%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 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 12:09:14 PM UTC 2026
% Result : Unsatisfiable 1.11s 0.71s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 4 RR)
% Number of literals : 18 ( 17 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(i_definition,axiom,
apply(i,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_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(weak_fixed_point,axiom,
weak_fixed_point(X1) = apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',weak_fixed_point) ).
cnf(prove_weak_fixed_point,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
cnf(c_0_5,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition ).
cnf(c_0_6,axiom,
apply(i,X1) = X1,
i_definition ).
cnf(c_0_7,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_8,plain,
apply(apply(apply(s,X1),i),X2) = apply(apply(X1,X2),X2),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
apply(apply(apply(s,apply(b,X1)),i),X2) = apply(X1,apply(X2,X2)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
apply(apply(apply(s,i),i),X1) = apply(X1,X1),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_11,axiom,
weak_fixed_point(X1) = apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i)),
weak_fixed_point ).
cnf(c_0_12,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
inference(fof_simplification,[status(thm)],[prove_weak_fixed_point]) ).
cnf(c_0_13,plain,
apply(apply(apply(s,apply(b,X1)),i),X2) = apply(X1,apply(apply(apply(s,i),i),X2)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
apply(apply(apply(s,i),i),apply(apply(s,apply(b,X1)),i)) = weak_fixed_point(X1),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
c_0_12 ).
cnf(c_0_16,plain,
apply(X1,weak_fixed_point(X1)) = weak_fixed_point(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_13]),c_0_14]),c_0_14]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n011.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 14:03:10 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.51 Running first-order theorem proving
% 0.27/0.52 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
% 1.11/0.71 % Version: 3.5.1
% 1.11/0.71 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.11/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.11/0.71 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.11/0.71 % Starting new_bool_3 with 300s (1) cores
% 1.11/0.71 % Starting new_bool_1 with 300s (1) cores
% 1.11/0.71 % Starting sh5l with 300s (1) cores
% 1.11/0.71 % new_bool_3 with pid 2101473 completed with status 0
% 1.11/0.71 % Result found by new_bool_3
% 1.11/0.71 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.11/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.11/0.71 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.11/0.71 % Starting new_bool_3 with 300s (1) cores
% 1.11/0.71 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.11/0.71 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.11/0.71 % Search class: FUUPM-FFSF21-MFFFFFNN
% 1.11/0.71 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 1.11/0.71 % Starting SubtermCWHack with 28s (1) cores
% 1.11/0.71 % SubtermCWHack with pid 2101480 completed with status 0
% 1.11/0.71 % Result found by SubtermCWHack
% 1.11/0.71 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.11/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.11/0.71 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.11/0.71 % Starting new_bool_3 with 300s (1) cores
% 1.11/0.71 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.11/0.71 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.11/0.71 % Search class: FUUPM-FFSF21-MFFFFFNN
% 1.11/0.71 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 1.11/0.71 % Starting SubtermCWHack with 28s (1) cores
% 1.11/0.71 % Preprocessing time : 0.002 s
% 1.11/0.71
% 1.11/0.71 % Proof found!
% 1.11/0.71 % SZS status Unsatisfiable
% 1.11/0.71 % SZS output start CNFRefutation
% See solution above
% 1.11/0.71 % Parsed axioms : 6
% 1.11/0.71 % Removed by relevancy pruning/SinE : 1
% 1.11/0.71 % Initial clauses : 5
% 1.11/0.71 % Removed in clause preprocessing : 0
% 1.11/0.71 % Initial clauses in saturation : 5
% 1.11/0.71 % Processed clauses : 219
% 1.11/0.71 % ...of these trivial : 11
% 1.11/0.71 % ...subsumed : 142
% 1.11/0.71 % ...remaining for further processing : 66
% 1.11/0.71 % Other redundant clauses eliminated : 0
% 1.11/0.71 % Clauses deleted for lack of memory : 0
% 1.11/0.71 % Backward-subsumed : 0
% 1.11/0.71 % Backward-rewritten : 7
% 1.11/0.71 % Generated clauses : 10363
% 1.11/0.71 % ...of the previous two non-redundant : 10047
% 1.11/0.71 % ...aggressively subsumed : 0
% 1.11/0.71 % Contextual simplify-reflections : 0
% 1.11/0.71 % Paramodulations : 10363
% 1.11/0.71 % Factorizations : 0
% 1.11/0.71 % NegExts : 0
% 1.11/0.71 % Equation resolutions : 0
% 1.11/0.71 % Disequality decompositions : 0
% 1.11/0.71 % Total rewrite steps : 2777
% 1.11/0.71 % ...of those cached : 1746
% 1.11/0.71 % Propositional unsat checks : 0
% 1.11/0.71 % Propositional check models : 0
% 1.11/0.71 % Propositional check unsatisfiable : 0
% 1.11/0.71 % Propositional clauses : 0
% 1.11/0.71 % Propositional clauses after purity: 0
% 1.11/0.71 % Propositional unsat core size : 0
% 1.11/0.71 % Propositional preprocessing time : 0.000
% 1.11/0.71 % Propositional encoding time : 0.000
% 1.11/0.71 % Propositional solver time : 0.000
% 1.11/0.71 % Success case prop preproc time : 0.000
% 1.11/0.71 % Success case prop encoding time : 0.000
% 1.11/0.71 % Success case prop solver time : 0.000
% 1.11/0.71 % Current number of processed clauses : 59
% 1.11/0.71 % Positive orientable unit clauses : 15
% 1.11/0.71 % Positive unorientable unit clauses: 44
% 1.11/0.71 % Negative unit clauses : 0
% 1.11/0.71 % Non-unit-clauses : 0
% 1.11/0.71 % Current number of unprocessed clauses: 9831
% 1.11/0.71 % ...number of literals in the above : 9831
% 1.11/0.71 % Current number of archived formulas : 0
% 1.11/0.71 % Current number of archived clauses : 7
% 1.11/0.71 % Clause-clause subsumption calls (NU) : 0
% 1.11/0.71 % Rec. Clause-clause subsumption calls : 0
% 1.11/0.71 % Non-unit clause-clause subsumptions : 0
% 1.11/0.71 % Unit Clause-clause subsumption calls : 96
% 1.11/0.71 % Rewrite failures with RHS unbound : 0
% 1.11/0.71 % BW rewrite match attempts : 2075
% 1.11/0.71 % BW rewrite match successes : 104
% 1.11/0.71 % Condensation attempts : 0
% 1.11/0.71 % Condensation successes : 0
% 1.11/0.71 % Termbank termtop insertions : 229841
% 1.11/0.71 % Search garbage collected termcells : 8
% 1.11/0.71
% 1.11/0.71 % -------------------------------------------------
% 1.11/0.71 % User time : 0.130 s
% 1.11/0.71 % System time : 0.013 s
% 1.11/0.71 % Total time : 0.143 s
% 1.11/0.71 % Maximum resident set size: 3632 pages
% 1.11/0.71
% 1.11/0.71 % -------------------------------------------------
% 1.11/0.71 % User time : 0.131 s
% 1.11/0.71 % System time : 0.020 s
% 1.11/0.71 % Total time : 0.151 s
% 1.11/0.71 % Maximum resident set size: 4608 pages
% 1.11/0.71 % E exiting
%------------------------------------------------------------------------------