%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : COL004-1 : 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 : n013.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 12:09:47 PM UTC 2026
% Result : Unsatisfiable 5.81s 6.57s
% Output : CNFRefutation 5.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 7 RR)
% Number of literals : 20 ( 19 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 38 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
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(prove_u_combinator,negated_conjecture,
apply(apply(X1,f(X1)),g(X1)) != apply(g(X1),apply(apply(f(X1),f(X1)),g(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_u_combinator) ).
cnf(c_0_3,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition ).
cnf(c_0_4,axiom,
apply(apply(k,X1),X2) = X1,
k_definition ).
cnf(c_0_5,plain,
apply(apply(apply(s,k),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,negated_conjecture,
apply(apply(X1,f(X1)),g(X1)) != apply(g(X1),apply(apply(f(X1),f(X1)),g(X1))),
inference(fof_simplification,[status(thm)],[prove_u_combinator]) ).
cnf(c_0_7,plain,
apply(apply(apply(s,apply(s,k)),X1),X2) = apply(X1,X2),
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_8,plain,
apply(apply(apply(apply(s,s),X1),X2),X3) = apply(apply(X2,X3),apply(apply(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_9,negated_conjecture,
apply(apply(X1,f(X1)),g(X1)) != apply(g(X1),apply(apply(f(X1),f(X1)),g(X1))),
c_0_6 ).
cnf(c_0_10,plain,
apply(apply(apply(s,apply(s,apply(s,k))),X1),X2) = apply(X2,apply(X1,X2)),
inference(spm,[status(thm)],[c_0_3,c_0_7]) ).
cnf(c_0_11,plain,
apply(apply(apply(apply(s,s),apply(apply(s,X1),X2)),X3),X4) = apply(apply(X3,X4),apply(apply(apply(X1,X3),apply(X2,X3)),X4)),
inference(spm,[status(thm)],[c_0_8,c_0_3]) ).
cnf(c_0_12,plain,
apply(apply(apply(apply(s,s),X1),apply(s,apply(s,k))),X2) = apply(X2,apply(apply(X1,apply(s,apply(s,k))),X2)),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_13,plain,
apply(apply(apply(apply(s,s),X1),apply(s,k)),X2) = apply(apply(X1,apply(s,k)),X2),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
apply(apply(apply(s,apply(s,apply(s,k))),apply(f(X1),f(X1))),g(X1)) != apply(apply(X1,f(X1)),g(X1)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),X1) = apply(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_5]),c_0_5]) ).
cnf(c_0_16,negated_conjecture,
apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),f(X1))),g(X1)) != apply(apply(X1,f(X1)),g(X1)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
apply(apply(apply(s,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_18,negated_conjecture,
apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2))) != apply(apply(X1,apply(X2,f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/5.47 % Computer : n013.cluster.edu
% 0.20/5.47 % Model : x86_64 x86_64
% 0.20/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.47 % Memory : 8046.5625MB
% 0.20/5.47 % OS : Linux 6.8.0-71-generic
% 0.20/5.47 % CPULimit : 300
% 0.20/5.47 % WCLimit : 300
% 0.20/5.47 % DateTime : Mon Sep 21 14:03:42 UTC 2026
% 0.20/5.48 % CPUTime :
% 0.20/5.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/5.54 Running first-order theorem proving
% 0.25/5.54 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
% 5.81/6.57 % Version: 3.5.1
% 5.81/6.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 5.81/6.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.81/6.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 5.81/6.57 % Starting new_bool_3 with 300s (1) cores
% 5.81/6.57 % Starting new_bool_1 with 300s (1) cores
% 5.81/6.57 % Starting sh5l with 300s (1) cores
% 5.81/6.57 % new_bool_3 with pid 949514 completed with status 9
% 5.81/6.57 % new_bool_1 with pid 949515 completed with status 9
% 5.81/6.57 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 949513 completed with status 0
% 5.81/6.57 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 5.81/6.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 5.81/6.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.81/6.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 5.81/6.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.81/6.57 % No SInE strategy applied
% 5.81/6.57 % Search class: FUUPS-FFSF21-MFFFFFNN
% 5.81/6.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.81/6.57 % Starting SubtermCWHack with 136s (1) cores
% 5.81/6.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 5.81/6.57 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 5.81/6.57 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 5.81/6.57 % Starting U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 5.81/6.57 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 949517 completed with status 0
% 5.81/6.57 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 5.81/6.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 5.81/6.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.81/6.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 5.81/6.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.81/6.57 % No SInE strategy applied
% 5.81/6.57 % Search class: FUUPS-FFSF21-MFFFFFNN
% 5.81/6.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.81/6.57 % Starting SubtermCWHack with 136s (1) cores
% 5.81/6.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 5.81/6.57 % Preprocessing time : 0.005 s
% 5.81/6.57
% 5.81/6.57 % Proof found!
% 5.81/6.57 % SZS status Unsatisfiable
% 5.81/6.57 % SZS output start CNFRefutation
% See solution above
% 5.81/6.57 % Parsed axioms : 3
% 5.81/6.57 % Removed by relevancy pruning/SinE : 0
% 5.81/6.57 % Initial clauses : 3
% 5.81/6.57 % Removed in clause preprocessing : 0
% 5.81/6.57 % Initial clauses in saturation : 3
% 5.81/6.57 % Processed clauses : 305
% 5.81/6.57 % ...of these trivial : 55
% 5.81/6.57 % ...subsumed : 102
% 5.81/6.57 % ...remaining for further processing : 148
% 5.81/6.57 % Other redundant clauses eliminated : 0
% 5.81/6.57 % Clauses deleted for lack of memory : 0
% 5.81/6.57 % Backward-subsumed : 0
% 5.81/6.57 % Backward-rewritten : 4
% 5.81/6.57 % Generated clauses : 17849
% 5.81/6.57 % ...of the previous two non-redundant : 17111
% 5.81/6.57 % ...aggressively subsumed : 0
% 5.81/6.57 % Contextual simplify-reflections : 0
% 5.81/6.57 % Paramodulations : 17848
% 5.81/6.57 % Factorizations : 0
% 5.81/6.57 % NegExts : 0
% 5.81/6.57 % Equation resolutions : 1
% 5.81/6.57 % Disequality decompositions : 0
% 5.81/6.57 % Total rewrite steps : 12778
% 5.81/6.57 % ...of those cached : 9114
% 5.81/6.57 % Propositional unsat checks : 0
% 5.81/6.57 % Propositional check models : 0
% 5.81/6.57 % Propositional check unsatisfiable : 0
% 5.81/6.57 % Propositional clauses : 0
% 5.81/6.57 % Propositional clauses after purity: 0
% 5.81/6.57 % Propositional unsat core size : 0
% 5.81/6.57 % Propositional preprocessing time : 0.000
% 5.81/6.57 % Propositional encoding time : 0.000
% 5.81/6.57 % Propositional solver time : 0.000
% 5.81/6.57 % Success case prop preproc time : 0.000
% 5.81/6.57 % Success case prop encoding time : 0.000
% 5.81/6.57 % Success case prop solver time : 0.000
% 5.81/6.57 % Current number of processed clauses : 144
% 5.81/6.57 % Positive orientable unit clauses : 88
% 5.81/6.57 % Positive unorientable unit clauses: 32
% 5.81/6.57 % Negative unit clauses : 24
% 5.81/6.57 % Non-unit-clauses : 0
% 5.81/6.57 % Current number of unprocessed clauses: 16809
% 5.81/6.57 % ...number of literals in the above : 16809
% 5.81/6.57 % Current number of archived formulas : 0
% 5.81/6.57 % Current number of archived clauses : 4
% 5.81/6.57 % Clause-clause subsumption calls (NU) : 0
% 5.81/6.57 % Rec. Clause-clause subsumption calls : 0
% 5.81/6.57 % Non-unit clause-clause subsumptions : 0
% 5.81/6.57 % Unit Clause-clause subsumption calls : 1018
% 5.81/6.57 % Rewrite failures with RHS unbound : 0
% 5.81/6.57 % BW rewrite match attempts : 7012
% 5.81/6.57 % BW rewrite match successes : 101
% 5.81/6.57 % Condensation attempts : 0
% 5.81/6.57 % Condensation successes : 0
% 5.81/6.57 % Termbank termtop insertions : 757327
% 5.81/6.57 % Search garbage collected termcells : 2
% 5.81/6.57
% 5.81/6.57 % -------------------------------------------------
% 5.81/6.57 % User time : 0.923 s
% 5.81/6.57 % System time : 0.045 s
% 5.81/6.57 % Total time : 0.967 s
% 5.81/6.57 % Maximum resident set size: 3580 pages
% 5.81/6.57
% 5.81/6.57 % -------------------------------------------------
% 5.81/6.57 % User time : 4.597 s
% 5.81/6.57 % System time : 0.253 s
% 5.81/6.57 % Total time : 4.849 s
% 5.81/6.57 % Maximum resident set size: 4864 pages
% 5.81/6.57 % E exiting
%------------------------------------------------------------------------------