%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : COL078-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:10:02 PM UTC 2026
% Result : Unsatisfiable 38.33s 6.17s
% Output : CNFRefutation 38.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 21 ( 15 unt; 0 nHn; 11 RR)
% Number of literals : 27 ( 26 equ; 10 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 : 33 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(extensionality2,axiom,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',extensionality2) ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',abstraction) ).
cnf(k_definition,axiom,
apply(k(X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',k_definition) ).
cnf(identity_definition,axiom,
apply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_definition) ).
cnf(prove_TRC1b,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
file('/export/starexec/sandbox/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,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
abstraction ).
cnf(c_0_7,axiom,
apply(k(X1),X2) = X1,
k_definition ).
cnf(c_0_8,plain,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
c_0_5 ).
cnf(c_0_9,axiom,
apply(identity,X1) = X1,
identity_definition ).
cnf(c_0_10,plain,
apply(apply(apply(apply(abstraction,abstraction),X1),X2),X3) = apply(X2,apply(apply(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_6]),c_0_7]) ).
cnf(c_0_11,plain,
( apply(X1,n(identity,X1)) != n(identity,X1)
| identity = X1 ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_10]),c_0_7]) ).
cnf(c_0_13,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
inference(fof_simplification,[status(thm)],[prove_TRC1b]) ).
cnf(c_0_14,plain,
( apply(X2,n(k(X1),X2)) != X1
| k(X1) = X2 ),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_15,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2) = identity,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
c_0_13 ).
cnf(c_0_17,plain,
( apply(X3,apply(apply(X2,X3),n(k(X1),apply(apply(apply(abstraction,abstraction),X2),X3)))) != X1
| k(X1) = apply(apply(apply(abstraction,abstraction),X2),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_18,plain,
apply(abstraction,apply(apply(abstraction,abstraction),X1)) = k(identity),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_19,negated_conjecture,
apply(apply(abstraction,k(abstraction)),apply(abstraction,abstraction)) != k(k(identity)),
inference(rw,[status(thm)],[c_0_16,c_0_6]) ).
cnf(c_0_20,plain,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_6])]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL078-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 14:10:18 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 38.33/6.17 % Version: 3.5.1
% 38.33/6.17 % Preprocessing class: FSSSSMSSSSSNFFN.
% 38.33/6.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 38.33/6.17 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 38.33/6.17 % Starting new_bool_3 with 300s (1) cores
% 38.33/6.17 % Starting new_bool_1 with 300s (1) cores
% 38.33/6.17 % Starting sh5l with 300s (1) cores
% 38.33/6.17 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3134695 completed with status 0
% 38.33/6.17 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 38.33/6.17 % Preprocessing class: FSSSSMSSSSSNFFN.
% 38.33/6.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 38.33/6.17 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 38.33/6.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 38.33/6.17 % No SInE strategy applied
% 38.33/6.17 % Search class: FGUPM-FFSF21-MFFFFFNN
% 38.33/6.17 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 38.33/6.17 % Starting SubtermCWHack with 136s (1) cores
% 38.33/6.17 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 38.33/6.17 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 136s (1) cores
% 38.33/6.17 % Starting new_bool_3 with 136s (1) cores
% 38.33/6.17 % Starting new_bool_1 with 136s (1) cores
% 38.33/6.17 % C12_02_nc_SAT001_MinMin_p005000_rr with pid 3134701 completed with status 0
% 38.33/6.17 % Result found by C12_02_nc_SAT001_MinMin_p005000_rr
% 38.33/6.17 % Preprocessing class: FSSSSMSSSSSNFFN.
% 38.33/6.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 38.33/6.17 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 38.33/6.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 38.33/6.17 % No SInE strategy applied
% 38.33/6.17 % Search class: FGUPM-FFSF21-MFFFFFNN
% 38.33/6.17 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 38.33/6.17 % Starting SubtermCWHack with 136s (1) cores
% 38.33/6.17 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 38.33/6.17 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 136s (1) cores
% 38.33/6.17 % Preprocessing time : 0.001 s
% 38.33/6.17 % Presaturation interreduction done
% 38.33/6.17
% 38.33/6.17 % Proof found!
% 38.33/6.17 % SZS status Unsatisfiable
% 38.33/6.17 % SZS output start CNFRefutation
% See solution above
% 38.33/6.17 % Parsed axioms : 12
% 38.33/6.17 % Removed by relevancy pruning/SinE : 0
% 38.33/6.17 % Initial clauses : 12
% 38.33/6.17 % Removed in clause preprocessing : 0
% 38.33/6.17 % Initial clauses in saturation : 12
% 38.33/6.17 % Processed clauses : 7090
% 38.33/6.17 % ...of these trivial : 162
% 38.33/6.17 % ...subsumed : 5578
% 38.33/6.17 % ...remaining for further processing : 1350
% 38.33/6.17 % Other redundant clauses eliminated : 148
% 38.33/6.17 % Clauses deleted for lack of memory : 0
% 38.33/6.17 % Backward-subsumed : 40
% 38.33/6.17 % Backward-rewritten : 244
% 38.33/6.17 % Generated clauses : 137225
% 38.33/6.17 % ...of the previous two non-redundant : 117247
% 38.33/6.17 % ...aggressively subsumed : 0
% 38.33/6.17 % Contextual simplify-reflections : 0
% 38.33/6.17 % Paramodulations : 137075
% 38.33/6.17 % Factorizations : 0
% 38.33/6.17 % NegExts : 0
% 38.33/6.17 % Equation resolutions : 150
% 38.33/6.17 % Disequality decompositions : 0
% 38.33/6.17 % Total rewrite steps : 207671
% 38.33/6.17 % ...of those cached : 155447
% 38.33/6.17 % Propositional unsat checks : 0
% 38.33/6.17 % Propositional check models : 0
% 38.33/6.17 % Propositional check unsatisfiable : 0
% 38.33/6.17 % Propositional clauses : 0
% 38.33/6.17 % Propositional clauses after purity: 0
% 38.33/6.17 % Propositional unsat core size : 0
% 38.33/6.17 % Propositional preprocessing time : 0.000
% 38.33/6.17 % Propositional encoding time : 0.000
% 38.33/6.17 % Propositional solver time : 0.000
% 38.33/6.17 % Success case prop preproc time : 0.000
% 38.33/6.17 % Success case prop encoding time : 0.000
% 38.33/6.17 % Success case prop solver time : 0.000
% 38.33/6.17 % Current number of processed clauses : 1054
% 38.33/6.17 % Positive orientable unit clauses : 751
% 38.33/6.17 % Positive unorientable unit clauses: 31
% 38.33/6.17 % Negative unit clauses : 124
% 38.33/6.17 % Non-unit-clauses : 148
% 38.33/6.17 % Current number of unprocessed clauses: 107422
% 38.33/6.17 % ...number of literals in the above : 135159
% 38.33/6.17 % Current number of archived formulas : 0
% 38.33/6.17 % Current number of archived clauses : 296
% 38.33/6.17 % Clause-clause subsumption calls (NU) : 2582
% 38.33/6.17 % Rec. Clause-clause subsumption calls : 2578
% 38.33/6.17 % Non-unit clause-clause subsumptions : 940
% 38.33/6.17 % Unit Clause-clause subsumption calls : 2153
% 38.33/6.17 % Rewrite failures with RHS unbound : 0
% 38.33/6.17 % BW rewrite match attempts : 33465
% 38.33/6.17 % BW rewrite match successes : 329
% 38.33/6.17 % Condensation attempts : 0
% 38.33/6.17 % Condensation successes : 0
% 38.33/6.17 % Termbank termtop insertions : 4373088
% 38.33/6.17 % Search garbage collected termcells : 7
% 38.33/6.17
% 38.33/6.17 % -------------------------------------------------
% 38.33/6.17 % User time : 5.244 s
% 38.33/6.17 % System time : 0.218 s
% 38.33/6.17 % Total time : 5.462 s
% 38.33/6.17 % Maximum resident set size: 3588 pages
% 38.33/6.17
% 38.33/6.17 % -------------------------------------------------
% 38.33/6.17 % User time : 26.224 s
% 38.33/6.17 % System time : 1.110 s
% 38.33/6.17 % Total time : 27.334 s
% 38.33/6.17 % Maximum resident set size: 4864 pages
% 38.33/6.17 % E exiting
%------------------------------------------------------------------------------