%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL003-20 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:09:15 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.64s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 6 RR)
% Number of literals : 20 ( 19 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(strong_fixed_point,axiom,
strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
cnf(prove_strong_fixed_point,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_0_4,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
w_definition ).
cnf(c_0_5,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_6,plain,
apply(apply(w,apply(w,X1)),X2) = apply(apply(w,apply(X1,X2)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_4]),c_0_4]) ).
cnf(c_0_7,plain,
apply(apply(w,apply(apply(b,X1),X2)),X3) = apply(apply(X1,apply(X2,X3)),X3),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_8,plain,
apply(apply(w,apply(b,X1)),X2) = apply(X1,apply(X2,X2)),
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_9,plain,
apply(apply(w,apply(apply(b,w),X1)),X2) = apply(apply(w,apply(w,X1)),X2),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,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_5,c_0_8]) ).
cnf(c_0_11,plain,
apply(apply(w,w),X1) = apply(apply(X1,X1),X1),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_12,axiom,
strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),
strong_fixed_point ).
cnf(c_0_13,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(fof_simplification,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_0_14,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_4,c_0_9]) ).
cnf(c_0_15,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_10,c_0_11]),c_0_4]) ).
cnf(c_0_16,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X1)))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_12]),c_0_5]),c_0_5]) ).
cnf(c_0_17,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
c_0_13 ).
cnf(c_0_18,plain,
apply(X1,apply(strong_fixed_point,X1)) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_16]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL003-20 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n001.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 14:09:15 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.51 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
% 0.27/0.64 % Version: 3.5.1
% 0.27/0.64 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.27/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.27/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.64 % Starting sh5l with 300s (1) cores
% 0.27/0.64 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3320754 completed with status 0
% 0.27/0.64 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.27/0.64 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.27/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.27/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.64 % No SInE strategy applied
% 0.27/0.64 % Search class: FUUPS-FFSF22-MFFFFFNN
% 0.27/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.27/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.27/0.64 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.64 % Starting new_bool_1 with 136s (1) cores
% 0.27/0.64 % new_bool_1 with pid 3320765 completed with status 0
% 0.27/0.64 % Result found by new_bool_1
% 0.27/0.64 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.27/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.27/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.64 % No SInE strategy applied
% 0.27/0.64 % Search class: FUUPS-FFSF22-MFFFFFNN
% 0.27/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.27/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.27/0.64 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.64 % Starting new_bool_1 with 136s (1) cores
% 0.27/0.64 % Preprocessing time : 0.002 s
% 0.27/0.64 % Presaturation interreduction done
% 0.27/0.64
% 0.27/0.64 % Proof found!
% 0.27/0.64 % SZS status Unsatisfiable
% 0.27/0.64 % SZS output start CNFRefutation
% See solution above
% 0.27/0.64 % Parsed axioms : 4
% 0.27/0.64 % Removed by relevancy pruning/SinE : 0
% 0.27/0.64 % Initial clauses : 4
% 0.27/0.64 % Removed in clause preprocessing : 0
% 0.27/0.64 % Initial clauses in saturation : 4
% 0.27/0.64 % Processed clauses : 148
% 0.27/0.64 % ...of these trivial : 34
% 0.27/0.64 % ...subsumed : 53
% 0.27/0.64 % ...remaining for further processing : 61
% 0.27/0.64 % Other redundant clauses eliminated : 0
% 0.27/0.64 % Clauses deleted for lack of memory : 0
% 0.27/0.64 % Backward-subsumed : 0
% 0.27/0.64 % Backward-rewritten : 6
% 0.27/0.64 % Generated clauses : 2700
% 0.27/0.64 % ...of the previous two non-redundant : 2585
% 0.27/0.64 % ...aggressively subsumed : 0
% 0.27/0.64 % Contextual simplify-reflections : 0
% 0.27/0.64 % Paramodulations : 2700
% 0.27/0.64 % Factorizations : 0
% 0.27/0.64 % NegExts : 0
% 0.27/0.64 % Equation resolutions : 0
% 0.27/0.64 % Disequality decompositions : 0
% 0.27/0.64 % Total rewrite steps : 856
% 0.27/0.64 % ...of those cached : 444
% 0.27/0.64 % Propositional unsat checks : 0
% 0.27/0.64 % Propositional check models : 0
% 0.27/0.64 % Propositional check unsatisfiable : 0
% 0.27/0.64 % Propositional clauses : 0
% 0.27/0.64 % Propositional clauses after purity: 0
% 0.27/0.64 % Propositional unsat core size : 0
% 0.27/0.64 % Propositional preprocessing time : 0.000
% 0.27/0.64 % Propositional encoding time : 0.000
% 0.27/0.64 % Propositional solver time : 0.000
% 0.27/0.64 % Success case prop preproc time : 0.000
% 0.27/0.64 % Success case prop encoding time : 0.000
% 0.27/0.64 % Success case prop solver time : 0.000
% 0.27/0.64 % Current number of processed clauses : 51
% 0.27/0.64 % Positive orientable unit clauses : 34
% 0.27/0.64 % Positive unorientable unit clauses: 17
% 0.27/0.64 % Negative unit clauses : 0
% 0.27/0.64 % Non-unit-clauses : 0
% 0.27/0.64 % Current number of unprocessed clauses: 2438
% 0.27/0.64 % ...number of literals in the above : 2438
% 0.27/0.64 % Current number of archived formulas : 0
% 0.27/0.64 % Current number of archived clauses : 10
% 0.27/0.64 % Clause-clause subsumption calls (NU) : 0
% 0.27/0.64 % Rec. Clause-clause subsumption calls : 0
% 0.27/0.64 % Non-unit clause-clause subsumptions : 0
% 0.27/0.64 % Unit Clause-clause subsumption calls : 86
% 0.27/0.64 % Rewrite failures with RHS unbound : 0
% 0.27/0.64 % BW rewrite match attempts : 1108
% 0.27/0.64 % BW rewrite match successes : 31
% 0.27/0.64 % Condensation attempts : 0
% 0.27/0.64 % Condensation successes : 0
% 0.27/0.64 % Termbank termtop insertions : 72786
% 0.27/0.64 % Search garbage collected termcells : 2
% 0.27/0.64
% 0.27/0.64 % -------------------------------------------------
% 0.27/0.64 % User time : 0.083 s
% 0.27/0.64 % System time : 0.010 s
% 0.27/0.64 % Total time : 0.094 s
% 0.27/0.64 % Maximum resident set size: 3580 pages
% 0.27/0.64
% 0.27/0.64 % -------------------------------------------------
% 0.27/0.64 % User time : 0.444 s
% 0.27/0.64 % System time : 0.038 s
% 0.27/0.64 % Total time : 0.482 s
% 0.27/0.64 % Maximum resident set size: 4608 pages
% 0.27/0.64 % E exiting
%------------------------------------------------------------------------------