%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP010-1 : 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 : n007.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 0.19s 1.05s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 29 ( 18 unt; 0 nHn; 19 RR)
% Number of literals : 50 ( 9 equ; 24 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 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 : 54 ( 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(a_multiply_b_is_identity,hypothesis,
product(a,b,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_multiply_b_is_identity) ).
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(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(prove_b_multiply_a_is_identity,negated_conjecture,
~ product(b,a,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_multiply_a_is_identity) ).
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,hypothesis,
product(a,b,identity),
a_multiply_b_is_identity ).
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,hypothesis,
( ~ product(X3,a,X1)
| ~ product(X3,identity,X2)
| product(X1,b,X2) ),
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,hypothesis,
( ~ product(X2,a,X1)
| product(X1,b,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_17]) ).
cnf(c_0_20,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
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(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
cnf(c_0_23,hypothesis,
product(identity,b,inverse(a)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_25,negated_conjecture,
~ product(b,a,identity),
inference(fof_simplification,[status(thm)],[prove_b_multiply_a_is_identity]) ).
cnf(c_0_26,hypothesis,
inverse(a) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_27,negated_conjecture,
~ product(b,a,identity),
c_0_25 ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.98 % Computer : n007.cluster.edu
% 0.11/0.98 % Model : x86_64 x86_64
% 0.11/0.98 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.98 % Memory : 8046.5625MB
% 0.11/0.98 % OS : Linux 6.8.0-71-generic
% 0.11/0.98 % CPULimit : 300
% 0.11/0.98 % WCLimit : 300
% 0.11/0.98 % DateTime : Sun Sep 20 19:51:22 UTC 2026
% 0.11/0.98 % CPUTime :
% 0.11/0.98 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/1.03 Running first-order theorem proving
% 0.11/1.03 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
% 0.19/1.05 % Version: 3.5.1
% 0.19/1.05 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.19/1.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/1.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.19/1.05 % Starting new_bool_3 with 300s (1) cores
% 0.19/1.05 % Starting new_bool_1 with 300s (1) cores
% 0.19/1.05 % Starting sh5l with 300s (1) cores
% 0.19/1.05 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3435481 completed with status 0
% 0.19/1.05 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.19/1.05 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.19/1.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/1.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.19/1.05 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/1.05 % No SInE strategy applied
% 0.19/1.05 % Search class: FHUSM-FFSF21-SFFFFFNN
% 0.19/1.05 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/1.05 % Starting SubtermCWHack with 136s (1) cores
% 0.19/1.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.19/1.05 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 136s (1) cores
% 0.19/1.05 % Starting new_bool_3 with 136s (1) cores
% 0.19/1.05 % Starting new_bool_1 with 136s (1) cores
% 0.19/1.05 % new_bool_3 with pid 3435490 completed with status 0
% 0.19/1.05 % Result found by new_bool_3
% 0.19/1.05 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.19/1.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/1.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.19/1.05 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/1.05 % No SInE strategy applied
% 0.19/1.05 % Search class: FHUSM-FFSF21-SFFFFFNN
% 0.19/1.05 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/1.05 % Starting SubtermCWHack with 136s (1) cores
% 0.19/1.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.19/1.05 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 136s (1) cores
% 0.19/1.05 % Starting new_bool_3 with 136s (1) cores
% 0.19/1.05 % Preprocessing time : 0.001 s
% 0.19/1.05 % Presaturation interreduction done
% 0.19/1.05
% 0.19/1.05 % Proof found!
% 0.19/1.05 % SZS status Unsatisfiable
% 0.19/1.05 % SZS output start CNFRefutation
% See solution above
% 0.19/1.05 % Parsed axioms : 10
% 0.19/1.05 % Removed by relevancy pruning/SinE : 0
% 0.19/1.05 % Initial clauses : 10
% 0.19/1.05 % Removed in clause preprocessing : 0
% 0.19/1.05 % Initial clauses in saturation : 10
% 0.19/1.05 % Processed clauses : 41
% 0.19/1.05 % ...of these trivial : 1
% 0.19/1.05 % ...subsumed : 3
% 0.19/1.05 % ...remaining for further processing : 37
% 0.19/1.05 % Other redundant clauses eliminated : 0
% 0.19/1.05 % Clauses deleted for lack of memory : 0
% 0.19/1.05 % Backward-subsumed : 1
% 0.19/1.05 % Backward-rewritten : 1
% 0.19/1.05 % Generated clauses : 65
% 0.19/1.05 % ...of the previous two non-redundant : 46
% 0.19/1.05 % ...aggressively subsumed : 0
% 0.19/1.05 % Contextual simplify-reflections : 0
% 0.19/1.05 % Paramodulations : 65
% 0.19/1.05 % Factorizations : 0
% 0.19/1.05 % NegExts : 0
% 0.19/1.05 % Equation resolutions : 0
% 0.19/1.05 % Disequality decompositions : 0
% 0.19/1.05 % Total rewrite steps : 26
% 0.19/1.05 % ...of those cached : 10
% 0.19/1.05 % Propositional unsat checks : 0
% 0.19/1.05 % Propositional check models : 0
% 0.19/1.05 % Propositional check unsatisfiable : 0
% 0.19/1.05 % Propositional clauses : 0
% 0.19/1.05 % Propositional clauses after purity: 0
% 0.19/1.05 % Propositional unsat core size : 0
% 0.19/1.05 % Propositional preprocessing time : 0.000
% 0.19/1.05 % Propositional encoding time : 0.000
% 0.19/1.05 % Propositional solver time : 0.000
% 0.19/1.05 % Success case prop preproc time : 0.000
% 0.19/1.05 % Success case prop encoding time : 0.000
% 0.19/1.05 % Success case prop solver time : 0.000
% 0.19/1.05 % Current number of processed clauses : 25
% 0.19/1.05 % Positive orientable unit clauses : 12
% 0.19/1.05 % Positive unorientable unit clauses: 0
% 0.19/1.05 % Negative unit clauses : 1
% 0.19/1.05 % Non-unit-clauses : 12
% 0.19/1.05 % Current number of unprocessed clauses: 23
% 0.19/1.05 % ...number of literals in the above : 53
% 0.19/1.05 % Current number of archived formulas : 0
% 0.19/1.05 % Current number of archived clauses : 12
% 0.19/1.05 % Clause-clause subsumption calls (NU) : 57
% 0.19/1.05 % Rec. Clause-clause subsumption calls : 53
% 0.19/1.05 % Non-unit clause-clause subsumptions : 4
% 0.19/1.05 % Unit Clause-clause subsumption calls : 0
% 0.19/1.05 % Rewrite failures with RHS unbound : 0
% 0.19/1.05 % BW rewrite match attempts : 13
% 0.19/1.05 % BW rewrite match successes : 1
% 0.19/1.05 % Condensation attempts : 0
% 0.19/1.05 % Condensation successes : 0
% 0.19/1.05 % Termbank termtop insertions : 860
% 0.19/1.05 % Search garbage collected termcells : 18
% 0.19/1.05
% 0.19/1.05 % -------------------------------------------------
% 0.19/1.05 % User time : 0.002 s
% 0.19/1.05 % System time : 0.003 s
% 0.19/1.05 % Total time : 0.006 s
% 0.19/1.05 % Maximum resident set size: 3640 pages
% 0.19/1.05
% 0.19/1.05 % -------------------------------------------------
% 0.19/1.05 % User time : 0.011 s
% 0.19/1.05 % System time : 0.015 s
% 0.19/1.05 % Total time : 0.026 s
% 0.19/1.05 % Maximum resident set size: 4864 pages
% 0.19/1.05 % E exiting
%------------------------------------------------------------------------------