%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL004-3 : 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 : n019.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 12:09:17 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 4 RR)
% Number of literals : 10 ( 9 equ; 3 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; 4 con; 0-2 aty)
% Number of variables : 15 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_u_combinator,negated_conjecture,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_u_combinator) ).
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(k_definition,axiom,
apply(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(c_0_3,negated_conjecture,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
inference(fof_simplification,[status(thm)],[prove_u_combinator]) ).
cnf(c_0_4,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition ).
cnf(c_0_5,axiom,
apply(apply(k,X1),X2) = X1,
k_definition ).
cnf(c_0_6,negated_conjecture,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
c_0_3 ).
cnf(c_0_7,plain,
apply(apply(apply(s,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_8,plain,
apply(apply(apply(s,k),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_9,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_4]),c_0_8]),c_0_8]),c_0_4]),c_0_8])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.38 % Computer : n019.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Mon Sep 21 14:04:25 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.44 % Version: 3.5.1
% 0.15/5.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.44 % Starting sh5l with 300s (1) cores
% 0.15/5.44 % new_bool_3 with pid 2766552 completed with status 0
% 0.15/5.44 % Result found by new_bool_3
% 0.15/5.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.44 % Search class: FUUPS-FFSF22-DFFFFFNN
% 0.15/5.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/5.44 % SubtermCWHack with pid 2766557 completed with status 0
% 0.15/5.44 % Result found by SubtermCWHack
% 0.15/5.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.44 % Search class: FUUPS-FFSF22-DFFFFFNN
% 0.15/5.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/5.44 % Preprocessing time : 0.001 s
% 0.15/5.44
% 0.15/5.44 % Proof found!
% 0.15/5.44 % SZS status Unsatisfiable
% 0.15/5.44 % SZS output start CNFRefutation
% See solution above
% 0.15/5.44 % Parsed axioms : 3
% 0.15/5.44 % Removed by relevancy pruning/SinE : 0
% 0.15/5.44 % Initial clauses : 3
% 0.15/5.44 % Removed in clause preprocessing : 0
% 0.15/5.44 % Initial clauses in saturation : 3
% 0.15/5.44 % Processed clauses : 11
% 0.15/5.44 % ...of these trivial : 0
% 0.15/5.44 % ...subsumed : 0
% 0.15/5.44 % ...remaining for further processing : 10
% 0.15/5.44 % Other redundant clauses eliminated : 0
% 0.15/5.44 % Clauses deleted for lack of memory : 0
% 0.15/5.44 % Backward-subsumed : 0
% 0.15/5.44 % Backward-rewritten : 0
% 0.15/5.44 % Generated clauses : 101
% 0.15/5.44 % ...of the previous two non-redundant : 86
% 0.15/5.44 % ...aggressively subsumed : 0
% 0.15/5.44 % Contextual simplify-reflections : 0
% 0.15/5.44 % Paramodulations : 101
% 0.15/5.44 % Factorizations : 0
% 0.15/5.44 % NegExts : 0
% 0.15/5.44 % Equation resolutions : 0
% 0.15/5.44 % Disequality decompositions : 0
% 0.15/5.44 % Total rewrite steps : 27
% 0.15/5.44 % ...of those cached : 6
% 0.15/5.44 % Propositional unsat checks : 0
% 0.15/5.44 % Propositional check models : 0
% 0.15/5.44 % Propositional check unsatisfiable : 0
% 0.15/5.44 % Propositional clauses : 0
% 0.15/5.44 % Propositional clauses after purity: 0
% 0.15/5.44 % Propositional unsat core size : 0
% 0.15/5.44 % Propositional preprocessing time : 0.000
% 0.15/5.44 % Propositional encoding time : 0.000
% 0.15/5.44 % Propositional solver time : 0.000
% 0.15/5.44 % Success case prop preproc time : 0.000
% 0.15/5.44 % Success case prop encoding time : 0.000
% 0.15/5.44 % Success case prop solver time : 0.000
% 0.15/5.44 % Current number of processed clauses : 10
% 0.15/5.44 % Positive orientable unit clauses : 7
% 0.15/5.44 % Positive unorientable unit clauses: 3
% 0.15/5.44 % Negative unit clauses : 0
% 0.15/5.44 % Non-unit-clauses : 0
% 0.15/5.44 % Current number of unprocessed clauses: 78
% 0.15/5.44 % ...number of literals in the above : 78
% 0.15/5.44 % Current number of archived formulas : 0
% 0.15/5.44 % Current number of archived clauses : 0
% 0.15/5.44 % Clause-clause subsumption calls (NU) : 0
% 0.15/5.44 % Rec. Clause-clause subsumption calls : 0
% 0.15/5.44 % Non-unit clause-clause subsumptions : 0
% 0.15/5.44 % Unit Clause-clause subsumption calls : 0
% 0.15/5.44 % Rewrite failures with RHS unbound : 4
% 0.15/5.44 % BW rewrite match attempts : 36
% 0.15/5.44 % BW rewrite match successes : 0
% 0.15/5.44 % Condensation attempts : 0
% 0.15/5.44 % Condensation successes : 0
% 0.15/5.44 % Termbank termtop insertions : 1795
% 0.15/5.44 % Search garbage collected termcells : 2
% 0.15/5.44
% 0.15/5.44 % -------------------------------------------------
% 0.15/5.44 % User time : 0.002 s
% 0.15/5.44 % System time : 0.003 s
% 0.15/5.44 % Total time : 0.004 s
% 0.15/5.44 % Maximum resident set size: 3636 pages
% 0.15/5.44
% 0.15/5.44 % -------------------------------------------------
% 0.15/5.44 % User time : 0.003 s
% 0.15/5.44 % System time : 0.007 s
% 0.15/5.44 % Total time : 0.010 s
% 0.15/5.44 % Maximum resident set size: 4864 pages
% 0.15/5.44 % E exiting
%------------------------------------------------------------------------------