%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL081-2 : 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 : n004.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 5.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 16 ( 11 unt; 0 nHn; 9 RR)
% Number of literals : 21 ( 20 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 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 : 27 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(extensionality2,axiom,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
cnf(k_definition,axiom,
apply(k(X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
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,plain,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
c_0_4 ).
cnf(c_0_6,axiom,
apply(k(X1),X2) = X1,
k_definition ).
cnf(c_0_7,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
abstraction ).
cnf(c_0_8,plain,
( apply(X2,n(k(X1),X2)) != X1
| k(X1) = X2 ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
apply(apply(apply(abstraction,k(X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_10,plain,
( apply(X2,apply(X3,n(k(X1),apply(apply(abstraction,k(X2)),X3)))) != X1
| k(X1) = apply(apply(abstraction,k(X2)),X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
inference(fof_simplification,[status(thm)],[prove_TRC2c]) ).
cnf(c_0_12,plain,
apply(apply(abstraction,k(k(X1))),X2) = k(X1),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_6])]) ).
cnf(c_0_13,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
c_0_11 ).
cnf(c_0_14,plain,
apply(abstraction,k(k(X1))) = k(k(X1)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_12])]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/5.38 % Computer : n004.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 14:09:41 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.45 % Version: 3.5.1
% 0.15/5.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.45 % Starting sh5l with 300s (1) cores
% 0.15/5.45 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3335096 completed with status 0
% 0.15/5.45 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.15/5.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.45 % No SInE strategy applied
% 0.15/5.45 % Search class: FHUPS-FFSF21-MFFFFFNN
% 0.15/5.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.45 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.15/5.45 % Starting U----_211g_00_C10_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/5.45 % Starting new_bool_3 with 136s (1) cores
% 0.15/5.45 % Starting new_bool_1 with 136s (1) cores
% 0.15/5.45 % U----_211g_00_C10_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3335104 completed with status 0
% 0.15/5.45 % Result found by U----_211g_00_C10_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.15/5.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.45 % No SInE strategy applied
% 0.15/5.45 % Search class: FHUPS-FFSF21-MFFFFFNN
% 0.15/5.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.45 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.15/5.45 % Starting U----_211g_00_C10_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/5.45 % Preprocessing time : 0.001 s
% 0.15/5.45 % Presaturation interreduction done
% 0.15/5.45
% 0.15/5.45 % Proof found!
% 0.15/5.45 % SZS status Unsatisfiable
% 0.15/5.45 % SZS output start CNFRefutation
% See solution above
% 0.15/5.45 % Parsed axioms : 5
% 0.15/5.45 % Removed by relevancy pruning/SinE : 0
% 0.15/5.45 % Initial clauses : 5
% 0.15/5.45 % Removed in clause preprocessing : 0
% 0.15/5.45 % Initial clauses in saturation : 5
% 0.15/5.45 % Processed clauses : 42
% 0.15/5.45 % ...of these trivial : 0
% 0.15/5.45 % ...subsumed : 8
% 0.15/5.45 % ...remaining for further processing : 34
% 0.15/5.45 % Other redundant clauses eliminated : 17
% 0.15/5.45 % Clauses deleted for lack of memory : 0
% 0.15/5.45 % Backward-subsumed : 0
% 0.15/5.45 % Backward-rewritten : 5
% 0.15/5.45 % Generated clauses : 214
% 0.15/5.45 % ...of the previous two non-redundant : 161
% 0.15/5.45 % ...aggressively subsumed : 0
% 0.15/5.45 % Contextual simplify-reflections : 0
% 0.15/5.45 % Paramodulations : 196
% 0.15/5.45 % Factorizations : 0
% 0.15/5.45 % NegExts : 0
% 0.15/5.45 % Equation resolutions : 18
% 0.15/5.45 % Disequality decompositions : 0
% 0.15/5.45 % Total rewrite steps : 103
% 0.15/5.45 % ...of those cached : 41
% 0.15/5.45 % Propositional unsat checks : 0
% 0.15/5.45 % Propositional check models : 0
% 0.15/5.45 % Propositional check unsatisfiable : 0
% 0.15/5.45 % Propositional clauses : 0
% 0.15/5.45 % Propositional clauses after purity: 0
% 0.15/5.45 % Propositional unsat core size : 0
% 0.15/5.45 % Propositional preprocessing time : 0.000
% 0.15/5.45 % Propositional encoding time : 0.000
% 0.15/5.45 % Propositional solver time : 0.000
% 0.15/5.45 % Success case prop preproc time : 0.000
% 0.15/5.45 % Success case prop encoding time : 0.000
% 0.15/5.45 % Success case prop solver time : 0.000
% 0.15/5.45 % Current number of processed clauses : 24
% 0.15/5.45 % Positive orientable unit clauses : 12
% 0.15/5.45 % Positive unorientable unit clauses: 0
% 0.15/5.45 % Negative unit clauses : 0
% 0.15/5.45 % Non-unit-clauses : 12
% 0.15/5.45 % Current number of unprocessed clauses: 113
% 0.15/5.45 % ...number of literals in the above : 170
% 0.15/5.45 % Current number of archived formulas : 0
% 0.15/5.45 % Current number of archived clauses : 10
% 0.15/5.45 % Clause-clause subsumption calls (NU) : 24
% 0.15/5.45 % Rec. Clause-clause subsumption calls : 24
% 0.15/5.45 % Non-unit clause-clause subsumptions : 8
% 0.15/5.45 % Unit Clause-clause subsumption calls : 0
% 0.15/5.45 % Rewrite failures with RHS unbound : 0
% 0.15/5.45 % BW rewrite match attempts : 17
% 0.15/5.45 % BW rewrite match successes : 5
% 0.15/5.45 % Condensation attempts : 0
% 0.15/5.45 % Condensation successes : 0
% 0.15/5.45 % Termbank termtop insertions : 3476
% 0.15/5.45 % Search garbage collected termcells : 5
% 0.15/5.45
% 0.15/5.45 % -------------------------------------------------
% 0.15/5.45 % User time : 0.006 s
% 0.15/5.45 % System time : 0.003 s
% 0.15/5.45 % Total time : 0.010 s
% 0.15/5.45 % Maximum resident set size: 3632 pages
% 0.15/5.45
% 0.15/5.45 % -------------------------------------------------
% 0.15/5.45 % User time : 0.033 s
% 0.15/5.45 % System time : 0.014 s
% 0.15/5.45 % Total time : 0.048 s
% 0.15/5.45 % Maximum resident set size: 4608 pages
% 0.15/5.45 % E exiting
%------------------------------------------------------------------------------