%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL062-1 : 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 : n006.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 12:09:28 PM UTC 2026
% Result : Unsatisfiable 1.57s 0.80s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 11 RR)
% Number of literals : 15 ( 14 equ; 10 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_c_combinator,negated_conjecture,
apply(apply(apply(X1,f(X1)),g(X1)),h(X1)) != apply(apply(f(X1),h(X1)),g(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_combinator) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(t_definition,axiom,
apply(apply(t,X1),X2) = apply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
cnf(c_0_3,negated_conjecture,
apply(apply(apply(X1,f(X1)),g(X1)),h(X1)) != apply(apply(f(X1),h(X1)),g(X1)),
inference(fof_simplification,[status(thm)],[prove_c_combinator]) ).
cnf(c_0_4,negated_conjecture,
apply(apply(apply(X1,f(X1)),g(X1)),h(X1)) != apply(apply(f(X1),h(X1)),g(X1)),
c_0_3 ).
cnf(c_0_5,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_6,negated_conjecture,
apply(apply(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))) != apply(apply(f(apply(apply(b,X1),X2)),h(apply(apply(b,X1),X2))),g(apply(apply(b,X1),X2))),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,axiom,
apply(apply(t,X1),X2) = apply(X2,X1),
t_definition ).
cnf(c_0_8,negated_conjecture,
apply(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),g(apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,apply(t,X2)),X1))) != apply(apply(f(apply(apply(b,apply(t,X2)),X1)),h(apply(apply(b,apply(t,X2)),X1))),g(apply(apply(b,apply(t,X2)),X1))),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,negated_conjecture,
apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))) != apply(apply(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_10,negated_conjecture,
apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))) != apply(apply(f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),
inference(spm,[status(thm)],[c_0_9,c_0_5]) ).
cnf(c_0_11,negated_conjecture,
apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_12,negated_conjecture,
apply(apply(apply(X1,apply(X2,g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),
inference(spm,[status(thm)],[c_0_11,c_0_5]) ).
cnf(c_0_13,negated_conjecture,
apply(apply(X1,g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),
inference(spm,[status(thm)],[c_0_12,c_0_5]) ).
cnf(c_0_14,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_13,c_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL062-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.46 % Computer : n006.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Mon Sep 21 14:07:41 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.55 Running first-order theorem proving
% 0.21/0.55 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
% 1.57/0.80 % Version: 3.5.1
% 1.57/0.80 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.57/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.57/0.80 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.57/0.80 % Starting new_bool_3 with 300s (1) cores
% 1.57/0.80 % Starting new_bool_1 with 300s (1) cores
% 1.57/0.80 % Starting sh5l with 300s (1) cores
% 1.57/0.80 % new_bool_3 with pid 3037418 completed with status 9
% 1.57/0.80 % new_bool_1 with pid 3037419 completed with status 9
% 1.57/0.80 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3037417 completed with status 0
% 1.57/0.80 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 1.57/0.80 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.57/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.57/0.80 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.57/0.80 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.57/0.80 % No SInE strategy applied
% 1.57/0.80 % Search class: FUUPS-FFSF21-MFFFFFNN
% 1.57/0.80 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.57/0.80 % Starting SubtermCWHack with 136s (1) cores
% 1.57/0.80 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 1.57/0.80 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 1.57/0.80 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.57/0.80 % Starting U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.57/0.80 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3037427 completed with status 0
% 1.57/0.80 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 1.57/0.80 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.57/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.57/0.80 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.57/0.80 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.57/0.80 % No SInE strategy applied
% 1.57/0.80 % Search class: FUUPS-FFSF21-MFFFFFNN
% 1.57/0.80 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.57/0.80 % Starting SubtermCWHack with 136s (1) cores
% 1.57/0.80 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 1.57/0.80 % Preprocessing time : 0.002 s
% 1.57/0.80
% 1.57/0.80 % Proof found!
% 1.57/0.80 % SZS status Unsatisfiable
% 1.57/0.80 % SZS output start CNFRefutation
% See solution above
% 1.57/0.80 % Parsed axioms : 3
% 1.57/0.80 % Removed by relevancy pruning/SinE : 0
% 1.57/0.80 % Initial clauses : 3
% 1.57/0.80 % Removed in clause preprocessing : 0
% 1.57/0.80 % Initial clauses in saturation : 3
% 1.57/0.80 % Processed clauses : 843
% 1.57/0.80 % ...of these trivial : 0
% 1.57/0.80 % ...subsumed : 195
% 1.57/0.80 % ...remaining for further processing : 648
% 1.57/0.80 % Other redundant clauses eliminated : 0
% 1.57/0.80 % Clauses deleted for lack of memory : 0
% 1.57/0.80 % Backward-subsumed : 0
% 1.57/0.80 % Backward-rewritten : 0
% 1.57/0.80 % Generated clauses : 2261
% 1.57/0.80 % ...of the previous two non-redundant : 2259
% 1.57/0.80 % ...aggressively subsumed : 0
% 1.57/0.80 % Contextual simplify-reflections : 0
% 1.57/0.80 % Paramodulations : 2261
% 1.57/0.80 % Factorizations : 0
% 1.57/0.80 % NegExts : 0
% 1.57/0.80 % Equation resolutions : 0
% 1.57/0.80 % Disequality decompositions : 0
% 1.57/0.80 % Total rewrite steps : 0
% 1.57/0.80 % ...of those cached : 0
% 1.57/0.80 % Propositional unsat checks : 0
% 1.57/0.80 % Propositional check models : 0
% 1.57/0.80 % Propositional check unsatisfiable : 0
% 1.57/0.80 % Propositional clauses : 0
% 1.57/0.80 % Propositional clauses after purity: 0
% 1.57/0.80 % Propositional unsat core size : 0
% 1.57/0.80 % Propositional preprocessing time : 0.000
% 1.57/0.80 % Propositional encoding time : 0.000
% 1.57/0.80 % Propositional solver time : 0.000
% 1.57/0.80 % Success case prop preproc time : 0.000
% 1.57/0.80 % Success case prop encoding time : 0.000
% 1.57/0.80 % Success case prop solver time : 0.000
% 1.57/0.80 % Current number of processed clauses : 648
% 1.57/0.80 % Positive orientable unit clauses : 2
% 1.57/0.80 % Positive unorientable unit clauses: 0
% 1.57/0.80 % Negative unit clauses : 646
% 1.57/0.80 % Non-unit-clauses : 0
% 1.57/0.80 % Current number of unprocessed clauses: 1417
% 1.57/0.80 % ...number of literals in the above : 1417
% 1.57/0.80 % Current number of archived formulas : 0
% 1.57/0.80 % Current number of archived clauses : 0
% 1.57/0.80 % Clause-clause subsumption calls (NU) : 0
% 1.57/0.80 % Rec. Clause-clause subsumption calls : 0
% 1.57/0.80 % Non-unit clause-clause subsumptions : 0
% 1.57/0.80 % Unit Clause-clause subsumption calls : 63421
% 1.57/0.80 % Rewrite failures with RHS unbound : 0
% 1.57/0.80 % BW rewrite match attempts : 1
% 1.57/0.80 % BW rewrite match successes : 0
% 1.57/0.80 % Condensation attempts : 0
% 1.57/0.80 % Condensation successes : 0
% 1.57/0.80 % Termbank termtop insertions : 271299
% 1.57/0.80 % Search garbage collected termcells : 2
% 1.57/0.80
% 1.57/0.80 % -------------------------------------------------
% 1.57/0.80 % User time : 0.161 s
% 1.57/0.80 % System time : 0.032 s
% 1.57/0.80 % Total time : 0.193 s
% 1.57/0.80 % Maximum resident set size: 3632 pages
% 1.57/0.80
% 1.57/0.80 % -------------------------------------------------
% 1.57/0.80 % User time : 0.886 s
% 1.57/0.80 % System time : 0.188 s
% 1.57/0.80 % Total time : 1.074 s
% 1.57/0.80 % Maximum resident set size: 4864 pages
% 1.57/0.80 % E exiting
%------------------------------------------------------------------------------