%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP167-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:38:48 PM UTC 2026
% Result : Unsatisfiable 16.53s 18.40s
% Output : CNFRefutation 16.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 9 RR)
% Number of literals : 56 ( 55 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 91 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(lat4_3,axiom,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_3) ).
cnf(lat4_1,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_1) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(lat4_2,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_2) ).
cnf(monotony_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(prove_lat4,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat4) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(lat4_4,axiom,
positive_part(X1) = least_upper_bound(X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_4) ).
cnf(lat4_5,axiom,
negative_part(X1) = greatest_lower_bound(X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_5) ).
cnf(lat4_7,axiom,
greatest_lower_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_7) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
cnf(c_0_17,axiom,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
lat4_3 ).
cnf(c_0_18,axiom,
inverse(identity) = identity,
lat4_1 ).
cnf(c_0_19,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_20,plain,
multiply(inverse(X1),identity) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_21,axiom,
inverse(inverse(X1)) = X1,
lat4_2 ).
cnf(c_0_22,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_23,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_25,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_26,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(identity,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_19]),c_0_25]) ).
cnf(c_0_28,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
inference(fof_simplification,[status(thm)],[prove_lat4]) ).
cnf(c_0_29,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_30,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_31,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_32,plain,
multiply(least_upper_bound(X1,identity),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_34,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
c_0_28 ).
cnf(c_0_35,axiom,
positive_part(X1) = least_upper_bound(X1,identity),
lat4_4 ).
cnf(c_0_36,axiom,
negative_part(X1) = greatest_lower_bound(X1,identity),
lat4_5 ).
cnf(c_0_37,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(identity,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_38,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_31]) ).
cnf(c_0_39,axiom,
greatest_lower_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,X3)),
lat4_7 ).
cnf(c_0_40,plain,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_25]) ).
cnf(c_0_41,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
associativity_of_glb ).
cnf(c_0_42,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_43,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_44,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld ).
cnf(c_0_45,plain,
multiply(greatest_lower_bound(X1,identity),X1) = multiply(X1,greatest_lower_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
least_upper_bound(greatest_lower_bound(X1,X2),multiply(X1,greatest_lower_bound(identity,X3))) = greatest_lower_bound(X1,least_upper_bound(X2,multiply(X1,X3))),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_47,plain,
multiply(greatest_lower_bound(X1,identity),least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_40]),c_0_38]) ).
cnf(c_0_48,plain,
greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),X3)) = greatest_lower_bound(X1,X3),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,a)) != a,
inference(rw,[status(thm)],[c_0_43,c_0_31]) ).
cnf(c_0_50,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_44]) ).
cnf(c_0_51,plain,
greatest_lower_bound(X1,least_upper_bound(identity,multiply(X1,X1))) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_45]),c_0_46]),c_0_47]) ).
cnf(c_0_52,plain,
greatest_lower_bound(X1,multiply(least_upper_bound(X2,X1),greatest_lower_bound(identity,X3))) = greatest_lower_bound(X1,multiply(least_upper_bound(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_48,c_0_37]) ).
cnf(c_0_53,negated_conjecture,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(rw,[status(thm)],[c_0_49,c_0_25]) ).
cnf(c_0_54,plain,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_40]),c_0_37]),c_0_33]),c_0_23]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP167-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/15.47 % Computer : n006.cluster.edu
% 0.18/15.47 % Model : x86_64 x86_64
% 0.18/15.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/15.47 % Memory : 8046.5625MB
% 0.18/15.47 % OS : Linux 6.8.0-71-generic
% 0.18/15.47 % CPULimit : 300
% 0.18/15.47 % WCLimit : 300
% 0.18/15.47 % DateTime : Sun Sep 20 20:03:12 UTC 2026
% 0.18/15.47 % CPUTime :
% 0.18/15.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/15.55 Running first-order theorem proving
% 0.24/15.55 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 16.53/18.40 % Version: 3.5.1
% 16.53/18.40 % Preprocessing class: FSMSSMSSSSSNFFN.
% 16.53/18.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.53/18.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 16.53/18.40 % Starting new_bool_3 with 300s (1) cores
% 16.53/18.40 % Starting new_bool_1 with 300s (1) cores
% 16.53/18.40 % Starting sh5l with 300s (1) cores
% 16.53/18.40 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1143202 completed with status 0
% 16.53/18.40 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 16.53/18.40 % Preprocessing class: FSMSSMSSSSSNFFN.
% 16.53/18.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.53/18.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 16.53/18.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 16.53/18.40 % No SInE strategy applied
% 16.53/18.40 % Search class: FUUPM-FFSF21-SFFFFFNN
% 16.53/18.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 16.53/18.40 % Starting SubtermCWHack with 136s (1) cores
% 16.53/18.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 16.53/18.40 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 16.53/18.40 % Starting new_bool_3 with 136s (1) cores
% 16.53/18.40 % Starting new_bool_1 with 136s (1) cores
% 16.53/18.40 % new_bool_1 with pid 1143213 completed with status 0
% 16.53/18.40 % Result found by new_bool_1
% 16.53/18.40 % Preprocessing class: FSMSSMSSSSSNFFN.
% 16.53/18.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.53/18.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 16.53/18.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 16.53/18.40 % No SInE strategy applied
% 16.53/18.40 % Search class: FUUPM-FFSF21-SFFFFFNN
% 16.53/18.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 16.53/18.40 % Starting SubtermCWHack with 136s (1) cores
% 16.53/18.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 16.53/18.40 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 16.53/18.40 % Starting new_bool_3 with 136s (1) cores
% 16.53/18.40 % Starting new_bool_1 with 136s (1) cores
% 16.53/18.40 % Preprocessing time : 0.002 s
% 16.53/18.40 % Presaturation interreduction done
% 16.53/18.40
% 16.53/18.40 % Proof found!
% 16.53/18.40 % SZS status Unsatisfiable
% 16.53/18.40 % SZS output start CNFRefutation
% See solution above
% 16.53/18.40 % Parsed axioms : 23
% 16.53/18.40 % Removed by relevancy pruning/SinE : 0
% 16.53/18.40 % Initial clauses : 23
% 16.53/18.40 % Removed in clause preprocessing : 2
% 16.53/18.40 % Initial clauses in saturation : 21
% 16.53/18.40 % Processed clauses : 4873
% 16.53/18.40 % ...of these trivial : 1807
% 16.53/18.40 % ...subsumed : 2459
% 16.53/18.40 % ...remaining for further processing : 607
% 16.53/18.40 % Other redundant clauses eliminated : 0
% 16.53/18.40 % Clauses deleted for lack of memory : 0
% 16.53/18.40 % Backward-subsumed : 0
% 16.53/18.40 % Backward-rewritten : 67
% 16.53/18.40 % Generated clauses : 142470
% 16.53/18.40 % ...of the previous two non-redundant : 88386
% 16.53/18.40 % ...aggressively subsumed : 0
% 16.53/18.40 % Contextual simplify-reflections : 0
% 16.53/18.40 % Paramodulations : 142470
% 16.53/18.40 % Factorizations : 0
% 16.53/18.40 % NegExts : 0
% 16.53/18.40 % Equation resolutions : 0
% 16.53/18.40 % Disequality decompositions : 0
% 16.53/18.40 % Total rewrite steps : 206906
% 16.53/18.40 % ...of those cached : 169515
% 16.53/18.40 % Propositional unsat checks : 0
% 16.53/18.40 % Propositional check models : 0
% 16.53/18.40 % Propositional check unsatisfiable : 0
% 16.53/18.40 % Propositional clauses : 0
% 16.53/18.40 % Propositional clauses after purity: 0
% 16.53/18.40 % Propositional unsat core size : 0
% 16.53/18.40 % Propositional preprocessing time : 0.000
% 16.53/18.40 % Propositional encoding time : 0.000
% 16.53/18.40 % Propositional solver time : 0.000
% 16.53/18.40 % Success case prop preproc time : 0.000
% 16.53/18.40 % Success case prop encoding time : 0.000
% 16.53/18.40 % Success case prop solver time : 0.000
% 16.53/18.40 % Current number of processed clauses : 519
% 16.53/18.40 % Positive orientable unit clauses : 478
% 16.53/18.40 % Positive unorientable unit clauses: 41
% 16.53/18.40 % Negative unit clauses : 0
% 16.53/18.40 % Non-unit-clauses : 0
% 16.53/18.40 % Current number of unprocessed clauses: 83148
% 16.53/18.40 % ...number of literals in the above : 83148
% 16.53/18.40 % Current number of archived formulas : 0
% 16.53/18.40 % Current number of archived clauses : 90
% 16.53/18.40 % Clause-clause subsumption calls (NU) : 0
% 16.53/18.40 % Rec. Clause-clause subsumption calls : 0
% 16.53/18.40 % Non-unit clause-clause subsumptions : 0
% 16.53/18.40 % Unit Clause-clause subsumption calls : 195
% 16.53/18.40 % Rewrite failures with RHS unbound : 0
% 16.53/18.40 % BW rewrite match attempts : 2358
% 16.53/18.40 % BW rewrite match successes : 466
% 16.53/18.40 % Condensation attempts : 0
% 16.53/18.40 % Condensation successes : 0
% 16.53/18.40 % Termbank termtop insertions : 1794040
% 16.53/18.40 % Search garbage collected termcells : 2
% 16.53/18.40
% 16.53/18.40 % -------------------------------------------------
% 16.53/18.40 % User time : 2.632 s
% 16.53/18.40 % System time : 0.114 s
% 16.53/18.40 % Total time : 2.746 s
% 16.53/18.40 % Maximum resident set size: 3592 pages
% 16.53/18.40
% 16.53/18.40 % -------------------------------------------------
% 16.53/18.40 % User time : 13.010 s
% 16.53/18.40 % System time : 0.599 s
% 16.53/18.40 % Total time : 13.609 s
% 16.53/18.40 % Maximum resident set size: 4608 pages
% 16.53/18.40 % E exiting
%------------------------------------------------------------------------------