%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:09:17 PM UTC 2026
% Result : Unsatisfiable 31.39s 6.86s
% Output : CNFRefutation 31.39s
% 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 : 8 ( 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 : 36 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_definition,axiom,
apply(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
cnf(s_definition,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(c_0_3,axiom,
apply(apply(k,X1),X2) = X1,
k_definition ).
cnf(c_0_4,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_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(apply(s,k),X1),X2) = X2,
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(apply(s,apply(apply(s,k),X1)),X2),X3) = apply(X3,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_9,plain,
apply(apply(apply(s,apply(apply(s,X1),X2)),X3),X4) = apply(apply(apply(X1,X4),apply(X2,X4)),apply(X3,X4)),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_10,negated_conjecture,
apply(apply(apply(s,apply(apply(s,k),X1)),X2),f(X2)) != apply(X2,f(X2)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
apply(apply(apply(s,apply(apply(s,apply(k,X1)),X2)),X3),X4) = apply(apply(X1,apply(X2,X4)),apply(X3,X4)),
inference(spm,[status(thm)],[c_0_9,c_0_3]) ).
cnf(c_0_12,plain,
apply(apply(apply(apply(s,s),X1),X2),X3) = apply(apply(X2,X3),apply(apply(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_13,negated_conjecture,
apply(apply(apply(apply(s,apply(apply(s,apply(k,s)),apply(s,k))),X1),X2),f(apply(X1,X2))) != apply(apply(X1,X2),f(apply(X1,X2))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
apply(apply(apply(apply(s,s),apply(s,k)),X1),X2) = apply(apply(X1,X2),X2),
inference(spm,[status(thm)],[c_0_12,c_0_6]) ).
cnf(c_0_15,negated_conjecture,
apply(apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(apply(s,apply(k,s)),apply(s,k)))),X1),f(apply(X1,X1))) != apply(apply(X1,X1),f(apply(X1,X1))),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n001.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 14:09:59 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.52 Running first-order theorem proving
% 0.18/0.52 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 31.39/6.86 % Version: 3.5.1
% 31.39/6.86 % Preprocessing class: FSSSSMSSSSSNFFN.
% 31.39/6.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 31.39/6.86 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 31.39/6.86 % Starting new_bool_3 with 300s (1) cores
% 31.39/6.86 % Starting new_bool_1 with 300s (1) cores
% 31.39/6.86 % Starting sh5l with 300s (1) cores
% 31.39/6.86 % new_bool_1 with pid 3322408 completed with status 9
% 31.39/6.86 % new_bool_3 with pid 3322407 completed with status 9
% 31.39/6.86 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3322406 completed with status 0
% 31.39/6.86 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 31.39/6.86 % Preprocessing class: FSSSSMSSSSSNFFN.
% 31.39/6.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 31.39/6.86 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 31.39/6.86 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 31.39/6.86 % No SInE strategy applied
% 31.39/6.86 % Search class: FUUPS-FFSF21-MFFFFFNN
% 31.39/6.86 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 31.39/6.86 % Starting SubtermCWHack with 136s (1) cores
% 31.39/6.86 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 31.39/6.86 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 31.39/6.86 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 31.39/6.86 % Starting U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 31.39/6.86 % U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3322416 completed with status 0
% 31.39/6.86 % Result found by U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 31.39/6.86 % Preprocessing class: FSSSSMSSSSSNFFN.
% 31.39/6.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 31.39/6.86 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 31.39/6.86 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 31.39/6.86 % No SInE strategy applied
% 31.39/6.86 % Search class: FUUPS-FFSF21-MFFFFFNN
% 31.39/6.86 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 31.39/6.86 % Starting SubtermCWHack with 136s (1) cores
% 31.39/6.86 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 31.39/6.86 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 31.39/6.86 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 31.39/6.86 % Preprocessing time : 0.002 s
% 31.39/6.86 % Presaturation interreduction done
% 31.39/6.86
% 31.39/6.86 % Proof found!
% 31.39/6.86 % SZS status Unsatisfiable
% 31.39/6.86 % SZS output start CNFRefutation
% See solution above
% 31.39/6.86 % Parsed axioms : 3
% 31.39/6.86 % Removed by relevancy pruning/SinE : 0
% 31.39/6.86 % Initial clauses : 3
% 31.39/6.86 % Removed in clause preprocessing : 0
% 31.39/6.86 % Initial clauses in saturation : 3
% 31.39/6.86 % Processed clauses : 2085
% 31.39/6.86 % ...of these trivial : 39
% 31.39/6.86 % ...subsumed : 1239
% 31.39/6.86 % ...remaining for further processing : 807
% 31.39/6.86 % Other redundant clauses eliminated : 0
% 31.39/6.86 % Clauses deleted for lack of memory : 0
% 31.39/6.86 % Backward-subsumed : 84
% 31.39/6.86 % Backward-rewritten : 14
% 31.39/6.86 % Generated clauses : 87875
% 31.39/6.86 % ...of the previous two non-redundant : 85976
% 31.39/6.86 % ...aggressively subsumed : 0
% 31.39/6.86 % Contextual simplify-reflections : 0
% 31.39/6.86 % Paramodulations : 87874
% 31.39/6.86 % Factorizations : 0
% 31.39/6.86 % NegExts : 0
% 31.39/6.86 % Equation resolutions : 1
% 31.39/6.86 % Disequality decompositions : 0
% 31.39/6.86 % Total rewrite steps : 35502
% 31.39/6.86 % ...of those cached : 23310
% 31.39/6.86 % Propositional unsat checks : 0
% 31.39/6.86 % Propositional check models : 0
% 31.39/6.86 % Propositional check unsatisfiable : 0
% 31.39/6.86 % Propositional clauses : 0
% 31.39/6.86 % Propositional clauses after purity: 0
% 31.39/6.86 % Propositional unsat core size : 0
% 31.39/6.86 % Propositional preprocessing time : 0.000
% 31.39/6.86 % Propositional encoding time : 0.000
% 31.39/6.86 % Propositional solver time : 0.000
% 31.39/6.86 % Success case prop preproc time : 0.000
% 31.39/6.86 % Success case prop encoding time : 0.000
% 31.39/6.86 % Success case prop solver time : 0.000
% 31.39/6.86 % Current number of processed clauses : 706
% 31.39/6.86 % Positive orientable unit clauses : 53
% 31.39/6.86 % Positive unorientable unit clauses: 59
% 31.39/6.86 % Negative unit clauses : 594
% 31.39/6.86 % Non-unit-clauses : 0
% 31.39/6.86 % Current number of unprocessed clauses: 83819
% 31.39/6.86 % ...number of literals in the above : 83819
% 31.39/6.86 % Current number of archived formulas : 0
% 31.39/6.86 % Current number of archived clauses : 101
% 31.39/6.86 % Clause-clause subsumption calls (NU) : 0
% 31.39/6.86 % Rec. Clause-clause subsumption calls : 0
% 31.39/6.86 % Non-unit clause-clause subsumptions : 0
% 31.39/6.86 % Unit Clause-clause subsumption calls : 90546
% 31.39/6.86 % Rewrite failures with RHS unbound : 0
% 31.39/6.86 % BW rewrite match attempts : 15853
% 31.39/6.86 % BW rewrite match successes : 180
% 31.39/6.86 % Condensation attempts : 0
% 31.39/6.86 % Condensation successes : 0
% 31.39/6.86 % Termbank termtop insertions : 3952128
% 31.39/6.86 % Search garbage collected termcells : 2
% 31.39/6.86
% 31.39/6.86 % -------------------------------------------------
% 31.39/6.86 % User time : 5.962 s
% 31.39/6.86 % System time : 0.211 s
% 31.39/6.86 % Total time : 6.172 s
% 31.39/6.86 % Maximum resident set size: 3628 pages
% 31.39/6.86
% 31.39/6.86 % -------------------------------------------------
% 31.39/6.86 % User time : 30.129 s
% 31.39/6.86 % System time : 1.092 s
% 31.39/6.86 % Total time : 31.221 s
% 31.39/6.86 % Maximum resident set size: 4608 pages
% 31.39/6.86 % E exiting
%------------------------------------------------------------------------------