%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP169-1 : 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 : 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 12:38:49 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 7 RR)
% Number of literals : 26 ( 25 equ; 3 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
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(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(p02a_1,hypothesis,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p02a_1) ).
cnf(prove_p02a,negated_conjecture,
least_upper_bound(a,b) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p02a) ).
cnf(c_0_8,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_9,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_10,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_11,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_12,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_13,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_14,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_15,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_16,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_11]) ).
cnf(c_0_17,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_12,c_0_9]),c_0_13]) ).
cnf(c_0_18,hypothesis,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
p02a_1 ).
cnf(c_0_19,plain,
least_upper_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(X1),least_upper_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_9]),c_0_13]) ).
cnf(c_0_20,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
least_upper_bound(a,b) != a,
inference(fof_simplification,[status(thm)],[prove_p02a]) ).
cnf(c_0_22,hypothesis,
multiply(inverse(a),least_upper_bound(a,b)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_9]),c_0_19]),c_0_13]) ).
cnf(c_0_23,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_20]),c_0_20]) ).
cnf(c_0_24,negated_conjecture,
least_upper_bound(a,b) != a,
c_0_21 ).
cnf(c_0_25,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_22]),c_0_23]),c_0_20]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:09:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.45 % Version: 3.5.1
% 0.09/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.45 % Starting sh5l with 300s (1) cores
% 0.09/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1284964 completed with status 0
% 0.09/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.09/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.45 % No SInE strategy applied
% 0.09/0.45 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.09/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.09/0.45 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.09/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.09/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.09/0.45 % new_bool_3 with pid 1284974 completed with status 0
% 0.09/0.45 % Result found by new_bool_3
% 0.09/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.45 % No SInE strategy applied
% 0.09/0.45 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.09/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.09/0.45 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.09/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.09/0.45 % Preprocessing time : 0.001 s
% 0.09/0.45 % Presaturation interreduction done
% 0.09/0.45
% 0.09/0.45 % Proof found!
% 0.09/0.45 % SZS status Unsatisfiable
% 0.09/0.45 % SZS output start CNFRefutation
% See solution above
% 0.09/0.45 % Parsed axioms : 17
% 0.09/0.45 % Removed by relevancy pruning/SinE : 0
% 0.09/0.45 % Initial clauses : 17
% 0.09/0.45 % Removed in clause preprocessing : 0
% 0.09/0.45 % Initial clauses in saturation : 17
% 0.09/0.45 % Processed clauses : 340
% 0.09/0.45 % ...of these trivial : 81
% 0.09/0.45 % ...subsumed : 140
% 0.09/0.45 % ...remaining for further processing : 119
% 0.09/0.45 % Other redundant clauses eliminated : 0
% 0.09/0.45 % Clauses deleted for lack of memory : 0
% 0.09/0.45 % Backward-subsumed : 0
% 0.09/0.45 % Backward-rewritten : 7
% 0.09/0.45 % Generated clauses : 3197
% 0.09/0.45 % ...of the previous two non-redundant : 2054
% 0.09/0.45 % ...aggressively subsumed : 0
% 0.09/0.45 % Contextual simplify-reflections : 0
% 0.09/0.45 % Paramodulations : 3197
% 0.09/0.45 % Factorizations : 0
% 0.09/0.45 % NegExts : 0
% 0.09/0.45 % Equation resolutions : 0
% 0.09/0.45 % Disequality decompositions : 0
% 0.09/0.45 % Total rewrite steps : 2951
% 0.09/0.45 % ...of those cached : 1872
% 0.09/0.45 % Propositional unsat checks : 0
% 0.09/0.45 % Propositional check models : 0
% 0.09/0.45 % Propositional check unsatisfiable : 0
% 0.09/0.45 % Propositional clauses : 0
% 0.09/0.45 % Propositional clauses after purity: 0
% 0.09/0.45 % Propositional unsat core size : 0
% 0.09/0.45 % Propositional preprocessing time : 0.000
% 0.09/0.45 % Propositional encoding time : 0.000
% 0.09/0.45 % Propositional solver time : 0.000
% 0.09/0.45 % Success case prop preproc time : 0.000
% 0.09/0.45 % Success case prop encoding time : 0.000
% 0.09/0.45 % Success case prop solver time : 0.000
% 0.09/0.45 % Current number of processed clauses : 95
% 0.09/0.45 % Positive orientable unit clauses : 85
% 0.09/0.45 % Positive unorientable unit clauses: 9
% 0.09/0.45 % Negative unit clauses : 1
% 0.09/0.45 % Non-unit-clauses : 0
% 0.09/0.45 % Current number of unprocessed clauses: 1736
% 0.09/0.45 % ...number of literals in the above : 1736
% 0.09/0.45 % Current number of archived formulas : 0
% 0.09/0.45 % Current number of archived clauses : 24
% 0.09/0.45 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.45 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.45 % Non-unit clause-clause subsumptions : 0
% 0.09/0.45 % Unit Clause-clause subsumption calls : 17
% 0.09/0.45 % Rewrite failures with RHS unbound : 0
% 0.09/0.45 % BW rewrite match attempts : 192
% 0.09/0.45 % BW rewrite match successes : 142
% 0.09/0.45 % Condensation attempts : 0
% 0.09/0.45 % Condensation successes : 0
% 0.09/0.45 % Termbank termtop insertions : 27698
% 0.09/0.45 % Search garbage collected termcells : 2
% 0.09/0.45
% 0.09/0.45 % -------------------------------------------------
% 0.09/0.45 % User time : 0.016 s
% 0.09/0.45 % System time : 0.007 s
% 0.09/0.45 % Total time : 0.023 s
% 0.09/0.45 % Maximum resident set size: 3640 pages
% 0.09/0.45
% 0.09/0.45 % -------------------------------------------------
% 0.09/0.45 % User time : 0.075 s
% 0.09/0.45 % System time : 0.021 s
% 0.09/0.45 % Total time : 0.096 s
% 0.09/0.45 % Maximum resident set size: 4608 pages
% 0.09/0.45 % E exiting
%------------------------------------------------------------------------------