%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP061-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:37:46 PM UTC 2026
% Result : Unsatisfiable 9.57s 6.95s
% Output : CNFRefutation 9.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of clauses : 46 ( 42 unt; 0 nHn; 6 RR)
% Number of literals : 53 ( 52 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 143 ( 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,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
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(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),X4),inverse(multiply(X5,multiply(X2,X4)))))),multiply(multiply(X5,X6),inverse(multiply(X7,multiply(X1,X6))))))) = X7,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_5,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_6,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_3,c_0_4]) ).
cnf(c_0_7,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(inverse(X4),multiply(X1,X3)))))) = X4,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,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_7]) ).
cnf(c_0_9,plain,
inverse(multiply(inverse(X1),multiply(X1,multiply(X2,inverse(multiply(X3,X2)))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_6]),c_0_5]) ).
cnf(c_0_10,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_6,c_0_9]),c_0_5]) ).
cnf(c_0_11,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_10]),c_0_10]) ).
cnf(c_0_12,plain,
multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X3),X1))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_10]),c_0_10]) ).
cnf(c_0_13,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_10,c_0_11]) ).
cnf(c_0_14,plain,
multiply(multiply(X1,multiply(X2,inverse(multiply(X3,X2)))),multiply(X4,multiply(inverse(X4),X3))) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_15,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_13,c_0_13]),c_0_13]) ).
cnf(c_0_16,plain,
multiply(X1,multiply(X2,inverse(multiply(multiply(multiply(X3,multiply(inverse(X3),inverse(X4))),X4),X2)))) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,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_11,c_0_11]) ).
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_16]) ).
cnf(c_0_19,plain,
inverse(inverse(multiply(inverse(X1),X1))) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_21,plain,
inverse(multiply(X1,multiply(inverse(multiply(X2,X1)),multiply(inverse(X3),X3)))) = X2,
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_22,plain,
inverse(multiply(X1,multiply(inverse(X2),X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_23,plain,
inverse(multiply(inverse(X1),multiply(X1,multiply(multiply(X2,multiply(X3,inverse(multiply(X4,X3)))),X4)))) = inverse(X2),
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_24,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_22]),c_0_5]) ).
cnf(c_0_25,plain,
multiply(inverse(X1),multiply(X1,multiply(multiply(X2,multiply(X3,inverse(multiply(X4,X3)))),X4))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_23]),c_0_5]) ).
cnf(c_0_26,plain,
multiply(X1,inverse(multiply(inverse(X2),X2))) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_27,plain,
multiply(X1,multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),X2)))) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_28,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_29,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_31,plain,
multiply(multiply(X1,multiply(X2,inverse(multiply(multiply(inverse(inverse(X3)),inverse(multiply(inverse(X4),X3))),X2)))),X4) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_32,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_24]) ).
cnf(c_0_33,plain,
inverse(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))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_6]) ).
cnf(c_0_34,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
c_0_30 ).
cnf(c_0_35,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29]),c_0_32]),c_0_29]) ).
cnf(c_0_36,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(X3,X4),inverse(multiply(X5,multiply(X6,X4))))),X5)),X6))) = X3,
inference(rw,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_37,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_38,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_32]),c_0_29]) ).
cnf(c_0_39,negated_conjecture,
( multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(sr,[status(thm)],[c_0_34,c_0_20]) ).
cnf(c_0_40,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_20]),c_0_29]) ).
cnf(c_0_41,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_36,c_0_32]),c_0_37]),c_0_38]),c_0_37]) ).
cnf(c_0_42,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_43,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
cnf(c_0_44,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_29]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP061-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/5.47 % Computer : n005.cluster.edu
% 0.19/5.47 % Model : x86_64 x86_64
% 0.19/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.47 % Memory : 8046.5625MB
% 0.19/5.47 % OS : Linux 6.8.0-71-generic
% 0.19/5.47 % CPULimit : 300
% 0.19/5.47 % WCLimit : 300
% 0.19/5.47 % DateTime : Sun Sep 20 19:56:08 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/5.54 Running first-order theorem proving
% 0.23/5.54 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
% 9.57/6.95 % Version: 3.5.1
% 9.57/6.95 % Preprocessing class: FSSSSMSSSSSNFFN.
% 9.57/6.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.57/6.95 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 9.57/6.95 % Starting new_bool_3 with 300s (1) cores
% 9.57/6.95 % Starting new_bool_1 with 300s (1) cores
% 9.57/6.95 % Starting sh5l with 300s (1) cores
% 9.57/6.95 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1625795 completed with status 0
% 9.57/6.95 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 9.57/6.95 % Preprocessing class: FSSSSMSSSSSNFFN.
% 9.57/6.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.57/6.95 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 9.57/6.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.57/6.95 % No SInE strategy applied
% 9.57/6.95 % Search class: FUHPF-FFSF21-DFFFFFNN
% 9.57/6.95 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.57/6.95 % Starting SubtermCWHack with 136s (1) cores
% 9.57/6.95 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 9.57/6.95 % Starting G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 9.57/6.95 % Starting new_bool_3 with 136s (1) cores
% 9.57/6.95 % Starting new_bool_1 with 136s (1) cores
% 9.57/6.95 % new_bool_1 with pid 1625806 completed with status 0
% 9.57/6.95 % Result found by new_bool_1
% 9.57/6.95 % Preprocessing class: FSSSSMSSSSSNFFN.
% 9.57/6.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.57/6.95 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 9.57/6.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.57/6.95 % No SInE strategy applied
% 9.57/6.95 % Search class: FUHPF-FFSF21-DFFFFFNN
% 9.57/6.95 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.57/6.95 % Starting SubtermCWHack with 136s (1) cores
% 9.57/6.95 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 9.57/6.95 % Starting G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 9.57/6.95 % Starting new_bool_3 with 136s (1) cores
% 9.57/6.95 % Starting new_bool_1 with 136s (1) cores
% 9.57/6.95 % Preprocessing time : 0.002 s
% 9.57/6.95 % Presaturation interreduction done
% 9.57/6.95
% 9.57/6.95 % Proof found!
% 9.57/6.95 % SZS status Unsatisfiable
% 9.57/6.95 % SZS output start CNFRefutation
% See solution above
% 9.57/6.95 % Parsed axioms : 2
% 9.57/6.95 % Removed by relevancy pruning/SinE : 0
% 9.57/6.95 % Initial clauses : 2
% 9.57/6.95 % Removed in clause preprocessing : 0
% 9.57/6.95 % Initial clauses in saturation : 2
% 9.57/6.95 % Processed clauses : 403
% 9.57/6.95 % ...of these trivial : 182
% 9.57/6.95 % ...subsumed : 121
% 9.57/6.95 % ...remaining for further processing : 100
% 9.57/6.95 % Other redundant clauses eliminated : 0
% 9.57/6.95 % Clauses deleted for lack of memory : 0
% 9.57/6.95 % Backward-subsumed : 0
% 9.57/6.95 % Backward-rewritten : 47
% 9.57/6.95 % Generated clauses : 29215
% 9.57/6.95 % ...of the previous two non-redundant : 27959
% 9.57/6.95 % ...aggressively subsumed : 0
% 9.57/6.95 % Contextual simplify-reflections : 0
% 9.57/6.95 % Paramodulations : 29214
% 9.57/6.95 % Factorizations : 0
% 9.57/6.95 % NegExts : 0
% 9.57/6.95 % Equation resolutions : 0
% 9.57/6.95 % Disequality decompositions : 0
% 9.57/6.95 % Total rewrite steps : 19593
% 9.57/6.95 % ...of those cached : 14793
% 9.57/6.95 % Propositional unsat checks : 0
% 9.57/6.95 % Propositional check models : 0
% 9.57/6.95 % Propositional check unsatisfiable : 0
% 9.57/6.95 % Propositional clauses : 0
% 9.57/6.95 % Propositional clauses after purity: 0
% 9.57/6.95 % Propositional unsat core size : 0
% 9.57/6.95 % Propositional preprocessing time : 0.000
% 9.57/6.95 % Propositional encoding time : 0.000
% 9.57/6.95 % Propositional solver time : 0.000
% 9.57/6.95 % Success case prop preproc time : 0.000
% 9.57/6.95 % Success case prop encoding time : 0.000
% 9.57/6.95 % Success case prop solver time : 0.000
% 9.57/6.95 % Current number of processed clauses : 50
% 9.57/6.95 % Positive orientable unit clauses : 46
% 9.57/6.95 % Positive unorientable unit clauses: 4
% 9.57/6.95 % Negative unit clauses : 0
% 9.57/6.95 % Non-unit-clauses : 0
% 9.57/6.95 % Current number of unprocessed clauses: 27424
% 9.57/6.95 % ...number of literals in the above : 27424
% 9.57/6.95 % Current number of archived formulas : 0
% 9.57/6.95 % Current number of archived clauses : 50
% 9.57/6.95 % Clause-clause subsumption calls (NU) : 0
% 9.57/6.95 % Rec. Clause-clause subsumption calls : 0
% 9.57/6.95 % Non-unit clause-clause subsumptions : 0
% 9.57/6.95 % Unit Clause-clause subsumption calls : 223
% 9.57/6.95 % Rewrite failures with RHS unbound : 167
% 9.57/6.95 % BW rewrite match attempts : 1446
% 9.57/6.95 % BW rewrite match successes : 78
% 9.57/6.95 % Condensation attempts : 0
% 9.57/6.95 % Condensation successes : 0
% 9.57/6.95 % Termbank termtop insertions : 984813
% 9.57/6.95 % Search garbage collected termcells : 8
% 9.57/6.95
% 9.57/6.95 % -------------------------------------------------
% 9.57/6.95 % User time : 1.269 s
% 9.57/6.95 % System time : 0.066 s
% 9.57/6.95 % Total time : 1.336 s
% 9.57/6.95 % Maximum resident set size: 3636 pages
% 9.57/6.95
% 9.57/6.95 % -------------------------------------------------
% 9.57/6.95 % User time : 6.371 s
% 9.57/6.95 % System time : 0.311 s
% 9.57/6.95 % Total time : 6.681 s
% 9.57/6.95 % Maximum resident set size: 4608 pages
% 9.57/6.95 % E exiting
%------------------------------------------------------------------------------