%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP420-1 : 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 : n026.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 12:39:46 PM UTC 2026
% Result : Unsatisfiable 1.99s 0.89s
% Output : CNFRefutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 2
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 4 RR)
% Number of literals : 44 ( 43 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c_0_2,axiom,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3))) = X2,
single_axiom ).
cnf(c_0_3,plain,
inverse(multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X2),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),multiply(X4,X5)),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(inverse(multiply(a3,inverse(multiply(inverse(inverse(X1)),inverse(multiply(a3,inverse(multiply(inverse(a3),a3)))))))),multiply(a3,a3)) = X1,
inference(rw,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3)) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X2),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),multiply(X4,X5)),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_6,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3)) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3)) = multiply(inverse(multiply(X4,inverse(multiply(X2,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),multiply(X4,X5)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_3]),c_0_3]),c_0_6]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3)) = multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X6,inverse(multiply(inverse(X6),X6)))))))),inverse(multiply(X2,inverse(multiply(multiply(X4,X6),inverse(multiply(inverse(multiply(X4,X6)),multiply(X4,X6))))))))),X5),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
inverse(multiply(inverse(multiply(X1,multiply(inverse(multiply(a3,inverse(multiply(inverse(X2),inverse(multiply(a3,inverse(multiply(inverse(a3),a3)))))))),multiply(a3,a3)))),multiply(X1,X3))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),inverse(multiply(X2,inverse(multiply(multiply(X4,X5),inverse(multiply(inverse(multiply(X4,X5)),multiply(X4,X5)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_8]),c_0_6]),c_0_3]) ).
cnf(c_0_10,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_9]),c_0_6]),c_0_6]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)) = multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_10]),c_0_6]) ).
cnf(c_0_12,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),multiply(X1,X3)) = multiply(inverse(X4),multiply(inverse(inverse(multiply(inverse(multiply(X5,inverse(X4))),multiply(X5,X2)))),X3)),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_13,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))) = multiply(inverse(X3),X3),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_14,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10]) ).
cnf(c_0_15,plain,
multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X2),inverse(multiply(inverse(a3),a3))))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_14]),c_0_14]) ).
cnf(c_0_16,plain,
multiply(inverse(X1),X1) = inverse(multiply(inverse(a3),a3)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,X3)) = multiply(X3,inverse(multiply(inverse(X3),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_14]),c_0_6]) ).
cnf(c_0_18,plain,
multiply(inverse(X1),X1) = inverse(multiply(inverse(X2),X2)),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_19,plain,
multiply(inverse(multiply(X1,multiply(inverse(a3),a3))),multiply(X1,X2)) = multiply(X2,multiply(inverse(a3),a3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
cnf(c_0_20,plain,
multiply(multiply(inverse(X1),X1),multiply(inverse(a3),a3)) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_16]),c_0_16]) ).
cnf(c_0_21,plain,
multiply(inverse(multiply(X1,multiply(inverse(X2),X2))),multiply(X1,X3)) = multiply(X3,multiply(inverse(X2),X2)),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_22,plain,
multiply(multiply(inverse(X1),X1),multiply(inverse(X2),X2)) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_23,plain,
multiply(inverse(multiply(inverse(X1),multiply(inverse(a3),a3))),multiply(inverse(X2),X2)) = multiply(multiply(inverse(a3),a3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_15]),c_0_18]),c_0_18]),c_0_22]),c_0_18]),c_0_18]) ).
cnf(c_0_24,plain,
multiply(multiply(inverse(a3),a3),inverse(multiply(inverse(X1),multiply(inverse(a3),a3)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_18]),c_0_18]),c_0_14]),c_0_18]) ).
cnf(c_0_25,plain,
multiply(multiply(inverse(a3),a3),X1) = multiply(X1,multiply(inverse(a3),a3)),
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_26,plain,
multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(X2),multiply(inverse(X1),X1)))) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_27,plain,
multiply(multiply(inverse(a3),a3),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_25]),c_0_26]) ).
cnf(c_0_28,plain,
multiply(X1,multiply(inverse(a3),a3)) = X1,
inference(rw,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_29,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_30,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_28]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_28]),c_0_27]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_27]),c_0_18]),c_0_27]),c_0_27]) ).
cnf(c_0_32,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_29]),c_0_30]),c_0_18]),c_0_28]),c_0_30]),c_0_29]) ).
cnf(c_0_33,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_31]),c_0_31]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_35,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_36,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_37,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
multiply(multiply(multiply(X1,inverse(X2)),multiply(X2,X3)),inverse(X3)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_30]),c_0_18]),c_0_28]),c_0_37]) ).
cnf(c_0_39,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(fof_simplification,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_0_40,plain,
multiply(multiply(X1,inverse(X2)),multiply(X2,X3)) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_38]),c_0_30]) ).
cnf(c_0_41,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
c_0_39 ).
cnf(c_0_42,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_33]),c_0_30]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP420-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:15:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 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
% 1.99/0.89 % Version: 3.5.1
% 1.99/0.89 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.99/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.99/0.89 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.99/0.89 % Starting new_bool_3 with 300s (1) cores
% 1.99/0.89 % Starting new_bool_1 with 300s (1) cores
% 1.99/0.89 % Starting sh5l with 300s (1) cores
% 1.99/0.89 % new_bool_1 with pid 505057 completed with status 9
% 1.99/0.89 % new_bool_3 with pid 505056 completed with status 9
% 1.99/0.89 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 505051 completed with status 0
% 1.99/0.89 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 1.99/0.89 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.99/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.99/0.89 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.99/0.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.99/0.89 % No SInE strategy applied
% 1.99/0.89 % Search class: FUUPF-FFSF21-DFFFFFNN
% 1.99/0.89 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.99/0.89 % Starting SubtermCWHack with 136s (1) cores
% 1.99/0.89 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 1.99/0.89 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.99/0.89 % Starting new_bool_3 with 136s (1) cores
% 1.99/0.89 % Starting new_bool_1 with 136s (1) cores
% 1.99/0.89 % U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 505054 completed with status 0
% 1.99/0.89 % Result found by U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 1.99/0.89 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.99/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.99/0.89 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.99/0.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.99/0.89 % No SInE strategy applied
% 1.99/0.89 % Search class: FUUPF-FFSF21-DFFFFFNN
% 1.99/0.89 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.99/0.89 % Starting SubtermCWHack with 136s (1) cores
% 1.99/0.89 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 1.99/0.89 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.99/0.89 % Preprocessing time : 0.002 s
% 1.99/0.89 % Presaturation interreduction done
% 1.99/0.89
% 1.99/0.89 % Proof found!
% 1.99/0.89 % SZS status Unsatisfiable
% 1.99/0.89 % SZS output start CNFRefutation
% See solution above
% 1.99/0.89 % Parsed axioms : 2
% 1.99/0.89 % Removed by relevancy pruning/SinE : 0
% 1.99/0.89 % Initial clauses : 2
% 1.99/0.89 % Removed in clause preprocessing : 0
% 1.99/0.89 % Initial clauses in saturation : 2
% 1.99/0.89 % Processed clauses : 335
% 1.99/0.89 % ...of these trivial : 77
% 1.99/0.89 % ...subsumed : 162
% 1.99/0.89 % ...remaining for further processing : 96
% 1.99/0.89 % Other redundant clauses eliminated : 0
% 1.99/0.89 % Clauses deleted for lack of memory : 0
% 1.99/0.89 % Backward-subsumed : 2
% 1.99/0.89 % Backward-rewritten : 75
% 1.99/0.89 % Generated clauses : 7550
% 1.99/0.89 % ...of the previous two non-redundant : 6773
% 1.99/0.89 % ...aggressively subsumed : 0
% 1.99/0.89 % Contextual simplify-reflections : 0
% 1.99/0.89 % Paramodulations : 7550
% 1.99/0.89 % Factorizations : 0
% 1.99/0.89 % NegExts : 0
% 1.99/0.89 % Equation resolutions : 0
% 1.99/0.89 % Disequality decompositions : 0
% 1.99/0.89 % Total rewrite steps : 20981
% 1.99/0.89 % ...of those cached : 19571
% 1.99/0.89 % Propositional unsat checks : 0
% 1.99/0.89 % Propositional check models : 0
% 1.99/0.89 % Propositional check unsatisfiable : 0
% 1.99/0.89 % Propositional clauses : 0
% 1.99/0.89 % Propositional clauses after purity: 0
% 1.99/0.89 % Propositional unsat core size : 0
% 1.99/0.89 % Propositional preprocessing time : 0.000
% 1.99/0.89 % Propositional encoding time : 0.000
% 1.99/0.89 % Propositional solver time : 0.000
% 1.99/0.89 % Success case prop preproc time : 0.000
% 1.99/0.89 % Success case prop encoding time : 0.000
% 1.99/0.89 % Success case prop solver time : 0.000
% 1.99/0.89 % Current number of processed clauses : 17
% 1.99/0.89 % Positive orientable unit clauses : 15
% 1.99/0.89 % Positive unorientable unit clauses: 2
% 1.99/0.89 % Negative unit clauses : 0
% 1.99/0.89 % Non-unit-clauses : 0
% 1.99/0.89 % Current number of unprocessed clauses: 2407
% 1.99/0.89 % ...number of literals in the above : 2407
% 1.99/0.89 % Current number of archived formulas : 0
% 1.99/0.89 % Current number of archived clauses : 79
% 1.99/0.89 % Clause-clause subsumption calls (NU) : 0
% 1.99/0.89 % Rec. Clause-clause subsumption calls : 0
% 1.99/0.89 % Non-unit clause-clause subsumptions : 0
% 1.99/0.89 % Unit Clause-clause subsumption calls : 133
% 1.99/0.89 % Rewrite failures with RHS unbound : 0
% 1.99/0.89 % BW rewrite match attempts : 628
% 1.99/0.89 % BW rewrite match successes : 142
% 1.99/0.89 % Condensation attempts : 0
% 1.99/0.89 % Condensation successes : 0
% 1.99/0.89 % Termbank termtop insertions : 426902
% 1.99/0.89 % Search garbage collected termcells : 2
% 1.99/0.89
% 1.99/0.89 % -------------------------------------------------
% 1.99/0.89 % User time : 0.325 s
% 1.99/0.89 % System time : 0.022 s
% 1.99/0.89 % Total time : 0.347 s
% 1.99/0.89 % Maximum resident set size: 3640 pages
% 1.99/0.89
% 1.99/0.89 % -------------------------------------------------
% 1.99/0.89 % User time : 1.784 s
% 1.99/0.89 % System time : 0.143 s
% 1.99/0.89 % Total time : 1.927 s
% 1.99/0.89 % Maximum resident set size: 4608 pages
% 1.99/0.89 % E exiting
%------------------------------------------------------------------------------