%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP053-1 : 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 : n004.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 12:37:45 PM UTC 2026
% Result : Unsatisfiable 2.14s 0.76s
% Output : CNFRefutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of clauses : 38 ( 34 unt; 0 nHn; 6 RR)
% Number of literals : 45 ( 44 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 16 ( 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 : 88 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X1),X1)))))) = X3,
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,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X1),X1)))))) = X3,
single_axiom ).
cnf(c_0_3,plain,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,X3))),inverse(multiply(inverse(X1),X1)))))) = multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,inverse(X3)))),inverse(multiply(inverse(X4),X4))))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X3))))),inverse(multiply(inverse(X1),X1))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),X3)),inverse(multiply(inverse(X1),X1)))))) = multiply(inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,inverse(inverse(X3))))),inverse(multiply(inverse(X2),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_4]) ).
cnf(c_0_6,plain,
multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),inverse(multiply(inverse(X2),X2)))))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_5]),c_0_2]) ).
cnf(c_0_7,plain,
inverse(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,X3))),inverse(multiply(inverse(X1),X1))))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(X3))))))),inverse(multiply(inverse(X2),X2))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_5]) ).
cnf(c_0_9,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X4)))),inverse(multiply(inverse(inverse(multiply(X2,X3))),inverse(multiply(X2,X3)))))) = multiply(X2,inverse(inverse(multiply(X3,inverse(multiply(X4,inverse(multiply(inverse(X3),X3)))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_3]),c_0_7]) ).
cnf(c_0_10,plain,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,inverse(inverse(multiply(X3,inverse(X4))))))),X1)),X4)),inverse(multiply(inverse(X1),X1)))))) = multiply(inverse(X3),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_8]),c_0_4]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))),inverse(multiply(inverse(X2),X2))) = multiply(inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,X3))),inverse(multiply(inverse(X2),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_3]),c_0_2]) ).
cnf(c_0_12,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2))))))))) = X3,
inference(spm,[status(thm)],[c_0_4,c_0_9]) ).
cnf(c_0_13,plain,
inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))))) = multiply(inverse(X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_8]) ).
cnf(c_0_14,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X3),X3),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X2),X2)))),inverse(multiply(inverse(multiply(X3,multiply(X2,inverse(X4)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X2),X2)))))))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_16,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_14,c_0_14]) ).
cnf(c_0_17,plain,
inverse(multiply(inverse(X1),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(inverse(X1)),inverse(X1))))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_8]),c_0_8]),c_0_8]) ).
cnf(c_0_18,plain,
inverse(multiply(inverse(X1),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),X3)))))) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_19,plain,
inverse(multiply(inverse(X1),multiply(inverse(X2),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_18]),c_0_18]) ).
cnf(c_0_20,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_21,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,X3)))))),inverse(multiply(inverse(X2),X2)))) = X3,
inference(spm,[status(thm)],[c_0_7,c_0_5]) ).
cnf(c_0_22,plain,
inverse(multiply(inverse(X1),inverse(multiply(inverse(X2),X2)))) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,X3))))) = X3,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
multiply(inverse(inverse(inverse(multiply(X1,X2)))),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_25,plain,
inverse(inverse(multiply(inverse(X1),X1))) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
multiply(inverse(multiply(inverse(X1),X1)),inverse(X2)) = inverse(X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,plain,
multiply(inverse(multiply(inverse(X1),X1)),X2) = X2,
inference(spm,[status(thm)],[c_0_26,c_0_7]) ).
cnf(c_0_28,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_29,plain,
inverse(inverse(multiply(X1,multiply(inverse(X1),X2)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_27]),c_0_22]),c_0_27]) ).
cnf(c_0_30,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_18]),c_0_22]) ).
cnf(c_0_31,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_28 ).
cnf(c_0_32,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_30]),c_0_27]) ).
cnf(c_0_33,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_31,c_0_16]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[c_0_29,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_30])]) ).
cnf(c_0_36,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_23]),c_0_32]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP053-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 19:55:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 2.14/0.76 % Version: 3.5.1
% 2.14/0.76 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.14/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.14/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.14/0.76 % Starting new_bool_3 with 300s (1) cores
% 2.14/0.76 % Starting new_bool_1 with 300s (1) cores
% 2.14/0.76 % Starting sh5l with 300s (1) cores
% 2.14/0.76 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1350516 completed with status 0
% 2.14/0.76 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 2.14/0.76 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.14/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.14/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.14/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.14/0.76 % No SInE strategy applied
% 2.14/0.76 % Search class: FUHPF-FFSF21-DFFFFFNN
% 2.14/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.14/0.76 % Starting SubtermCWHack with 136s (1) cores
% 2.14/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.14/0.76 % Starting G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.14/0.76 % Starting new_bool_3 with 136s (1) cores
% 2.14/0.76 % Starting new_bool_1 with 136s (1) cores
% 2.14/0.76 % new_bool_1 with pid 1350527 completed with status 0
% 2.14/0.76 % Result found by new_bool_1
% 2.14/0.76 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.14/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.14/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.14/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.14/0.76 % No SInE strategy applied
% 2.14/0.76 % Search class: FUHPF-FFSF21-DFFFFFNN
% 2.14/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.14/0.76 % Starting SubtermCWHack with 136s (1) cores
% 2.14/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.14/0.76 % Starting G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.14/0.76 % Starting new_bool_3 with 136s (1) cores
% 2.14/0.76 % Starting new_bool_1 with 136s (1) cores
% 2.14/0.76 % Preprocessing time : 0.001 s
% 2.14/0.76 % Presaturation interreduction done
% 2.14/0.76
% 2.14/0.76 % Proof found!
% 2.14/0.76 % SZS status Unsatisfiable
% 2.14/0.76 % SZS output start CNFRefutation
% See solution above
% 2.14/0.76 % Parsed axioms : 2
% 2.14/0.76 % Removed by relevancy pruning/SinE : 0
% 2.14/0.76 % Initial clauses : 2
% 2.14/0.76 % Removed in clause preprocessing : 0
% 2.14/0.76 % Initial clauses in saturation : 2
% 2.14/0.76 % Processed clauses : 187
% 2.14/0.76 % ...of these trivial : 48
% 2.14/0.76 % ...subsumed : 69
% 2.14/0.76 % ...remaining for further processing : 70
% 2.14/0.76 % Other redundant clauses eliminated : 0
% 2.14/0.76 % Clauses deleted for lack of memory : 0
% 2.14/0.76 % Backward-subsumed : 3
% 2.14/0.76 % Backward-rewritten : 48
% 2.14/0.76 % Generated clauses : 8465
% 2.14/0.76 % ...of the previous two non-redundant : 7763
% 2.14/0.76 % ...aggressively subsumed : 0
% 2.14/0.76 % Contextual simplify-reflections : 0
% 2.14/0.76 % Paramodulations : 8464
% 2.14/0.76 % Factorizations : 0
% 2.14/0.76 % NegExts : 0
% 2.14/0.76 % Equation resolutions : 0
% 2.14/0.76 % Disequality decompositions : 0
% 2.14/0.76 % Total rewrite steps : 6071
% 2.14/0.76 % ...of those cached : 4227
% 2.14/0.76 % Propositional unsat checks : 0
% 2.14/0.76 % Propositional check models : 0
% 2.14/0.76 % Propositional check unsatisfiable : 0
% 2.14/0.76 % Propositional clauses : 0
% 2.14/0.76 % Propositional clauses after purity: 0
% 2.14/0.76 % Propositional unsat core size : 0
% 2.14/0.76 % Propositional preprocessing time : 0.000
% 2.14/0.76 % Propositional encoding time : 0.000
% 2.14/0.76 % Propositional solver time : 0.000
% 2.14/0.76 % Success case prop preproc time : 0.000
% 2.14/0.76 % Success case prop encoding time : 0.000
% 2.14/0.76 % Success case prop solver time : 0.000
% 2.14/0.76 % Current number of processed clauses : 16
% 2.14/0.76 % Positive orientable unit clauses : 13
% 2.14/0.76 % Positive unorientable unit clauses: 3
% 2.14/0.76 % Negative unit clauses : 0
% 2.14/0.76 % Non-unit-clauses : 0
% 2.14/0.76 % Current number of unprocessed clauses: 7535
% 2.14/0.76 % ...number of literals in the above : 7535
% 2.14/0.76 % Current number of archived formulas : 0
% 2.14/0.76 % Current number of archived clauses : 54
% 2.14/0.76 % Clause-clause subsumption calls (NU) : 0
% 2.14/0.76 % Rec. Clause-clause subsumption calls : 0
% 2.14/0.76 % Non-unit clause-clause subsumptions : 0
% 2.14/0.76 % Unit Clause-clause subsumption calls : 158
% 2.14/0.76 % Rewrite failures with RHS unbound : 602
% 2.14/0.76 % BW rewrite match attempts : 499
% 2.14/0.76 % BW rewrite match successes : 129
% 2.14/0.76 % Condensation attempts : 0
% 2.14/0.76 % Condensation successes : 0
% 2.14/0.76 % Termbank termtop insertions : 397861
% 2.14/0.76 % Search garbage collected termcells : 8
% 2.14/0.76
% 2.14/0.76 % -------------------------------------------------
% 2.14/0.76 % User time : 0.296 s
% 2.14/0.76 % System time : 0.020 s
% 2.14/0.76 % Total time : 0.316 s
% 2.14/0.76 % Maximum resident set size: 3636 pages
% 2.14/0.76
% 2.14/0.76 % -------------------------------------------------
% 2.14/0.76 % User time : 1.514 s
% 2.14/0.76 % System time : 0.089 s
% 2.14/0.76 % Total time : 1.603 s
% 2.14/0.76 % Maximum resident set size: 4608 pages
% 2.14/0.76 % E exiting
%------------------------------------------------------------------------------