%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL036-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:09:21 PM UTC 2026
% Result : Unsatisfiable 42.45s 17.60s
% Output : CNFRefutation 42.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 6 RR)
% Number of literals : 20 ( 19 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t_definition,axiom,
apply(apply(t,X1),X2) = apply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
cnf(s_definition,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
cnf(prove_fixed_point,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
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(c_0_4,axiom,
apply(apply(t,X1),X2) = apply(X2,X1),
t_definition ).
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,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
inference(fof_simplification,[status(thm)],[prove_fixed_point]) ).
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,t),X1),X2) = apply(apply(X1,X2),X2),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_9,plain,
apply(apply(t,X1),apply(t,X2)) = apply(X1,X2),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_10,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
c_0_6 ).
cnf(c_0_11,plain,
apply(apply(apply(s,t),apply(b,X1)),X2) = apply(X1,apply(X2,X2)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
apply(apply(apply(t,t),apply(s,t)),X1) = apply(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_4]) ).
cnf(c_0_13,negated_conjecture,
apply(f(apply(apply(b,X1),X2)),apply(X1,apply(X2,f(apply(apply(b,X1),X2))))) != apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_14,plain,
apply(apply(t,X1),apply(apply(s,t),X2)) = apply(apply(X2,X1),X1),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_15,plain,
apply(apply(t,X1),apply(apply(s,t),apply(b,X2))) = apply(X2,apply(X1,X1)),
inference(spm,[status(thm)],[c_0_4,c_0_11]) ).
cnf(c_0_16,plain,
apply(apply(t,X1),apply(apply(t,t),apply(s,t))) = apply(X1,X1),
inference(spm,[status(thm)],[c_0_4,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
apply(f(apply(apply(b,X1),apply(apply(b,X2),X3))),apply(X1,apply(X2,apply(X3,f(apply(apply(b,X1),apply(apply(b,X2),X3))))))) != apply(X1,apply(X2,apply(X3,f(apply(apply(b,X1),apply(apply(b,X2),X3)))))),
inference(spm,[status(thm)],[c_0_13,c_0_7]) ).
cnf(c_0_18,plain,
apply(X1,apply(apply(apply(t,t),apply(s,t)),apply(apply(s,t),apply(b,X1)))) = apply(apply(apply(t,t),apply(s,t)),apply(apply(s,t),apply(b,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_4]),c_0_16]),c_0_12]),c_0_12]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_17,c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL036-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/10.39 % Computer : n016.cluster.edu
% 0.09/10.39 % Model : x86_64 x86_64
% 0.09/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.39 % Memory : 8046.5625MB
% 0.09/10.39 % OS : Linux 6.8.0-71-generic
% 0.09/10.39 % CPULimit : 300
% 0.09/10.39 % WCLimit : 300
% 0.09/10.39 % DateTime : Mon Sep 21 14:10:35 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.09/10.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/10.44 Running first-order theorem proving
% 0.14/10.44 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
% 42.45/17.60 % Version: 3.5.1
% 42.45/17.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 42.45/17.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 42.45/17.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 42.45/17.60 % Starting new_bool_3 with 300s (1) cores
% 42.45/17.60 % Starting new_bool_1 with 300s (1) cores
% 42.45/17.60 % Starting sh5l with 300s (1) cores
% 42.45/17.60 % new_bool_1 with pid 2621540 completed with status 9
% 42.45/17.60 % new_bool_3 with pid 2621539 completed with status 9
% 42.45/17.60 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2621538 completed with status 0
% 42.45/17.60 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 42.45/17.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 42.45/17.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 42.45/17.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 42.45/17.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 42.45/17.60 % No SInE strategy applied
% 42.45/17.60 % Search class: FUUPS-FFSF21-MFFFFFNN
% 42.45/17.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 42.45/17.60 % Starting SubtermCWHack with 136s (1) cores
% 42.45/17.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 42.45/17.60 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 42.45/17.60 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 42.45/17.60 % Starting U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 42.45/17.60 % U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 2621549 completed with status 0
% 42.45/17.60 % Result found by U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 42.45/17.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 42.45/17.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 42.45/17.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 42.45/17.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 42.45/17.60 % No SInE strategy applied
% 42.45/17.60 % Search class: FUUPS-FFSF21-MFFFFFNN
% 42.45/17.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 42.45/17.60 % Starting SubtermCWHack with 136s (1) cores
% 42.45/17.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 42.45/17.60 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 42.45/17.60 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 42.45/17.60 % Starting U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 42.45/17.60 % Preprocessing time : 0.001 s
% 42.45/17.60 % Presaturation interreduction done
% 42.45/17.60
% 42.45/17.60 % Proof found!
% 42.45/17.60 % SZS status Unsatisfiable
% 42.45/17.60 % SZS output start CNFRefutation
% See solution above
% 42.45/17.60 % Parsed axioms : 4
% 42.45/17.60 % Removed by relevancy pruning/SinE : 0
% 42.45/17.60 % Initial clauses : 4
% 42.45/17.60 % Removed in clause preprocessing : 0
% 42.45/17.60 % Initial clauses in saturation : 4
% 42.45/17.60 % Processed clauses : 2290
% 42.45/17.60 % ...of these trivial : 18
% 42.45/17.60 % ...subsumed : 1950
% 42.45/17.60 % ...remaining for further processing : 322
% 42.45/17.60 % Other redundant clauses eliminated : 0
% 42.45/17.60 % Clauses deleted for lack of memory : 0
% 42.45/17.60 % Backward-subsumed : 13
% 42.45/17.60 % Backward-rewritten : 34
% 42.45/17.60 % Generated clauses : 212735
% 42.45/17.60 % ...of the previous two non-redundant : 211406
% 42.45/17.60 % ...aggressively subsumed : 0
% 42.45/17.60 % Contextual simplify-reflections : 0
% 42.45/17.60 % Paramodulations : 212735
% 42.45/17.60 % Factorizations : 0
% 42.45/17.60 % NegExts : 0
% 42.45/17.60 % Equation resolutions : 0
% 42.45/17.60 % Disequality decompositions : 0
% 42.45/17.60 % Total rewrite steps : 67033
% 42.45/17.60 % ...of those cached : 58711
% 42.45/17.60 % Propositional unsat checks : 0
% 42.45/17.60 % Propositional check models : 0
% 42.45/17.60 % Propositional check unsatisfiable : 0
% 42.45/17.60 % Propositional clauses : 0
% 42.45/17.60 % Propositional clauses after purity: 0
% 42.45/17.60 % Propositional unsat core size : 0
% 42.45/17.60 % Propositional preprocessing time : 0.000
% 42.45/17.60 % Propositional encoding time : 0.000
% 42.45/17.60 % Propositional solver time : 0.000
% 42.45/17.60 % Success case prop preproc time : 0.000
% 42.45/17.60 % Success case prop encoding time : 0.000
% 42.45/17.60 % Success case prop solver time : 0.000
% 42.45/17.60 % Current number of processed clauses : 271
% 42.45/17.60 % Positive orientable unit clauses : 18
% 42.45/17.60 % Positive unorientable unit clauses: 150
% 42.45/17.60 % Negative unit clauses : 103
% 42.45/17.60 % Non-unit-clauses : 0
% 42.45/17.60 % Current number of unprocessed clauses: 208956
% 42.45/17.60 % ...number of literals in the above : 208956
% 42.45/17.60 % Current number of archived formulas : 0
% 42.45/17.60 % Current number of archived clauses : 51
% 42.45/17.60 % Clause-clause subsumption calls (NU) : 0
% 42.45/17.60 % Rec. Clause-clause subsumption calls : 0
% 42.45/17.60 % Non-unit clause-clause subsumptions : 0
% 42.45/17.60 % Unit Clause-clause subsumption calls : 3442
% 42.45/17.60 % Rewrite failures with RHS unbound : 0
% 42.45/17.60 % BW rewrite match attempts : 19783
% 42.45/17.60 % BW rewrite match successes : 3998
% 42.45/17.60 % Condensation attempts : 0
% 42.45/17.60 % Condensation successes : 0
% 42.45/17.60 % Termbank termtop insertions : 7713649
% 42.45/17.60 % Search garbage collected termcells : 2
% 42.45/17.60
% 42.45/17.60 % -------------------------------------------------
% 42.45/17.60 % User time : 6.698 s
% 42.45/17.60 % System time : 0.244 s
% 42.45/17.60 % Total time : 6.941 s
% 42.45/17.60 % Maximum resident set size: 3632 pages
% 42.45/17.60
% 42.45/17.60 % -------------------------------------------------
% 42.45/17.60 % User time : 33.849 s
% 42.45/17.60 % System time : 1.278 s
% 42.45/17.60 % Total time : 35.127 s
% 42.45/17.60 % Maximum resident set size: 4864 pages
% 42.45/17.60 % E exiting
%------------------------------------------------------------------------------