%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP167-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 69.39s 11.21s
% Output : CNFRefutation 69.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 6 RR)
% Number of literals : 60 ( 59 equ; 5 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 99 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
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/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(lat4_4,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/sandbox/benchmark/theBenchmark.p',lat4_4) ).
cnf(monotony_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
cnf(prove_lat4,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lat4) ).
cnf(lat4_1,axiom,
positive_part(X1) = least_upper_bound(X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_1) ).
cnf(lat4_2,axiom,
negative_part(X1) = greatest_lower_bound(X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_2) ).
cnf(c_0_15,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_16,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_17,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_18,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_19,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_20,plain,
multiply(inverse(inverse(inverse(X1))),X1) = identity,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_20]),c_0_19]) ).
cnf(c_0_22,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_23,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_24,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_25,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_26,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_27,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_28,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_29,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_30,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_31,axiom,
greatest_lower_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,X3)),
lat4_4 ).
cnf(c_0_32,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_33,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_34,plain,
greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,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_28,c_0_17]),c_0_29]) ).
cnf(c_0_36,plain,
multiply(inverse(X1),greatest_lower_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_16]),c_0_24]) ).
cnf(c_0_37,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,least_upper_bound(X1,X3)),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_38,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld ).
cnf(c_0_39,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_32]),c_0_23]) ).
cnf(c_0_40,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_23]),c_0_29]) ).
cnf(c_0_41,plain,
greatest_lower_bound(X1,multiply(least_upper_bound(X1,X2),greatest_lower_bound(X3,identity))) = greatest_lower_bound(X1,multiply(least_upper_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_42,plain,
multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(X1,identity)) = greatest_lower_bound(identity,least_upper_bound(X1,inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_29]),c_0_37]) ).
cnf(c_0_43,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_38]) ).
cnf(c_0_44,plain,
multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_16]),c_0_29]) ).
cnf(c_0_45,plain,
multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(X2,multiply(X2,X1)))) = inverse(X2),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,plain,
greatest_lower_bound(identity,least_upper_bound(X1,inverse(X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44]),c_0_17]),c_0_27]) ).
cnf(c_0_47,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
inference(fof_simplification,[status(thm)],[prove_lat4]) ).
cnf(c_0_48,plain,
multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_16]),c_0_29]),c_0_21]) ).
cnf(c_0_49,plain,
multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(X1,identity)) = identity,
inference(rw,[status(thm)],[c_0_42,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
c_0_47 ).
cnf(c_0_51,axiom,
positive_part(X1) = least_upper_bound(X1,identity),
lat4_1 ).
cnf(c_0_52,axiom,
negative_part(X1) = greatest_lower_bound(X1,identity),
lat4_2 ).
cnf(c_0_53,plain,
multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(identity,inverse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_29]) ).
cnf(c_0_54,plain,
inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(X1,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_49]),c_0_23]) ).
cnf(c_0_55,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_56,plain,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)) = X1,
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,negated_conjecture,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_29]),c_0_24]) ).
cnf(c_0_58,plain,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) = X1,
inference(spm,[status(thm)],[c_0_56,c_0_24]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP167-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:08:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 69.39/11.21 % Version: 3.5.1
% 69.39/11.21 % Preprocessing class: FSMSSMSSSSSNFFN.
% 69.39/11.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 69.39/11.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 69.39/11.21 % Starting new_bool_3 with 300s (1) cores
% 69.39/11.21 % Starting new_bool_1 with 300s (1) cores
% 69.39/11.21 % Starting sh5l with 300s (1) cores
% 69.39/11.21 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1283771 completed with status 0
% 69.39/11.21 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 69.39/11.21 % Preprocessing class: FSMSSMSSSSSNFFN.
% 69.39/11.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 69.39/11.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 69.39/11.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 69.39/11.21 % No SInE strategy applied
% 69.39/11.21 % Search class: FUUPM-FFSF21-SFFFFFNN
% 69.39/11.21 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 69.39/11.21 % Starting SubtermCWHack with 136s (1) cores
% 69.39/11.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 69.39/11.21 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 69.39/11.21 % Starting new_bool_3 with 136s (1) cores
% 69.39/11.21 % Starting new_bool_1 with 136s (1) cores
% 69.39/11.21 % SubtermCWHack with pid 1283776 completed with status 0
% 69.39/11.21 % Result found by SubtermCWHack
% 69.39/11.21 % Preprocessing class: FSMSSMSSSSSNFFN.
% 69.39/11.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 69.39/11.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 69.39/11.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 69.39/11.21 % No SInE strategy applied
% 69.39/11.21 % Search class: FUUPM-FFSF21-SFFFFFNN
% 69.39/11.21 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 69.39/11.21 % Starting SubtermCWHack with 136s (1) cores
% 69.39/11.21 % Preprocessing time : 0.002 s
% 69.39/11.21
% 69.39/11.21 % Proof found!
% 69.39/11.21 % SZS status Unsatisfiable
% 69.39/11.21 % SZS output start CNFRefutation
% See solution above
% 69.39/11.21 % Parsed axioms : 20
% 69.39/11.21 % Removed by relevancy pruning/SinE : 0
% 69.39/11.21 % Initial clauses : 20
% 69.39/11.21 % Removed in clause preprocessing : 2
% 69.39/11.21 % Initial clauses in saturation : 18
% 69.39/11.21 % Processed clauses : 17848
% 69.39/11.21 % ...of these trivial : 5565
% 69.39/11.21 % ...subsumed : 11092
% 69.39/11.21 % ...remaining for further processing : 1191
% 69.39/11.21 % Other redundant clauses eliminated : 0
% 69.39/11.21 % Clauses deleted for lack of memory : 0
% 69.39/11.21 % Backward-subsumed : 0
% 69.39/11.21 % Backward-rewritten : 179
% 69.39/11.21 % Generated clauses : 716684
% 69.39/11.21 % ...of the previous two non-redundant : 479864
% 69.39/11.21 % ...aggressively subsumed : 0
% 69.39/11.21 % Contextual simplify-reflections : 0
% 69.39/11.21 % Paramodulations : 716684
% 69.39/11.21 % Factorizations : 0
% 69.39/11.21 % NegExts : 0
% 69.39/11.21 % Equation resolutions : 0
% 69.39/11.21 % Disequality decompositions : 0
% 69.39/11.21 % Total rewrite steps : 954440
% 69.39/11.21 % ...of those cached : 746901
% 69.39/11.21 % Propositional unsat checks : 0
% 69.39/11.21 % Propositional check models : 0
% 69.39/11.21 % Propositional check unsatisfiable : 0
% 69.39/11.21 % Propositional clauses : 0
% 69.39/11.21 % Propositional clauses after purity: 0
% 69.39/11.21 % Propositional unsat core size : 0
% 69.39/11.21 % Propositional preprocessing time : 0.000
% 69.39/11.21 % Propositional encoding time : 0.000
% 69.39/11.21 % Propositional solver time : 0.000
% 69.39/11.21 % Success case prop preproc time : 0.000
% 69.39/11.21 % Success case prop encoding time : 0.000
% 69.39/11.21 % Success case prop solver time : 0.000
% 69.39/11.21 % Current number of processed clauses : 1012
% 69.39/11.21 % Positive orientable unit clauses : 940
% 69.39/11.21 % Positive unorientable unit clauses: 72
% 69.39/11.21 % Negative unit clauses : 0
% 69.39/11.21 % Non-unit-clauses : 0
% 69.39/11.21 % Current number of unprocessed clauses: 460777
% 69.39/11.21 % ...number of literals in the above : 460777
% 69.39/11.21 % Current number of archived formulas : 0
% 69.39/11.21 % Current number of archived clauses : 181
% 69.39/11.21 % Clause-clause subsumption calls (NU) : 0
% 69.39/11.21 % Rec. Clause-clause subsumption calls : 0
% 69.39/11.21 % Non-unit clause-clause subsumptions : 0
% 69.39/11.21 % Unit Clause-clause subsumption calls : 637
% 69.39/11.21 % Rewrite failures with RHS unbound : 0
% 69.39/11.21 % BW rewrite match attempts : 9688
% 69.39/11.21 % BW rewrite match successes : 742
% 69.39/11.21 % Condensation attempts : 0
% 69.39/11.21 % Condensation successes : 0
% 69.39/11.21 % Termbank termtop insertions : 9226714
% 69.39/11.21 % Search garbage collected termcells : 2
% 69.39/11.21
% 69.39/11.21 % -------------------------------------------------
% 69.39/11.21 % User time : 9.868 s
% 69.39/11.21 % System time : 0.410 s
% 69.39/11.21 % Total time : 10.278 s
% 69.39/11.21 % Maximum resident set size: 3640 pages
% 69.39/11.21
% 69.39/11.21 % -------------------------------------------------
% 69.39/11.21 % User time : 46.265 s
% 69.39/11.21 % System time : 1.942 s
% 69.39/11.21 % Total time : 48.207 s
% 69.39/11.21 % Maximum resident set size: 4864 pages
% 69.39/11.21 % E exiting
%------------------------------------------------------------------------------