%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL044-6 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:09:24 PM UTC 2026
% Result : Unsatisfiable 152.52s 19.96s
% Output : CNFRefutation 152.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 6 RR)
% Number of literals : 22 ( 21 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 : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(n_definition,axiom,
apply(apply(apply(n,X1),X2),X3) = apply(apply(apply(X1,X3),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_definition) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(strong_fixed_point,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b),
file('/export/starexec/sandbox/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/sandbox/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(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b),
strong_fixed_point ).
cnf(c_0_7,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_8,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_9,plain,
apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),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(apply(b,b),X1)),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_11,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_12,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_8]) ).
cnf(c_0_13,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_14,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_12]) ).
cnf(c_0_15,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_8]) ).
cnf(c_0_16,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_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)),
inference(fof_simplification,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_0_18,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_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)),
c_0_17 ).
cnf(c_0_20,plain,
apply(X1,apply(strong_fixed_point,X1)) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL044-6 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n004.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 14:06:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 152.52/19.96 % Version: 3.5.1
% 152.52/19.96 % Preprocessing class: FSSSSMSSSSSNFFN.
% 152.52/19.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 152.52/19.96 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 152.52/19.96 % Starting new_bool_3 with 300s (1) cores
% 152.52/19.96 % Starting new_bool_1 with 300s (1) cores
% 152.52/19.96 % Starting sh5l with 300s (1) cores
% 152.52/19.96 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3330079 completed with status 0
% 152.52/19.96 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 152.52/19.96 % Preprocessing class: FSSSSMSSSSSNFFN.
% 152.52/19.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 152.52/19.96 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 152.52/19.96 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 152.52/19.96 % No SInE strategy applied
% 152.52/19.96 % Search class: FUUPS-FFSF22-DFFFFFNN
% 152.52/19.96 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 152.52/19.96 % Starting SubtermCWHack with 136s (1) cores
% 152.52/19.96 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 152.52/19.96 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 152.52/19.96 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 152.52/19.96 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 152.52/19.96 % U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3330090 completed with status 0
% 152.52/19.96 % Result found by U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 152.52/19.96 % Preprocessing class: FSSSSMSSSSSNFFN.
% 152.52/19.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 152.52/19.96 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 152.52/19.96 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 152.52/19.96 % No SInE strategy applied
% 152.52/19.96 % Search class: FUUPS-FFSF22-DFFFFFNN
% 152.52/19.96 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 152.52/19.96 % Starting SubtermCWHack with 136s (1) cores
% 152.52/19.96 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 152.52/19.96 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 152.52/19.96 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 152.52/19.96 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 152.52/19.96 % Preprocessing time : 0.001 s
% 152.52/19.96 % Presaturation interreduction done
% 152.52/19.96
% 152.52/19.96 % Proof found!
% 152.52/19.96 % SZS status Unsatisfiable
% 152.52/19.96 % SZS output start CNFRefutation
% See solution above
% 152.52/19.96 % Parsed axioms : 4
% 152.52/19.96 % Removed by relevancy pruning/SinE : 0
% 152.52/19.96 % Initial clauses : 4
% 152.52/19.96 % Removed in clause preprocessing : 0
% 152.52/19.96 % Initial clauses in saturation : 4
% 152.52/19.96 % Processed clauses : 1821
% 152.52/19.96 % ...of these trivial : 453
% 152.52/19.96 % ...subsumed : 572
% 152.52/19.96 % ...remaining for further processing : 796
% 152.52/19.96 % Other redundant clauses eliminated : 0
% 152.52/19.96 % Clauses deleted for lack of memory : 0
% 152.52/19.96 % Backward-subsumed : 9
% 152.52/19.96 % Backward-rewritten : 100
% 152.52/19.96 % Generated clauses : 314114
% 152.52/19.96 % ...of the previous two non-redundant : 312124
% 152.52/19.96 % ...aggressively subsumed : 0
% 152.52/19.96 % Contextual simplify-reflections : 0
% 152.52/19.96 % Paramodulations : 314114
% 152.52/19.96 % Factorizations : 0
% 152.52/19.96 % NegExts : 0
% 152.52/19.96 % Equation resolutions : 0
% 152.52/19.96 % Disequality decompositions : 0
% 152.52/19.96 % Total rewrite steps : 73140
% 152.52/19.96 % ...of those cached : 53625
% 152.52/19.96 % Propositional unsat checks : 0
% 152.52/19.96 % Propositional check models : 0
% 152.52/19.96 % Propositional check unsatisfiable : 0
% 152.52/19.96 % Propositional clauses : 0
% 152.52/19.96 % Propositional clauses after purity: 0
% 152.52/19.96 % Propositional unsat core size : 0
% 152.52/19.96 % Propositional preprocessing time : 0.000
% 152.52/19.96 % Propositional encoding time : 0.000
% 152.52/19.96 % Propositional solver time : 0.000
% 152.52/19.96 % Success case prop preproc time : 0.000
% 152.52/19.96 % Success case prop encoding time : 0.000
% 152.52/19.96 % Success case prop solver time : 0.000
% 152.52/19.96 % Current number of processed clauses : 683
% 152.52/19.96 % Positive orientable unit clauses : 446
% 152.52/19.96 % Positive unorientable unit clauses: 237
% 152.52/19.96 % Negative unit clauses : 0
% 152.52/19.96 % Non-unit-clauses : 0
% 152.52/19.96 % Current number of unprocessed clauses: 310048
% 152.52/19.96 % ...number of literals in the above : 310048
% 152.52/19.96 % Current number of archived formulas : 0
% 152.52/19.96 % Current number of archived clauses : 113
% 152.52/19.96 % Clause-clause subsumption calls (NU) : 0
% 152.52/19.96 % Rec. Clause-clause subsumption calls : 0
% 152.52/19.96 % Non-unit clause-clause subsumptions : 0
% 152.52/19.96 % Unit Clause-clause subsumption calls : 38677
% 152.52/19.96 % Rewrite failures with RHS unbound : 0
% 152.52/19.96 % BW rewrite match attempts : 211699
% 152.52/19.96 % BW rewrite match successes : 976
% 152.52/19.96 % Condensation attempts : 0
% 152.52/19.96 % Condensation successes : 0
% 152.52/19.96 % Termbank termtop insertions : 16222900
% 152.52/19.96 % Search garbage collected termcells : 2
% 152.52/19.96
% 152.52/19.96 % -------------------------------------------------
% 152.52/19.96 % User time : 18.510 s
% 152.52/19.96 % System time : 0.464 s
% 152.52/19.96 % Total time : 18.973 s
% 152.52/19.96 % Maximum resident set size: 3640 pages
% 152.52/19.96
% 152.52/19.96 % -------------------------------------------------
% 152.52/19.96 % User time : 91.250 s
% 152.52/19.96 % System time : 2.773 s
% 152.52/19.96 % Total time : 94.023 s
% 152.52/19.96 % Maximum resident set size: 4608 pages
% 152.52/19.96 % E exiting
%------------------------------------------------------------------------------