%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP505-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:39:58 PM UTC 2026
% Result : Unsatisfiable 157.90s 30.33s
% Output : CNFRefutation 157.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 4 RR)
% Number of literals : 36 ( 35 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 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 : 151 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(multiply(X5,inverse(X6)),inverse(X4))))))),X6) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c_0_2,axiom,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(multiply(X5,inverse(X6)),inverse(X4))))))),X6) = X5,
single_axiom ).
cnf(c_0_3,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(X5,inverse(X4))))))),X6) = inverse(multiply(inverse(multiply(inverse(multiply(X7,X8)),multiply(X8,X7))),multiply(inverse(multiply(X9,X10)),multiply(X9,inverse(multiply(multiply(X5,inverse(inverse(X6))),inverse(X10))))))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(X5,inverse(X4))))))),X6),inverse(X6)) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(X5,inverse(X4))))))),X6),X7),inverse(X7)) = multiply(X5,inverse(inverse(X6))),
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_6,plain,
multiply(multiply(X1,X2),inverse(X2)) = multiply(multiply(X1,inverse(X3)),inverse(inverse(X3))),
inference(spm,[status(thm)],[c_0_5,c_0_2]) ).
cnf(c_0_7,plain,
multiply(multiply(X1,X2),inverse(X2)) = multiply(multiply(X1,X3),inverse(X3)),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,inverse(X4))),multiply(X3,inverse(multiply(multiply(X5,X6),inverse(X6))))))),X4) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_9,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(multiply(X3,multiply(multiply(X4,X5),inverse(X5))),inverse(X6))),multiply(multiply(X3,X7),inverse(X7))))),X6) = X4,
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_10,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(multiply(X5,X6),inverse(X6))))))),X7),inverse(X7)) = multiply(X5,X4),
inference(spm,[status(thm)],[c_0_4,c_0_7]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(X3),X3))),multiply(multiply(X4,X5),inverse(X5))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_4]),c_0_4]) ).
cnf(c_0_12,plain,
multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X2)))) = multiply(X3,inverse(multiply(multiply(X3,X4),inverse(X4)))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
multiply(multiply(multiply(X1,X2),inverse(X2)),inverse(inverse(X3))) = multiply(multiply(multiply(X1,X3),X4),inverse(X4)),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_14,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1)))),multiply(inverse(X3),X3))),multiply(multiply(X4,X5),inverse(X5))) = X4,
inference(spm,[status(thm)],[c_0_11,c_0_11]) ).
cnf(c_0_15,plain,
multiply(multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X2)))),inverse(inverse(X3))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_12]),c_0_4]) ).
cnf(c_0_16,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,a1)),multiply(a1,a1))),multiply(inverse(multiply(a1,a1)),multiply(a1,inverse(multiply(X3,inverse(a1))))))),multiply(inverse(multiply(inverse(multiply(X4,X5)),multiply(X5,X4))),inverse(multiply(X6,inverse(multiply(inverse(multiply(X7,X8)),multiply(X7,inverse(multiply(X3,inverse(X8)))))))))))),X9) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,a1)),multiply(a1,a1))),multiply(inverse(multiply(a1,a1)),multiply(a1,inverse(multiply(X6,inverse(a1))))))),X9),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_3]),c_0_3]),c_0_3]) ).
cnf(c_0_17,plain,
multiply(multiply(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1)))),multiply(inverse(X3),X3))),X4),X5),inverse(X5)) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
multiply(X1,multiply(inverse(multiply(X2,X3)),multiply(X2,inverse(multiply(X4,inverse(X3)))))) = multiply(X1,multiply(inverse(multiply(a1,a1)),multiply(a1,inverse(multiply(X4,inverse(a1)))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_16]),c_0_4]) ).
cnf(c_0_19,plain,
multiply(multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X2)))),inverse(multiply(X3,inverse(inverse(inverse(X3)))))) = multiply(X4,inverse(multiply(multiply(X4,X5),inverse(X5)))),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_20,plain,
multiply(X1,inverse(inverse(inverse(X1)))) = multiply(X2,inverse(inverse(inverse(X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_15]),c_0_4]) ).
cnf(c_0_21,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(a1,a1)),multiply(a1,inverse(multiply(X3,inverse(a1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_17]) ).
cnf(c_0_22,plain,
multiply(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1)))),multiply(inverse(X3),X3))),X4),inverse(X4)) = multiply(a1,inverse(multiply(multiply(a1,a1),inverse(a1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_19]) ).
cnf(c_0_23,plain,
multiply(X1,inverse(inverse(inverse(X1)))) = inverse(multiply(X2,inverse(multiply(multiply(X2,X3),inverse(X3))))),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_24,plain,
multiply(inverse(multiply(multiply(X1,multiply(X2,inverse(X3))),X3)),multiply(multiply(X1,X4),inverse(X4))) = multiply(inverse(multiply(a1,a1)),multiply(a1,inverse(multiply(X2,inverse(a1))))),
inference(spm,[status(thm)],[c_0_21,c_0_7]) ).
cnf(c_0_25,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(multiply(X3,multiply(X4,inverse(X5))),X5)),multiply(multiply(X3,X6),inverse(X6))))),X7),inverse(X7)) = X4,
inference(spm,[status(thm)],[c_0_4,c_0_7]) ).
cnf(c_0_26,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1)))),multiply(inverse(X3),X3))),multiply(a1,inverse(inverse(inverse(a1))))) = multiply(a1,inverse(multiply(multiply(a1,a1),inverse(a1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_22]),c_0_19]),c_0_23]) ).
cnf(c_0_27,plain,
multiply(inverse(multiply(multiply(X1,multiply(multiply(X2,X3),inverse(X3))),X4)),multiply(multiply(X1,X5),inverse(X5))) = multiply(inverse(multiply(a1,a1)),multiply(a1,inverse(multiply(multiply(X2,X4),inverse(a1))))),
inference(spm,[status(thm)],[c_0_24,c_0_7]) ).
cnf(c_0_28,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(a1),multiply(a1,inverse(multiply(multiply(a1,a1),inverse(a1))))))),X3),inverse(X3)) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_15]),c_0_22]) ).
cnf(c_0_29,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(X4,X5)),multiply(X4,inverse(multiply(X3,inverse(X5))))),
inference(spm,[status(thm)],[c_0_21,c_0_21]) ).
cnf(c_0_30,plain,
multiply(inverse(multiply(a1,a1)),multiply(a1,inverse(multiply(multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X2)))),inverse(a1))))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
cnf(c_0_31,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(fof_simplification,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_0_32,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(multiply(X3,inverse(multiply(multiply(X3,X4),inverse(X4)))),inverse(X2))))) = multiply(inverse(a1),a1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
c_0_31 ).
cnf(c_0_34,plain,
multiply(inverse(X1),X1) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_4]),c_0_15]),c_0_4]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_33,c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP505-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.43 % Computer : n004.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Sun Sep 20 20:14:57 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/5.51 Running first-order theorem proving
% 0.21/5.51 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
% 157.90/30.33 % Version: 3.5.1
% 157.90/30.33 % Preprocessing class: FSSSSMSSSSSNFFN.
% 157.90/30.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 157.90/30.33 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 157.90/30.33 % Starting new_bool_3 with 300s (1) cores
% 157.90/30.33 % Starting new_bool_1 with 300s (1) cores
% 157.90/30.33 % Starting sh5l with 300s (1) cores
% 157.90/30.33 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1395014 completed with status 0
% 157.90/30.33 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 157.90/30.33 % Preprocessing class: FSSSSMSSSSSNFFN.
% 157.90/30.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 157.90/30.33 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 157.90/30.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 157.90/30.33 % No SInE strategy applied
% 157.90/30.33 % Search class: FUUPF-FFSF21-DFFFFFNN
% 157.90/30.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 157.90/30.33 % Starting SubtermCWHack with 136s (1) cores
% 157.90/30.33 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 157.90/30.33 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 157.90/30.33 % Starting new_bool_3 with 136s (1) cores
% 157.90/30.33 % Starting new_bool_1 with 136s (1) cores
% 157.90/30.33 % U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 1395020 completed with status 0
% 157.90/30.33 % Result found by U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 157.90/30.33 % Preprocessing class: FSSSSMSSSSSNFFN.
% 157.90/30.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 157.90/30.33 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 157.90/30.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 157.90/30.33 % No SInE strategy applied
% 157.90/30.33 % Search class: FUUPF-FFSF21-DFFFFFNN
% 157.90/30.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 157.90/30.33 % Starting SubtermCWHack with 136s (1) cores
% 157.90/30.33 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 157.90/30.33 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 157.90/30.33 % Preprocessing time : 0.002 s
% 157.90/30.33 % Presaturation interreduction done
% 157.90/30.33
% 157.90/30.33 % Proof found!
% 157.90/30.33 % SZS status Unsatisfiable
% 157.90/30.33 % SZS output start CNFRefutation
% See solution above
% 157.90/30.33 % Parsed axioms : 2
% 157.90/30.33 % Removed by relevancy pruning/SinE : 0
% 157.90/30.33 % Initial clauses : 2
% 157.90/30.33 % Removed in clause preprocessing : 0
% 157.90/30.33 % Initial clauses in saturation : 2
% 157.90/30.33 % Processed clauses : 3465
% 157.90/30.33 % ...of these trivial : 316
% 157.90/30.33 % ...subsumed : 2950
% 157.90/30.33 % ...remaining for further processing : 199
% 157.90/30.33 % Other redundant clauses eliminated : 0
% 157.90/30.33 % Clauses deleted for lack of memory : 0
% 157.90/30.33 % Backward-subsumed : 15
% 157.90/30.33 % Backward-rewritten : 50
% 157.90/30.33 % Generated clauses : 237135
% 157.90/30.33 % ...of the previous two non-redundant : 226446
% 157.90/30.33 % ...aggressively subsumed : 0
% 157.90/30.33 % Contextual simplify-reflections : 0
% 157.90/30.33 % Paramodulations : 237134
% 157.90/30.33 % Factorizations : 0
% 157.90/30.33 % NegExts : 0
% 157.90/30.33 % Equation resolutions : 0
% 157.90/30.33 % Disequality decompositions : 0
% 157.90/30.33 % Total rewrite steps : 59909
% 157.90/30.33 % ...of those cached : 45969
% 157.90/30.33 % Propositional unsat checks : 0
% 157.90/30.33 % Propositional check models : 0
% 157.90/30.33 % Propositional check unsatisfiable : 0
% 157.90/30.33 % Propositional clauses : 0
% 157.90/30.33 % Propositional clauses after purity: 0
% 157.90/30.33 % Propositional unsat core size : 0
% 157.90/30.33 % Propositional preprocessing time : 0.000
% 157.90/30.33 % Propositional encoding time : 0.000
% 157.90/30.33 % Propositional solver time : 0.000
% 157.90/30.33 % Success case prop preproc time : 0.000
% 157.90/30.33 % Success case prop encoding time : 0.000
% 157.90/30.33 % Success case prop solver time : 0.000
% 157.90/30.33 % Current number of processed clauses : 131
% 157.90/30.33 % Positive orientable unit clauses : 88
% 157.90/30.33 % Positive unorientable unit clauses: 43
% 157.90/30.33 % Negative unit clauses : 0
% 157.90/30.33 % Non-unit-clauses : 0
% 157.90/30.33 % Current number of unprocessed clauses: 222196
% 157.90/30.33 % ...number of literals in the above : 222196
% 157.90/30.33 % Current number of archived formulas : 0
% 157.90/30.33 % Current number of archived clauses : 68
% 157.90/30.33 % Clause-clause subsumption calls (NU) : 0
% 157.90/30.33 % Rec. Clause-clause subsumption calls : 0
% 157.90/30.33 % Non-unit clause-clause subsumptions : 0
% 157.90/30.33 % Unit Clause-clause subsumption calls : 1755
% 157.90/30.33 % Rewrite failures with RHS unbound : 0
% 157.90/30.33 % BW rewrite match attempts : 7625
% 157.90/30.33 % BW rewrite match successes : 487
% 157.90/30.33 % Condensation attempts : 0
% 157.90/30.33 % Condensation successes : 0
% 157.90/30.33 % Termbank termtop insertions : 20099472
% 157.90/30.33 % Search garbage collected termcells : 2
% 157.90/30.33
% 157.90/30.33 % -------------------------------------------------
% 157.90/30.33 % User time : 18.245 s
% 157.90/30.33 % System time : 0.513 s
% 157.90/30.33 % Total time : 18.758 s
% 157.90/30.33 % Maximum resident set size: 3636 pages
% 157.90/30.33
% 157.90/30.33 % -------------------------------------------------
% 157.90/30.33 % User time : 106.317 s
% 157.90/30.33 % System time : 3.096 s
% 157.90/30.33 % Total time : 109.413 s
% 157.90/30.33 % Maximum resident set size: 4608 pages
% 157.90/30.33 % E exiting
%------------------------------------------------------------------------------