%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL043-3 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:09:23 PM UTC 2026
% Result : Unsatisfiable 217.07s 47.33s
% Output : CNFRefutation 217.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 6 RR)
% Number of literals : 20 ( 19 equ; 3 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(strong_fixed_point,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
cnf(h_definition,axiom,
apply(apply(apply(h,X1),X2),X3) = apply(apply(apply(X1,X2),X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_definition) ).
cnf(prove_strong_fixed_point,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_0_4,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_5,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),
strong_fixed_point ).
cnf(c_0_6,axiom,
apply(apply(apply(h,X1),X2),X3) = apply(apply(apply(X1,X2),X3),X2),
h_definition ).
cnf(c_0_7,plain,
apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,X1))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_5]),c_0_4]) ).
cnf(c_0_8,plain,
apply(apply(apply(h,apply(apply(b,X1),X2)),X3),X4) = apply(apply(apply(X1,apply(X2,X3)),X4),X3),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
cnf(c_0_9,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,X1))),h) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_4]) ).
cnf(c_0_10,plain,
apply(apply(apply(h,apply(apply(b,b),X1)),X2),X3) = apply(apply(X1,X2),apply(X3,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_11,plain,
apply(apply(apply(h,apply(b,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
cnf(c_0_12,plain,
apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,X1))),h),apply(h,apply(b,apply(b,X1)))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_8]) ).
cnf(c_0_13,plain,
apply(apply(apply(h,apply(b,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X2)),
inference(spm,[status(thm)],[c_0_4,c_0_11]) ).
cnf(c_0_14,plain,
apply(apply(apply(h,apply(b,apply(b,X1))),apply(h,apply(b,apply(b,X1)))),apply(h,apply(b,apply(b,X1)))) = apply(strong_fixed_point,X1),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(fof_simplification,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_0_16,plain,
apply(apply(apply(h,apply(b,apply(b,X1))),apply(h,apply(b,apply(b,X2)))),apply(h,apply(b,apply(b,X2)))) = apply(X1,apply(strong_fixed_point,X2)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
c_0_15 ).
cnf(c_0_18,plain,
apply(X1,apply(strong_fixed_point,X1)) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL043-3 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/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 14:02:13 UTC 2026
% 0.09/15.60 % CPUTime :
% 0.09/15.60 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.49/15.67 Running first-order theorem proving
% 0.49/15.67 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
% 217.07/47.33 % Version: 3.5.1
% 217.07/47.33 % Preprocessing class: FSSSSMSSSSSNFFN.
% 217.07/47.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 217.07/47.33 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 217.07/47.33 % Starting new_bool_3 with 300s (1) cores
% 217.07/47.33 % Starting new_bool_1 with 300s (1) cores
% 217.07/47.33 % Starting sh5l with 300s (1) cores
% 217.07/47.33 % new_bool_3 with pid 2505899 completed with status 0
% 217.07/47.33 % Result found by new_bool_3
% 217.07/47.33 % Preprocessing class: FSSSSMSSSSSNFFN.
% 217.07/47.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 217.07/47.33 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 217.07/47.33 % Starting new_bool_3 with 300s (1) cores
% 217.07/47.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 217.07/47.33 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 217.07/47.33 % Search class: FUUPS-FFSF22-DFFFFFNN
% 217.07/47.33 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 217.07/47.33 % Starting SubtermCWHack with 31s (1) cores
% 217.07/47.33 % SubtermCWHack with pid 2505902 completed with status 8
% 217.07/47.33 % Starting Y1006__C12_02_nc_F1_AE_CS_SP_S2S with 181s (1) cores
% 217.07/47.33 % Y1006__C12_02_nc_F1_AE_CS_SP_S2S with pid 2506459 completed with status 0
% 217.07/47.33 % Result found by Y1006__C12_02_nc_F1_AE_CS_SP_S2S
% 217.07/47.33 % Preprocessing class: FSSSSMSSSSSNFFN.
% 217.07/47.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 217.07/47.33 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 217.07/47.33 % Starting new_bool_3 with 300s (1) cores
% 217.07/47.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 217.07/47.33 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 217.07/47.33 % Search class: FUUPS-FFSF22-DFFFFFNN
% 217.07/47.33 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 217.07/47.33 % Starting SubtermCWHack with 31s (1) cores
% 217.07/47.33 % SubtermCWHack with pid 2505902 completed with status 8
% 217.07/47.33 % Starting Y1006__C12_02_nc_F1_AE_CS_SP_S2S with 181s (1) cores
% 217.07/47.33 % Preprocessing time : 0.001 s
% 217.07/47.33 % Presaturation interreduction done
% 217.07/47.33
% 217.07/47.33 % Proof found!
% 217.07/47.33 % SZS status Unsatisfiable
% 217.07/47.33 % SZS output start CNFRefutation
% See solution above
% 217.07/47.33 % Parsed axioms : 4
% 217.07/47.33 % Removed by relevancy pruning/SinE : 0
% 217.07/47.33 % Initial clauses : 4
% 217.07/47.33 % Removed in clause preprocessing : 0
% 217.07/47.33 % Initial clauses in saturation : 4
% 217.07/47.33 % Processed clauses : 171
% 217.07/47.33 % ...of these trivial : 45
% 217.07/47.33 % ...subsumed : 42
% 217.07/47.33 % ...remaining for further processing : 84
% 217.07/47.33 % Other redundant clauses eliminated : 0
% 217.07/47.33 % Clauses deleted for lack of memory : 0
% 217.07/47.33 % Backward-subsumed : 0
% 217.07/47.33 % Backward-rewritten : 9
% 217.07/47.33 % Generated clauses : 6260
% 217.07/47.33 % ...of the previous two non-redundant : 6087
% 217.07/47.33 % ...aggressively subsumed : 0
% 217.07/47.33 % Contextual simplify-reflections : 0
% 217.07/47.33 % Paramodulations : 6260
% 217.07/47.33 % Factorizations : 0
% 217.07/47.33 % NegExts : 0
% 217.07/47.33 % Equation resolutions : 0
% 217.07/47.33 % Disequality decompositions : 0
% 217.07/47.33 % Total rewrite steps : 1175
% 217.07/47.33 % ...of those cached : 413
% 217.07/47.33 % Propositional unsat checks : 0
% 217.07/47.33 % Propositional check models : 0
% 217.07/47.33 % Propositional check unsatisfiable : 0
% 217.07/47.33 % Propositional clauses : 0
% 217.07/47.33 % Propositional clauses after purity: 0
% 217.07/47.33 % Propositional unsat core size : 0
% 217.07/47.33 % Propositional preprocessing time : 0.000
% 217.07/47.33 % Propositional encoding time : 0.000
% 217.07/47.33 % Propositional solver time : 0.000
% 217.07/47.33 % Success case prop preproc time : 0.000
% 217.07/47.33 % Success case prop encoding time : 0.000
% 217.07/47.33 % Success case prop solver time : 0.000
% 217.07/47.33 % Current number of processed clauses : 71
% 217.07/47.33 % Positive orientable unit clauses : 44
% 217.07/47.33 % Positive unorientable unit clauses: 27
% 217.07/47.33 % Negative unit clauses : 0
% 217.07/47.33 % Non-unit-clauses : 0
% 217.07/47.33 % Current number of unprocessed clauses: 5919
% 217.07/47.33 % ...number of literals in the above : 5919
% 217.07/47.33 % Current number of archived formulas : 0
% 217.07/47.33 % Current number of archived clauses : 13
% 217.07/47.33 % Clause-clause subsumption calls (NU) : 0
% 217.07/47.33 % Rec. Clause-clause subsumption calls : 0
% 217.07/47.33 % Non-unit clause-clause subsumptions : 0
% 217.07/47.33 % Unit Clause-clause subsumption calls : 302
% 217.07/47.33 % Rewrite failures with RHS unbound : 0
% 217.07/47.33 % BW rewrite match attempts : 2078
% 217.07/47.33 % BW rewrite match successes : 47
% 217.07/47.33 % Condensation attempts : 0
% 217.07/47.33 % Condensation successes : 0
% 217.07/47.33 % Termbank termtop insertions : 184093
% 217.07/47.33 % Search garbage collected termcells : 2
% 217.07/47.33
% 217.07/47.33 % -------------------------------------------------
% 217.07/47.33 % User time : 30.286 s
% 217.07/47.33 % System time : 0.912 s
% 217.07/47.33 % Total time : 31.197 s
% 217.07/47.33 % Maximum resident set size: 3588 pages
% 217.07/47.33
% 217.07/47.33 % -------------------------------------------------
% 217.07/47.33 % User time : 30.287 s
% 217.07/47.33 % System time : 0.921 s
% 217.07/47.33 % Total time : 31.208 s
% 217.07/47.33 % Maximum resident set size: 4608 pages
% 217.07/47.33 % E exiting
%------------------------------------------------------------------------------