%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL078-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:09:32 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 29 ( 21 unt; 0 nHn; 14 RR)
% Number of literals : 37 ( 36 equ; 12 neg)
% Maximal clause size : 2 ( 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; 2 con; 0-2 aty)
% Number of variables : 43 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(extensionality2,axiom,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
cnf(k_definition,axiom,
apply(k(X1),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstraction) ).
cnf(identity_definition,axiom,
apply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_definition) ).
cnf(prove_TRC1b,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_TRC1b) ).
cnf(c_0_5,plain,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[extensionality2]) ).
cnf(c_0_6,plain,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
c_0_5 ).
cnf(c_0_7,axiom,
apply(k(X1),X2) = X1,
k_definition ).
cnf(c_0_8,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
abstraction ).
cnf(c_0_9,plain,
( apply(X2,n(k(X1),X2)) != X1
| k(X1) = X2 ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
apply(apply(apply(abstraction,k(X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_11,plain,
( apply(X2,apply(X3,n(k(X1),apply(apply(abstraction,k(X2)),X3)))) != X1
| k(X1) = apply(apply(abstraction,k(X2)),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
apply(apply(abstraction,k(k(X1))),X2) = k(X1),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_7])]) ).
cnf(c_0_13,axiom,
apply(identity,X1) = X1,
identity_definition ).
cnf(c_0_14,plain,
apply(abstraction,k(k(X1))) = k(k(X1)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_12])]) ).
cnf(c_0_15,plain,
( apply(X1,n(X1,identity)) != n(X1,identity)
| X1 = identity ),
inference(spm,[status(thm)],[c_0_6,c_0_13]) ).
cnf(c_0_16,plain,
apply(apply(apply(abstraction,identity),X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_13]),c_0_7]) ).
cnf(c_0_17,plain,
apply(apply(apply(abstraction,abstraction),X1),k(X2)) = k(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_14]),c_0_7]) ).
cnf(c_0_18,plain,
apply(apply(abstraction,identity),X1) = identity,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( apply(X1,n(identity,X1)) != n(identity,X1)
| identity = X1 ),
inference(spm,[status(thm)],[c_0_6,c_0_13]) ).
cnf(c_0_20,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_17]),c_0_7]) ).
cnf(c_0_21,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
inference(fof_simplification,[status(thm)],[prove_TRC1b]) ).
cnf(c_0_22,plain,
( apply(X1,n(apply(abstraction,identity),X1)) != identity
| apply(abstraction,identity) = X1 ),
inference(spm,[status(thm)],[c_0_6,c_0_18]) ).
cnf(c_0_23,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2) = identity,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
c_0_21 ).
cnf(c_0_25,plain,
k(identity) = apply(abstraction,identity),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_7])]) ).
cnf(c_0_26,plain,
apply(abstraction,apply(apply(abstraction,abstraction),X1)) = apply(abstraction,identity),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(apply(abstraction,identity)),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_26]),c_0_8])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL078-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 14:14:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2628230 completed with status 0
% 0.14/0.44 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.14/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FHUPS-FFSF21-MFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/0.44 % Starting U----_211g_00_C10_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.44 % new_bool_3 with pid 2628240 completed with status 0
% 0.14/0.44 % Result found by new_bool_3
% 0.14/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FHUPS-FFSF21-MFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/0.44 % Starting U----_211g_00_C10_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.44 % Preprocessing time : 0.001 s
% 0.14/0.44 % Presaturation interreduction done
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Unsatisfiable
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 5
% 0.14/0.44 % Removed by relevancy pruning/SinE : 0
% 0.14/0.44 % Initial clauses : 5
% 0.14/0.44 % Removed in clause preprocessing : 0
% 0.14/0.44 % Initial clauses in saturation : 5
% 0.14/0.44 % Processed clauses : 110
% 0.14/0.44 % ...of these trivial : 11
% 0.14/0.44 % ...subsumed : 19
% 0.14/0.44 % ...remaining for further processing : 80
% 0.14/0.44 % Other redundant clauses eliminated : 48
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 0
% 0.14/0.44 % Backward-rewritten : 22
% 0.14/0.44 % Generated clauses : 729
% 0.14/0.44 % ...of the previous two non-redundant : 534
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 0
% 0.14/0.44 % Paramodulations : 680
% 0.14/0.44 % Factorizations : 0
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 49
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 801
% 0.14/0.44 % ...of those cached : 551
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 53
% 0.14/0.44 % Positive orientable unit clauses : 34
% 0.14/0.44 % Positive unorientable unit clauses: 0
% 0.14/0.44 % Negative unit clauses : 1
% 0.14/0.44 % Non-unit-clauses : 18
% 0.14/0.44 % Current number of unprocessed clauses: 390
% 0.14/0.44 % ...number of literals in the above : 521
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 27
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 61
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 61
% 0.14/0.44 % Non-unit clause-clause subsumptions : 19
% 0.14/0.44 % Unit Clause-clause subsumption calls : 2
% 0.14/0.45 % Rewrite failures with RHS unbound : 0
% 0.14/0.45 % BW rewrite match attempts : 133
% 0.14/0.45 % BW rewrite match successes : 19
% 0.14/0.45 % Condensation attempts : 0
% 0.14/0.45 % Condensation successes : 0
% 0.14/0.45 % Termbank termtop insertions : 14020
% 0.14/0.45 % Search garbage collected termcells : 5
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.016 s
% 0.14/0.45 % System time : 0.003 s
% 0.14/0.45 % Total time : 0.020 s
% 0.14/0.45 % Maximum resident set size: 3632 pages
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.082 s
% 0.14/0.45 % System time : 0.016 s
% 0.14/0.45 % Total time : 0.099 s
% 0.14/0.45 % Maximum resident set size: 4864 pages
% 0.14/0.45 % E exiting
%------------------------------------------------------------------------------