%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL044-5 : 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 12:09:24 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.62s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 20 ( 17 unt; 0 nHn; 8 RR)
% Number of literals : 23 ( 16 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 12 ( 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 : 40 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(n_definition,axiom,
apply(apply(apply(n,X1),X2),X3) = apply(apply(apply(X1,X3),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_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(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),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(n,X1),X2),X3) = apply(apply(apply(X1,X3),X2),X3),
n_definition ).
cnf(c_0_5,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_6,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),b)),b)),
inference(fof_simplification,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_0_7,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_8,plain,
apply(apply(apply(n,apply(b,X1)),X2),X3) = apply(apply(X1,apply(X3,X2)),X3),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_9,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),b)),b)),
c_0_6 ).
cnf(c_0_10,plain,
( apply(X1,fixed_pt) != apply(fixed_pt,apply(X1,fixed_pt))
| fixed_point(X1) ),
c_0_7 ).
cnf(c_0_11,plain,
apply(apply(apply(n,apply(X1,X2)),X2),X3) = apply(apply(apply(n,apply(n,X1)),X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_4]),c_0_4]) ).
cnf(c_0_12,plain,
apply(apply(apply(n,apply(apply(b,X1),X2)),X3),X4) = apply(apply(apply(X1,apply(X2,X4)),X3),X4),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_13,plain,
apply(apply(apply(apply(n,apply(b,b)),X1),X2),X3) = apply(apply(X2,X1),apply(X2,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
apply(fixed_pt,apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_5]),c_0_5]),c_0_5]),c_0_5]) ).
cnf(c_0_15,plain,
apply(apply(apply(n,apply(X1,apply(X2,X3))),X3),X4) = apply(apply(apply(n,apply(n,apply(apply(b,X1),X2))),X3),X4),
inference(spm,[status(thm)],[c_0_11,c_0_5]) ).
cnf(c_0_16,plain,
apply(apply(apply(n,apply(apply(b,b),X1)),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_12]) ).
cnf(c_0_17,plain,
apply(apply(apply(n,apply(n,apply(b,b))),X1),X2) = apply(apply(X1,X2),apply(X1,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_13]) ).
cnf(c_0_18,plain,
apply(apply(apply(n,apply(b,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X3,X2),X3)),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[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(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]),c_0_18]),c_0_15]),c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-5 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/5.37 % Computer : n004.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % 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 14:06:42 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
% 0.15/5.62 % Version: 3.5.1
% 0.15/5.62 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.62 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.62 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.62 % Starting sh5l with 300s (1) cores
% 0.15/5.62 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3329458 completed with status 0
% 0.15/5.62 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.15/5.62 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.62 % No SInE strategy applied
% 0.15/5.62 % Search class: FHUSS-FFSF22-DFFFFFNN
% 0.15/5.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.62 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.15/5.62 % Starting U----_206e_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/5.62 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/5.62 % Starting new_bool_3 with 136s (1) cores
% 0.15/5.62 % U----_206e_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3329466 completed with status 0
% 0.15/5.62 % Result found by U----_206e_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.15/5.62 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.62 % No SInE strategy applied
% 0.15/5.62 % Search class: FHUSS-FFSF22-DFFFFFNN
% 0.15/5.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.62 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.15/5.62 % Starting U----_206e_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/5.62 % Preprocessing time : 0.001 s
% 0.15/5.62 % Presaturation interreduction done
% 0.15/5.62
% 0.15/5.62 % Proof found!
% 0.15/5.62 % SZS status Unsatisfiable
% 0.15/5.62 % SZS output start CNFRefutation
% See solution above
% 0.15/5.62 % Parsed axioms : 4
% 0.15/5.62 % Removed by relevancy pruning/SinE : 0
% 0.15/5.62 % Initial clauses : 4
% 0.15/5.62 % Removed in clause preprocessing : 0
% 0.15/5.62 % Initial clauses in saturation : 4
% 0.15/5.62 % Processed clauses : 131
% 0.15/5.62 % ...of these trivial : 19
% 0.15/5.62 % ...subsumed : 52
% 0.15/5.62 % ...remaining for further processing : 60
% 0.15/5.62 % Other redundant clauses eliminated : 0
% 0.15/5.62 % Clauses deleted for lack of memory : 0
% 0.15/5.62 % Backward-subsumed : 0
% 0.15/5.62 % Backward-rewritten : 3
% 0.15/5.62 % Generated clauses : 7840
% 0.15/5.62 % ...of the previous two non-redundant : 7419
% 0.15/5.62 % ...aggressively subsumed : 0
% 0.15/5.62 % Contextual simplify-reflections : 0
% 0.15/5.62 % Paramodulations : 7840
% 0.15/5.62 % Factorizations : 0
% 0.15/5.62 % NegExts : 0
% 0.15/5.62 % Equation resolutions : 0
% 0.15/5.62 % Disequality decompositions : 0
% 0.15/5.62 % Total rewrite steps : 452
% 0.15/5.62 % ...of those cached : 192
% 0.15/5.62 % Propositional unsat checks : 0
% 0.15/5.62 % Propositional check models : 0
% 0.15/5.62 % Propositional check unsatisfiable : 0
% 0.15/5.62 % Propositional clauses : 0
% 0.15/5.62 % Propositional clauses after purity: 0
% 0.15/5.62 % Propositional unsat core size : 0
% 0.15/5.62 % Propositional preprocessing time : 0.000
% 0.15/5.62 % Propositional encoding time : 0.000
% 0.15/5.62 % Propositional solver time : 0.000
% 0.15/5.62 % Success case prop preproc time : 0.000
% 0.15/5.62 % Success case prop encoding time : 0.000
% 0.15/5.62 % Success case prop solver time : 0.000
% 0.15/5.62 % Current number of processed clauses : 53
% 0.15/5.62 % Positive orientable unit clauses : 13
% 0.15/5.62 % Positive unorientable unit clauses: 38
% 0.15/5.62 % Negative unit clauses : 1
% 0.15/5.62 % Non-unit-clauses : 1
% 0.15/5.62 % Current number of unprocessed clauses: 7295
% 0.15/5.62 % ...number of literals in the above : 7295
% 0.15/5.62 % Current number of archived formulas : 0
% 0.15/5.62 % Current number of archived clauses : 7
% 0.15/5.62 % Clause-clause subsumption calls (NU) : 0
% 0.15/5.62 % Rec. Clause-clause subsumption calls : 0
% 0.15/5.62 % Non-unit clause-clause subsumptions : 0
% 0.15/5.62 % Unit Clause-clause subsumption calls : 95
% 0.15/5.62 % Rewrite failures with RHS unbound : 0
% 0.15/5.62 % BW rewrite match attempts : 2057
% 0.15/5.62 % BW rewrite match successes : 17
% 0.15/5.62 % Condensation attempts : 0
% 0.15/5.62 % Condensation successes : 0
% 0.15/5.62 % Termbank termtop insertions : 212342
% 0.15/5.62 % Search garbage collected termcells : 5
% 0.15/5.62
% 0.15/5.62 % -------------------------------------------------
% 0.15/5.62 % User time : 0.167 s
% 0.15/5.62 % System time : 0.012 s
% 0.15/5.62 % Total time : 0.179 s
% 0.15/5.62 % Maximum resident set size: 3592 pages
% 0.15/5.62
% 0.15/5.62 % -------------------------------------------------
% 0.15/5.62 % User time : 0.838 s
% 0.15/5.62 % System time : 0.068 s
% 0.15/5.62 % Total time : 0.906 s
% 0.15/5.62 % Maximum resident set size: 4864 pages
% 0.15/5.62 % E exiting
%------------------------------------------------------------------------------