%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL061-1 : 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 : n012.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 12:09:27 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 12 equ; 8 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 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 : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_q1_combinator,negated_conjecture,
apply(apply(apply(X1,f(X1)),g(X1)),h(X1)) != apply(f(X1),apply(h(X1),g(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_q1_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(f(X1),apply(h(X1),g(X1))),
inference(fof_simplification,[status(thm)],[prove_q1_combinator]) ).
cnf(c_0_4,negated_conjecture,
apply(apply(apply(X1,f(X1)),g(X1)),h(X1)) != apply(f(X1),apply(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(f(apply(apply(b,X1),X2)),apply(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(f(apply(apply(b,apply(t,X2)),X1)),apply(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(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),apply(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(f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),apply(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(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))),apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))))) != apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))))),
inference(spm,[status(thm)],[c_0_10,c_0_5]) ).
cnf(c_0_12,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_11,c_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL061-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 14:07:21 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.44 % Version: 3.5.1
% 0.13/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.44 % Starting sh5l with 300s (1) cores
% 0.13/0.44 % new_bool_3 with pid 2534231 completed with status 9
% 0.13/0.44 % new_bool_1 with pid 2534232 completed with status 9
% 0.13/0.44 % sh5l with pid 2534233 completed with status 0
% 0.13/0.44 % Result found by sh5l
% 0.13/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.44 % Starting sh5l with 300s (1) cores
% 0.13/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.13/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.13/0.44 % Search class: FUUPS-FFSF21-MFFFFFNN
% 0.13/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.13/0.44 % SubtermCWHack with pid 2534240 completed with status 0
% 0.13/0.44 % Result found by SubtermCWHack
% 0.13/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.44 % Starting sh5l with 300s (1) cores
% 0.13/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.13/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.13/0.44 % Search class: FUUPS-FFSF21-MFFFFFNN
% 0.13/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.13/0.44 % Preprocessing time : 0.001 s
% 0.13/0.44
% 0.13/0.44 % Proof found!
% 0.13/0.44 % SZS status Unsatisfiable
% 0.13/0.44 % SZS output start CNFRefutation
% See solution above
% 0.13/0.44 % Parsed axioms : 3
% 0.13/0.44 % Removed by relevancy pruning/SinE : 0
% 0.13/0.44 % Initial clauses : 3
% 0.13/0.44 % Removed in clause preprocessing : 0
% 0.13/0.44 % Initial clauses in saturation : 3
% 0.13/0.44 % Processed clauses : 178
% 0.13/0.44 % ...of these trivial : 0
% 0.13/0.44 % ...subsumed : 27
% 0.13/0.44 % ...remaining for further processing : 151
% 0.13/0.44 % Other redundant clauses eliminated : 0
% 0.13/0.44 % Clauses deleted for lack of memory : 0
% 0.13/0.44 % Backward-subsumed : 0
% 0.13/0.44 % Backward-rewritten : 0
% 0.13/0.44 % Generated clauses : 450
% 0.13/0.44 % ...of the previous two non-redundant : 448
% 0.13/0.44 % ...aggressively subsumed : 0
% 0.13/0.44 % Contextual simplify-reflections : 0
% 0.13/0.44 % Paramodulations : 450
% 0.13/0.44 % Factorizations : 0
% 0.13/0.44 % NegExts : 0
% 0.13/0.44 % Equation resolutions : 0
% 0.13/0.44 % Disequality decompositions : 0
% 0.13/0.44 % Total rewrite steps : 0
% 0.13/0.44 % ...of those cached : 0
% 0.13/0.44 % Propositional unsat checks : 0
% 0.13/0.44 % Propositional check models : 0
% 0.13/0.44 % Propositional check unsatisfiable : 0
% 0.13/0.44 % Propositional clauses : 0
% 0.13/0.44 % Propositional clauses after purity: 0
% 0.13/0.44 % Propositional unsat core size : 0
% 0.13/0.44 % Propositional preprocessing time : 0.000
% 0.13/0.44 % Propositional encoding time : 0.000
% 0.13/0.44 % Propositional solver time : 0.000
% 0.13/0.44 % Success case prop preproc time : 0.000
% 0.13/0.44 % Success case prop encoding time : 0.000
% 0.13/0.44 % Success case prop solver time : 0.000
% 0.13/0.44 % Current number of processed clauses : 151
% 0.13/0.44 % Positive orientable unit clauses : 2
% 0.13/0.44 % Positive unorientable unit clauses: 0
% 0.13/0.44 % Negative unit clauses : 149
% 0.13/0.44 % Non-unit-clauses : 0
% 0.13/0.44 % Current number of unprocessed clauses: 271
% 0.13/0.44 % ...number of literals in the above : 271
% 0.13/0.44 % Current number of archived formulas : 0
% 0.13/0.44 % Current number of archived clauses : 0
% 0.13/0.44 % Clause-clause subsumption calls (NU) : 0
% 0.13/0.44 % Rec. Clause-clause subsumption calls : 0
% 0.13/0.44 % Non-unit clause-clause subsumptions : 0
% 0.13/0.44 % Unit Clause-clause subsumption calls : 2935
% 0.13/0.44 % Rewrite failures with RHS unbound : 0
% 0.13/0.44 % BW rewrite match attempts : 0
% 0.13/0.44 % BW rewrite match successes : 0
% 0.13/0.44 % Condensation attempts : 0
% 0.13/0.44 % Condensation successes : 0
% 0.13/0.44 % Termbank termtop insertions : 45164
% 0.13/0.44 % Search garbage collected termcells : 2
% 0.13/0.44
% 0.13/0.44 % -------------------------------------------------
% 0.13/0.44 % User time : 0.022 s
% 0.13/0.44 % System time : 0.007 s
% 0.13/0.44 % Total time : 0.029 s
% 0.13/0.44 % Maximum resident set size: 3632 pages
% 0.13/0.44
% 0.13/0.44 % -------------------------------------------------
% 0.13/0.44 % User time : 0.054 s
% 0.13/0.44 % System time : 0.026 s
% 0.13/0.44 % Total time : 0.080 s
% 0.13/0.44 % Maximum resident set size: 4864 pages
% 0.13/0.44 % E exiting
%------------------------------------------------------------------------------