%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP433-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:43:47 PM UTC 2026
% Result : Unsatisfiable 0.24s 5.66s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 4 RR)
% Number of literals : 25 ( 24 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X1,X2),X3)),X1),X2),multiply(X4,inverse(X4)))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c_0_2,axiom,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X1,X2),X3)),X1),X2),multiply(X4,inverse(X4)))) = X3,
single_axiom ).
cnf(c_0_3,plain,
inverse(multiply(multiply(multiply(X1,multiply(inverse(multiply(multiply(X2,X3),X1)),X2)),X3),multiply(X4,inverse(X4)))) = multiply(X5,inverse(X5)),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),X3),multiply(X4,inverse(X4)))) = inverse(multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_6,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X1,X2),inverse(multiply(X3,inverse(X3))))),X1),X2)) = multiply(X4,inverse(X4)),
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_7,plain,
inverse(multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),inverse(X2))) = multiply(X3,inverse(X3)),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
cnf(c_0_8,plain,
inverse(multiply(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))),X3),multiply(X4,inverse(X4)))) = inverse(X3),
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_9,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X1,inverse(X1)),X2)),X3),inverse(X3)),multiply(X4,inverse(X4)))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_10,plain,
inverse(multiply(multiply(multiply(X1,inverse(X1)),X2),multiply(X3,inverse(X3)))) = inverse(X2),
inference(spm,[status(thm)],[c_0_8,c_0_4]) ).
cnf(c_0_11,plain,
inverse(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),X2))))) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
inverse(inverse(multiply(X1,inverse(X1)))) = multiply(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_8]),c_0_11]) ).
cnf(c_0_13,plain,
inverse(multiply(inverse(inverse(multiply(X1,inverse(X1)))),X2)) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_14,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_15,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_16,plain,
inverse(multiply(X1,multiply(X2,inverse(X2)))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_15]),c_0_13]) ).
cnf(c_0_17,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_16]),c_0_14]) ).
cnf(c_0_18,plain,
inverse(multiply(multiply(inverse(X1),X2),inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_16]),c_0_15]) ).
cnf(c_0_19,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(fof_simplification,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_0_21,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_12]),c_0_19]),c_0_17]) ).
cnf(c_0_22,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
c_0_20 ).
cnf(c_0_23,plain,
multiply(inverse(X1),X1) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_4,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP433-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/5.45 % Computer : n004.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.46 % CPULimit : 300
% 0.17/5.46 % WCLimit : 300
% 0.17/5.46 % DateTime : Sun Sep 20 20:12:40 UTC 2026
% 0.17/5.46 % CPUTime :
% 0.17/5.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/5.52 Running first-order theorem proving
% 0.24/5.52 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
% 0.24/5.66 % Version: 3.5.1
% 0.24/5.66 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/5.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.66 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/5.66 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.66 % Starting new_bool_1 with 300s (1) cores
% 0.24/5.66 % Starting sh5l with 300s (1) cores
% 0.24/5.66 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1390184 completed with status 0
% 0.24/5.66 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.24/5.66 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/5.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.66 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/5.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/5.66 % No SInE strategy applied
% 0.24/5.66 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.24/5.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/5.66 % Starting SubtermCWHack with 136s (1) cores
% 0.24/5.66 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.24/5.66 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.24/5.66 % Starting new_bool_3 with 136s (1) cores
% 0.24/5.66 % Starting new_bool_1 with 136s (1) cores
% 0.24/5.66 % new_bool_3 with pid 1390191 completed with status 0
% 0.24/5.66 % Result found by new_bool_3
% 0.24/5.66 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/5.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.66 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/5.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/5.66 % No SInE strategy applied
% 0.24/5.66 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.24/5.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/5.66 % Starting SubtermCWHack with 136s (1) cores
% 0.24/5.66 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.24/5.66 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.24/5.66 % Starting new_bool_3 with 136s (1) cores
% 0.24/5.66 % Preprocessing time : 0.002 s
% 0.24/5.66 % Presaturation interreduction done
% 0.24/5.66
% 0.24/5.66 % Proof found!
% 0.24/5.66 % SZS status Unsatisfiable
% 0.24/5.66 % SZS output start CNFRefutation
% See solution above
% 0.24/5.66 % Parsed axioms : 2
% 0.24/5.66 % Removed by relevancy pruning/SinE : 0
% 0.24/5.66 % Initial clauses : 2
% 0.24/5.66 % Removed in clause preprocessing : 0
% 0.24/5.66 % Initial clauses in saturation : 2
% 0.24/5.66 % Processed clauses : 100
% 0.24/5.66 % ...of these trivial : 21
% 0.24/5.66 % ...subsumed : 40
% 0.24/5.66 % ...remaining for further processing : 39
% 0.24/5.66 % Other redundant clauses eliminated : 0
% 0.24/5.66 % Clauses deleted for lack of memory : 0
% 0.24/5.66 % Backward-subsumed : 0
% 0.24/5.66 % Backward-rewritten : 18
% 0.24/5.66 % Generated clauses : 2525
% 0.24/5.66 % ...of the previous two non-redundant : 2372
% 0.24/5.66 % ...aggressively subsumed : 0
% 0.24/5.66 % Contextual simplify-reflections : 0
% 0.24/5.66 % Paramodulations : 2525
% 0.24/5.66 % Factorizations : 0
% 0.24/5.66 % NegExts : 0
% 0.24/5.66 % Equation resolutions : 0
% 0.24/5.66 % Disequality decompositions : 0
% 0.24/5.66 % Total rewrite steps : 935
% 0.24/5.66 % ...of those cached : 484
% 0.24/5.66 % Propositional unsat checks : 0
% 0.24/5.66 % Propositional check models : 0
% 0.24/5.66 % Propositional check unsatisfiable : 0
% 0.24/5.66 % Propositional clauses : 0
% 0.24/5.66 % Propositional clauses after purity: 0
% 0.24/5.66 % Propositional unsat core size : 0
% 0.24/5.66 % Propositional preprocessing time : 0.000
% 0.24/5.66 % Propositional encoding time : 0.000
% 0.24/5.66 % Propositional solver time : 0.000
% 0.24/5.66 % Success case prop preproc time : 0.000
% 0.24/5.66 % Success case prop encoding time : 0.000
% 0.24/5.66 % Success case prop solver time : 0.000
% 0.24/5.66 % Current number of processed clauses : 19
% 0.24/5.66 % Positive orientable unit clauses : 13
% 0.24/5.66 % Positive unorientable unit clauses: 5
% 0.24/5.66 % Negative unit clauses : 1
% 0.24/5.66 % Non-unit-clauses : 0
% 0.24/5.66 % Current number of unprocessed clauses: 2229
% 0.24/5.66 % ...number of literals in the above : 2229
% 0.24/5.66 % Current number of archived formulas : 0
% 0.24/5.66 % Current number of archived clauses : 20
% 0.24/5.66 % Clause-clause subsumption calls (NU) : 0
% 0.24/5.66 % Rec. Clause-clause subsumption calls : 0
% 0.24/5.66 % Non-unit clause-clause subsumptions : 0
% 0.24/5.66 % Unit Clause-clause subsumption calls : 42
% 0.24/5.66 % Rewrite failures with RHS unbound : 246
% 0.24/5.66 % BW rewrite match attempts : 169
% 0.24/5.66 % BW rewrite match successes : 66
% 0.24/5.66 % Condensation attempts : 0
% 0.24/5.66 % Condensation successes : 0
% 0.24/5.66 % Termbank termtop insertions : 51326
% 0.24/5.66 % Search garbage collected termcells : 2
% 0.24/5.66
% 0.24/5.66 % -------------------------------------------------
% 0.24/5.66 % User time : 0.065 s
% 0.24/5.66 % System time : 0.007 s
% 0.24/5.66 % Total time : 0.073 s
% 0.24/5.66 % Maximum resident set size: 3376 pages
% 0.24/5.66
% 0.24/5.66 % -------------------------------------------------
% 0.24/5.66 % User time : 0.224 s
% 0.24/5.66 % System time : 0.030 s
% 0.24/5.66 % Total time : 0.254 s
% 0.24/5.66 % Maximum resident set size: 4608 pages
% 0.24/5.66 % E exiting
%------------------------------------------------------------------------------