0.15/1.25 % C12_02_nc_SAT001_MinMin_p005000_rr with pid 1062343 completed with status 0
% 0.15/1.25 % Result found by C12_02_nc_SAT001_MinMin_p005000_rr
% 0.15/1.25 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/1.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/1.25 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/1.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/1.25 % No SInE strategy applied
% 0.15/1.25 % Search class: FGUPM-FFSF21-MFFFFFNN
% 0.15/1.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/1.25 % Starting SubtermCWHack with 136s (1) cores
% 0.15/1.25 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.15/1.25 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 136s (1) cores
% 0.15/1.25 % Preprocessing time : 0.001 s
% 0.15/1.25 % Presaturation interreduction done
% 0.15/1.25
% 0.15/1.25 % Proof found!
% 0.15/1.25 % SZS status Unsatisfiable
% 0.15/1.25 % SZS output start CNFRefutation
% See solution above
% 0.15/1.25 % Parsed axioms : 12
% 0.15/1.25 % Removed by relevancy pruning/SinE : 0
% 0.15/1.25 % Initial clauses : 12
% 0.15/1.25 % Removed in clause preprocessing : 0
% 0.15/1.25 % Initial clauses in saturation : 12
% 0.15/1.25 % Processed clauses : 345
% 0.15/1.25 % ...of these trivial : 17
% 0.15/1.25 % ...subsumed : 77
% 0.15/1.25 % ...remaining for further processing : 251
% 0.15/1.25 % Other redundant clauses eliminated : 18
% 0.15/1.25 % Clauses deleted for lack of memory : 0
% 0.15/1.25 % Backward-subsumed : 0
% 0.15/1.25 % Backward-rewritten : 55
% 0.15/1.25 % Generated clauses : 3665
% 0.15/1.25 % ...of the previous two non-redundant : 2919
% 0.15/1.25 % ...aggressively subsumed : 0
% 0.15/1.25 % Contextual simplify-reflections : 0
% 0.15/1.25 % Paramodulations : 3646
% 0.15/1.25 % Factorizations : 0
% 0.15/1.25 % NegExts : 0
% 0.15/1.25 % Equation resolutions : 19
% 0.15/1.25 % Disequality decompositions : 0
% 0.15/1.25 % Total rewrite steps : 2906
% 0.15/1.25 % ...of those cached : 1776
% 0.15/1.25 % Propositional unsat checks : 0
% 0.15/1.25 % Propositional check models : 0
% 0.15/1.25 % Propositional check unsatisfiable : 0
% 0.15/1.25 % Propositional clauses : 0
% 0.15/1.25 % Propositional clauses after purity: 0
% 0.15/1.25 % Propositional unsat core size : 0
% 0.15/1.25 % Propositional preprocessing time : 0.000
% 0.15/1.25 % Propositional encoding time : 0.000
% 0.15/1.25 % Propositional solver time : 0.000
% 0.15/1.25 % Success case prop preproc time : 0.000
% 0.15/1.25 % Success case prop encoding time : 0.000
% 0.15/1.25 % Success case prop solver time : 0.000
% 0.15/1.25 % Current number of processed clauses : 184
% 0.15/1.25 % Positive orientable unit clauses : 159
% 0.15/1.25 % Positive unorientable unit clauses: 4
% 0.15/1.25 % Negative unit clauses : 1
% 0.15/1.25 % Non-unit-clauses : 20
% 0.15/1.25 % Current number of unprocessed clauses: 2408
% 0.15/1.25 % ...number of literals in the above : 2799
% 0.15/1.25 % Current number of archived formulas : 0
% 0.15/1.25 % Current number of archived clauses : 67
% 0.15/1.25 % Clause-clause subsumption calls (NU) : 128
% 0.15/1.25 % Rec. Clause-clause subsumption calls : 128
% 0.15/1.25 % Non-unit clause-clause subsumptions : 76
% 0.15/1.25 % Unit Clause-clause subsumption calls : 56
% 0.15/1.25 % Rewrite failures with RHS unbound : 0
% 0.15/1.25 % BW rewrite match attempts : 628
% 0.15/1.25 % BW rewrite match successes : 64
% 0.15/1.25 % Condensation attempts : 0
% 0.15/1.25 % Condensation successes : 0
% 0.15/1.25 % Termbank termtop insertions : 59193
% 0.15/1.25 % Search garbage collected termcells : 7
% 0.15/1.25
% 0.15/1.25 % -------------------------------------------------
% 0.15/1.25 % User time : 0.056 s
% 0.15/1.25 % System time : 0.007 s
% 0.15/1.25 % Total time : 0.063 s
% 0.15/1.25 % Maximum resident set size: 3640 pages
% 0.15/1.25
% 0.15/1.25 % -------------------------------------------------
% 0.15/1.25 % User time : 0.291 s
% 0.15/1.25 % System time : 0.027 s
% 0.15/1.25 % Total time : 0.318 s
% 0.15/1.25 % Maximum resident set size: 4864 pages
% 0.15/1.25 % E exiting
%------------------------------------------------------------------------------