%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP050-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:37:44 PM UTC 2026
% Result : Unsatisfiable 7.77s 1.60s
% Output : CNFRefutation 7.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of clauses : 32 ( 29 unt; 0 nHn; 5 RR)
% Number of literals : 38 ( 37 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(X2),multiply(inverse(X2),X2))))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_2,axiom,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(X2),multiply(inverse(X2),X2))))) = X3,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),multiply(inverse(X3),X3))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4)))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(X1,X2)),X4))),multiply(inverse(X3),multiply(inverse(X3),X3)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(X3),multiply(inverse(X2),multiply(inverse(X2),X2)))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_6,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X3,
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_7,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(X1,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X1,X3)) = multiply(X4,multiply(inverse(multiply(inverse(multiply(X5,X2)),multiply(X5,X4))),X3)),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,multiply(inverse(X2),X2)))))) = multiply(inverse(X2),X4),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_10,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),multiply(inverse(X2),multiply(inverse(X2),X2))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_8]),c_0_9]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(X1,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X1,multiply(inverse(X2),multiply(inverse(X2),X2)))) = multiply(inverse(X3),X3),
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_12,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_11,c_0_11]) ).
cnf(c_0_13,plain,
inverse(multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_12]) ).
cnf(c_0_14,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(inverse(X2),X2)))) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_7]) ).
cnf(c_0_15,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(inverse(X3),X3)))) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_16,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_5,c_0_15]) ).
cnf(c_0_17,plain,
inverse(multiply(inverse(X1),multiply(inverse(X2),X2))) = X1,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_17]),c_0_16]),c_0_16]),c_0_17]) ).
cnf(c_0_19,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_20,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_21,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_22,plain,
multiply(X1,inverse(multiply(inverse(X2),X2))) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_17]),c_0_16]),c_0_16]),c_0_17]) ).
cnf(c_0_24,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_20]),c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
c_0_21 ).
cnf(c_0_27,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_28,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_25]),c_0_24]) ).
cnf(c_0_29,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_26,c_0_12]),c_0_27])]) ).
cnf(c_0_30,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_28]),c_0_24]),c_0_24]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP050-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 19:55:55 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.46 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
% 7.77/1.60 % Version: 3.5.1
% 7.77/1.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 7.77/1.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.77/1.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 7.77/1.60 % Starting new_bool_3 with 300s (1) cores
% 7.77/1.60 % Starting new_bool_1 with 300s (1) cores
% 7.77/1.60 % Starting sh5l with 300s (1) cores
% 7.77/1.60 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 29681 completed with status 0
% 7.77/1.60 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 7.77/1.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 7.77/1.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.77/1.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 7.77/1.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.77/1.60 % No SInE strategy applied
% 7.77/1.60 % Search class: FUHPF-FFSF21-DFFFFFNN
% 7.77/1.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.77/1.60 % Starting SubtermCWHack with 136s (1) cores
% 7.77/1.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 7.77/1.60 % Starting G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 7.77/1.60 % Starting new_bool_3 with 136s (1) cores
% 7.77/1.60 % Starting new_bool_1 with 136s (1) cores
% 7.77/1.60 % SubtermCWHack with pid 29685 completed with status 0
% 7.77/1.60 % Result found by SubtermCWHack
% 7.77/1.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 7.77/1.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.77/1.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 7.77/1.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.77/1.60 % No SInE strategy applied
% 7.77/1.60 % Search class: FUHPF-FFSF21-DFFFFFNN
% 7.77/1.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.77/1.60 % Starting SubtermCWHack with 136s (1) cores
% 7.77/1.60 % Preprocessing time : 0.002 s
% 7.77/1.60
% 7.77/1.60 % Proof found!
% 7.77/1.60 % SZS status Unsatisfiable
% 7.77/1.60 % SZS output start CNFRefutation
% See solution above
% 7.77/1.60 % Parsed axioms : 2
% 7.77/1.60 % Removed by relevancy pruning/SinE : 0
% 7.77/1.60 % Initial clauses : 2
% 7.77/1.60 % Removed in clause preprocessing : 0
% 7.77/1.60 % Initial clauses in saturation : 2
% 7.77/1.60 % Processed clauses : 437
% 7.77/1.60 % ...of these trivial : 96
% 7.77/1.60 % ...subsumed : 257
% 7.77/1.60 % ...remaining for further processing : 84
% 7.77/1.60 % Other redundant clauses eliminated : 0
% 7.77/1.60 % Clauses deleted for lack of memory : 0
% 7.77/1.60 % Backward-subsumed : 1
% 7.77/1.60 % Backward-rewritten : 67
% 7.77/1.60 % Generated clauses : 20737
% 7.77/1.60 % ...of the previous two non-redundant : 19361
% 7.77/1.60 % ...aggressively subsumed : 0
% 7.77/1.60 % Contextual simplify-reflections : 0
% 7.77/1.60 % Paramodulations : 20736
% 7.77/1.60 % Factorizations : 0
% 7.77/1.60 % NegExts : 0
% 7.77/1.60 % Equation resolutions : 0
% 7.77/1.60 % Disequality decompositions : 0
% 7.77/1.60 % Total rewrite steps : 43188
% 7.77/1.60 % ...of those cached : 38755
% 7.77/1.60 % Propositional unsat checks : 0
% 7.77/1.60 % Propositional check models : 0
% 7.77/1.60 % Propositional check unsatisfiable : 0
% 7.77/1.60 % Propositional clauses : 0
% 7.77/1.60 % Propositional clauses after purity: 0
% 7.77/1.60 % Propositional unsat core size : 0
% 7.77/1.60 % Propositional preprocessing time : 0.000
% 7.77/1.60 % Propositional encoding time : 0.000
% 7.77/1.60 % Propositional solver time : 0.000
% 7.77/1.60 % Success case prop preproc time : 0.000
% 7.77/1.60 % Success case prop encoding time : 0.000
% 7.77/1.60 % Success case prop solver time : 0.000
% 7.77/1.60 % Current number of processed clauses : 15
% 7.77/1.60 % Positive orientable unit clauses : 12
% 7.77/1.60 % Positive unorientable unit clauses: 3
% 7.77/1.60 % Negative unit clauses : 0
% 7.77/1.60 % Non-unit-clauses : 0
% 7.77/1.60 % Current number of unprocessed clauses: 10283
% 7.77/1.60 % ...number of literals in the above : 10283
% 7.77/1.60 % Current number of archived formulas : 0
% 7.77/1.60 % Current number of archived clauses : 69
% 7.77/1.60 % Clause-clause subsumption calls (NU) : 0
% 7.77/1.60 % Rec. Clause-clause subsumption calls : 0
% 7.77/1.60 % Non-unit clause-clause subsumptions : 0
% 7.77/1.60 % Unit Clause-clause subsumption calls : 331
% 7.77/1.60 % Rewrite failures with RHS unbound : 868
% 7.77/1.60 % BW rewrite match attempts : 1352
% 7.77/1.60 % BW rewrite match successes : 166
% 7.77/1.60 % Condensation attempts : 0
% 7.77/1.60 % Condensation successes : 0
% 7.77/1.60 % Termbank termtop insertions : 1008395
% 7.77/1.60 % Search garbage collected termcells : 8
% 7.77/1.60
% 7.77/1.60 % -------------------------------------------------
% 7.77/1.60 % User time : 0.903 s
% 7.77/1.60 % System time : 0.057 s
% 7.77/1.60 % Total time : 0.960 s
% 7.77/1.60 % Maximum resident set size: 3636 pages
% 7.77/1.60
% 7.77/1.60 % -------------------------------------------------
% 7.77/1.60 % User time : 4.660 s
% 7.77/1.60 % System time : 0.235 s
% 7.77/1.60 % Total time : 4.896 s
% 7.77/1.60 % Maximum resident set size: 4864 pages
% 7.77/1.60 % E exiting
%------------------------------------------------------------------------------