%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL076-2 : 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 : n005.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 50.95s 7.90s
% Output : CNFRefutation 50.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 30 ( 24 unt; 0 nHn; 14 RR)
% Number of literals : 36 ( 35 equ; 13 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 60 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(extensionality2,axiom,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
cnf(k_definition,axiom,
apply(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(pairwise_application,axiom,
apply(pair(X1,X2),X3) = pair(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairwise_application) ).
cnf(prove_self_referential,negated_conjecture,
X1 != apply(eq,pair(apply(k,X1),apply(k,projection2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_self_referential) ).
cnf(projection2,axiom,
apply(projection2,pair(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection2) ).
cnf(diagonal_combinator,axiom,
apply(apply(f,X1),X2) = apply(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagonal_combinator) ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,apply(k,X3)),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
cnf(c_0_7,plain,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[extensionality2]) ).
cnf(c_0_8,plain,
( apply(X1,n(X1,X2)) != apply(X2,n(X1,X2))
| X1 = X2 ),
c_0_7 ).
cnf(c_0_9,axiom,
apply(apply(k,X1),X2) = X1,
k_definition ).
cnf(c_0_10,axiom,
apply(pair(X1,X2),X3) = pair(apply(X1,X3),apply(X2,X3)),
pairwise_application ).
cnf(c_0_11,plain,
( apply(X2,n(apply(k,X1),X2)) != X1
| apply(k,X1) = X2 ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
apply(pair(X1,apply(k,X2)),X3) = pair(apply(X1,X3),X2),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
X1 != apply(eq,pair(apply(k,X1),apply(k,projection2))),
inference(fof_simplification,[status(thm)],[prove_self_referential]) ).
cnf(c_0_14,plain,
( pair(apply(X2,n(apply(k,X1),pair(X2,apply(k,X3)))),X3) != X1
| apply(k,X1) = pair(X2,apply(k,X3)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
X1 != apply(eq,pair(apply(k,X1),apply(k,projection2))),
c_0_13 ).
cnf(c_0_16,plain,
pair(apply(k,X1),apply(k,X2)) = apply(k,pair(X1,X2)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_9])]) ).
cnf(c_0_17,axiom,
apply(projection2,pair(X1,X2)) = X2,
projection2 ).
cnf(c_0_18,plain,
( apply(X1,n(X1,apply(k,X2))) != X2
| X1 = apply(k,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_19,axiom,
apply(apply(f,X1),X2) = apply(X1,X1),
diagonal_combinator ).
cnf(c_0_20,negated_conjecture,
apply(eq,apply(k,pair(X1,projection2))) != X1,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
pair(apply(X1,pair(X2,X3)),X3) = apply(pair(X1,projection2),pair(X2,X3)),
inference(spm,[status(thm)],[c_0_10,c_0_17]) ).
cnf(c_0_22,plain,
apply(k,apply(X1,X1)) = apply(f,X1),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_23,negated_conjecture,
apply(eq,apply(k,apply(pair(X1,projection2),pair(X2,projection2)))) != apply(X1,pair(X2,projection2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
apply(k,apply(apply(f,X1),X2)) = apply(f,X1),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_25,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,apply(k,X3)),apply(X2,X3)),
abstraction ).
cnf(c_0_26,negated_conjecture,
apply(eq,apply(f,pair(X1,projection2))) != apply(X1,pair(X1,projection2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_19]),c_0_24]) ).
cnf(c_0_27,plain,
apply(apply(apply(abstraction,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_25,c_0_9]) ).
cnf(c_0_28,negated_conjecture,
apply(eq,apply(f,pair(apply(apply(abstraction,apply(k,X1)),X2),projection2))) != apply(X1,apply(X2,pair(apply(apply(abstraction,apply(k,X1)),X2),projection2))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL076-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 14:09:18 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 50.95/7.90 % Version: 3.5.1
% 50.95/7.90 % Preprocessing class: FSSSSMSSSSSNFFN.
% 50.95/7.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 50.95/7.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 50.95/7.90 % Starting new_bool_3 with 300s (1) cores
% 50.95/7.90 % Starting new_bool_1 with 300s (1) cores
% 50.95/7.90 % Starting sh5l with 300s (1) cores
% 50.95/7.90 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3687613 completed with status 0
% 50.95/7.90 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 50.95/7.90 % Preprocessing class: FSSSSMSSSSSNFFN.
% 50.95/7.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 50.95/7.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 50.95/7.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 50.95/7.90 % No SInE strategy applied
% 50.95/7.90 % Search class: FHUPM-FFSF22-MFFFFFNN
% 50.95/7.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 50.95/7.90 % Starting SubtermCWHack with 136s (1) cores
% 50.95/7.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 50.95/7.90 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 50.95/7.90 % Starting U----_210g_05_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 50.95/7.90 % Starting new_bool_3 with 136s (1) cores
% 50.95/7.90 % U----_210g_05_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3687620 completed with status 0
% 50.95/7.90 % Result found by U----_210g_05_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 50.95/7.90 % Preprocessing class: FSSSSMSSSSSNFFN.
% 50.95/7.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 50.95/7.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 50.95/7.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 50.95/7.90 % No SInE strategy applied
% 50.95/7.90 % Search class: FHUPM-FFSF22-MFFFFFNN
% 50.95/7.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 50.95/7.90 % Starting SubtermCWHack with 136s (1) cores
% 50.95/7.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 50.95/7.90 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 50.95/7.90 % Starting U----_210g_05_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 50.95/7.90 % Preprocessing time : 0.001 s
% 50.95/7.90 % Presaturation interreduction done
% 50.95/7.90
% 50.95/7.90 % Proof found!
% 50.95/7.90 % SZS status Unsatisfiable
% 50.95/7.90 % SZS output start CNFRefutation
% See solution above
% 50.95/7.90 % Parsed axioms : 9
% 50.95/7.90 % Removed by relevancy pruning/SinE : 0
% 50.95/7.90 % Initial clauses : 9
% 50.95/7.90 % Removed in clause preprocessing : 0
% 50.95/7.90 % Initial clauses in saturation : 9
% 50.95/7.90 % Processed clauses : 9792
% 50.95/7.90 % ...of these trivial : 865
% 50.95/7.90 % ...subsumed : 6397
% 50.95/7.90 % ...remaining for further processing : 2530
% 50.95/7.90 % Other redundant clauses eliminated : 248
% 50.95/7.90 % Clauses deleted for lack of memory : 0
% 50.95/7.90 % Backward-subsumed : 160
% 50.95/7.90 % Backward-rewritten : 354
% 50.95/7.90 % Generated clauses : 275014
% 50.95/7.90 % ...of the previous two non-redundant : 257698
% 50.95/7.90 % ...aggressively subsumed : 0
% 50.95/7.90 % Contextual simplify-reflections : 0
% 50.95/7.90 % Paramodulations : 274761
% 50.95/7.90 % Factorizations : 0
% 50.95/7.90 % NegExts : 0
% 50.95/7.90 % Equation resolutions : 253
% 50.95/7.90 % Disequality decompositions : 0
% 50.95/7.90 % Total rewrite steps : 188347
% 50.95/7.90 % ...of those cached : 128450
% 50.95/7.90 % Propositional unsat checks : 0
% 50.95/7.90 % Propositional check models : 0
% 50.95/7.90 % Propositional check unsatisfiable : 0
% 50.95/7.90 % Propositional clauses : 0
% 50.95/7.90 % Propositional clauses after purity: 0
% 50.95/7.90 % Propositional unsat core size : 0
% 50.95/7.90 % Propositional preprocessing time : 0.000
% 50.95/7.90 % Propositional encoding time : 0.000
% 50.95/7.90 % Propositional solver time : 0.000
% 50.95/7.90 % Success case prop preproc time : 0.000
% 50.95/7.90 % Success case prop encoding time : 0.000
% 50.95/7.90 % Success case prop solver time : 0.000
% 50.95/7.90 % Current number of processed clauses : 2007
% 50.95/7.90 % Positive orientable unit clauses : 1048
% 50.95/7.90 % Positive unorientable unit clauses: 119
% 50.95/7.90 % Negative unit clauses : 815
% 50.95/7.90 % Non-unit-clauses : 25
% 50.95/7.90 % Current number of unprocessed clauses: 246612
% 50.95/7.90 % ...number of literals in the above : 254962
% 50.95/7.90 % Current number of archived formulas : 0
% 50.95/7.90 % Current number of archived clauses : 523
% 50.95/7.90 % Clause-clause subsumption calls (NU) : 2242
% 58.48/7.90 % Rec. Clause-clause subsumption calls : 2187
% 58.48/7.90 % Non-unit clause-clause subsumptions : 239
% 58.48/7.90 % Unit Clause-clause subsumption calls : 58008
% 58.48/7.90 % Rewrite failures with RHS unbound : 0
% 58.48/7.90 % BW rewrite match attempts : 67080
% 58.48/7.90 % BW rewrite match successes : 1544
% 58.48/7.90 % Condensation attempts : 0
% 58.48/7.90 % Condensation successes : 0
% 58.48/7.90 % Termbank termtop insertions : 7999785
% 58.48/7.90 % Search garbage collected termcells : 5
% 58.48/7.90
% 58.48/7.90 % -------------------------------------------------
% 58.48/7.90 % User time : 6.962 s
% 58.48/7.90 % System time : 0.275 s
% 58.48/7.90 % Total time : 7.237 s
% 58.48/7.90 % Maximum resident set size: 3636 pages
% 58.48/7.90
% 58.48/7.90 % -------------------------------------------------
% 58.48/7.90 % User time : 34.733 s
% 58.48/7.90 % System time : 1.456 s
% 58.48/7.90 % Total time : 36.189 s
% 58.48/7.90 % Maximum resident set size: 4608 pages
% 58.48/7.90 % E exiting
%------------------------------------------------------------------------------