%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL003-19 : 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 : n020.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 0.60s 0.54s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 6 RR)
% Number of literals : 21 ( 20 equ; 3 neg)
% Maximal clause size : 1 ( 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; 4 con; 0-2 aty)
% Number of variables : 29 ( 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(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),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(b,X1)),X2) = apply(X1,apply(X2,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
apply(apply(w,apply(w,apply(b,X1))),X2) = apply(apply(X1,apply(X2,X2)),X2),
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_8,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_9,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_10,plain,
apply(apply(w,apply(w,apply(b,apply(b,X1)))),X2) = apply(X1,apply(apply(X2,X2),X2)),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
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,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,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),
strong_fixed_point ).
cnf(c_0_14,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_15,plain,
apply(apply(w,apply(w,apply(b,apply(b,X1)))),X2) = apply(X1,apply(apply(w,w),X2)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
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_4,c_0_12]) ).
cnf(c_0_17,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_13]),c_0_5]),c_0_5]) ).
cnf(c_0_18,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
c_0_14 ).
cnf(c_0_19,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_15,c_0_16]),c_0_17]),c_0_17]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-19 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n020.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 14:04:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 0.60/0.54 % Version: 3.5.1
% 0.60/0.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.60/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.60/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.60/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.60/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.60/0.54 % Starting sh5l with 300s (1) cores
% 0.60/0.54 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3124490 completed with status 0
% 0.60/0.54 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.60/0.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.60/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.60/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.60/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.60/0.54 % No SInE strategy applied
% 0.60/0.54 % Search class: FUUPS-FFSF22-DFFFFFNN
% 0.60/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.60/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.60/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.60/0.54 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.60/0.54 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 0.60/0.54 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.60/0.54 % G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 3124499 completed with status 0
% 0.60/0.54 % Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 0.60/0.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.60/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.60/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.60/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.60/0.54 % No SInE strategy applied
% 0.60/0.54 % Search class: FUUPS-FFSF22-DFFFFFNN
% 0.60/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.60/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.60/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.60/0.54 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.60/0.54 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 0.60/0.54 % Preprocessing time : 0.001 s
% 0.60/0.54 % Presaturation interreduction done
% 0.60/0.54
% 0.60/0.54 % Proof found!
% 0.60/0.54 % SZS status Unsatisfiable
% 0.60/0.54 % SZS output start CNFRefutation
% See solution above
% 0.60/0.54 % Parsed axioms : 4
% 0.60/0.54 % Removed by relevancy pruning/SinE : 0
% 0.60/0.54 % Initial clauses : 4
% 0.60/0.54 % Removed in clause preprocessing : 0
% 0.60/0.54 % Initial clauses in saturation : 4
% 0.60/0.54 % Processed clauses : 208
% 0.60/0.54 % ...of these trivial : 52
% 0.60/0.54 % ...subsumed : 86
% 0.60/0.54 % ...remaining for further processing : 70
% 0.60/0.54 % Other redundant clauses eliminated : 0
% 0.60/0.54 % Clauses deleted for lack of memory : 0
% 0.60/0.54 % Backward-subsumed : 0
% 0.60/0.54 % Backward-rewritten : 8
% 0.60/0.54 % Generated clauses : 5107
% 0.60/0.54 % ...of the previous two non-redundant : 4979
% 0.60/0.54 % ...aggressively subsumed : 0
% 0.60/0.54 % Contextual simplify-reflections : 0
% 0.60/0.54 % Paramodulations : 5107
% 0.60/0.54 % Factorizations : 0
% 0.60/0.54 % NegExts : 0
% 0.60/0.54 % Equation resolutions : 0
% 0.60/0.54 % Disequality decompositions : 0
% 0.60/0.54 % Total rewrite steps : 1155
% 0.60/0.54 % ...of those cached : 726
% 0.60/0.54 % Propositional unsat checks : 0
% 0.60/0.54 % Propositional check models : 0
% 0.60/0.54 % Propositional check unsatisfiable : 0
% 0.60/0.54 % Propositional clauses : 0
% 0.60/0.54 % Propositional clauses after purity: 0
% 0.60/0.54 % Propositional unsat core size : 0
% 0.60/0.54 % Propositional preprocessing time : 0.000
% 0.60/0.54 % Propositional encoding time : 0.000
% 0.60/0.54 % Propositional solver time : 0.000
% 0.60/0.54 % Success case prop preproc time : 0.000
% 0.60/0.54 % Success case prop encoding time : 0.000
% 0.60/0.54 % Success case prop solver time : 0.000
% 0.60/0.54 % Current number of processed clauses : 58
% 0.60/0.54 % Positive orientable unit clauses : 28
% 0.60/0.54 % Positive unorientable unit clauses: 30
% 0.60/0.54 % Negative unit clauses : 0
% 0.60/0.54 % Non-unit-clauses : 0
% 0.60/0.54 % Current number of unprocessed clauses: 4768
% 0.60/0.54 % ...number of literals in the above : 4768
% 0.60/0.54 % Current number of archived formulas : 0
% 0.60/0.54 % Current number of archived clauses : 12
% 0.60/0.54 % Clause-clause subsumption calls (NU) : 0
% 0.60/0.54 % Rec. Clause-clause subsumption calls : 0
% 0.60/0.54 % Non-unit clause-clause subsumptions : 0
% 0.60/0.54 % Unit Clause-clause subsumption calls : 169
% 0.60/0.54 % Rewrite failures with RHS unbound : 0
% 0.60/0.54 % BW rewrite match attempts : 1247
% 0.60/0.54 % BW rewrite match successes : 63
% 0.60/0.54 % Condensation attempts : 0
% 0.60/0.54 % Condensation successes : 0
% 0.60/0.54 % Termbank termtop insertions : 128384
% 0.60/0.54 % Search garbage collected termcells : 2
% 0.60/0.54
% 0.60/0.54 % -------------------------------------------------
% 0.60/0.54 % User time : 0.087 s
% 0.60/0.54 % System time : 0.007 s
% 0.60/0.54 % Total time : 0.094 s
% 0.60/0.54 % Maximum resident set size: 3636 pages
% 0.60/0.54
% 0.60/0.54 % -------------------------------------------------
% 0.60/0.54 % User time : 0.400 s
% 0.60/0.54 % System time : 0.037 s
% 0.60/0.54 % Total time : 0.437 s
% 0.60/0.54 % Maximum resident set size: 4864 pages
% 0.60/0.54 % E exiting
%------------------------------------------------------------------------------