%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL042-1 : 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 : 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 12:09:22 PM UTC 2026
% Result : Unsatisfiable 2.54s 0.93s
% Output : CNFRefutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 7 RR)
% Number of literals : 17 ( 16 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(w1_definition,axiom,
apply(apply(w1,X1),X2) = apply(apply(X2,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w1_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_fixed_point,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(c_0_3,axiom,
apply(apply(w1,X1),X2) = apply(apply(X2,X1),X1),
w1_definition ).
cnf(c_0_4,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_5,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
inference(fof_simplification,[status(thm)],[prove_fixed_point]) ).
cnf(c_0_6,plain,
apply(apply(w1,X1),apply(apply(b,X2),X3)) = apply(apply(X2,apply(X3,X1)),X1),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_7,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
c_0_5 ).
cnf(c_0_8,plain,
apply(apply(w1,X1),apply(apply(b,apply(b,X2)),X3)) = apply(X2,apply(apply(X3,X1),X1)),
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_9,negated_conjecture,
apply(f(apply(apply(b,X1),X2)),apply(X1,apply(X2,f(apply(apply(b,X1),X2))))) != apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),
inference(spm,[status(thm)],[c_0_7,c_0_4]) ).
cnf(c_0_10,plain,
apply(apply(apply(w1,X1),b),X2) = apply(X1,apply(X1,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_11,plain,
apply(apply(w1,X1),apply(apply(b,apply(b,X2)),X3)) = apply(X2,apply(apply(w1,X1),X3)),
inference(spm,[status(thm)],[c_0_8,c_0_3]) ).
cnf(c_0_12,negated_conjecture,
apply(f(apply(apply(b,X1),apply(apply(w1,X2),b))),apply(X1,apply(X2,apply(X2,f(apply(apply(b,X1),apply(apply(w1,X2),b))))))) != apply(X1,apply(X2,apply(X2,f(apply(apply(b,X1),apply(apply(w1,X2),b)))))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
apply(apply(w1,apply(apply(b,apply(b,X1)),X2)),w1) = apply(X1,apply(apply(w1,X2),apply(apply(b,w1),apply(b,apply(b,X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_11]),c_0_6]) ).
cnf(c_0_14,negated_conjecture,
apply(f(apply(apply(b,apply(apply(b,X1),X2)),apply(apply(w1,X3),b))),apply(X1,apply(X2,apply(X3,apply(X3,f(apply(apply(b,apply(apply(b,X1),X2)),apply(apply(w1,X3),b)))))))) != apply(X1,apply(X2,apply(X3,apply(X3,f(apply(apply(b,apply(apply(b,X1),X2)),apply(apply(w1,X3),b))))))),
inference(spm,[status(thm)],[c_0_12,c_0_4]) ).
cnf(c_0_15,plain,
apply(X1,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X1))))) = apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X1)))),
inference(spm,[status(thm)],[c_0_6,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_14,c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL042-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.36 % Computer : n011.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8046.5625MB
% 0.13/0.36 % OS : Linux 6.8.0-71-generic
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Sep 21 14:05:40 UTC 2026
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 2.54/0.93 % Version: 3.5.1
% 2.54/0.93 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.54/0.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.54/0.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.54/0.93 % Starting new_bool_3 with 300s (1) cores
% 2.54/0.93 % Starting new_bool_1 with 300s (1) cores
% 2.54/0.93 % Starting sh5l with 300s (1) cores
% 2.54/0.93 % new_bool_1 with pid 2105087 completed with status 9
% 2.54/0.93 % new_bool_3 with pid 2105086 completed with status 9
% 2.54/0.93 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2105085 completed with status 0
% 2.54/0.93 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 2.54/0.93 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.54/0.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.54/0.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.54/0.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.54/0.93 % No SInE strategy applied
% 2.54/0.93 % Search class: FUUPS-FFSF21-MFFFFFNN
% 2.54/0.93 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.54/0.93 % Starting SubtermCWHack with 136s (1) cores
% 2.54/0.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.54/0.93 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 2.54/0.93 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.54/0.93 % Starting U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.54/0.93 % U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 2105096 completed with status 0
% 2.54/0.93 % Result found by U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 2.54/0.93 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.54/0.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.54/0.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.54/0.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.54/0.93 % No SInE strategy applied
% 2.54/0.93 % Search class: FUUPS-FFSF21-MFFFFFNN
% 2.54/0.93 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.54/0.93 % Starting SubtermCWHack with 136s (1) cores
% 2.54/0.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.54/0.93 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 2.54/0.93 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.54/0.93 % Starting U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.54/0.93 % Preprocessing time : 0.001 s
% 2.54/0.93 % Presaturation interreduction done
% 2.54/0.93
% 2.54/0.93 % Proof found!
% 2.54/0.93 % SZS status Unsatisfiable
% 2.54/0.93 % SZS output start CNFRefutation
% See solution above
% 2.54/0.93 % Parsed axioms : 3
% 2.54/0.93 % Removed by relevancy pruning/SinE : 0
% 2.54/0.93 % Initial clauses : 3
% 2.54/0.93 % Removed in clause preprocessing : 0
% 2.54/0.93 % Initial clauses in saturation : 3
% 2.54/0.93 % Processed clauses : 585
% 2.54/0.93 % ...of these trivial : 79
% 2.54/0.93 % ...subsumed : 327
% 2.54/0.93 % ...remaining for further processing : 179
% 2.54/0.93 % Other redundant clauses eliminated : 0
% 2.54/0.93 % Clauses deleted for lack of memory : 0
% 2.54/0.93 % Backward-subsumed : 2
% 2.54/0.93 % Backward-rewritten : 11
% 2.54/0.93 % Generated clauses : 12258
% 2.54/0.93 % ...of the previous two non-redundant : 11869
% 2.54/0.93 % ...aggressively subsumed : 0
% 2.54/0.93 % Contextual simplify-reflections : 0
% 2.54/0.93 % Paramodulations : 12258
% 2.54/0.93 % Factorizations : 0
% 2.54/0.93 % NegExts : 0
% 2.54/0.93 % Equation resolutions : 0
% 2.54/0.93 % Disequality decompositions : 0
% 2.54/0.93 % Total rewrite steps : 12109
% 2.54/0.93 % ...of those cached : 9769
% 2.54/0.93 % Propositional unsat checks : 0
% 2.54/0.93 % Propositional check models : 0
% 2.54/0.93 % Propositional check unsatisfiable : 0
% 2.54/0.93 % Propositional clauses : 0
% 2.54/0.93 % Propositional clauses after purity: 0
% 2.54/0.93 % Propositional unsat core size : 0
% 2.54/0.93 % Propositional preprocessing time : 0.000
% 2.54/0.93 % Propositional encoding time : 0.000
% 2.54/0.93 % Propositional solver time : 0.000
% 2.54/0.93 % Success case prop preproc time : 0.000
% 2.54/0.93 % Success case prop encoding time : 0.000
% 2.54/0.93 % Success case prop solver time : 0.000
% 2.54/0.93 % Current number of processed clauses : 163
% 2.54/0.93 % Positive orientable unit clauses : 46
% 2.54/0.93 % Positive unorientable unit clauses: 46
% 2.54/0.93 % Negative unit clauses : 71
% 2.54/0.93 % Non-unit-clauses : 0
% 2.54/0.93 % Current number of unprocessed clauses: 11267
% 2.54/0.93 % ...number of literals in the above : 11267
% 2.54/0.93 % Current number of archived formulas : 0
% 2.54/0.93 % Current number of archived clauses : 16
% 2.54/0.93 % Clause-clause subsumption calls (NU) : 0
% 2.54/0.93 % Rec. Clause-clause subsumption calls : 0
% 2.54/0.93 % Non-unit clause-clause subsumptions : 0
% 2.54/0.93 % Unit Clause-clause subsumption calls : 1222
% 2.54/0.93 % Rewrite failures with RHS unbound : 0
% 2.54/0.93 % BW rewrite match attempts : 1858
% 2.54/0.93 % BW rewrite match successes : 92
% 2.54/0.93 % Condensation attempts : 0
% 2.54/0.93 % Condensation successes : 0
% 2.54/0.93 % Termbank termtop insertions : 530252
% 2.54/0.93 % Search garbage collected termcells : 2
% 2.54/0.93
% 2.54/0.93 % -------------------------------------------------
% 2.54/0.93 % User time : 0.458 s
% 2.54/0.93 % System time : 0.025 s
% 2.54/0.93 % Total time : 0.482 s
% 2.54/0.93 % Maximum resident set size: 3628 pages
% 2.54/0.93
% 2.54/0.93 % -------------------------------------------------
% 2.54/0.93 % User time : 2.341 s
% 2.54/0.93 % System time : 0.148 s
% 2.54/0.93 % Total time : 2.489 s
% 2.54/0.93 % Maximum resident set size: 4864 pages
% 2.54/0.93 % E exiting
%------------------------------------------------------------------------------