%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP058-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 2.04s 0.94s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 2
% Syntax : Number of clauses : 51 ( 47 unt; 0 nHn; 6 RR)
% Number of literals : 58 ( 57 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 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 : 144 ( 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,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/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
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(multiply(multiply(multiply(X2,inverse(X2)),inverse(X3)),multiply(X4,inverse(X4))),multiply(X5,X1)))) = inverse(multiply(X6,multiply(multiply(multiply(X7,inverse(X7)),inverse(multiply(X3,X6))),X5))),
inference(spm,[status(thm)],[c_0_3,c_0_2]) ).
cnf(c_0_9,plain,
multiply(X1,inverse(multiply(multiply(multiply(X2,inverse(X2)),multiply(X3,inverse(X3))),multiply(X4,X1)))) = inverse(X4),
inference(spm,[status(thm)],[c_0_3,c_0_7]) ).
cnf(c_0_10,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_11,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_12,plain,
inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X3,X4),X1))),X3))) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_8]) ).
cnf(c_0_13,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))) = multiply(X3,inverse(X3)),
inference(spm,[status(thm)],[c_0_5,c_0_9]) ).
cnf(c_0_14,plain,
multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X3,inverse(X3)),X1))),X4)) = X4,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X1))),X2)),multiply(X3,inverse(X3)))) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
multiply(inverse(multiply(X1,inverse(X1))),multiply(multiply(X2,inverse(X2)),X3)) = X3,
inference(spm,[status(thm)],[c_0_14,c_0_7]) ).
cnf(c_0_17,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(multiply(X3,inverse(X3)),X1))) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_18,plain,
inverse(multiply(inverse(X1),multiply(X2,inverse(X2)))) = multiply(multiply(X3,inverse(X3)),X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
multiply(multiply(X1,inverse(X1)),multiply(inverse(multiply(X2,inverse(X2))),X3)) = X3,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
inverse(multiply(inverse(multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),X3)),X2)) = X3,
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_21,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_20,c_0_14]),c_0_19]) ).
cnf(c_0_22,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_23,plain,
multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X1),multiply(X3,X2)))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_21]) ).
cnf(c_0_24,plain,
multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),inverse(multiply(inverse(X3),X2))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_9]) ).
cnf(c_0_25,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X3)))) = multiply(X3,inverse(X2)),
inference(spm,[status(thm)],[c_0_23,c_0_2]) ).
cnf(c_0_26,plain,
multiply(inverse(multiply(X1,inverse(X1))),inverse(inverse(X2))) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_28,plain,
multiply(inverse(multiply(X1,inverse(X1))),inverse(multiply(inverse(X2),multiply(X3,inverse(X3))))) = X2,
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_29,plain,
multiply(inverse(inverse(inverse(X1))),X2) = inverse(multiply(inverse(X2),X1)),
inference(rw,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_30,plain,
multiply(inverse(multiply(X1,inverse(X1))),X2) = inverse(inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]) ).
cnf(c_0_31,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_32,plain,
inverse(multiply(inverse(X1),inverse(X2))) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_29,c_0_31]) ).
cnf(c_0_33,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_31]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_33]),c_0_32]) ).
cnf(c_0_35,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,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_37,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_38,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_27,c_0_35]) ).
cnf(c_0_39,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_33]),c_0_21]),c_0_27]),c_0_31]) ).
cnf(c_0_40,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_14]),c_0_27]),c_0_31]) ).
cnf(c_0_41,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(X3,inverse(X3))),multiply(X4,X1)))) = inverse(multiply(inverse(multiply(X5,inverse(X5))),multiply(X2,X4))),
inference(rw,[status(thm)],[c_0_4,c_0_21]) ).
cnf(c_0_42,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_37 ).
cnf(c_0_43,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_38,c_0_35]) ).
cnf(c_0_44,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,X1)))) = inverse(multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_30]),c_0_33]),c_0_35]) ).
cnf(c_0_46,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
cnf(c_0_47,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_35]),c_0_35]) ).
cnf(c_0_48,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_49,plain,
multiply(inverse(X1),X1) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP058-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n001.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 20 20:01:43 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.55 Running first-order theorem proving
% 0.24/0.55 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
% 2.04/0.94 % Version: 3.5.1
% 2.04/0.94 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.04/0.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.04/0.94 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.04/0.94 % Starting new_bool_3 with 300s (1) cores
% 2.04/0.94 % Starting new_bool_1 with 300s (1) cores
% 2.04/0.94 % Starting sh5l with 300s (1) cores
% 2.04/0.94 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1267110 completed with status 0
% 2.04/0.94 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 2.04/0.94 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.04/0.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.04/0.94 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.04/0.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.04/0.94 % No SInE strategy applied
% 2.04/0.94 % Search class: FUHPF-FFSF21-DFFFFFNN
% 2.04/0.94 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.04/0.94 % Starting SubtermCWHack with 136s (1) cores
% 2.04/0.94 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.04/0.94 % Starting G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.04/0.94 % Starting new_bool_3 with 136s (1) cores
% 2.04/0.94 % Starting new_bool_1 with 136s (1) cores
% 2.04/0.94 % new_bool_1 with pid 1267119 completed with status 0
% 2.04/0.94 % Result found by new_bool_1
% 2.04/0.94 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.04/0.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.04/0.94 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.04/0.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.04/0.94 % No SInE strategy applied
% 2.04/0.94 % Search class: FUHPF-FFSF21-DFFFFFNN
% 2.04/0.94 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.04/0.94 % Starting SubtermCWHack with 136s (1) cores
% 2.04/0.94 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.04/0.94 % Starting G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.04/0.94 % Starting new_bool_3 with 136s (1) cores
% 2.04/0.94 % Starting new_bool_1 with 136s (1) cores
% 2.04/0.94 % Preprocessing time : 0.002 s
% 2.04/0.94 % Presaturation interreduction done
% 2.04/0.94
% 2.04/0.94 % Proof found!
% 2.04/0.94 % SZS status Unsatisfiable
% 2.04/0.94 % SZS output start CNFRefutation
% See solution above
% 2.04/0.94 % Parsed axioms : 2
% 2.04/0.94 % Removed by relevancy pruning/SinE : 0
% 2.04/0.94 % Initial clauses : 2
% 2.04/0.94 % Removed in clause preprocessing : 0
% 2.04/0.94 % Initial clauses in saturation : 2
% 2.04/0.94 % Processed clauses : 230
% 2.04/0.94 % ...of these trivial : 64
% 2.04/0.94 % ...subsumed : 98
% 2.04/0.94 % ...remaining for further processing : 68
% 2.04/0.94 % Other redundant clauses eliminated : 0
% 2.04/0.94 % Clauses deleted for lack of memory : 0
% 2.04/0.94 % Backward-subsumed : 1
% 2.04/0.94 % Backward-rewritten : 48
% 2.04/0.94 % Generated clauses : 7760
% 2.04/0.94 % ...of the previous two non-redundant : 7137
% 2.04/0.94 % ...aggressively subsumed : 0
% 2.04/0.94 % Contextual simplify-reflections : 0
% 2.04/0.94 % Paramodulations : 7760
% 2.04/0.94 % Factorizations : 0
% 2.04/0.94 % NegExts : 0
% 2.04/0.94 % Equation resolutions : 0
% 2.04/0.94 % Disequality decompositions : 0
% 2.04/0.94 % Total rewrite steps : 8061
% 2.04/0.94 % ...of those cached : 5617
% 2.04/0.94 % Propositional unsat checks : 0
% 2.04/0.94 % Propositional check models : 0
% 2.04/0.94 % Propositional check unsatisfiable : 0
% 2.04/0.94 % Propositional clauses : 0
% 2.04/0.94 % Propositional clauses after purity: 0
% 2.04/0.94 % Propositional unsat core size : 0
% 2.04/0.94 % Propositional preprocessing time : 0.000
% 2.04/0.94 % Propositional encoding time : 0.000
% 2.04/0.94 % Propositional solver time : 0.000
% 2.04/0.94 % Success case prop preproc time : 0.000
% 2.04/0.94 % Success case prop encoding time : 0.000
% 2.04/0.94 % Success case prop solver time : 0.000
% 2.04/0.94 % Current number of processed clauses : 17
% 2.04/0.94 % Positive orientable unit clauses : 14
% 2.04/0.94 % Positive unorientable unit clauses: 2
% 2.04/0.94 % Negative unit clauses : 1
% 2.04/0.94 % Non-unit-clauses : 0
% 2.04/0.94 % Current number of unprocessed clauses: 6838
% 2.04/0.94 % ...number of literals in the above : 6838
% 2.04/0.94 % Current number of archived formulas : 0
% 2.04/0.94 % Current number of archived clauses : 51
% 2.04/0.94 % Clause-clause subsumption calls (NU) : 0
% 2.04/0.94 % Rec. Clause-clause subsumption calls : 0
% 2.04/0.94 % Non-unit clause-clause subsumptions : 0
% 2.04/0.94 % Unit Clause-clause subsumption calls : 80
% 2.04/0.94 % Rewrite failures with RHS unbound : 269
% 2.04/0.94 % BW rewrite match attempts : 454
% 2.04/0.94 % BW rewrite match successes : 97
% 2.04/0.94 % Condensation attempts : 0
% 2.04/0.94 % Condensation successes : 0
% 2.04/0.94 % Termbank termtop insertions : 185727
% 2.04/0.94 % Search garbage collected termcells : 8
% 2.04/0.94
% 2.04/0.94 % -------------------------------------------------
% 2.04/0.94 % User time : 0.255 s
% 2.04/0.94 % System time : 0.019 s
% 2.04/0.94 % Total time : 0.274 s
% 2.04/0.94 % Maximum resident set size: 3636 pages
% 2.04/0.94
% 2.04/0.94 % -------------------------------------------------
% 2.04/0.94 % User time : 1.464 s
% 2.04/0.94 % System time : 0.096 s
% 2.04/0.94 % Total time : 1.560 s
% 2.04/0.94 % Maximum resident set size: 4864 pages
% 2.04/0.94 % E exiting
%------------------------------------------------------------------------------