%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP432-1 : 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 : n015.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 0.40s 0.48s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 2
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 4 RR)
% Number of literals : 41 ( 40 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 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 : 128 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X2))),X1)))) = X4,
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,
multiply(X1,inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X2))),X1)))) = X4,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X4))),multiply(X5,inverse(X5))),multiply(X3,X1)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(X3,inverse(X3))),multiply(X4,X1)))) = multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X2,X4))),multiply(X6,inverse(X6))),
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,inverse(multiply(multiply(X4,multiply(X5,inverse(X5))),multiply(X2,X3))))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_6,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))) = multiply(multiply(X4,inverse(X4)),inverse(multiply(X2,X3))),
inference(spm,[status(thm)],[c_0_5,c_0_3]) ).
cnf(c_0_7,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_6]),c_0_2]) ).
cnf(c_0_8,plain,
multiply(X1,inverse(multiply(inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X2))),X5))),multiply(multiply(multiply(X6,inverse(X6)),inverse(X4)),X1)))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_9,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(multiply(X3,inverse(X3)),X1)))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_10,plain,
multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X3,inverse(X3)),X1))),X4)) = X4,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
multiply(multiply(X1,inverse(multiply(multiply(X2,multiply(X3,inverse(X3))),multiply(multiply(X4,inverse(X4)),X1)))),multiply(X2,X5)) = X5,
inference(spm,[status(thm)],[c_0_10,c_0_5]) ).
cnf(c_0_12,plain,
multiply(inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),multiply(multiply(X4,inverse(X4)),inverse(multiply(X5,X6)))))),inverse(multiply(X6,X3))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_13,plain,
multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(multiply(X2,inverse(X2)),X3))),multiply(X3,X4)) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_10]),c_0_9]) ).
cnf(c_0_14,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(multiply(X3,multiply(X4,inverse(X4))),multiply(X1,X2)))))),inverse(multiply(inverse(X5),X3))) = X5,
inference(spm,[status(thm)],[c_0_12,c_0_4]) ).
cnf(c_0_15,plain,
multiply(inverse(multiply(X1,inverse(X1))),multiply(multiply(X2,inverse(X2)),X3)) = X3,
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_16,plain,
multiply(X1,inverse(multiply(multiply(X2,inverse(multiply(multiply(X3,multiply(X4,inverse(X4))),multiply(X5,X2)))),multiply(X3,X1)))) = X5,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_17,plain,
multiply(multiply(multiply(X1,inverse(X1)),inverse(X2)),X3) = inverse(multiply(inverse(X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_5]) ).
cnf(c_0_18,plain,
multiply(multiply(X1,inverse(X1)),multiply(inverse(multiply(X2,inverse(X2))),X3)) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_15]),c_0_15]) ).
cnf(c_0_19,plain,
multiply(X1,inverse(multiply(inverse(multiply(multiply(X2,inverse(multiply(multiply(X3,multiply(X4,inverse(X4))),multiply(X5,X2)))),multiply(X3,X6))),inverse(multiply(inverse(X1),X5))))) = X6,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_16]),c_0_17]) ).
cnf(c_0_20,plain,
multiply(inverse(multiply(multiply(X1,inverse(multiply(multiply(X2,multiply(X3,inverse(X3))),multiply(X4,X1)))),multiply(X2,multiply(multiply(X5,inverse(X5)),inverse(multiply(X6,X7)))))),inverse(multiply(X7,X4))) = X6,
inference(spm,[status(thm)],[c_0_2,c_0_16]) ).
cnf(c_0_21,plain,
multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),inverse(multiply(inverse(X3),X2))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_18]) ).
cnf(c_0_22,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X3)))) = multiply(X3,inverse(X2)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
multiply(inverse(multiply(X1,inverse(X1))),inverse(inverse(X2))) = X2,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_25,plain,
multiply(inverse(multiply(X1,inverse(X1))),inverse(multiply(inverse(X2),multiply(X3,inverse(X3))))) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_26,plain,
multiply(inverse(inverse(inverse(X1))),X2) = inverse(multiply(inverse(X2),X1)),
inference(rw,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_27,plain,
multiply(inverse(multiply(X1,inverse(X1))),X2) = inverse(inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).
cnf(c_0_28,plain,
multiply(X1,inverse(X1)) = inverse(inverse(inverse(multiply(X2,inverse(X2))))),
inference(spm,[status(thm)],[c_0_7,c_0_24]) ).
cnf(c_0_29,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_30,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(multiply(X3,inverse(X3)),X1))) = X2,
inference(rw,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_31,plain,
multiply(X1,inverse(X1)) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]),c_0_29]) ).
cnf(c_0_32,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_24]),c_0_27]),c_0_29]) ).
cnf(c_0_33,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_34,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_24]),c_0_32]) ).
cnf(c_0_35,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(fof_simplification,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_0_36,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_33]),c_0_17]),c_0_34]),c_0_33]),c_0_34]) ).
cnf(c_0_37,plain,
multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X2,X3))) = 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_12,c_0_7]),c_0_24]),c_0_32]),c_0_33]),c_0_34]),c_0_32]) ).
cnf(c_0_38,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
c_0_35 ).
cnf(c_0_39,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_32]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP432-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 20 20:15:52 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.40/0.48 % Version: 3.5.1
% 0.40/0.48 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.40/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.40/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.40/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.40/0.48 % Starting sh5l with 300s (1) cores
% 0.40/0.48 % new_bool_3 with pid 3834137 completed with status 9
% 0.40/0.48 % new_bool_1 with pid 3834138 completed with status 9
% 0.40/0.48 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3834136 completed with status 0
% 0.40/0.48 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.40/0.48 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.40/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.40/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.40/0.48 % No SInE strategy applied
% 0.40/0.48 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.40/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.40/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.40/0.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.40/0.48 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.40/0.48 % Starting new_bool_3 with 136s (1) cores
% 0.40/0.48 % Starting new_bool_1 with 136s (1) cores
% 0.40/0.48 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3834141 completed with status 0
% 0.40/0.48 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.40/0.48 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.40/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.40/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.40/0.48 % No SInE strategy applied
% 0.40/0.48 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.40/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.40/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.40/0.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.40/0.48 % Preprocessing time : 0.001 s
% 0.40/0.48
% 0.40/0.48 % Proof found!
% 0.40/0.48 % SZS status Unsatisfiable
% 0.40/0.48 % SZS output start CNFRefutation
% See solution above
% 0.40/0.48 % Parsed axioms : 2
% 0.40/0.48 % Removed by relevancy pruning/SinE : 0
% 0.40/0.48 % Initial clauses : 2
% 0.40/0.48 % Removed in clause preprocessing : 0
% 0.40/0.48 % Initial clauses in saturation : 2
% 0.40/0.48 % Processed clauses : 142
% 0.40/0.48 % ...of these trivial : 11
% 0.40/0.48 % ...subsumed : 70
% 0.40/0.48 % ...remaining for further processing : 61
% 0.40/0.48 % Other redundant clauses eliminated : 0
% 0.40/0.48 % Clauses deleted for lack of memory : 0
% 0.40/0.48 % Backward-subsumed : 2
% 0.40/0.48 % Backward-rewritten : 44
% 0.40/0.48 % Generated clauses : 4605
% 0.40/0.48 % ...of the previous two non-redundant : 4206
% 0.40/0.48 % ...aggressively subsumed : 0
% 0.40/0.48 % Contextual simplify-reflections : 0
% 0.40/0.48 % Paramodulations : 4605
% 0.40/0.48 % Factorizations : 0
% 0.40/0.48 % NegExts : 0
% 0.40/0.48 % Equation resolutions : 0
% 0.40/0.48 % Disequality decompositions : 0
% 0.40/0.48 % Total rewrite steps : 2752
% 0.40/0.48 % ...of those cached : 1470
% 0.40/0.48 % Propositional unsat checks : 0
% 0.40/0.48 % Propositional check models : 0
% 0.40/0.48 % Propositional check unsatisfiable : 0
% 0.40/0.48 % Propositional clauses : 0
% 0.40/0.48 % Propositional clauses after purity: 0
% 0.40/0.48 % Propositional unsat core size : 0
% 0.40/0.48 % Propositional preprocessing time : 0.000
% 0.40/0.48 % Propositional encoding time : 0.000
% 0.40/0.48 % Propositional solver time : 0.000
% 0.40/0.48 % Success case prop preproc time : 0.000
% 0.40/0.48 % Success case prop encoding time : 0.000
% 0.40/0.48 % Success case prop solver time : 0.000
% 0.40/0.48 % Current number of processed clauses : 15
% 0.40/0.48 % Positive orientable unit clauses : 13
% 0.40/0.48 % Positive unorientable unit clauses: 2
% 0.40/0.48 % Negative unit clauses : 0
% 0.40/0.48 % Non-unit-clauses : 0
% 0.40/0.48 % Current number of unprocessed clauses: 3889
% 0.40/0.48 % ...number of literals in the above : 3889
% 0.40/0.48 % Current number of archived formulas : 0
% 0.40/0.48 % Current number of archived clauses : 46
% 0.40/0.48 % Clause-clause subsumption calls (NU) : 0
% 0.40/0.48 % Rec. Clause-clause subsumption calls : 0
% 0.40/0.48 % Non-unit clause-clause subsumptions : 0
% 0.40/0.48 % Unit Clause-clause subsumption calls : 90
% 0.40/0.48 % Rewrite failures with RHS unbound : 0
% 0.40/0.48 % BW rewrite match attempts : 386
% 0.40/0.48 % BW rewrite match successes : 95
% 0.40/0.48 % Condensation attempts : 0
% 0.40/0.48 % Condensation successes : 0
% 0.40/0.48 % Termbank termtop insertions : 94668
% 0.40/0.48 % Search garbage collected termcells : 2
% 0.40/0.48
% 0.40/0.48 % -------------------------------------------------
% 0.40/0.48 % User time : 0.054 s
% 0.40/0.48 % System time : 0.007 s
% 0.40/0.48 % Total time : 0.060 s
% 0.40/0.48 % Maximum resident set size: 3636 pages
% 0.40/0.48
% 0.40/0.48 % -------------------------------------------------
% 0.40/0.48 % User time : 0.283 s
% 0.40/0.48 % System time : 0.063 s
% 0.40/0.48 % Total time : 0.345 s
% 0.40/0.48 % Maximum resident set size: 4608 pages
% 0.40/0.48 % E exiting
%------------------------------------------------------------------------------