%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP442-1 : 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 : n018.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 12:39:49 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.76s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 2
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 4 RR)
% Number of literals : 47 ( 46 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 135 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(X1,X2))))))) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c_0_2,axiom,
inverse(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(X1,X2))))))) = X4,
single_axiom ).
cnf(c_0_3,plain,
inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X4,X1)))),multiply(multiply(X5,inverse(X5)),X3)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
inverse(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X4)))),multiply(multiply(multiply(X5,inverse(X5)),X2),multiply(multiply(X6,inverse(X6)),X3)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
inverse(multiply(multiply(multiply(X1,inverse(X1)),X2),multiply(multiply(multiply(X3,inverse(X3)),X4),multiply(multiply(X5,inverse(X5)),X6)))) = multiply(multiply(X7,inverse(X7)),inverse(multiply(X2,multiply(X4,X6)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_6,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,X2)))) = X3,
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
multiply(multiply(a1,inverse(a1)),X1) = multiply(multiply(X2,inverse(X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_3]),c_0_2]) ).
cnf(c_0_8,plain,
multiply(a1,inverse(a1)) = multiply(X1,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_7]),c_0_2]) ).
cnf(c_0_9,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_10,plain,
inverse(multiply(X1,multiply(inverse(X1),multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X4,inverse(X4)))))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_9]) ).
cnf(c_0_11,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X3,X4))),multiply(X2,X3)))) = X4,
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_12,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(X1,multiply(X2,inverse(X2)))),multiply(X1,X3)))) = inverse(X3),
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_13,plain,
inverse(multiply(X1,multiply(inverse(X1),X2))) = inverse(multiply(X3,multiply(inverse(X3),X2))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X3,inverse(X3)))),multiply(X2,X4)))) = inverse(X4),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_15,plain,
inverse(multiply(inverse(X1),multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(inverse(X4),X2))))))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_13]) ).
cnf(c_0_16,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(inverse(X2),X3))),multiply(X4,inverse(X4))))) = X3,
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_17,plain,
inverse(multiply(X1,multiply(inverse(X1),inverse(inverse(X2))))) = inverse(multiply(X2,multiply(X3,inverse(X3)))),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_18,plain,
multiply(X1,inverse(X1)) = multiply(multiply(X2,multiply(inverse(X2),X3)),inverse(multiply(X4,multiply(inverse(X4),X3)))),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_19,plain,
inverse(multiply(inverse(X1),multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),X3))) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
multiply(X1,multiply(inverse(X1),inverse(inverse(X2)))) = multiply(X2,multiply(X3,inverse(X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_17]),c_0_15]) ).
cnf(c_0_21,plain,
multiply(multiply(inverse(X1),multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),X3)),X1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_18]) ).
cnf(c_0_22,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(X3,multiply(inverse(X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_15]) ).
cnf(c_0_23,plain,
multiply(X1,multiply(inverse(X1),inverse(multiply(X2,inverse(X2))))) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).
cnf(c_0_24,plain,
multiply(X1,multiply(X2,multiply(inverse(X2),X3))) = multiply(X4,multiply(inverse(X4),multiply(inverse(inverse(X1)),X3))),
inference(spm,[status(thm)],[c_0_22,c_0_22]) ).
cnf(c_0_25,plain,
multiply(inverse(X1),inverse(multiply(X2,inverse(X2)))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_23]),c_0_14]) ).
cnf(c_0_26,plain,
multiply(X1,multiply(inverse(X1),multiply(inverse(multiply(X2,multiply(inverse(X2),X3))),X3))) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24]),c_0_19]) ).
cnf(c_0_27,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_28,plain,
multiply(inverse(X1),multiply(inverse(multiply(X2,multiply(inverse(X2),X3))),X3)) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_26]),c_0_14]) ).
cnf(c_0_29,plain,
inverse(multiply(X1,multiply(X2,multiply(multiply(multiply(X3,multiply(X4,multiply(multiply(X5,inverse(X5)),inverse(multiply(X6,multiply(X3,X4)))))),X6),inverse(multiply(X7,multiply(X1,X2))))))) = X7,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_30,plain,
inverse(multiply(inverse(X1),multiply(inverse(multiply(X2,inverse(X2))),multiply(X3,inverse(X3))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_27]),c_0_27]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(inverse(multiply(X2,multiply(inverse(X2),X3))),X3)) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_32,plain,
multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(inverse(X4),multiply(X1,X2)))))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27]) ).
cnf(c_0_33,plain,
multiply(multiply(X1,inverse(X1)),multiply(inverse(multiply(X2,inverse(X2))),multiply(multiply(X3,inverse(X3)),X4))) = X4,
inference(spm,[status(thm)],[c_0_11,c_0_30]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(inverse(multiply(X2,multiply(X3,inverse(X3)))),inverse(inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_9]) ).
cnf(c_0_35,plain,
inverse(multiply(inverse(X1),multiply(X2,inverse(X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_27]) ).
cnf(c_0_36,plain,
inverse(inverse(multiply(X1,multiply(X2,inverse(X2))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_33]),c_0_27]) ).
cnf(c_0_37,plain,
multiply(X1,multiply(X2,inverse(inverse(inverse(X2))))) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
multiply(multiply(inverse(X1),multiply(inverse(multiply(X2,inverse(X2))),multiply(X3,inverse(X3)))),X1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_30]),c_0_18]) ).
cnf(c_0_39,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(X2)))),X1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_36]),c_0_18]) ).
cnf(c_0_40,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(inverse(inverse(X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_37]),c_0_36]) ).
cnf(c_0_41,plain,
inverse(multiply(X1,inverse(X1))) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_36]),c_0_35]) ).
cnf(c_0_42,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(fof_simplification,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_0_43,plain,
multiply(X1,multiply(a1,inverse(a1))) = X1,
inference(rw,[status(thm)],[c_0_27,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
c_0_42 ).
cnf(c_0_45,plain,
multiply(inverse(X1),X1) = multiply(a1,inverse(a1)),
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_43]),c_0_43]),c_0_41]),c_0_41]),c_0_41]),c_0_43]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP442-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.57 % Computer : n018.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Sun Sep 20 20:15:45 UTC 2026
% 0.11/0.57 % CPUTime :
% 0.11/0.57 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.62 Running first-order theorem proving
% 0.16/0.62 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
% 0.16/0.76 % Version: 3.5.1
% 0.16/0.76 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.16/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.16/0.76 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.76 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.76 % Starting sh5l with 300s (1) cores
% 0.16/0.76 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 94681 completed with status 0
% 0.16/0.76 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.16/0.76 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.16/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.16/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.76 % No SInE strategy applied
% 0.16/0.76 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.16/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.76 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.16/0.76 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/0.76 % Starting new_bool_3 with 136s (1) cores
% 0.16/0.76 % Starting new_bool_1 with 136s (1) cores
% 0.16/0.76 % U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 94689 completed with status 0
% 0.16/0.76 % Result found by U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.76 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.16/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.16/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.76 % No SInE strategy applied
% 0.16/0.76 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.16/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.76 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.16/0.76 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/0.76 % Preprocessing time : 0.001 s
% 0.16/0.76 % Presaturation interreduction done
% 0.16/0.76
% 0.16/0.76 % Proof found!
% 0.16/0.76 % SZS status Unsatisfiable
% 0.16/0.76 % SZS output start CNFRefutation
% See solution above
% 0.16/0.76 % Parsed axioms : 2
% 0.16/0.76 % Removed by relevancy pruning/SinE : 0
% 0.16/0.76 % Initial clauses : 2
% 0.16/0.76 % Removed in clause preprocessing : 0
% 0.16/0.76 % Initial clauses in saturation : 2
% 0.16/0.76 % Processed clauses : 370
% 0.16/0.76 % ...of these trivial : 63
% 0.16/0.76 % ...subsumed : 235
% 0.16/0.76 % ...remaining for further processing : 72
% 0.16/0.76 % Other redundant clauses eliminated : 0
% 0.16/0.76 % Clauses deleted for lack of memory : 0
% 0.16/0.76 % Backward-subsumed : 3
% 0.16/0.76 % Backward-rewritten : 24
% 0.16/0.76 % Generated clauses : 9168
% 0.16/0.76 % ...of the previous two non-redundant : 8143
% 0.16/0.76 % ...aggressively subsumed : 0
% 0.16/0.76 % Contextual simplify-reflections : 0
% 0.16/0.76 % Paramodulations : 9168
% 0.16/0.76 % Factorizations : 0
% 0.16/0.76 % NegExts : 0
% 0.16/0.76 % Equation resolutions : 0
% 0.16/0.76 % Disequality decompositions : 0
% 0.16/0.76 % Total rewrite steps : 4135
% 0.16/0.76 % ...of those cached : 3087
% 0.16/0.76 % Propositional unsat checks : 0
% 0.16/0.76 % Propositional check models : 0
% 0.16/0.76 % Propositional check unsatisfiable : 0
% 0.16/0.76 % Propositional clauses : 0
% 0.16/0.76 % Propositional clauses after purity: 0
% 0.16/0.76 % Propositional unsat core size : 0
% 0.16/0.76 % Propositional preprocessing time : 0.000
% 0.16/0.76 % Propositional encoding time : 0.000
% 0.16/0.76 % Propositional solver time : 0.000
% 0.16/0.76 % Success case prop preproc time : 0.000
% 0.16/0.76 % Success case prop encoding time : 0.000
% 0.16/0.76 % Success case prop solver time : 0.000
% 0.16/0.76 % Current number of processed clauses : 43
% 0.16/0.76 % Positive orientable unit clauses : 37
% 0.16/0.76 % Positive unorientable unit clauses: 6
% 0.16/0.76 % Negative unit clauses : 0
% 0.16/0.76 % Non-unit-clauses : 0
% 0.16/0.76 % Current number of unprocessed clauses: 7643
% 0.16/0.76 % ...number of literals in the above : 7643
% 0.16/0.76 % Current number of archived formulas : 0
% 0.16/0.76 % Current number of archived clauses : 29
% 0.16/0.76 % Clause-clause subsumption calls (NU) : 0
% 0.16/0.76 % Rec. Clause-clause subsumption calls : 0
% 0.16/0.76 % Non-unit clause-clause subsumptions : 0
% 0.16/0.76 % Unit Clause-clause subsumption calls : 78
% 0.16/0.76 % Rewrite failures with RHS unbound : 0
% 0.16/0.76 % BW rewrite match attempts : 494
% 0.16/0.76 % BW rewrite match successes : 62
% 0.16/0.76 % Condensation attempts : 0
% 0.16/0.76 % Condensation successes : 0
% 0.16/0.76 % Termbank termtop insertions : 232385
% 0.16/0.76 % Search garbage collected termcells : 2
% 0.16/0.76
% 0.16/0.76 % -------------------------------------------------
% 0.16/0.76 % User time : 0.103 s
% 0.16/0.76 % System time : 0.008 s
% 0.16/0.76 % Total time : 0.111 s
% 0.16/0.76 % Maximum resident set size: 3632 pages
% 0.16/0.76
% 0.16/0.76 % -------------------------------------------------
% 0.16/0.76 % User time : 0.512 s
% 0.16/0.76 % System time : 0.055 s
% 0.16/0.76 % Total time : 0.567 s
% 0.16/0.76 % Maximum resident set size: 4864 pages
% 0.16/0.76 % E exiting
%------------------------------------------------------------------------------