%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP031-1 : 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 : n017.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 12:37:30 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.54s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 29 ( 16 unt; 0 nHn; 17 RR)
% Number of literals : 53 ( 9 equ; 27 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
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/GRP002-0.ax',associativity2) ).
cnf(total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax',total_function2) ).
cnf(left_identity,hypothesis,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax',total_function1) ).
cnf(left_inverse,hypothesis,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(prove_a_has_an_inverse,negated_conjecture,
~ product(a,X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_has_an_inverse) ).
cnf(c_0_6,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_7,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_8,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_6 ).
cnf(c_0_9,hypothesis,
product(identity,X1,X1),
left_identity ).
cnf(c_0_10,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_7 ).
cnf(c_0_11,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_12,hypothesis,
( ~ product(X4,X2,X3)
| ~ product(X4,identity,X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,hypothesis,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_14,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,hypothesis,
( ~ product(X1,X2,X3)
| product(multiply(X1,identity),X2,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_16,hypothesis,
( ~ product(X4,identity,X3)
| ~ product(X4,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_17,hypothesis,
( ~ product(X2,X3,X1)
| X1 = multiply(multiply(X2,identity),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,hypothesis,
( ~ product(inverse(inverse(X1)),identity,X2)
| product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_19,hypothesis,
( ~ product(identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_20,hypothesis,
multiply(multiply(inverse(X1),identity),X1) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_21,hypothesis,
product(identity,X1,multiply(inverse(inverse(X1)),identity)),
inference(spm,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_22,hypothesis,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_23,negated_conjecture,
~ product(a,X1,identity),
inference(fof_simplification,[status(thm)],[prove_a_has_an_inverse]) ).
cnf(c_0_24,hypothesis,
product(multiply(inverse(X1),identity),X1,identity),
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_25,hypothesis,
multiply(inverse(inverse(X1)),identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_21]),c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ product(a,X1,identity),
c_0_23 ).
cnf(c_0_27,hypothesis,
product(X1,inverse(X1),identity),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_26,c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP031-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n017.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 20 19:49:56 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.51 Running first-order theorem proving
% 0.18/0.51 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
% 0.27/0.54 % Version: 3.5.1
% 0.27/0.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.27/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.27/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.54 % Starting sh5l with 300s (1) cores
% 0.27/0.54 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 481200 completed with status 0
% 0.27/0.54 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.27/0.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.27/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.27/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.54 % No SInE strategy applied
% 0.27/0.54 % Search class: FHUSS-FFSF21-SFFFFFNN
% 0.27/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.27/0.54 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S064A with 136s (1) cores
% 0.27/0.54 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.54 % Starting new_bool_1 with 136s (1) cores
% 0.27/0.54 % SubtermCWHack with pid 481205 completed with status 0
% 0.27/0.54 % Result found by SubtermCWHack
% 0.27/0.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.27/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.27/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.54 % No SInE strategy applied
% 0.27/0.54 % Search class: FHUSS-FFSF21-SFFFFFNN
% 0.27/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.54 % Preprocessing time : 0.002 s
% 0.27/0.54
% 0.27/0.54 % Proof found!
% 0.27/0.54 % SZS status Unsatisfiable
% 0.27/0.54 % SZS output start CNFRefutation
% See solution above
% 0.27/0.54 % Parsed axioms : 7
% 0.27/0.54 % Removed by relevancy pruning/SinE : 0
% 0.27/0.54 % Initial clauses : 7
% 0.27/0.54 % Removed in clause preprocessing : 0
% 0.27/0.54 % Initial clauses in saturation : 7
% 0.27/0.54 % Processed clauses : 47
% 0.27/0.54 % ...of these trivial : 1
% 0.27/0.54 % ...subsumed : 11
% 0.27/0.54 % ...remaining for further processing : 35
% 0.27/0.54 % Other redundant clauses eliminated : 0
% 0.27/0.54 % Clauses deleted for lack of memory : 0
% 0.27/0.54 % Backward-subsumed : 0
% 0.27/0.54 % Backward-rewritten : 9
% 0.27/0.54 % Generated clauses : 157
% 0.27/0.54 % ...of the previous two non-redundant : 104
% 0.27/0.54 % ...aggressively subsumed : 0
% 0.27/0.54 % Contextual simplify-reflections : 0
% 0.27/0.54 % Paramodulations : 157
% 0.27/0.54 % Factorizations : 0
% 0.27/0.54 % NegExts : 0
% 0.27/0.54 % Equation resolutions : 0
% 0.27/0.54 % Disequality decompositions : 0
% 0.27/0.54 % Total rewrite steps : 75
% 0.27/0.54 % ...of those cached : 57
% 0.27/0.54 % Propositional unsat checks : 0
% 0.27/0.54 % Propositional check models : 0
% 0.27/0.54 % Propositional check unsatisfiable : 0
% 0.27/0.54 % Propositional clauses : 0
% 0.27/0.54 % Propositional clauses after purity: 0
% 0.27/0.54 % Propositional unsat core size : 0
% 0.27/0.54 % Propositional preprocessing time : 0.000
% 0.27/0.54 % Propositional encoding time : 0.000
% 0.27/0.54 % Propositional solver time : 0.000
% 0.27/0.54 % Success case prop preproc time : 0.000
% 0.27/0.54 % Success case prop encoding time : 0.000
% 0.27/0.54 % Success case prop solver time : 0.000
% 0.27/0.54 % Current number of processed clauses : 26
% 0.27/0.54 % Positive orientable unit clauses : 12
% 0.27/0.54 % Positive unorientable unit clauses: 0
% 0.27/0.54 % Negative unit clauses : 1
% 0.27/0.54 % Non-unit-clauses : 13
% 0.27/0.54 % Current number of unprocessed clauses: 61
% 0.27/0.54 % ...number of literals in the above : 150
% 0.27/0.54 % Current number of archived formulas : 0
% 0.27/0.54 % Current number of archived clauses : 9
% 0.27/0.54 % Clause-clause subsumption calls (NU) : 87
% 0.27/0.54 % Rec. Clause-clause subsumption calls : 77
% 0.27/0.54 % Non-unit clause-clause subsumptions : 11
% 0.27/0.54 % Unit Clause-clause subsumption calls : 3
% 0.27/0.54 % Rewrite failures with RHS unbound : 0
% 0.27/0.54 % BW rewrite match attempts : 24
% 0.27/0.54 % BW rewrite match successes : 5
% 0.27/0.54 % Condensation attempts : 0
% 0.27/0.54 % Condensation successes : 0
% 0.27/0.54 % Termbank termtop insertions : 1636
% 0.27/0.54 % Search garbage collected termcells : 18
% 0.27/0.54
% 0.27/0.54 % -------------------------------------------------
% 0.27/0.54 % User time : 0.008 s
% 0.27/0.54 % System time : 0.004 s
% 0.27/0.54 % Total time : 0.013 s
% 0.27/0.54 % Maximum resident set size: 3636 pages
% 0.27/0.54
% 0.27/0.54 % -------------------------------------------------
% 0.27/0.54 % User time : 0.023 s
% 0.27/0.54 % System time : 0.016 s
% 0.27/0.54 % Total time : 0.039 s
% 0.27/0.54 % Maximum resident set size: 4608 pages
% 0.27/0.54 % E exiting
%------------------------------------------------------------------------------