%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL002-3 : 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 : n012.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 12:09:14 PM UTC 2026
% Result : Unsatisfiable 32.46s 5.14s
% Output : CNFRefutation 32.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 18 ( 15 unt; 0 nHn; 10 RR)
% Number of literals : 21 ( 13 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_weak_fixed_point,negated_conjecture,
~ fixed_point(apply(apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1)))),apply(s,apply(c,apply(b,X1))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
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(weak_fixed_point,axiom,
( X1 != apply(fixed_pt,X1)
| fixed_point(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',weak_fixed_point) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
cnf(c_definition,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_definition) ).
cnf(c_0_5,negated_conjecture,
~ fixed_point(apply(apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1)))),apply(s,apply(c,apply(b,X1))))),
inference(fof_simplification,[status(thm)],[prove_weak_fixed_point]) ).
cnf(c_0_6,negated_conjecture,
~ fixed_point(apply(apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1)))),apply(s,apply(c,apply(b,X1))))),
c_0_5 ).
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,plain,
( X1 != apply(fixed_pt,X1)
| fixed_point(X1) ),
inference(fof_simplification,[status(thm)],[weak_fixed_point]) ).
cnf(c_0_9,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_10,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
c_definition ).
cnf(c_0_11,negated_conjecture,
~ fixed_point(apply(apply(apply(c,apply(b,X1)),apply(s,apply(c,apply(b,X1)))),apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1)))))),
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_12,plain,
( X1 != apply(fixed_pt,X1)
| fixed_point(X1) ),
c_0_8 ).
cnf(c_0_13,plain,
apply(apply(apply(c,apply(b,X1)),X2),X3) = apply(X1,apply(X3,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
apply(fixed_pt,apply(apply(apply(c,apply(b,X1)),apply(s,apply(c,apply(b,X1)))),apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1)))))) != apply(apply(apply(c,apply(b,X1)),apply(s,apply(c,apply(b,X1)))),apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1))))),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
apply(apply(apply(c,apply(b,X1)),X2),apply(apply(s,X3),X4)) = apply(X1,apply(apply(X3,X2),apply(X4,X2))),
inference(spm,[status(thm)],[c_0_13,c_0_7]) ).
cnf(c_0_16,negated_conjecture,
apply(apply(apply(c,apply(b,fixed_pt)),apply(s,apply(c,apply(b,X1)))),apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1))))) != apply(apply(apply(c,apply(b,X1)),apply(s,apply(c,apply(b,X1)))),apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1))))),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 14:02:51 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 32.46/5.14 % Version: 3.5.1
% 32.46/5.14 % Preprocessing class: FSSSSMSSSSSNFFN.
% 32.46/5.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 32.46/5.14 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 32.46/5.14 % Starting new_bool_3 with 300s (1) cores
% 32.46/5.14 % Starting new_bool_1 with 300s (1) cores
% 32.46/5.14 % Starting sh5l with 300s (1) cores
% 32.46/5.14 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2527340 completed with status 0
% 32.46/5.14 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 32.46/5.14 % Preprocessing class: FSSSSMSSSSSNFFN.
% 32.46/5.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 32.46/5.14 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 32.46/5.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 32.46/5.14 % No SInE strategy applied
% 32.46/5.14 % Search class: FHUSM-FFSF22-MFFFFFNN
% 32.46/5.14 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 32.46/5.14 % Starting SubtermCWHack with 136s (1) cores
% 32.46/5.14 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 32.46/5.14 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 32.46/5.14 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 32.46/5.14 % Starting new_bool_3 with 136s (1) cores
% 32.46/5.14 % U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 2527347 completed with status 0
% 32.46/5.14 % Result found by U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 32.46/5.14 % Preprocessing class: FSSSSMSSSSSNFFN.
% 32.46/5.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 32.46/5.14 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 32.46/5.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 32.46/5.14 % No SInE strategy applied
% 32.46/5.14 % Search class: FHUSM-FFSF22-MFFFFFNN
% 32.46/5.14 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 32.46/5.14 % Starting SubtermCWHack with 136s (1) cores
% 32.46/5.14 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 32.46/5.14 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 32.46/5.14 % Preprocessing time : 0.001 s
% 32.46/5.14 % Presaturation interreduction done
% 32.46/5.14
% 32.46/5.14 % Proof found!
% 32.46/5.14 % SZS status Unsatisfiable
% 32.46/5.14 % SZS output start CNFRefutation
% See solution above
% 32.46/5.14 % Parsed axioms : 6
% 32.46/5.14 % Removed by relevancy pruning/SinE : 0
% 32.46/5.14 % Initial clauses : 6
% 32.46/5.14 % Removed in clause preprocessing : 0
% 32.46/5.14 % Initial clauses in saturation : 6
% 32.46/5.14 % Processed clauses : 4402
% 32.46/5.14 % ...of these trivial : 5
% 32.46/5.14 % ...subsumed : 2426
% 32.46/5.14 % ...remaining for further processing : 1971
% 32.46/5.14 % Other redundant clauses eliminated : 0
% 32.46/5.14 % Clauses deleted for lack of memory : 0
% 32.46/5.14 % Backward-subsumed : 23
% 32.46/5.14 % Backward-rewritten : 93
% 32.46/5.14 % Generated clauses : 221104
% 32.46/5.14 % ...of the previous two non-redundant : 220962
% 32.46/5.14 % ...aggressively subsumed : 0
% 32.46/5.14 % Contextual simplify-reflections : 0
% 32.46/5.14 % Paramodulations : 221103
% 32.46/5.14 % Factorizations : 0
% 32.46/5.14 % NegExts : 0
% 32.46/5.14 % Equation resolutions : 1
% 32.46/5.14 % Disequality decompositions : 0
% 32.46/5.14 % Total rewrite steps : 28524
% 32.46/5.14 % ...of those cached : 21777
% 32.46/5.14 % Propositional unsat checks : 0
% 32.46/5.14 % Propositional check models : 0
% 32.46/5.14 % Propositional check unsatisfiable : 0
% 32.46/5.14 % Propositional clauses : 0
% 32.46/5.14 % Propositional clauses after purity: 0
% 32.46/5.14 % Propositional unsat core size : 0
% 32.46/5.14 % Propositional preprocessing time : 0.000
% 32.46/5.14 % Propositional encoding time : 0.000
% 32.46/5.14 % Propositional solver time : 0.000
% 32.46/5.14 % Success case prop preproc time : 0.000
% 32.46/5.14 % Success case prop encoding time : 0.000
% 32.46/5.14 % Success case prop solver time : 0.000
% 32.46/5.14 % Current number of processed clauses : 1849
% 32.46/5.14 % Positive orientable unit clauses : 11
% 32.46/5.14 % Positive unorientable unit clauses: 130
% 32.46/5.14 % Negative unit clauses : 1707
% 32.46/5.14 % Non-unit-clauses : 1
% 32.46/5.14 % Current number of unprocessed clauses: 216422
% 32.46/5.14 % ...number of literals in the above : 216422
% 32.46/5.14 % Current number of archived formulas : 0
% 32.46/5.14 % Current number of archived clauses : 122
% 32.46/5.14 % Clause-clause subsumption calls (NU) : 0
% 32.46/5.14 % Rec. Clause-clause subsumption calls : 0
% 32.46/5.14 % Non-unit clause-clause subsumptions : 0
% 32.46/5.14 % Unit Clause-clause subsumption calls : 148982
% 32.46/5.14 % Rewrite failures with RHS unbound : 0
% 32.46/5.14 % BW rewrite match attempts : 175492
% 32.46/5.14 % BW rewrite match successes : 39668
% 32.46/5.14 % Condensation attempts : 0
% 32.46/5.14 % Condensation successes : 0
% 32.46/5.14 % Termbank termtop insertions : 7602300
% 32.46/5.14 % Search garbage collected termcells : 5
% 32.46/5.14
% 32.46/5.14 % -------------------------------------------------
% 32.46/5.14 % User time : 4.364 s
% 32.46/5.14 % System time : 0.150 s
% 32.46/5.14 % Total time : 4.514 s
% 32.46/5.14 % Maximum resident set size: 3636 pages
% 32.46/5.14
% 32.46/5.14 % -------------------------------------------------
% 32.46/5.14 % User time : 22.136 s
% 32.46/5.14 % System time : 0.826 s
% 32.46/5.14 % Total time : 22.963 s
% 32.46/5.14 % Maximum resident set size: 4608 pages
% 32.46/5.14 % E exiting
%------------------------------------------------------------------------------