%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL037-1 : 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 12:09:21 PM UTC 2026
% Result : Unsatisfiable 4.04s 16.39s
% Output : CNFRefutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 6 RR)
% Number of literals : 18 ( 17 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_definition,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_definition) ).
cnf(s_definition,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_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(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(c_0_4,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
c_definition ).
cnf(c_0_5,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition ).
cnf(c_0_6,plain,
apply(apply(apply(s,apply(c,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X3),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
inference(fof_simplification,[status(thm)],[prove_fixed_point]) ).
cnf(c_0_8,plain,
apply(apply(apply(apply(s,apply(c,c)),X1),X2),X3) = apply(apply(apply(X1,X2),X3),X2),
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_9,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_10,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
c_0_7 ).
cnf(c_0_11,plain,
apply(apply(apply(apply(s,apply(c,c)),c),X1),X2) = apply(apply(X1,X1),X2),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_12,plain,
apply(apply(apply(apply(s,b),X1),X2),X3) = apply(X2,apply(apply(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_9,c_0_5]) ).
cnf(c_0_13,negated_conjecture,
apply(f(apply(X1,X1)),apply(apply(apply(apply(s,apply(c,c)),c),X1),f(apply(X1,X1)))) != apply(apply(apply(apply(s,apply(c,c)),c),X1),f(apply(X1,X1))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
apply(apply(apply(apply(s,b),apply(c,X1)),X2),X3) = apply(X2,apply(apply(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_12,c_0_4]) ).
cnf(c_0_15,negated_conjecture,
apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),c))),f(apply(X1,X1))),X1) != apply(apply(apply(apply(s,apply(c,c)),c),X1),f(apply(X1,X1))),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
apply(apply(apply(apply(s,apply(c,c)),c),apply(c,X1)),X2) = apply(apply(X1,X2),apply(c,X1)),
inference(spm,[status(thm)],[c_0_4,c_0_11]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_15,c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL037-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.59 % CPULimit : 300
% 0.09/15.59 % WCLimit : 300
% 0.09/15.59 % DateTime : Mon Sep 21 14:05:22 UTC 2026
% 0.09/15.60 % CPUTime :
% 0.50/15.60 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.50/15.67 Running first-order theorem proving
% 0.50/15.67 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
% 4.04/16.39 % Version: 3.5.1
% 4.04/16.39 % Preprocessing class: FSSSSMSSSSSNFFN.
% 4.04/16.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.04/16.39 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 4.04/16.39 % Starting new_bool_3 with 300s (1) cores
% 4.04/16.39 % Starting new_bool_1 with 300s (1) cores
% 4.04/16.39 % Starting sh5l with 300s (1) cores
% 4.04/16.39 % new_bool_1 with pid 951951 completed with status 9
% 4.04/16.39 % new_bool_3 with pid 951950 completed with status 9
% 4.04/16.39 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 951949 completed with status 0
% 4.04/16.39 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 4.04/16.39 % Preprocessing class: FSSSSMSSSSSNFFN.
% 4.04/16.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.04/16.39 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 4.04/16.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.04/16.39 % No SInE strategy applied
% 4.04/16.39 % Search class: FUUPS-FFSF21-MFFFFFNN
% 4.04/16.39 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.04/16.39 % Starting SubtermCWHack with 136s (1) cores
% 4.04/16.39 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 4.04/16.39 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 4.04/16.39 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 4.04/16.39 % Starting U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 4.04/16.39 % G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 951954 completed with status 0
% 4.04/16.39 % Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 4.04/16.39 % Preprocessing class: FSSSSMSSSSSNFFN.
% 4.04/16.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.04/16.39 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 4.04/16.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.04/16.39 % No SInE strategy applied
% 4.04/16.39 % Search class: FUUPS-FFSF21-MFFFFFNN
% 4.04/16.39 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.04/16.39 % Starting SubtermCWHack with 136s (1) cores
% 4.04/16.39 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 4.04/16.39 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 4.04/16.39 % Preprocessing time : 0.001 s
% 4.04/16.39 % Presaturation interreduction done
% 4.04/16.39
% 4.04/16.39 % Proof found!
% 4.04/16.39 % SZS status Unsatisfiable
% 4.04/16.39 % SZS output start CNFRefutation
% See solution above
% 4.04/16.39 % Parsed axioms : 4
% 4.04/16.39 % Removed by relevancy pruning/SinE : 0
% 4.04/16.39 % Initial clauses : 4
% 4.04/16.39 % Removed in clause preprocessing : 0
% 4.04/16.39 % Initial clauses in saturation : 4
% 4.04/16.39 % Processed clauses : 335
% 4.04/16.39 % ...of these trivial : 26
% 4.04/16.39 % ...subsumed : 135
% 4.04/16.39 % ...remaining for further processing : 174
% 4.04/16.39 % Other redundant clauses eliminated : 0
% 4.04/16.39 % Clauses deleted for lack of memory : 0
% 4.04/16.39 % Backward-subsumed : 1
% 4.04/16.39 % Backward-rewritten : 7
% 4.04/16.39 % Generated clauses : 30211
% 4.04/16.39 % ...of the previous two non-redundant : 29556
% 4.04/16.39 % ...aggressively subsumed : 0
% 4.04/16.39 % Contextual simplify-reflections : 0
% 4.04/16.39 % Paramodulations : 30211
% 4.04/16.39 % Factorizations : 0
% 4.04/16.39 % NegExts : 0
% 4.04/16.39 % Equation resolutions : 0
% 4.04/16.39 % Disequality decompositions : 0
% 4.04/16.39 % Total rewrite steps : 3429
% 4.04/16.39 % ...of those cached : 1585
% 4.04/16.39 % Propositional unsat checks : 0
% 4.04/16.39 % Propositional check models : 0
% 4.04/16.39 % Propositional check unsatisfiable : 0
% 4.04/16.39 % Propositional clauses : 0
% 4.04/16.39 % Propositional clauses after purity: 0
% 4.04/16.39 % Propositional unsat core size : 0
% 4.04/16.39 % Propositional preprocessing time : 0.000
% 4.04/16.39 % Propositional encoding time : 0.000
% 4.04/16.39 % Propositional solver time : 0.000
% 4.04/16.39 % Success case prop preproc time : 0.000
% 4.04/16.39 % Success case prop encoding time : 0.000
% 4.04/16.39 % Success case prop solver time : 0.000
% 4.04/16.39 % Current number of processed clauses : 162
% 4.04/16.39 % Positive orientable unit clauses : 18
% 4.04/16.39 % Positive unorientable unit clauses: 57
% 4.04/16.39 % Negative unit clauses : 87
% 4.04/16.39 % Non-unit-clauses : 0
% 4.04/16.39 % Current number of unprocessed clauses: 29100
% 4.04/16.39 % ...number of literals in the above : 29100
% 4.04/16.39 % Current number of archived formulas : 0
% 4.04/16.39 % Current number of archived clauses : 12
% 4.04/16.39 % Clause-clause subsumption calls (NU) : 0
% 4.04/16.39 % Rec. Clause-clause subsumption calls : 0
% 4.04/16.39 % Non-unit clause-clause subsumptions : 0
% 4.04/16.39 % Unit Clause-clause subsumption calls : 1323
% 4.04/16.39 % Rewrite failures with RHS unbound : 0
% 4.04/16.39 % BW rewrite match attempts : 10759
% 4.04/16.39 % BW rewrite match successes : 112
% 4.04/16.39 % Condensation attempts : 0
% 4.04/16.39 % Condensation successes : 0
% 4.04/16.39 % Termbank termtop insertions : 862442
% 4.04/16.39 % Search garbage collected termcells : 2
% 4.04/16.39
% 4.04/16.39 % -------------------------------------------------
% 4.04/16.39 % User time : 0.635 s
% 4.04/16.39 % System time : 0.034 s
% 4.04/16.39 % Total time : 0.669 s
% 4.04/16.39 % Maximum resident set size: 3376 pages
% 4.04/16.39
% 4.04/16.39 % -------------------------------------------------
% 4.04/16.39 % User time : 3.153 s
% 4.04/16.39 % System time : 0.203 s
% 4.04/16.39 % Total time : 3.357 s
% 4.04/16.39 % Maximum resident set size: 4608 pages
% 4.04/16.39 % E exiting
%------------------------------------------------------------------------------