%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : COL006-2 : 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 : n016.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 12:09:47 PM UTC 2026
% Result : Unsatisfiable 26.94s 4.48s
% Output : CNFRefutation 26.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of clauses : 24 ( 21 unt; 0 nHn; 14 RR)
% Number of literals : 27 ( 20 equ; 13 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 8 ( 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 : 37 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_strong_fixed_point,negated_conjecture,
~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)))),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
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(c_0_4,negated_conjecture,
~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)))),
inference(fof_simplification,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_0_5,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_6,axiom,
apply(apply(k,X1),X2) = X1,
k_definition ).
cnf(c_0_7,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition ).
cnf(c_0_8,negated_conjecture,
~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)))),
c_0_4 ).
cnf(c_0_9,plain,
( apply(X1,fixed_pt) != apply(fixed_pt,apply(X1,fixed_pt))
| fixed_point(X1) ),
c_0_5 ).
cnf(c_0_10,plain,
apply(apply(apply(s,k),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,negated_conjecture,
apply(fixed_pt,apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))))) != apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))),
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)],[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_7]),c_0_6]),c_0_7]),c_0_6]),c_0_7]),c_0_6]),c_0_7]),c_0_7]),c_0_7]),c_0_6]),c_0_7]),c_0_6]),c_0_7]),c_0_6]),c_0_7]),c_0_7]) ).
cnf(c_0_12,plain,
apply(apply(apply(s,X1),apply(apply(s,k),X2)),X3) = apply(apply(X1,X3),X3),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) != apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_10]),c_0_10]),c_0_10]) ).
cnf(c_0_14,plain,
apply(apply(apply(s,X1),apply(apply(s,k),X2)),X3) = apply(apply(apply(s,X1),apply(apply(s,k),X4)),X3),
inference(spm,[status(thm)],[c_0_12,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),s)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) != apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),s)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_16,plain,
apply(apply(apply(s,X1),apply(k,X2)),X3) = apply(apply(X1,X3),X2),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_17,plain,
apply(apply(apply(s,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_18,negated_conjecture,
apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),X1)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) != apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),X1)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_19,plain,
apply(apply(apply(s,apply(s,apply(k,X1))),apply(k,X2)),X3) = apply(X1,apply(X3,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),X1))) != apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),X1)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,negated_conjecture,
apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),X1))) != apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_22,negated_conjecture,
apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),X1)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) != apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_7]),c_0_6]),c_0_17]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_7]),c_0_10]),c_0_17]),c_0_14]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n016.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 14:09:08 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 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
% 26.94/4.48 % Version: 3.5.1
% 26.94/4.48 % Preprocessing class: FSSSSMSSSSSNFFN.
% 26.94/4.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 26.94/4.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 26.94/4.48 % Starting new_bool_3 with 300s (1) cores
% 26.94/4.48 % Starting new_bool_1 with 300s (1) cores
% 26.94/4.48 % Starting sh5l with 300s (1) cores
% 26.94/4.48 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2617313 completed with status 0
% 26.94/4.48 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 26.94/4.48 % Preprocessing class: FSSSSMSSSSSNFFN.
% 26.94/4.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 26.94/4.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 26.94/4.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 26.94/4.48 % No SInE strategy applied
% 26.94/4.48 % Search class: FHUSS-FFSF22-DFFFFFNN
% 26.94/4.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 26.94/4.48 % Starting SubtermCWHack with 136s (1) cores
% 26.94/4.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 26.94/4.48 % Starting U----_206e_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 26.94/4.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 26.94/4.48 % Starting new_bool_3 with 136s (1) cores
% 26.94/4.48 % U----_206e_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 2617320 completed with status 0
% 26.94/4.48 % Result found by U----_206e_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 26.94/4.48 % Preprocessing class: FSSSSMSSSSSNFFN.
% 26.94/4.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 26.94/4.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 26.94/4.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 26.94/4.48 % No SInE strategy applied
% 26.94/4.48 % Search class: FHUSS-FFSF22-DFFFFFNN
% 26.94/4.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 26.94/4.48 % Starting SubtermCWHack with 136s (1) cores
% 26.94/4.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 26.94/4.48 % Starting U----_206e_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 26.94/4.48 % Preprocessing time : 0.002 s
% 26.94/4.48 % Presaturation interreduction done
% 26.94/4.48
% 26.94/4.48 % Proof found!
% 26.94/4.48 % SZS status Unsatisfiable
% 26.94/4.48 % SZS output start CNFRefutation
% See solution above
% 26.94/4.48 % Parsed axioms : 4
% 26.94/4.48 % Removed by relevancy pruning/SinE : 0
% 26.94/4.48 % Initial clauses : 4
% 26.94/4.48 % Removed in clause preprocessing : 0
% 26.94/4.48 % Initial clauses in saturation : 4
% 26.94/4.48 % Processed clauses : 802
% 26.94/4.48 % ...of these trivial : 87
% 26.94/4.48 % ...subsumed : 547
% 26.94/4.48 % ...remaining for further processing : 168
% 26.94/4.48 % Other redundant clauses eliminated : 0
% 26.94/4.48 % Clauses deleted for lack of memory : 0
% 26.94/4.48 % Backward-subsumed : 5
% 26.94/4.48 % Backward-rewritten : 7
% 26.94/4.48 % Generated clauses : 89837
% 26.94/4.48 % ...of the previous two non-redundant : 88310
% 26.94/4.48 % ...aggressively subsumed : 0
% 26.94/4.48 % Contextual simplify-reflections : 0
% 26.94/4.48 % Paramodulations : 89837
% 26.94/4.48 % Factorizations : 0
% 26.94/4.48 % NegExts : 0
% 26.94/4.48 % Equation resolutions : 0
% 26.94/4.48 % Disequality decompositions : 0
% 26.94/4.48 % Total rewrite steps : 14172
% 26.94/4.48 % ...of those cached : 11172
% 26.94/4.48 % Propositional unsat checks : 0
% 26.94/4.48 % Propositional check models : 0
% 26.94/4.48 % Propositional check unsatisfiable : 0
% 26.94/4.48 % Propositional clauses : 0
% 26.94/4.48 % Propositional clauses after purity: 0
% 26.94/4.48 % Propositional unsat core size : 0
% 26.94/4.48 % Propositional preprocessing time : 0.000
% 26.94/4.48 % Propositional encoding time : 0.000
% 26.94/4.48 % Propositional solver time : 0.000
% 26.94/4.48 % Success case prop preproc time : 0.000
% 26.94/4.48 % Success case prop encoding time : 0.000
% 26.94/4.48 % Success case prop solver time : 0.000
% 26.94/4.48 % Current number of processed clauses : 152
% 26.94/4.48 % Positive orientable unit clauses : 41
% 26.94/4.48 % Positive unorientable unit clauses: 97
% 26.94/4.48 % Negative unit clauses : 13
% 26.94/4.48 % Non-unit-clauses : 1
% 26.94/4.48 % Current number of unprocessed clauses: 87490
% 26.94/4.48 % ...number of literals in the above : 87490
% 26.94/4.48 % Current number of archived formulas : 0
% 26.94/4.48 % Current number of archived clauses : 16
% 26.94/4.48 % Clause-clause subsumption calls (NU) : 0
% 26.94/4.48 % Rec. Clause-clause subsumption calls : 0
% 26.94/4.48 % Non-unit clause-clause subsumptions : 0
% 26.94/4.48 % Unit Clause-clause subsumption calls : 814
% 26.94/4.48 % Rewrite failures with RHS unbound : 0
% 26.94/4.48 % BW rewrite match attempts : 13083
% 26.94/4.48 % BW rewrite match successes : 1677
% 26.94/4.48 % Condensation attempts : 0
% 26.94/4.48 % Condensation successes : 0
% 26.94/4.48 % Termbank termtop insertions : 3035441
% 26.94/4.48 % Search garbage collected termcells : 5
% 26.94/4.48
% 26.94/4.48 % -------------------------------------------------
% 26.94/4.48 % User time : 3.672 s
% 26.94/4.48 % System time : 0.137 s
% 26.94/4.48 % Total time : 3.809 s
% 26.94/4.48 % Maximum resident set size: 3640 pages
% 26.94/4.48
% 26.94/4.48 % -------------------------------------------------
% 26.94/4.48 % User time : 18.149 s
% 26.94/4.48 % System time : 0.703 s
% 26.94/4.48 % Total time : 18.853 s
% 26.94/4.48 % Maximum resident set size: 4864 pages
% 26.94/4.48 % E exiting
%------------------------------------------------------------------------------