%------------------------------------------------------------------------------
% File : E---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 : n013.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 12:39:48 PM UTC 2026
% Result : Unsatisfiable 0.33s 0.46s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 4 RR)
% Number of literals : 27 ( 26 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 : 56 ( 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,inverse(X1))) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_15]),c_0_7]) ).
cnf(c_0_17,plain,
inverse(multiply(X1,multiply(a1,inverse(a1)))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_16]),c_0_15]),c_0_16]),c_0_15]),c_0_15]) ).
cnf(c_0_18,plain,
multiply(X1,multiply(a1,inverse(a1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_17]),c_0_14]) ).
cnf(c_0_19,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_4]) ).
cnf(c_0_20,plain,
inverse(multiply(multiply(inverse(X1),X2),inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_19]),c_0_15]) ).
cnf(c_0_21,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(fof_simplification,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_0_22,plain,
multiply(inverse(inverse(inverse(X1))),X1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_14]),c_0_7]) ).
cnf(c_0_23,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_19]),c_0_19]) ).
cnf(c_0_24,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
c_0_21 ).
cnf(c_0_25,plain,
multiply(inverse(X1),X1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP433-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 20:12:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 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
% 0.33/0.46 % Version: 3.5.1
% 0.33/0.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.33/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.33/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.33/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.33/0.46 % Starting sh5l with 300s (1) cores
% 0.33/0.46 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3312887 completed with status 0
% 0.33/0.46 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.33/0.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.33/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.33/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.33/0.46 % No SInE strategy applied
% 0.33/0.46 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.33/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.33/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.33/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.33/0.46 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.33/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.33/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.33/0.46 % U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3312893 completed with status 0
% 0.33/0.46 % Result found by U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.33/0.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.33/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.33/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.33/0.46 % No SInE strategy applied
% 0.33/0.46 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.33/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.33/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.33/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.33/0.46 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.33/0.46 % Preprocessing time : 0.001 s
% 0.33/0.46 % Presaturation interreduction done
% 0.33/0.46
% 0.33/0.46 % Proof found!
% 0.33/0.46 % SZS status Unsatisfiable
% 0.33/0.46 % SZS output start CNFRefutation
% See solution above
% 0.33/0.46 % Parsed axioms : 2
% 0.33/0.46 % Removed by relevancy pruning/SinE : 0
% 0.33/0.46 % Initial clauses : 2
% 0.33/0.46 % Removed in clause preprocessing : 0
% 0.33/0.46 % Initial clauses in saturation : 2
% 0.33/0.46 % Processed clauses : 105
% 0.33/0.46 % ...of these trivial : 7
% 0.33/0.46 % ...subsumed : 69
% 0.33/0.46 % ...remaining for further processing : 29
% 0.33/0.46 % Other redundant clauses eliminated : 0
% 0.33/0.46 % Clauses deleted for lack of memory : 0
% 0.33/0.46 % Backward-subsumed : 0
% 0.33/0.46 % Backward-rewritten : 17
% 0.33/0.46 % Generated clauses : 1299
% 0.33/0.46 % ...of the previous two non-redundant : 1190
% 0.33/0.46 % ...aggressively subsumed : 0
% 0.33/0.46 % Contextual simplify-reflections : 0
% 0.33/0.46 % Paramodulations : 1299
% 0.33/0.46 % Factorizations : 0
% 0.33/0.46 % NegExts : 0
% 0.33/0.46 % Equation resolutions : 0
% 0.33/0.46 % Disequality decompositions : 0
% 0.33/0.46 % Total rewrite steps : 637
% 0.33/0.46 % ...of those cached : 443
% 0.33/0.46 % Propositional unsat checks : 0
% 0.33/0.46 % Propositional check models : 0
% 0.33/0.46 % Propositional check unsatisfiable : 0
% 0.33/0.46 % Propositional clauses : 0
% 0.33/0.46 % Propositional clauses after purity: 0
% 0.33/0.46 % Propositional unsat core size : 0
% 0.33/0.46 % Propositional preprocessing time : 0.000
% 0.33/0.46 % Propositional encoding time : 0.000
% 0.33/0.46 % Propositional solver time : 0.000
% 0.33/0.46 % Success case prop preproc time : 0.000
% 0.33/0.46 % Success case prop encoding time : 0.000
% 0.33/0.46 % Success case prop solver time : 0.000
% 0.33/0.46 % Current number of processed clauses : 10
% 0.33/0.46 % Positive orientable unit clauses : 8
% 0.33/0.46 % Positive unorientable unit clauses: 2
% 0.33/0.46 % Negative unit clauses : 0
% 0.33/0.46 % Non-unit-clauses : 0
% 0.33/0.46 % Current number of unprocessed clauses: 965
% 0.33/0.46 % ...number of literals in the above : 965
% 0.33/0.46 % Current number of archived formulas : 0
% 0.33/0.46 % Current number of archived clauses : 19
% 0.33/0.46 % Clause-clause subsumption calls (NU) : 0
% 0.33/0.46 % Rec. Clause-clause subsumption calls : 0
% 0.33/0.46 % Non-unit clause-clause subsumptions : 0
% 0.33/0.46 % Unit Clause-clause subsumption calls : 22
% 0.33/0.46 % Rewrite failures with RHS unbound : 0
% 0.33/0.46 % BW rewrite match attempts : 86
% 0.33/0.46 % BW rewrite match successes : 41
% 0.33/0.46 % Condensation attempts : 0
% 0.33/0.46 % Condensation successes : 0
% 0.33/0.46 % Termbank termtop insertions : 21021
% 0.33/0.46 % Search garbage collected termcells : 2
% 0.33/0.46
% 0.33/0.46 % -------------------------------------------------
% 0.33/0.46 % User time : 0.019 s
% 0.33/0.46 % System time : 0.002 s
% 0.33/0.46 % Total time : 0.021 s
% 0.33/0.46 % Maximum resident set size: 3632 pages
% 0.33/0.46
% 0.33/0.46 % -------------------------------------------------
% 0.33/0.46 % User time : 0.072 s
% 0.33/0.46 % System time : 0.016 s
% 0.33/0.46 % Total time : 0.088 s
% 0.33/0.46 % Maximum resident set size: 4864 pages
% 0.33/0.46 % E exiting
%------------------------------------------------------------------------------