%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL042-7 : 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 : 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 13.89s 2.26s
% Output : CNFRefutation 13.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% 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 : 7 ( 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 : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(w1_definition,axiom,
apply(apply(w1,X1),X2) = apply(apply(X2,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w1_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(w1,w1)),apply(b,w1))),apply(apply(b,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(w1,X1),X2) = apply(apply(X2,X1),X1),
w1_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(w1,X1),apply(apply(b,X2),X3)) = apply(apply(X2,apply(X3,X1)),X1),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
apply(apply(w1,X1),apply(apply(b,apply(b,X2)),X3)) = apply(X2,apply(apply(X3,X1),X1)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
apply(apply(w1,X1),apply(apply(b,apply(b,X2)),X3)) = apply(X2,apply(apply(w1,X1),X3)),
inference(spm,[status(thm)],[c_0_7,c_0_4]) ).
cnf(c_0_9,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,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(X1,apply(apply(w1,apply(apply(b,apply(b,X1)),X2)),X2)) = apply(apply(w1,apply(apply(b,apply(b,X1)),X2)),w1),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_12,plain,
apply(apply(w1,apply(apply(b,apply(b,X1)),w1)),w1) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_5]),c_0_5]),c_0_6]) ).
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(spm,[status(thm)],[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
% 0.00/0.03 % Problem : COL042-7 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 14:05:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 13.89/2.26 % Version: 3.5.1
% 13.89/2.26 % Preprocessing class: FSSSSMSSSSSNFFN.
% 13.89/2.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.89/2.26 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 13.89/2.26 % Starting new_bool_3 with 300s (1) cores
% 13.89/2.26 % Starting new_bool_1 with 300s (1) cores
% 13.89/2.26 % Starting sh5l with 300s (1) cores
% 13.89/2.26 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2105943 completed with status 0
% 13.89/2.26 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 13.89/2.26 % Preprocessing class: FSSSSMSSSSSNFFN.
% 13.89/2.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.89/2.26 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 13.89/2.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.89/2.26 % No SInE strategy applied
% 13.89/2.26 % Search class: FUUPS-FFSF22-MFFFFFNN
% 13.89/2.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 13.89/2.26 % Starting SubtermCWHack with 136s (1) cores
% 13.89/2.26 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 13.89/2.26 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 13.89/2.26 % Starting new_bool_3 with 136s (1) cores
% 13.89/2.26 % Starting new_bool_1 with 136s (1) cores
% 13.89/2.26 % new_bool_3 with pid 2105953 completed with status 0
% 13.89/2.26 % Result found by new_bool_3
% 13.89/2.26 % Preprocessing class: FSSSSMSSSSSNFFN.
% 13.89/2.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.89/2.26 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 13.89/2.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.89/2.26 % No SInE strategy applied
% 13.89/2.26 % Search class: FUUPS-FFSF22-MFFFFFNN
% 13.89/2.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 13.89/2.26 % Starting SubtermCWHack with 136s (1) cores
% 13.89/2.26 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 13.89/2.26 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 13.89/2.26 % Starting new_bool_3 with 136s (1) cores
% 13.89/2.26 % Preprocessing time : 0.002 s
% 13.89/2.26 % Presaturation interreduction done
% 13.89/2.26
% 13.89/2.26 % Proof found!
% 13.89/2.26 % SZS status Unsatisfiable
% 13.89/2.26 % SZS output start CNFRefutation
% See solution above
% 13.89/2.26 % Parsed axioms : 4
% 13.89/2.26 % Removed by relevancy pruning/SinE : 0
% 13.89/2.26 % Initial clauses : 4
% 13.89/2.26 % Removed in clause preprocessing : 0
% 13.89/2.26 % Initial clauses in saturation : 4
% 13.89/2.26 % Processed clauses : 802
% 13.89/2.26 % ...of these trivial : 282
% 13.89/2.26 % ...subsumed : 258
% 13.89/2.26 % ...remaining for further processing : 262
% 13.89/2.26 % Other redundant clauses eliminated : 0
% 13.89/2.26 % Clauses deleted for lack of memory : 0
% 13.89/2.26 % Backward-subsumed : 2
% 13.89/2.26 % Backward-rewritten : 35
% 13.89/2.26 % Generated clauses : 44736
% 13.89/2.26 % ...of the previous two non-redundant : 43327
% 13.89/2.26 % ...aggressively subsumed : 0
% 13.89/2.26 % Contextual simplify-reflections : 0
% 13.89/2.26 % Paramodulations : 44736
% 13.89/2.26 % Factorizations : 0
% 13.89/2.26 % NegExts : 0
% 13.89/2.26 % Equation resolutions : 0
% 13.89/2.26 % Disequality decompositions : 0
% 13.89/2.26 % Total rewrite steps : 28740
% 13.89/2.26 % ...of those cached : 21979
% 13.89/2.26 % Propositional unsat checks : 0
% 13.89/2.26 % Propositional check models : 0
% 13.89/2.26 % Propositional check unsatisfiable : 0
% 13.89/2.26 % Propositional clauses : 0
% 13.89/2.26 % Propositional clauses after purity: 0
% 13.89/2.26 % Propositional unsat core size : 0
% 13.89/2.26 % Propositional preprocessing time : 0.000
% 13.89/2.26 % Propositional encoding time : 0.000
% 13.89/2.26 % Propositional solver time : 0.000
% 13.89/2.26 % Success case prop preproc time : 0.000
% 13.89/2.26 % Success case prop encoding time : 0.000
% 13.89/2.26 % Success case prop solver time : 0.000
% 13.89/2.26 % Current number of processed clauses : 221
% 13.89/2.26 % Positive orientable unit clauses : 154
% 13.89/2.26 % Positive unorientable unit clauses: 67
% 13.89/2.26 % Negative unit clauses : 0
% 13.89/2.26 % Non-unit-clauses : 0
% 13.89/2.26 % Current number of unprocessed clauses: 42436
% 13.89/2.26 % ...number of literals in the above : 42436
% 13.89/2.26 % Current number of archived formulas : 0
% 13.89/2.26 % Current number of archived clauses : 41
% 13.89/2.26 % Clause-clause subsumption calls (NU) : 0
% 13.89/2.26 % Rec. Clause-clause subsumption calls : 0
% 13.89/2.26 % Non-unit clause-clause subsumptions : 0
% 13.89/2.26 % Unit Clause-clause subsumption calls : 2899
% 13.89/2.26 % Rewrite failures with RHS unbound : 0
% 13.89/2.26 % BW rewrite match attempts : 8803
% 13.89/2.26 % BW rewrite match successes : 277
% 13.89/2.26 % Condensation attempts : 0
% 13.89/2.26 % Condensation successes : 0
% 13.89/2.26 % Termbank termtop insertions : 1485225
% 13.89/2.26 % Search garbage collected termcells : 2
% 13.89/2.26
% 13.89/2.26 % -------------------------------------------------
% 13.89/2.26 % User time : 1.693 s
% 13.89/2.26 % System time : 0.066 s
% 13.89/2.26 % Total time : 1.759 s
% 13.89/2.26 % Maximum resident set size: 3324 pages
% 13.89/2.26
% 13.89/2.26 % -------------------------------------------------
% 13.89/2.26 % User time : 8.377 s
% 13.89/2.26 % System time : 0.297 s
% 13.89/2.26 % Total time : 8.674 s
% 13.89/2.26 % Maximum resident set size: 4608 pages
% 13.89/2.26 % E exiting
%------------------------------------------------------------------------------