%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP012-3 : 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 : n009.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 12:37:26 PM UTC 2026
% Result : Unsatisfiable 0.16s 10.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of clauses : 41 ( 25 unt; 0 nHn; 19 RR)
% Number of literals : 74 ( 18 equ; 36 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(associativity2,axiom,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(associativity1,axiom,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity1) ).
cnf(prove_inverse_of_product_is_product_of_inverses,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).
cnf(c_0_8,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_9,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity2]) ).
cnf(c_0_10,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_8 ).
cnf(c_0_11,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_12,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_9 ).
cnf(c_0_13,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_14,plain,
( ~ product(X2,identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_16,plain,
( ~ product(X4,identity,X3)
| ~ product(X4,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_19,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity1]) ).
cnf(c_0_20,plain,
( ~ product(X3,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_17]) ).
cnf(c_0_21,plain,
( ~ product(identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_22,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_19 ).
cnf(c_0_23,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
cnf(c_0_24,plain,
product(identity,X1,inverse(inverse(X1))),
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_25,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_26,plain,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_27,plain,
product(multiply(X1,inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_28,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_29,plain,
( ~ product(X1,X2,identity)
| product(X1,multiply(X2,X3),X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_30,plain,
product(multiply(X1,X2),inverse(X2),X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
product(X1,multiply(inverse(X1),X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_25]) ).
cnf(c_0_32,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_33,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_35,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_36,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
inference(fof_simplification,[status(thm)],[prove_inverse_of_product_is_product_of_inverses]) ).
cnf(c_0_37,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
c_0_36 ).
cnf(c_0_39,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/10.39 % Computer : n009.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Sun Sep 20 19:53:54 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/10.46 Running first-order theorem proving
% 0.16/10.46 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
% 0.16/10.50 % Version: 3.5.1
% 0.16/10.50 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.16/10.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/10.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.16/10.50 % Starting new_bool_3 with 300s (1) cores
% 0.16/10.50 % Starting new_bool_1 with 300s (1) cores
% 0.16/10.50 % Starting sh5l with 300s (1) cores
% 0.16/10.50 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 4096384 completed with status 0
% 0.16/10.50 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.16/10.50 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.16/10.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/10.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.16/10.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/10.50 % No SInE strategy applied
% 0.16/10.50 % Search class: FHUSM-FFSF21-SFFFFFNN
% 0.16/10.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/10.50 % Starting SubtermCWHack with 136s (1) cores
% 0.16/10.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.16/10.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 136s (1) cores
% 0.16/10.50 % Starting new_bool_3 with 136s (1) cores
% 0.16/10.50 % Starting new_bool_1 with 136s (1) cores
% 0.16/10.50 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 4096392 completed with status 0
% 0.16/10.50 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 0.16/10.50 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.16/10.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/10.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.16/10.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/10.50 % No SInE strategy applied
% 0.16/10.50 % Search class: FHUSM-FFSF21-SFFFFFNN
% 0.16/10.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/10.50 % Starting SubtermCWHack with 136s (1) cores
% 0.16/10.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.16/10.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 136s (1) cores
% 0.16/10.50 % Preprocessing time : 0.001 s
% 0.16/10.50 % Presaturation interreduction done
% 0.16/10.50
% 0.16/10.50 % Proof found!
% 0.16/10.50 % SZS status Unsatisfiable
% 0.16/10.50 % SZS output start CNFRefutation
% See solution above
% 0.16/10.50 % Parsed axioms : 9
% 0.16/10.50 % Removed by relevancy pruning/SinE : 0
% 0.16/10.50 % Initial clauses : 9
% 0.16/10.50 % Removed in clause preprocessing : 0
% 0.16/10.50 % Initial clauses in saturation : 9
% 0.16/10.50 % Processed clauses : 144
% 0.16/10.50 % ...of these trivial : 2
% 0.16/10.50 % ...subsumed : 50
% 0.16/10.50 % ...remaining for further processing : 92
% 0.16/10.50 % Other redundant clauses eliminated : 0
% 0.16/10.50 % Clauses deleted for lack of memory : 0
% 0.16/10.50 % Backward-subsumed : 2
% 0.16/10.50 % Backward-rewritten : 2
% 0.16/10.50 % Generated clauses : 569
% 0.16/10.50 % ...of the previous two non-redundant : 265
% 0.16/10.50 % ...aggressively subsumed : 0
% 0.16/10.50 % Contextual simplify-reflections : 0
% 0.16/10.50 % Paramodulations : 569
% 0.16/10.50 % Factorizations : 0
% 0.16/10.50 % NegExts : 0
% 0.16/10.50 % Equation resolutions : 0
% 0.16/10.50 % Disequality decompositions : 0
% 0.16/10.50 % Total rewrite steps : 489
% 0.16/10.50 % ...of those cached : 442
% 0.16/10.50 % Propositional unsat checks : 0
% 0.16/10.50 % Propositional check models : 0
% 0.16/10.50 % Propositional check unsatisfiable : 0
% 0.16/10.50 % Propositional clauses : 0
% 0.16/10.50 % Propositional clauses after purity: 0
% 0.16/10.50 % Propositional unsat core size : 0
% 0.16/10.50 % Propositional preprocessing time : 0.000
% 0.16/10.50 % Propositional encoding time : 0.000
% 0.16/10.50 % Propositional solver time : 0.000
% 0.16/10.50 % Success case prop preproc time : 0.000
% 0.16/10.50 % Success case prop encoding time : 0.000
% 0.16/10.50 % Success case prop solver time : 0.000
% 0.16/10.50 % Current number of processed clauses : 79
% 0.16/10.50 % Positive orientable unit clauses : 22
% 0.16/10.50 % Positive unorientable unit clauses: 0
% 0.16/10.50 % Negative unit clauses : 0
% 0.16/10.50 % Non-unit-clauses : 57
% 0.16/10.50 % Current number of unprocessed clauses: 131
% 0.16/10.50 % ...number of literals in the above : 228
% 0.16/10.50 % Current number of archived formulas : 0
% 0.16/10.50 % Current number of archived clauses : 13
% 0.16/10.50 % Clause-clause subsumption calls (NU) : 1116
% 0.16/10.50 % Rec. Clause-clause subsumption calls : 1093
% 0.16/10.50 % Non-unit clause-clause subsumptions : 52
% 0.16/10.50 % Unit Clause-clause subsumption calls : 0
% 0.16/10.50 % Rewrite failures with RHS unbound : 0
% 0.16/10.50 % BW rewrite match attempts : 15
% 0.16/10.50 % BW rewrite match successes : 2
% 0.16/10.50 % Condensation attempts : 0
% 0.16/10.50 % Condensation successes : 0
% 0.16/10.50 % Termbank termtop insertions : 4953
% 0.16/10.50 % Search garbage collected termcells : 18
% 0.16/10.50
% 0.16/10.50 % -------------------------------------------------
% 0.16/10.50 % User time : 0.009 s
% 0.16/10.50 % System time : 0.004 s
% 0.16/10.50 % Total time : 0.014 s
% 0.16/10.50 % Maximum resident set size: 3588 pages
% 0.16/10.50
% 0.16/10.50 % -------------------------------------------------
% 0.16/10.50 % User time : 0.044 s
% 0.16/10.50 % System time : 0.018 s
% 0.16/10.50 % Total time : 0.063 s
% 0.16/10.50 % Maximum resident set size: 4864 pages
% 0.16/10.50 % E exiting
%------------------------------------------------------------------------------