%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL044-9 : 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 : 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 12:09:25 PM UTC 2026
% Result : Unsatisfiable 110.79s 16.48s
% Output : CNFRefutation 110.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 6 RR)
% Number of literals : 24 ( 23 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 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 : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(n_definition,axiom,
apply(apply(apply(n,X1),X2),X3) = apply(apply(apply(X1,X3),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_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(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),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(apply(n,X1),X2),X3) = apply(apply(apply(X1,X3),X2),X3),
n_definition ).
cnf(c_0_5,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_6,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),b)),b),
strong_fixed_point ).
cnf(c_0_7,plain,
apply(apply(apply(n,apply(X1,X2)),X2),X3) = apply(apply(apply(n,apply(n,X1)),X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_4]),c_0_4]) ).
cnf(c_0_8,plain,
apply(apply(apply(n,apply(apply(b,X1),X2)),X3),X4) = apply(apply(apply(X1,apply(X2,X4)),X3),X4),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_9,plain,
apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n),apply(b,apply(b,X1))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_5]) ).
cnf(c_0_10,plain,
apply(apply(apply(n,apply(X1,apply(X2,X3))),X3),X4) = apply(apply(apply(n,apply(n,apply(apply(b,X1),X2))),X3),X4),
inference(spm,[status(thm)],[c_0_7,c_0_5]) ).
cnf(c_0_11,plain,
apply(apply(apply(n,apply(b,X1)),X2),X3) = apply(apply(X1,apply(X3,X2)),X3),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_12,plain,
apply(apply(apply(n,apply(apply(b,b),X1)),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_13,plain,
apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,X1))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
apply(apply(apply(apply(n,apply(b,b)),X1),X2),X3) = apply(apply(X2,X1),apply(X2,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_11]) ).
cnf(c_0_15,plain,
apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,X1))),apply(n,apply(b,apply(b,X1)))) = apply(strong_fixed_point,X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
apply(apply(apply(n,apply(n,apply(b,b))),X1),X2) = apply(apply(X1,X2),apply(X1,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_14]) ).
cnf(c_0_17,plain,
apply(apply(apply(n,apply(b,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X3,X2),X3)),
inference(spm,[status(thm)],[c_0_5,c_0_11]) ).
cnf(c_0_18,plain,
apply(apply(apply(n,apply(b,apply(b,X1))),apply(n,apply(b,apply(b,X1)))),apply(n,apply(b,apply(b,X1)))) = apply(strong_fixed_point,X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,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_20,plain,
apply(apply(apply(n,apply(b,apply(b,X1))),apply(n,apply(b,apply(b,X2)))),apply(n,apply(b,apply(b,X2)))) = apply(X1,apply(strong_fixed_point,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
c_0_19 ).
cnf(c_0_22,plain,
apply(X1,apply(strong_fixed_point,X1)) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL044-9 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 14:07:06 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.35 Running first-order theorem proving
% 0.04/0.35 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
% 110.79/16.48 % Version: 3.5.1
% 110.79/16.48 % Preprocessing class: FSSSSMSSSSSNFFN.
% 110.79/16.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 110.79/16.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 110.79/16.48 % Starting new_bool_3 with 300s (1) cores
% 110.79/16.48 % Starting new_bool_1 with 300s (1) cores
% 110.79/16.48 % Starting sh5l with 300s (1) cores
% 110.79/16.48 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2533839 completed with status 0
% 110.79/16.48 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 110.79/16.48 % Preprocessing class: FSSSSMSSSSSNFFN.
% 110.79/16.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 110.79/16.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 110.79/16.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 110.79/16.48 % No SInE strategy applied
% 110.79/16.48 % Search class: FUUPS-FFSF22-DFFFFFNN
% 110.79/16.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 110.79/16.48 % Starting SubtermCWHack with 136s (1) cores
% 110.79/16.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 110.79/16.48 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 110.79/16.48 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 110.79/16.48 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 110.79/16.48 % U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 2533847 completed with status 0
% 110.79/16.48 % Result found by U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 110.79/16.48 % Preprocessing class: FSSSSMSSSSSNFFN.
% 110.79/16.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 110.79/16.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 110.79/16.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 110.79/16.48 % No SInE strategy applied
% 110.79/16.48 % Search class: FUUPS-FFSF22-DFFFFFNN
% 110.79/16.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 110.79/16.48 % Starting SubtermCWHack with 136s (1) cores
% 110.79/16.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 110.79/16.48 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 110.79/16.48 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 110.79/16.48 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 110.79/16.48 % Preprocessing time : 0.001 s
% 110.79/16.48 % Presaturation interreduction done
% 110.79/16.48
% 110.79/16.48 % Proof found!
% 110.79/16.48 % SZS status Unsatisfiable
% 110.79/16.48 % SZS output start CNFRefutation
% See solution above
% 110.79/16.48 % Parsed axioms : 4
% 110.79/16.48 % Removed by relevancy pruning/SinE : 0
% 110.79/16.48 % Initial clauses : 4
% 110.79/16.48 % Removed in clause preprocessing : 0
% 110.79/16.48 % Initial clauses in saturation : 4
% 110.79/16.48 % Processed clauses : 2939
% 110.79/16.48 % ...of these trivial : 754
% 110.79/16.48 % ...subsumed : 1000
% 110.79/16.48 % ...remaining for further processing : 1185
% 110.79/16.48 % Other redundant clauses eliminated : 0
% 110.79/16.48 % Clauses deleted for lack of memory : 0
% 110.79/16.48 % Backward-subsumed : 14
% 110.79/16.48 % Backward-rewritten : 161
% 110.79/16.48 % Generated clauses : 593216
% 110.79/16.48 % ...of the previous two non-redundant : 590166
% 110.79/16.48 % ...aggressively subsumed : 0
% 110.79/16.48 % Contextual simplify-reflections : 0
% 110.79/16.48 % Paramodulations : 593216
% 110.79/16.48 % Factorizations : 0
% 110.79/16.48 % NegExts : 0
% 110.79/16.48 % Equation resolutions : 0
% 110.79/16.48 % Disequality decompositions : 0
% 110.79/16.48 % Total rewrite steps : 139227
% 110.79/16.48 % ...of those cached : 102644
% 110.79/16.48 % Propositional unsat checks : 0
% 110.79/16.48 % Propositional check models : 0
% 110.79/16.48 % Propositional check unsatisfiable : 0
% 110.79/16.48 % Propositional clauses : 0
% 110.79/16.48 % Propositional clauses after purity: 0
% 110.79/16.48 % Propositional unsat core size : 0
% 110.79/16.48 % Propositional preprocessing time : 0.000
% 110.79/16.48 % Propositional encoding time : 0.000
% 110.79/16.48 % Propositional solver time : 0.000
% 110.79/16.48 % Success case prop preproc time : 0.000
% 110.79/16.48 % Success case prop encoding time : 0.000
% 110.79/16.48 % Success case prop solver time : 0.000
% 110.79/16.48 % Current number of processed clauses : 1006
% 110.79/16.48 % Positive orientable unit clauses : 696
% 110.79/16.48 % Positive unorientable unit clauses: 310
% 110.79/16.48 % Negative unit clauses : 0
% 110.79/16.48 % Non-unit-clauses : 0
% 110.79/16.48 % Current number of unprocessed clauses: 586823
% 110.79/16.48 % ...number of literals in the above : 586823
% 110.79/16.48 % Current number of archived formulas : 0
% 110.79/16.48 % Current number of archived clauses : 179
% 110.79/16.48 % Clause-clause subsumption calls (NU) : 0
% 110.79/16.48 % Rec. Clause-clause subsumption calls : 0
% 110.79/16.48 % Non-unit clause-clause subsumptions : 0
% 110.79/16.48 % Unit Clause-clause subsumption calls : 77017
% 110.79/16.48 % Rewrite failures with RHS unbound : 0
% 110.79/16.48 % BW rewrite match attempts : 430325
% 110.79/16.48 % BW rewrite match successes : 1459
% 110.79/16.48 % Condensation attempts : 0
% 110.79/16.48 % Condensation successes : 0
% 110.79/16.48 % Termbank termtop insertions : 32899029
% 110.79/16.48 % Search garbage collected termcells : 2
% 110.79/16.48
% 110.79/16.48 % -------------------------------------------------
% 110.79/16.48 % User time : 15.407 s
% 110.79/16.48 % System time : 0.423 s
% 110.79/16.48 % Total time : 15.829 s
% 110.79/16.48 % Maximum resident set size: 3588 pages
% 110.79/16.48
% 110.79/16.48 % -------------------------------------------------
% 110.79/16.48 % User time : 76.553 s
% 110.79/16.48 % System time : 2.278 s
% 110.79/16.48 % Total time : 78.832 s
% 110.79/16.48 % Maximum resident set size: 4864 pages
% 110.79/16.48 % E exiting
%------------------------------------------------------------------------------