%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG005-1 : 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 : n018.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 17.75s 2.90s
% Output : CNFRefutation 17.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 8 RR)
% Number of literals : 55 ( 54 equ; 7 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 133 ( 19 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_associativity_of_multiply,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
cnf(intersection,axiom,
multiply(X1,X2) = difference(X1,difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
cnf(c_0_5,axiom,
difference(X1,difference(X2,X1)) = X1,
set_difference_1 ).
cnf(c_0_6,axiom,
difference(X1,difference(X1,X2)) = difference(X2,difference(X2,X1)),
set_difference_2 ).
cnf(c_0_7,plain,
difference(difference(X1,X2),X2) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_8,axiom,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),difference(X2,X3)),
set_difference_3 ).
cnf(c_0_9,plain,
difference(X1,X1) = difference(difference(X2,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_5]),c_0_8]) ).
cnf(c_0_10,plain,
difference(difference(X1,X1),difference(X2,X2)) = difference(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_9]),c_0_8]),c_0_7]) ).
cnf(c_0_11,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_6,c_0_10]),c_0_10]),c_0_10]),c_0_10]) ).
cnf(c_0_12,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_13,plain,
difference(difference(X1,difference(X2,X3)),X3) = difference(difference(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_7]),c_0_8]) ).
cnf(c_0_14,plain,
difference(difference(X1,X2),X1) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_15,plain,
difference(X1,difference(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_11]) ).
cnf(c_0_16,plain,
difference(difference(X1,difference(X2,X3)),X2) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_17,plain,
difference(difference(X1,X2),difference(X1,difference(X2,X3))) = difference(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_16]),c_0_8]),c_0_12]) ).
cnf(c_0_18,plain,
difference(X1,difference(X1,difference(X1,X2))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_14]),c_0_15]) ).
cnf(c_0_19,plain,
difference(X1,difference(X1,difference(difference(X2,X1),X3))) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_17,c_0_5]) ).
cnf(c_0_20,plain,
difference(difference(X1,X2),difference(X3,X1)) = difference(X1,difference(X2,difference(X3,X1))),
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_21,plain,
difference(X1,difference(difference(X2,X1),X3)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_5]) ).
cnf(c_0_22,plain,
difference(X1,difference(X2,difference(X3,X1))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_16]) ).
cnf(c_0_23,plain,
difference(difference(difference(X1,X2),X3),X2) = difference(difference(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_7]),c_0_8]) ).
cnf(c_0_24,plain,
difference(difference(difference(X1,X2),X3),X1) = difference(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_14]),c_0_12]) ).
cnf(c_0_25,plain,
difference(X1,difference(difference(X2,difference(X3,X1)),X4)) = difference(X1,difference(X2,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_22]) ).
cnf(c_0_26,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
inference(fof_simplification,[status(thm)],[prove_associativity_of_multiply]) ).
cnf(c_0_27,plain,
difference(difference(X1,X2),difference(X2,X3)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_5]) ).
cnf(c_0_28,plain,
difference(X1,difference(X1,difference(difference(X1,X2),X3))) = difference(difference(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_24]),c_0_15]) ).
cnf(c_0_29,plain,
difference(X1,difference(difference(X1,difference(X1,X2)),X3)) = difference(X1,difference(X2,X3)),
inference(spm,[status(thm)],[c_0_25,c_0_6]) ).
cnf(c_0_30,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
c_0_26 ).
cnf(c_0_31,axiom,
multiply(X1,X2) = difference(X1,difference(X1,X2)),
intersection ).
cnf(c_0_32,plain,
difference(difference(X1,difference(X1,X2)),difference(X3,difference(X2,X1))) = difference(difference(X2,X3),difference(X2,X1)),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_33,plain,
difference(difference(X1,X2),difference(X3,difference(X4,X1))) = difference(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_34,plain,
difference(difference(X1,difference(X1,X2)),X3) = difference(X1,difference(X1,difference(X2,X3))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
difference(difference(X1,difference(X2,X3)),difference(X3,difference(X3,X2))) = difference(difference(X1,X2),difference(X2,X3)),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_36,negated_conjecture,
difference(difference(a,difference(a,b)),difference(difference(a,difference(a,b)),c)) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_31]),c_0_31]) ).
cnf(c_0_37,plain,
difference(difference(X1,difference(X1,X2)),X3) = difference(difference(X2,X3),difference(X2,X1)),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
difference(difference(X1,X2),difference(X1,X3)) = difference(X1,difference(X1,difference(X3,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_34]),c_0_22]) ).
cnf(c_0_39,plain,
difference(difference(X1,difference(X2,X3)),difference(X3,difference(X3,X2))) = difference(X1,X2),
inference(rw,[status(thm)],[c_0_35,c_0_27]) ).
cnf(c_0_40,plain,
difference(difference(X1,difference(X2,X3)),difference(difference(X4,X2),X3)) = difference(difference(X1,difference(X4,X3)),difference(X2,X3)),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_41,plain,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_21]),c_0_23]) ).
cnf(c_0_42,negated_conjecture,
difference(c,difference(c,difference(a,difference(a,b)))) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(rw,[status(thm)],[c_0_36,c_0_6]) ).
cnf(c_0_43,plain,
difference(X1,difference(X1,difference(X2,X3))) = difference(X2,difference(X2,difference(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_34]),c_0_38]) ).
cnf(c_0_44,plain,
difference(X1,difference(X2,difference(X1,difference(X1,X3)))) = difference(X1,difference(X2,X3)),
inference(spm,[status(thm)],[c_0_25,c_0_39]) ).
cnf(c_0_45,plain,
difference(X1,difference(X2,difference(X2,difference(X1,X3)))) = difference(X1,difference(X2,X3)),
inference(spm,[status(thm)],[c_0_25,c_0_34]) ).
cnf(c_0_46,plain,
difference(difference(X1,difference(X2,X3)),difference(X4,difference(X3,difference(X4,X2)))) = difference(difference(X1,difference(X2,X3)),difference(X4,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_5]),c_0_22]),c_0_41]),c_0_22]) ).
cnf(c_0_47,plain,
difference(X1,difference(X2,difference(difference(X3,X1),X4))) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
difference(a,difference(a,difference(c,difference(a,b)))) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
difference(X1,difference(X2,difference(X1,X3))) = difference(X1,difference(X2,difference(X2,X3))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
difference(X1,difference(X2,difference(X1,difference(X2,X3)))) = difference(X1,difference(X2,X3)),
inference(spm,[status(thm)],[c_0_46,c_0_5]) ).
cnf(c_0_51,plain,
difference(X1,difference(X2,difference(X3,difference(X4,X1)))) = difference(X1,difference(X2,X3)),
inference(spm,[status(thm)],[c_0_47,c_0_39]) ).
cnf(c_0_52,negated_conjecture,
difference(a,difference(a,difference(c,difference(a,b)))) != difference(a,difference(a,difference(b,difference(a,c)))),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
difference(X1,difference(X2,difference(X1,X3))) = difference(X1,difference(X3,difference(X3,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_6]),c_0_51]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53]),c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG005-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 12:54:30 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 17.75/2.90 % Version: 3.5.1
% 17.75/2.90 % Preprocessing class: FSSSSMSSSSSNFFN.
% 17.75/2.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.75/2.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 17.75/2.90 % Starting new_bool_3 with 300s (1) cores
% 17.75/2.90 % Starting new_bool_1 with 300s (1) cores
% 17.75/2.90 % Starting sh5l with 300s (1) cores
% 17.75/2.90 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1926941 completed with status 0
% 17.75/2.90 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 17.75/2.90 % Preprocessing class: FSSSSMSSSSSNFFN.
% 17.75/2.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.75/2.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 17.75/2.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.75/2.90 % No SInE strategy applied
% 17.75/2.90 % Search class: FUUPS-FFSF22-MFFFFFNN
% 17.75/2.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 17.75/2.90 % Starting SubtermCWHack with 136s (1) cores
% 17.75/2.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 17.75/2.90 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 17.75/2.90 % Starting new_bool_3 with 136s (1) cores
% 17.75/2.90 % Starting new_bool_1 with 136s (1) cores
% 17.75/2.90 % new_bool_3 with pid 1926948 completed with status 0
% 17.75/2.90 % Result found by new_bool_3
% 17.75/2.90 % Preprocessing class: FSSSSMSSSSSNFFN.
% 17.75/2.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.75/2.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 17.75/2.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.75/2.90 % No SInE strategy applied
% 17.75/2.90 % Search class: FUUPS-FFSF22-MFFFFFNN
% 17.75/2.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 17.75/2.90 % Starting SubtermCWHack with 136s (1) cores
% 17.75/2.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 17.75/2.90 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 17.75/2.90 % Starting new_bool_3 with 136s (1) cores
% 17.75/2.90 % Preprocessing time : 0.001 s
% 17.75/2.90 % Presaturation interreduction done
% 17.75/2.90
% 17.75/2.90 % Proof found!
% 17.75/2.90 % SZS status Unsatisfiable
% 17.75/2.90 % SZS output start CNFRefutation
% See solution above
% 17.75/2.90 % Parsed axioms : 5
% 17.75/2.90 % Removed by relevancy pruning/SinE : 0
% 17.75/2.90 % Initial clauses : 5
% 17.75/2.90 % Removed in clause preprocessing : 1
% 17.75/2.90 % Initial clauses in saturation : 4
% 17.75/2.90 % Processed clauses : 4866
% 17.75/2.90 % ...of these trivial : 716
% 17.75/2.90 % ...subsumed : 3890
% 17.75/2.90 % ...remaining for further processing : 260
% 17.75/2.90 % Other redundant clauses eliminated : 0
% 17.75/2.90 % Clauses deleted for lack of memory : 0
% 17.75/2.90 % Backward-subsumed : 0
% 17.75/2.90 % Backward-rewritten : 90
% 17.75/2.90 % Generated clauses : 197988
% 17.75/2.90 % ...of the previous two non-redundant : 124077
% 17.75/2.90 % ...aggressively subsumed : 0
% 17.75/2.90 % Contextual simplify-reflections : 0
% 17.75/2.90 % Paramodulations : 197988
% 17.75/2.90 % Factorizations : 0
% 17.75/2.90 % NegExts : 0
% 17.75/2.90 % Equation resolutions : 0
% 17.75/2.90 % Disequality decompositions : 0
% 17.75/2.90 % Total rewrite steps : 358247
% 17.75/2.90 % ...of those cached : 278623
% 17.75/2.90 % Propositional unsat checks : 0
% 17.75/2.90 % Propositional check models : 0
% 17.75/2.90 % Propositional check unsatisfiable : 0
% 17.75/2.90 % Propositional clauses : 0
% 17.75/2.90 % Propositional clauses after purity: 0
% 17.75/2.90 % Propositional unsat core size : 0
% 17.75/2.90 % Propositional preprocessing time : 0.000
% 17.75/2.90 % Propositional encoding time : 0.000
% 17.75/2.90 % Propositional solver time : 0.000
% 17.75/2.90 % Success case prop preproc time : 0.000
% 17.75/2.90 % Success case prop encoding time : 0.000
% 17.75/2.90 % Success case prop solver time : 0.000
% 17.75/2.90 % Current number of processed clauses : 166
% 17.75/2.90 % Positive orientable unit clauses : 154
% 17.75/2.90 % Positive unorientable unit clauses: 12
% 17.75/2.90 % Negative unit clauses : 0
% 17.75/2.90 % Non-unit-clauses : 0
% 17.75/2.90 % Current number of unprocessed clauses: 112229
% 17.75/2.90 % ...number of literals in the above : 112229
% 17.75/2.90 % Current number of archived formulas : 0
% 17.75/2.90 % Current number of archived clauses : 95
% 17.75/2.90 % Clause-clause subsumption calls (NU) : 0
% 17.75/2.90 % Rec. Clause-clause subsumption calls : 0
% 17.75/2.90 % Non-unit clause-clause subsumptions : 0
% 17.75/2.90 % Unit Clause-clause subsumption calls : 625
% 17.75/2.90 % Rewrite failures with RHS unbound : 50
% 17.75/2.90 % BW rewrite match attempts : 6642
% 17.75/2.90 % BW rewrite match successes : 469
% 17.75/2.90 % Condensation attempts : 0
% 17.75/2.90 % Condensation successes : 0
% 17.75/2.90 % Termbank termtop insertions : 3600172
% 17.75/2.90 % Search garbage collected termcells : 2
% 17.75/2.90
% 17.75/2.90 % -------------------------------------------------
% 17.75/2.90 % User time : 2.284 s
% 17.75/2.90 % System time : 0.091 s
% 17.75/2.90 % Total time : 2.374 s
% 17.75/2.90 % Maximum resident set size: 3628 pages
% 17.75/2.90
% 17.75/2.90 % -------------------------------------------------
% 17.75/2.90 % User time : 10.688 s
% 17.75/2.90 % System time : 0.418 s
% 17.75/2.90 % Total time : 11.106 s
% 17.75/2.90 % Maximum resident set size: 4608 pages
% 17.75/2.90 % E exiting
%------------------------------------------------------------------------------