%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG006-1 : TPTP v9.3.1. Released v2.2.0.
% 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 11:50:12 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.49s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 4 RR)
% Number of literals : 26 ( 25 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(set_difference_1,axiom,
difference(X1,difference(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_1) ).
cnf(set_difference_2,axiom,
difference(X1,difference(X1,X2)) = difference(X2,difference(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_2) ).
cnf(set_difference_3,axiom,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),difference(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_3) ).
cnf(prove_set_difference_3_simplified,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_difference_3_simplified) ).
cnf(c_0_4,axiom,
difference(X1,difference(X2,X1)) = X1,
set_difference_1 ).
cnf(c_0_5,axiom,
difference(X1,difference(X1,X2)) = difference(X2,difference(X2,X1)),
set_difference_2 ).
cnf(c_0_6,plain,
difference(difference(X1,X2),X2) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_7,plain,
difference(difference(X1,X2),difference(X1,X2)) = difference(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_4]) ).
cnf(c_0_8,plain,
difference(X1,X1) = difference(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_5]),c_0_7]),c_0_7]),c_0_7]) ).
cnf(c_0_9,axiom,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),difference(X2,X3)),
set_difference_3 ).
cnf(c_0_10,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_11,plain,
difference(difference(X1,X2),X1) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
difference(X1,difference(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_13,plain,
difference(X1,difference(X1,difference(X1,X2))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_11]),c_0_12]) ).
cnf(c_0_14,plain,
difference(X1,difference(X2,difference(X2,X1))) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_5]) ).
cnf(c_0_15,plain,
difference(difference(X1,difference(X2,X3)),X2) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_11]),c_0_12]) ).
cnf(c_0_16,plain,
difference(X1,difference(difference(X2,difference(X1,X3)),difference(X2,X1))) = difference(X1,difference(X2,difference(X1,X3))),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
difference(X1,difference(difference(X2,X1),difference(X1,X3))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_6]),c_0_11]),c_0_7]),c_0_4]) ).
cnf(c_0_18,plain,
difference(difference(X1,X2),difference(X2,X3)) = difference(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_17]),c_0_15]),c_0_6]) ).
cnf(c_0_19,plain,
difference(difference(difference(X1,X2),X3),X2) = difference(difference(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_6]),c_0_9]) ).
cnf(c_0_20,plain,
difference(X1,difference(difference(X2,X1),X3)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_4]) ).
cnf(c_0_21,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c),
inference(fof_simplification,[status(thm)],[prove_set_difference_3_simplified]) ).
cnf(c_0_22,plain,
difference(difference(difference(X1,X2),X3),difference(difference(X1,X3),X2)) = difference(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_19]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c),
c_0_21 ).
cnf(c_0_24,plain,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_19]),c_0_22]),c_0_12]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG006-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n006.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 12:52:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.13/0.49 % Version: 3.5.1
% 0.13/0.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.49 % Starting sh5l with 300s (1) cores
% 0.13/0.49 % new_bool_1 with pid 2881397 completed with status 0
% 0.13/0.49 % Result found by new_bool_1
% 0.13/0.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.49 % Search class: FUUPS-FFSF22-SFFFFFNN
% 0.13/0.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.49 % SubtermCWHack with pid 2881404 completed with status 0
% 0.13/0.49 % Result found by SubtermCWHack
% 0.13/0.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.49 % Search class: FUUPS-FFSF22-SFFFFFNN
% 0.13/0.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.49 % Preprocessing time : 0.001 s
% 0.13/0.49
% 0.13/0.49 % Proof found!
% 0.13/0.49 % SZS status Unsatisfiable
% 0.13/0.49 % SZS output start CNFRefutation
% See solution above
% 0.13/0.49 % Parsed axioms : 4
% 0.13/0.49 % Removed by relevancy pruning/SinE : 0
% 0.13/0.49 % Initial clauses : 4
% 0.13/0.49 % Removed in clause preprocessing : 0
% 0.13/0.49 % Initial clauses in saturation : 4
% 0.13/0.49 % Processed clauses : 869
% 0.13/0.49 % ...of these trivial : 55
% 0.13/0.49 % ...subsumed : 754
% 0.13/0.49 % ...remaining for further processing : 60
% 0.13/0.49 % Other redundant clauses eliminated : 0
% 0.13/0.49 % Clauses deleted for lack of memory : 0
% 0.13/0.49 % Backward-subsumed : 1
% 0.13/0.49 % Backward-rewritten : 22
% 0.13/0.49 % Generated clauses : 8577
% 0.13/0.49 % ...of the previous two non-redundant : 5277
% 0.13/0.49 % ...aggressively subsumed : 0
% 0.13/0.49 % Contextual simplify-reflections : 0
% 0.13/0.49 % Paramodulations : 8577
% 0.13/0.49 % Factorizations : 0
% 0.13/0.49 % NegExts : 0
% 0.13/0.49 % Equation resolutions : 0
% 0.13/0.49 % Disequality decompositions : 0
% 0.13/0.49 % Total rewrite steps : 14841
% 0.13/0.49 % ...of those cached : 12392
% 0.13/0.49 % Propositional unsat checks : 0
% 0.13/0.49 % Propositional check models : 0
% 0.13/0.49 % Propositional check unsatisfiable : 0
% 0.13/0.49 % Propositional clauses : 0
% 0.13/0.49 % Propositional clauses after purity: 0
% 0.13/0.49 % Propositional unsat core size : 0
% 0.13/0.49 % Propositional preprocessing time : 0.000
% 0.13/0.49 % Propositional encoding time : 0.000
% 0.13/0.49 % Propositional solver time : 0.000
% 0.13/0.49 % Success case prop preproc time : 0.000
% 0.13/0.49 % Success case prop encoding time : 0.000
% 0.13/0.49 % Success case prop solver time : 0.000
% 0.13/0.49 % Current number of processed clauses : 37
% 0.13/0.49 % Positive orientable unit clauses : 32
% 0.13/0.49 % Positive unorientable unit clauses: 5
% 0.13/0.49 % Negative unit clauses : 0
% 0.13/0.49 % Non-unit-clauses : 0
% 0.13/0.49 % Current number of unprocessed clauses: 4365
% 0.13/0.49 % ...number of literals in the above : 4365
% 0.13/0.49 % Current number of archived formulas : 0
% 0.13/0.49 % Current number of archived clauses : 23
% 0.13/0.49 % Clause-clause subsumption calls (NU) : 0
% 0.13/0.49 % Rec. Clause-clause subsumption calls : 0
% 0.13/0.49 % Non-unit clause-clause subsumptions : 0
% 0.13/0.49 % Unit Clause-clause subsumption calls : 50
% 0.13/0.49 % Rewrite failures with RHS unbound : 24
% 0.13/0.49 % BW rewrite match attempts : 460
% 0.13/0.49 % BW rewrite match successes : 122
% 0.13/0.49 % Condensation attempts : 0
% 0.13/0.49 % Condensation successes : 0
% 0.13/0.49 % Termbank termtop insertions : 105386
% 0.13/0.49 % Search garbage collected termcells : 2
% 0.13/0.49
% 0.13/0.49 % -------------------------------------------------
% 0.13/0.49 % User time : 0.047 s
% 0.13/0.49 % System time : 0.005 s
% 0.13/0.49 % Total time : 0.052 s
% 0.13/0.49 % Maximum resident set size: 3628 pages
% 0.13/0.49
% 0.13/0.49 % -------------------------------------------------
% 0.13/0.49 % User time : 0.047 s
% 0.13/0.49 % System time : 0.010 s
% 0.13/0.49 % Total time : 0.057 s
% 0.13/0.49 % Maximum resident set size: 4864 pages
% 0.13/0.49 % E exiting
%------------------------------------------------------------------------------