%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL003-9 : 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 : n011.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 101.75s 15.54s
% Output : CNFRefutation 101.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 23 ( 17 unt; 0 nHn; 10 RR)
% Number of literals : 29 ( 19 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 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 : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(w_definition,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
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(prove_strong_fixed_point,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_0_4,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_5,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
w_definition ).
cnf(c_0_6,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_7,plain,
( apply(X1,fixed_pt) != apply(fixed_pt,apply(X1,fixed_pt))
| fixed_point(X1) ),
c_0_4 ).
cnf(c_0_8,plain,
apply(apply(w,apply(X1,X2)),X2) = apply(apply(w,apply(w,X1)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_5]),c_0_5]) ).
cnf(c_0_9,plain,
apply(apply(w,apply(apply(b,X1),X2)),X3) = apply(apply(X1,apply(X2,X3)),X3),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_10,plain,
apply(apply(w,apply(b,X1)),X2) = apply(X1,apply(X2,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_11,plain,
( apply(fixed_pt,apply(X1,apply(X2,fixed_pt))) != apply(X1,apply(X2,fixed_pt))
| fixed_point(apply(apply(b,X1),X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_12,plain,
apply(apply(w,apply(apply(b,w),X1)),X2) = apply(apply(w,apply(w,X1)),X2),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,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_6,c_0_10]) ).
cnf(c_0_14,plain,
apply(apply(w,w),X1) = apply(apply(X1,X1),X1),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_15,plain,
( apply(fixed_pt,apply(X1,apply(X2,apply(X3,fixed_pt)))) != apply(X1,apply(X2,apply(X3,fixed_pt)))
| fixed_point(apply(apply(b,apply(apply(b,X1),X2)),X3)) ),
inference(spm,[status(thm)],[c_0_11,c_0_6]) ).
cnf(c_0_16,plain,
apply(apply(w,apply(w,X1)),apply(apply(b,w),X1)) = apply(apply(w,w),apply(apply(b,w),X1)),
inference(spm,[status(thm)],[c_0_5,c_0_12]) ).
cnf(c_0_17,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_13,c_0_14]),c_0_5]) ).
cnf(c_0_18,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),
inference(fof_simplification,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_0_19,plain,
( apply(fixed_pt,apply(X1,apply(X2,apply(X3,apply(X4,fixed_pt))))) != apply(X1,apply(X2,apply(X3,apply(X4,fixed_pt))))
| fixed_point(apply(apply(b,apply(apply(b,X1),apply(apply(b,X2),X3))),X4)) ),
inference(spm,[status(thm)],[c_0_15,c_0_6]) ).
cnf(c_0_20,plain,
apply(X1,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X1))))) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X1)))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),
c_0_18 ).
cnf(c_0_22,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-9 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 14:04:11 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 101.75/15.54 % Version: 3.5.1
% 101.75/15.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 101.75/15.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 101.75/15.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 101.75/15.54 % Starting new_bool_3 with 300s (1) cores
% 101.75/15.54 % Starting new_bool_1 with 300s (1) cores
% 101.75/15.54 % Starting sh5l with 300s (1) cores
% 101.75/15.54 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2102834 completed with status 0
% 101.75/15.54 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 101.75/15.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 101.75/15.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 101.75/15.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 101.75/15.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 101.75/15.54 % No SInE strategy applied
% 101.75/15.54 % Search class: FHUSS-FFSF22-DFFFFFNN
% 101.75/15.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 101.75/15.54 % Starting SubtermCWHack with 136s (1) cores
% 101.75/15.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 101.75/15.54 % Starting U----_206e_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 101.75/15.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 101.75/15.54 % Starting new_bool_3 with 136s (1) cores
% 101.75/15.54 % new_bool_3 with pid 2102845 completed with status 0
% 101.75/15.54 % Result found by new_bool_3
% 101.75/15.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 101.75/15.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 101.75/15.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 101.75/15.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 101.75/15.54 % No SInE strategy applied
% 101.75/15.54 % Search class: FHUSS-FFSF22-DFFFFFNN
% 101.75/15.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 101.75/15.54 % Starting SubtermCWHack with 136s (1) cores
% 101.75/15.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 101.75/15.54 % Starting U----_206e_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 101.75/15.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 101.75/15.54 % Starting new_bool_3 with 136s (1) cores
% 101.75/15.54 % Preprocessing time : 0.001 s
% 101.75/15.54 % Presaturation interreduction done
% 101.75/15.54
% 101.75/15.54 % Proof found!
% 101.75/15.54 % SZS status Unsatisfiable
% 101.75/15.54 % SZS output start CNFRefutation
% See solution above
% 101.75/15.54 % Parsed axioms : 4
% 101.75/15.54 % Removed by relevancy pruning/SinE : 0
% 101.75/15.54 % Initial clauses : 4
% 101.75/15.54 % Removed in clause preprocessing : 0
% 101.75/15.54 % Initial clauses in saturation : 4
% 101.75/15.54 % Processed clauses : 6106
% 101.75/15.54 % ...of these trivial : 1493
% 101.75/15.54 % ...subsumed : 2447
% 101.75/15.54 % ...remaining for further processing : 2166
% 101.75/15.54 % Other redundant clauses eliminated : 0
% 101.75/15.54 % Clauses deleted for lack of memory : 0
% 101.75/15.54 % Backward-subsumed : 14
% 101.75/15.54 % Backward-rewritten : 179
% 101.75/15.54 % Generated clauses : 396992
% 101.75/15.54 % ...of the previous two non-redundant : 393163
% 101.75/15.54 % ...aggressively subsumed : 0
% 101.75/15.54 % Contextual simplify-reflections : 0
% 101.75/15.54 % Paramodulations : 396985
% 101.75/15.54 % Factorizations : 0
% 101.75/15.54 % NegExts : 0
% 101.75/15.54 % Equation resolutions : 7
% 101.75/15.54 % Disequality decompositions : 0
% 101.75/15.54 % Total rewrite steps : 260231
% 101.75/15.54 % ...of those cached : 228770
% 101.75/15.54 % Propositional unsat checks : 0
% 101.75/15.54 % Propositional check models : 0
% 101.75/15.54 % Propositional check unsatisfiable : 0
% 101.75/15.54 % Propositional clauses : 0
% 101.75/15.54 % Propositional clauses after purity: 0
% 101.75/15.54 % Propositional unsat core size : 0
% 101.75/15.54 % Propositional preprocessing time : 0.000
% 101.75/15.54 % Propositional encoding time : 0.000
% 101.75/15.54 % Propositional solver time : 0.000
% 101.75/15.54 % Success case prop preproc time : 0.000
% 101.75/15.54 % Success case prop encoding time : 0.000
% 101.75/15.54 % Success case prop solver time : 0.000
% 101.75/15.54 % Current number of processed clauses : 1969
% 101.75/15.54 % Positive orientable unit clauses : 1291
% 101.75/15.54 % Positive unorientable unit clauses: 99
% 101.75/15.54 % Negative unit clauses : 1
% 101.75/15.54 % Non-unit-clauses : 578
% 101.75/15.54 % Current number of unprocessed clauses: 386539
% 101.75/15.54 % ...number of literals in the above : 597821
% 101.75/15.54 % Current number of archived formulas : 0
% 101.75/15.54 % Current number of archived clauses : 197
% 101.75/15.54 % Clause-clause subsumption calls (NU) : 65539
% 101.75/15.54 % Rec. Clause-clause subsumption calls : 65459
% 101.75/15.54 % Non-unit clause-clause subsumptions : 1848
% 101.75/15.54 % Unit Clause-clause subsumption calls : 50420
% 101.75/15.54 % Rewrite failures with RHS unbound : 0
% 101.75/15.54 % BW rewrite match attempts : 319835
% 101.75/15.54 % BW rewrite match successes : 2193
% 101.75/15.54 % Condensation attempts : 0
% 101.75/15.54 % Condensation successes : 0
% 101.75/15.54 % Termbank termtop insertions : 19572925
% 101.75/15.54 % Search garbage collected termcells : 5
% 101.75/15.54
% 101.75/15.54 % -------------------------------------------------
% 101.75/15.54 % User time : 13.719 s
% 101.75/15.54 % System time : 0.471 s
% 101.75/15.54 % Total time : 14.189 s
% 101.75/15.54 % Maximum resident set size: 3584 pages
% 101.75/15.54
% 101.75/15.54 % -------------------------------------------------
% 101.75/15.54 % User time : 68.255 s
% 101.75/15.54 % System time : 3.430 s
% 101.75/15.54 % Total time : 71.685 s
% 101.75/15.54 % Maximum resident set size: 4608 pages
% 101.75/15.54 % E exiting
%------------------------------------------------------------------------------