%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL003-16 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:09:15 PM UTC 2026
% Result : Unsatisfiable 0.33s 0.61s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 6 RR)
% Number of literals : 16 ( 15 equ; 3 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; 4 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(w_definition,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
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(b,apply(w,w)),w)),b)),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
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(w,X1),X2) = apply(apply(X1,X2),X2),
w_definition ).
cnf(c_0_5,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_6,plain,
apply(apply(w,apply(b,X1)),X2) = apply(X1,apply(X2,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
apply(apply(apply(w,apply(b,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X2),X3)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
apply(apply(w,w),X1) = apply(apply(X1,X1),X1),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_9,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(b,apply(w,w)),w)),b)),b),
strong_fixed_point ).
cnf(c_0_10,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_11,plain,
apply(apply(w,apply(w,apply(b,apply(b,X1)))),X2) = apply(X1,apply(apply(w,w),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_4]) ).
cnf(c_0_12,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,X1)))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_5]),c_0_5]) ).
cnf(c_0_13,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
c_0_10 ).
cnf(c_0_14,plain,
apply(X1,apply(strong_fixed_point,X1)) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_11]),c_0_12]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL003-16 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 14:02:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 Running first-order theorem proving
% 0.16/0.45 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
% 0.33/0.61 % Version: 3.5.1
% 0.33/0.61 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.33/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.61 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.33/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.33/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.33/0.61 % Starting sh5l with 300s (1) cores
% 0.33/0.61 % new_bool_3 with pid 948292 completed with status 0
% 0.33/0.61 % Result found by new_bool_3
% 0.33/0.61 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.33/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.61 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.33/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.33/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.33/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.33/0.61 % Search class: FUUPS-FFSF22-DFFFFFNN
% 0.33/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.33/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.33/0.61 % SubtermCWHack with pid 948297 completed with status 0
% 0.33/0.61 % Result found by SubtermCWHack
% 0.33/0.61 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.33/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.61 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.33/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.33/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.33/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.33/0.61 % Search class: FUUPS-FFSF22-DFFFFFNN
% 0.33/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.33/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.33/0.61 % Preprocessing time : 0.002 s
% 0.33/0.61
% 0.33/0.61 % Proof found!
% 0.33/0.61 % SZS status Unsatisfiable
% 0.33/0.61 % SZS output start CNFRefutation
% See solution above
% 0.33/0.61 % Parsed axioms : 4
% 0.33/0.61 % Removed by relevancy pruning/SinE : 0
% 0.33/0.61 % Initial clauses : 4
% 0.33/0.61 % Removed in clause preprocessing : 0
% 0.33/0.61 % Initial clauses in saturation : 4
% 0.33/0.61 % Processed clauses : 145
% 0.33/0.61 % ...of these trivial : 25
% 0.33/0.61 % ...subsumed : 67
% 0.33/0.61 % ...remaining for further processing : 53
% 0.33/0.61 % Other redundant clauses eliminated : 0
% 0.33/0.61 % Clauses deleted for lack of memory : 0
% 0.33/0.61 % Backward-subsumed : 0
% 0.33/0.61 % Backward-rewritten : 7
% 0.33/0.61 % Generated clauses : 4734
% 0.33/0.61 % ...of the previous two non-redundant : 4621
% 0.33/0.61 % ...aggressively subsumed : 0
% 0.33/0.61 % Contextual simplify-reflections : 0
% 0.33/0.61 % Paramodulations : 4734
% 0.33/0.61 % Factorizations : 0
% 0.33/0.61 % NegExts : 0
% 0.33/0.61 % Equation resolutions : 0
% 0.33/0.61 % Disequality decompositions : 0
% 0.33/0.61 % Total rewrite steps : 906
% 0.33/0.61 % ...of those cached : 504
% 0.33/0.61 % Propositional unsat checks : 0
% 0.33/0.61 % Propositional check models : 0
% 0.33/0.61 % Propositional check unsatisfiable : 0
% 0.33/0.61 % Propositional clauses : 0
% 0.33/0.61 % Propositional clauses after purity: 0
% 0.33/0.61 % Propositional unsat core size : 0
% 0.33/0.61 % Propositional preprocessing time : 0.000
% 0.33/0.61 % Propositional encoding time : 0.000
% 0.33/0.61 % Propositional solver time : 0.000
% 0.33/0.61 % Success case prop preproc time : 0.000
% 0.33/0.61 % Success case prop encoding time : 0.000
% 0.33/0.61 % Success case prop solver time : 0.000
% 0.33/0.61 % Current number of processed clauses : 46
% 0.33/0.61 % Positive orientable unit clauses : 16
% 0.33/0.61 % Positive unorientable unit clauses: 30
% 0.33/0.61 % Negative unit clauses : 0
% 0.33/0.61 % Non-unit-clauses : 0
% 0.33/0.61 % Current number of unprocessed clauses: 4467
% 0.33/0.61 % ...number of literals in the above : 4467
% 0.33/0.61 % Current number of archived formulas : 0
% 0.33/0.61 % Current number of archived clauses : 7
% 0.33/0.61 % Clause-clause subsumption calls (NU) : 0
% 0.33/0.61 % Rec. Clause-clause subsumption calls : 0
% 0.33/0.61 % Non-unit clause-clause subsumptions : 0
% 0.33/0.61 % Unit Clause-clause subsumption calls : 85
% 0.33/0.61 % Rewrite failures with RHS unbound : 0
% 0.33/0.61 % BW rewrite match attempts : 825
% 0.33/0.61 % BW rewrite match successes : 39
% 0.33/0.61 % Condensation attempts : 0
% 0.33/0.61 % Condensation successes : 0
% 0.33/0.61 % Termbank termtop insertions : 113888
% 0.33/0.61 % Search garbage collected termcells : 2
% 0.33/0.61
% 0.33/0.61 % -------------------------------------------------
% 0.33/0.61 % User time : 0.107 s
% 0.33/0.61 % System time : 0.017 s
% 0.33/0.61 % Total time : 0.124 s
% 0.33/0.61 % Maximum resident set size: 3636 pages
% 0.33/0.61
% 0.33/0.61 % -------------------------------------------------
% 0.33/0.61 % User time : 0.107 s
% 0.33/0.61 % System time : 0.025 s
% 0.33/0.61 % Total time : 0.132 s
% 0.33/0.61 % Maximum resident set size: 4864 pages
% 0.33/0.61 % E exiting
%------------------------------------------------------------------------------