%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP441-1 : 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 : n007.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 12:43:48 PM UTC 2026
% Result : Unsatisfiable 2.39s 0.84s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 4 RR)
% Number of literals : 43 ( 42 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 130 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3))))))) = X4,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c_0_2,axiom,
inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3))))))) = X4,
single_axiom ).
cnf(c_0_3,plain,
inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(inverse(X3),X4),inverse(multiply(X5,multiply(X6,X4))))),X5)),X6)))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(X3,X4),inverse(multiply(X5,multiply(X6,X4))))),X5)),X6)))) = multiply(X7,multiply(X8,multiply(multiply(inverse(X8),X9),inverse(multiply(X3,multiply(X7,X9)))))),
inference(spm,[status(thm)],[c_0_4,c_0_2]) ).
cnf(c_0_6,plain,
multiply(a3,multiply(a3,multiply(multiply(inverse(a3),a3),inverse(multiply(inverse(X1),multiply(a3,a3)))))) = X1,
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3)))))) = multiply(X5,multiply(X6,multiply(multiply(inverse(X6),X7),inverse(multiply(X4,multiply(X5,X7)))))),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_8,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(inverse(X4),multiply(X1,X3)))))) = X4,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
inverse(multiply(X1,multiply(X2,multiply(X3,inverse(multiply(X4,multiply(X1,multiply(X5,multiply(multiply(inverse(X5),X6),inverse(multiply(inverse(X3),multiply(inverse(X2),X6)))))))))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_8]) ).
cnf(c_0_10,plain,
inverse(multiply(inverse(X1),multiply(X1,multiply(X2,inverse(multiply(X3,X2)))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_7]),c_0_8]) ).
cnf(c_0_11,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,inverse(multiply(X4,X3)))),X4))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_10]),c_0_8]) ).
cnf(c_0_12,plain,
inverse(multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(X3,X1)))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_11]),c_0_11]) ).
cnf(c_0_13,plain,
multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X3),X1))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_11]),c_0_11]) ).
cnf(c_0_14,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(X3,multiply(inverse(X3),inverse(multiply(X4,X5)))),X4)),X5))) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
multiply(multiply(X1,multiply(X2,inverse(multiply(X3,X2)))),multiply(X4,multiply(inverse(X4),X3))) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_16,plain,
multiply(X1,multiply(X2,multiply(inverse(X2),multiply(multiply(X3,multiply(inverse(X3),inverse(X4))),X4)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_14]),c_0_14]) ).
cnf(c_0_17,plain,
multiply(X1,multiply(X2,inverse(multiply(multiply(multiply(X3,multiply(inverse(X3),inverse(X4))),X4),X2)))) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
inverse(multiply(inverse(X1),X1)) = multiply(multiply(X2,multiply(inverse(X2),inverse(X3))),X3),
inference(spm,[status(thm)],[c_0_2,c_0_17]) ).
cnf(c_0_19,plain,
inverse(multiply(multiply(X1,multiply(inverse(X1),inverse(multiply(X2,X3)))),multiply(X4,multiply(inverse(X4),X2)))) = X3,
inference(spm,[status(thm)],[c_0_12,c_0_12]) ).
cnf(c_0_20,plain,
multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X3),X3))))) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_21,plain,
inverse(inverse(multiply(inverse(X1),X1))) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_22,plain,
multiply(X1,multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(a3),a3))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_23,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_21,c_0_21]) ).
cnf(c_0_24,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
multiply(X1,inverse(multiply(inverse(X2),X1))) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_24]) ).
cnf(c_0_26,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_25]),c_0_8]) ).
cnf(c_0_27,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_28,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),X3),inverse(multiply(X4,multiply(inverse(X5),X3))))),X4))) = X5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_7]),c_0_2]) ).
cnf(c_0_30,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_24]),c_0_20]) ).
cnf(c_0_32,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_33,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(spm,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X1),inverse(multiply(X3,inverse(X4))))),X3))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_11]),c_0_11]) ).
cnf(c_0_35,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_32]),c_0_30]) ).
cnf(c_0_37,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(fof_simplification,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_0_39,plain,
multiply(X1,multiply(X2,multiply(inverse(multiply(X1,X2)),X3))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_31]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
c_0_38 ).
cnf(c_0_41,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_30]),c_0_27]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP441-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n007.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 20:11:35 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.42 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
% 2.39/0.84 % Version: 3.5.1
% 2.39/0.84 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.39/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.39/0.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.39/0.84 % Starting new_bool_3 with 300s (1) cores
% 2.39/0.84 % Starting new_bool_1 with 300s (1) cores
% 2.39/0.84 % Starting sh5l with 300s (1) cores
% 2.39/0.84 % new_bool_3 with pid 3488053 completed with status 9
% 2.39/0.84 % new_bool_1 with pid 3488054 completed with status 9
% 2.39/0.84 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3488052 completed with status 0
% 2.39/0.84 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 2.39/0.84 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.39/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.39/0.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.39/0.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.39/0.84 % No SInE strategy applied
% 2.39/0.84 % Search class: FUUPF-FFSF21-DFFFFFNN
% 2.39/0.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.39/0.84 % Starting SubtermCWHack with 136s (1) cores
% 2.39/0.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.39/0.84 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.39/0.84 % Starting new_bool_3 with 136s (1) cores
% 2.39/0.84 % Starting new_bool_1 with 136s (1) cores
% 2.39/0.84 % U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3488060 completed with status 0
% 2.39/0.84 % Result found by U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 2.39/0.84 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.39/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.39/0.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.39/0.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.39/0.84 % No SInE strategy applied
% 2.39/0.84 % Search class: FUUPF-FFSF21-DFFFFFNN
% 2.39/0.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.39/0.84 % Starting SubtermCWHack with 136s (1) cores
% 2.39/0.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.39/0.84 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.39/0.84 % Preprocessing time : 0.001 s
% 2.39/0.84 % Presaturation interreduction done
% 2.39/0.84
% 2.39/0.84 % Proof found!
% 2.39/0.84 % SZS status Unsatisfiable
% 2.39/0.84 % SZS output start CNFRefutation
% See solution above
% 2.39/0.84 % Parsed axioms : 2
% 2.39/0.84 % Removed by relevancy pruning/SinE : 0
% 2.39/0.84 % Initial clauses : 2
% 2.39/0.84 % Removed in clause preprocessing : 0
% 2.39/0.84 % Initial clauses in saturation : 2
% 2.39/0.84 % Processed clauses : 300
% 2.39/0.84 % ...of these trivial : 138
% 2.39/0.84 % ...subsumed : 66
% 2.39/0.84 % ...remaining for further processing : 96
% 2.39/0.84 % Other redundant clauses eliminated : 0
% 2.39/0.84 % Clauses deleted for lack of memory : 0
% 2.39/0.84 % Backward-subsumed : 1
% 2.39/0.84 % Backward-rewritten : 50
% 2.39/0.84 % Generated clauses : 17925
% 2.39/0.84 % ...of the previous two non-redundant : 16837
% 2.39/0.84 % ...aggressively subsumed : 0
% 2.39/0.84 % Contextual simplify-reflections : 0
% 2.39/0.84 % Paramodulations : 17925
% 2.39/0.84 % Factorizations : 0
% 2.39/0.84 % NegExts : 0
% 2.39/0.84 % Equation resolutions : 0
% 2.39/0.84 % Disequality decompositions : 0
% 2.39/0.84 % Total rewrite steps : 9613
% 2.39/0.84 % ...of those cached : 6580
% 2.39/0.84 % Propositional unsat checks : 0
% 2.39/0.84 % Propositional check models : 0
% 2.39/0.84 % Propositional check unsatisfiable : 0
% 2.39/0.84 % Propositional clauses : 0
% 2.39/0.84 % Propositional clauses after purity: 0
% 2.39/0.84 % Propositional unsat core size : 0
% 2.39/0.84 % Propositional preprocessing time : 0.000
% 2.39/0.84 % Propositional encoding time : 0.000
% 2.39/0.84 % Propositional solver time : 0.000
% 2.39/0.84 % Success case prop preproc time : 0.000
% 2.39/0.84 % Success case prop encoding time : 0.000
% 2.39/0.84 % Success case prop solver time : 0.000
% 2.39/0.84 % Current number of processed clauses : 43
% 2.39/0.84 % Positive orientable unit clauses : 42
% 2.39/0.84 % Positive unorientable unit clauses: 1
% 2.39/0.84 % Negative unit clauses : 0
% 2.39/0.84 % Non-unit-clauses : 0
% 2.39/0.84 % Current number of unprocessed clauses: 16389
% 2.39/0.84 % ...number of literals in the above : 16389
% 2.39/0.84 % Current number of archived formulas : 0
% 2.39/0.84 % Current number of archived clauses : 53
% 2.39/0.84 % Clause-clause subsumption calls (NU) : 0
% 2.39/0.84 % Rec. Clause-clause subsumption calls : 0
% 2.39/0.84 % Non-unit clause-clause subsumptions : 0
% 2.39/0.84 % Unit Clause-clause subsumption calls : 153
% 2.39/0.84 % Rewrite failures with RHS unbound : 0
% 2.39/0.84 % BW rewrite match attempts : 839
% 2.39/0.84 % BW rewrite match successes : 74
% 2.39/0.84 % Condensation attempts : 0
% 2.39/0.84 % Condensation successes : 0
% 2.39/0.84 % Termbank termtop insertions : 506082
% 2.39/0.84 % Search garbage collected termcells : 2
% 2.39/0.84
% 2.39/0.84 % -------------------------------------------------
% 2.39/0.84 % User time : 0.369 s
% 2.39/0.84 % System time : 0.028 s
% 2.39/0.84 % Total time : 0.397 s
% 2.39/0.84 % Maximum resident set size: 3636 pages
% 2.39/0.84
% 2.39/0.84 % -------------------------------------------------
% 2.39/0.84 % User time : 1.862 s
% 2.39/0.84 % System time : 0.171 s
% 2.39/0.84 % Total time : 2.033 s
% 2.39/0.84 % Maximum resident set size: 4864 pages
% 2.39/0.84 % E exiting
%------------------------------------------------------------------------------