%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:09:16 PM UTC 2026
% Result : Unsatisfiable 0.14s 6.01s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 17 ( 14 unt; 0 nHn; 8 RR)
% Number of literals : 20 ( 13 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(w_definition,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
cnf(prove_strong_fixed_point,negated_conjecture,
~ fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(strong_fixed_point,axiom,
( apply(X1,fixed_pt) != apply(fixed_pt,apply(X1,fixed_pt))
| fixed_point(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
cnf(c_0_4,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_5,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
w_definition ).
cnf(c_0_6,plain,
apply(apply(w,apply(b,X1)),X2) = apply(X1,apply(X2,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,negated_conjecture,
~ fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b)))),
inference(fof_simplification,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_0_8,plain,
( apply(X1,fixed_pt) != apply(fixed_pt,apply(X1,fixed_pt))
| fixed_point(X1) ),
inference(fof_simplification,[status(thm)],[strong_fixed_point]) ).
cnf(c_0_9,plain,
apply(apply(apply(w,apply(b,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X2),X3)),
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_10,plain,
apply(apply(w,w),X1) = apply(apply(X1,X1),X1),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_11,negated_conjecture,
~ fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b)))),
c_0_7 ).
cnf(c_0_12,plain,
( apply(X1,fixed_pt) != apply(fixed_pt,apply(X1,fixed_pt))
| fixed_point(X1) ),
c_0_8 ).
cnf(c_0_13,plain,
apply(apply(w,apply(w,apply(b,apply(b,X1)))),X2) = apply(X1,apply(apply(w,w),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_5]) ).
cnf(c_0_14,negated_conjecture,
apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))) != apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))),
inference(rw,[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_11,c_0_12]),c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_4]) ).
cnf(c_0_15,plain,
apply(X1,apply(apply(w,w),apply(w,apply(b,apply(b,X1))))) = apply(apply(w,w),apply(w,apply(b,apply(b,X1)))),
inference(spm,[status(thm)],[c_0_5,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.58 % Computer : n026.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.58 % DateTime : Mon Sep 21 14:06:43 UTC 2026
% 0.11/5.58 % CPUTime :
% 0.11/5.58 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.63 Running first-order theorem proving
% 0.14/5.63 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
% 0.14/6.01 % Version: 3.5.1
% 0.14/6.01 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/6.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/6.01 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/6.01 % Starting new_bool_3 with 300s (1) cores
% 0.14/6.01 % Starting new_bool_1 with 300s (1) cores
% 0.14/6.01 % Starting sh5l with 300s (1) cores
% 0.14/6.01 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2465708 completed with status 0
% 0.14/6.01 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.14/6.01 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/6.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/6.01 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/6.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/6.01 % No SInE strategy applied
% 0.14/6.01 % Search class: FHUSS-FFSF22-MFFFFFNN
% 0.14/6.01 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/6.01 % Starting SubtermCWHack with 136s (1) cores
% 0.14/6.01 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/6.01 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/6.01 % Starting new_bool_3 with 136s (1) cores
% 0.14/6.01 % Starting new_bool_1 with 136s (1) cores
% 0.14/6.01 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 2465716 completed with status 0
% 0.14/6.01 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.14/6.01 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/6.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/6.01 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/6.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/6.01 % No SInE strategy applied
% 0.14/6.01 % Search class: FHUSS-FFSF22-MFFFFFNN
% 0.14/6.01 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/6.01 % Starting SubtermCWHack with 136s (1) cores
% 0.14/6.01 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/6.01 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/6.01 % Preprocessing time : 0.001 s
% 0.14/6.01 % Presaturation interreduction done
% 0.14/6.01
% 0.14/6.01 % Proof found!
% 0.14/6.01 % SZS status Unsatisfiable
% 0.14/6.01 % SZS output start CNFRefutation
% See solution above
% 0.14/6.01 % Parsed axioms : 4
% 0.14/6.01 % Removed by relevancy pruning/SinE : 0
% 0.14/6.01 % Initial clauses : 4
% 0.14/6.01 % Removed in clause preprocessing : 0
% 0.14/6.01 % Initial clauses in saturation : 4
% 0.14/6.01 % Processed clauses : 535
% 0.14/6.01 % ...of these trivial : 175
% 0.14/6.01 % ...subsumed : 134
% 0.14/6.01 % ...remaining for further processing : 226
% 0.14/6.01 % Other redundant clauses eliminated : 0
% 0.14/6.01 % Clauses deleted for lack of memory : 0
% 0.14/6.01 % Backward-subsumed : 2
% 0.14/6.01 % Backward-rewritten : 23
% 0.14/6.01 % Generated clauses : 16033
% 0.14/6.01 % ...of the previous two non-redundant : 15598
% 0.14/6.01 % ...aggressively subsumed : 0
% 0.14/6.01 % Contextual simplify-reflections : 0
% 0.14/6.01 % Paramodulations : 16033
% 0.14/6.01 % Factorizations : 0
% 0.14/6.01 % NegExts : 0
% 0.14/6.01 % Equation resolutions : 0
% 0.14/6.01 % Disequality decompositions : 0
% 0.14/6.01 % Total rewrite steps : 5754
% 0.14/6.01 % ...of those cached : 3723
% 0.14/6.01 % Propositional unsat checks : 0
% 0.14/6.01 % Propositional check models : 0
% 0.14/6.01 % Propositional check unsatisfiable : 0
% 0.14/6.01 % Propositional clauses : 0
% 0.14/6.01 % Propositional clauses after purity: 0
% 0.14/6.01 % Propositional unsat core size : 0
% 0.14/6.01 % Propositional preprocessing time : 0.000
% 0.14/6.01 % Propositional encoding time : 0.000
% 0.14/6.01 % Propositional solver time : 0.000
% 0.14/6.01 % Success case prop preproc time : 0.000
% 0.14/6.01 % Success case prop encoding time : 0.000
% 0.14/6.01 % Success case prop solver time : 0.000
% 0.14/6.01 % Current number of processed clauses : 197
% 0.14/6.01 % Positive orientable unit clauses : 158
% 0.14/6.01 % Positive unorientable unit clauses: 37
% 0.14/6.01 % Negative unit clauses : 1
% 0.14/6.01 % Non-unit-clauses : 1
% 0.14/6.01 % Current number of unprocessed clauses: 15026
% 0.14/6.01 % ...number of literals in the above : 15026
% 0.14/6.01 % Current number of archived formulas : 0
% 0.14/6.01 % Current number of archived clauses : 29
% 0.14/6.01 % Clause-clause subsumption calls (NU) : 0
% 0.14/6.01 % Rec. Clause-clause subsumption calls : 0
% 0.14/6.01 % Non-unit clause-clause subsumptions : 0
% 0.14/6.01 % Unit Clause-clause subsumption calls : 2914
% 0.14/6.01 % Rewrite failures with RHS unbound : 0
% 0.14/6.01 % BW rewrite match attempts : 11618
% 0.14/6.01 % BW rewrite match successes : 339
% 0.14/6.01 % Condensation attempts : 0
% 0.14/6.01 % Condensation successes : 0
% 0.14/6.01 % Termbank termtop insertions : 554441
% 0.14/6.01 % Search garbage collected termcells : 5
% 0.14/6.01
% 0.14/6.01 % -------------------------------------------------
% 0.14/6.01 % User time : 0.341 s
% 0.14/6.01 % System time : 0.015 s
% 0.14/6.01 % Total time : 0.357 s
% 0.14/6.01 % Maximum resident set size: 3632 pages
% 0.14/6.01
% 0.14/6.01 % -------------------------------------------------
% 0.14/6.01 % User time : 1.670 s
% 0.14/6.01 % System time : 0.090 s
% 0.14/6.01 % Total time : 1.760 s
% 0.14/6.01 % Maximum resident set size: 4864 pages
% 0.14/6.01 % E exiting
%------------------------------------------------------------------------------