%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP003-2 : 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 : n005.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 12:41:20 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of clauses : 40 ( 15 unt; 0 nHn; 29 RR)
% Number of literals : 86 ( 0 equ; 49 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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/GRP005-0.ax',associativity1) ).
cnf(total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function2) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',left_identity) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',left_inverse) ).
cnf(product_substitution3,axiom,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).
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/GRP005-0.ax',associativity2) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function1) ).
cnf(prove_right_identity,negated_conjecture,
~ product(a,identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_right_identity) ).
cnf(c_0_8,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_9,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_10,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_8 ).
cnf(c_0_11,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_12,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_9 ).
cnf(c_0_13,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_14,plain,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ product(inverse(X2),X2,X1)
| equalish(X1,identity) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( ~ product(X1,X3,X2)
| product(inverse(X1),X2,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_17,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
inference(fof_simplification,[status(thm)],[product_substitution3]) ).
cnf(c_0_18,plain,
( ~ product(X2,X1,X2)
| equalish(X1,identity) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,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_20,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
c_0_17 ).
cnf(c_0_21,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_22,plain,
( ~ product(X2,inverse(X2),X1)
| equalish(X1,identity) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_23,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_19 ).
cnf(c_0_24,plain,
( ~ equalish(multiply(X1,X2),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
equalish(multiply(X1,inverse(X1)),identity),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_26,plain,
( ~ product(X4,identity,X3)
| ~ product(X4,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_27,plain,
product(X1,inverse(X1),identity),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( ~ equalish(X1,X2)
| product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_29,plain,
( ~ product(identity,X2,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_30,plain,
( ~ product(X1,identity,X2)
| product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( ~ product(identity,X2,X1)
| product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
product(identity,X1,multiply(X1,identity)),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_33,plain,
( ~ product(X4,X5,X1)
| ~ product(X4,multiply(X5,X2),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_34,plain,
product(identity,multiply(X1,identity),X1),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
~ product(a,identity,a),
inference(fof_simplification,[status(thm)],[prove_right_identity]) ).
cnf(c_0_36,plain,
( ~ product(identity,X2,X1)
| product(X1,identity,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
~ product(a,identity,a),
c_0_35 ).
cnf(c_0_38,plain,
product(X1,identity,X1),
inference(spm,[status(thm)],[c_0_36,c_0_11]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.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 19:53:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.42 % Version: 3.5.1
% 0.09/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.42 % Starting sh5l with 300s (1) cores
% 0.09/0.42 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1617985 completed with status 0
% 0.09/0.42 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.09/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.42 % No SInE strategy applied
% 0.09/0.42 % Search class: FHUNS-FFSF21-SFFFFFNN
% 0.09/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.09/0.42 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with 136s (1) cores
% 0.09/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.09/0.42 % Starting new_bool_1 with 136s (1) cores
% 0.09/0.42 % G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with pid 1617992 completed with status 0
% 0.09/0.42 % Result found by G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y
% 0.09/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.42 % No SInE strategy applied
% 0.09/0.42 % Search class: FHUNS-FFSF21-SFFFFFNN
% 0.09/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.09/0.42 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with 136s (1) cores
% 0.09/0.42 % Preprocessing time : 0.001 s
% 0.09/0.42
% 0.09/0.42 % Proof found!
% 0.09/0.42 % SZS status Unsatisfiable
% 0.09/0.42 % SZS output start CNFRefutation
% See solution above
% 0.09/0.42 % Parsed axioms : 8
% 0.09/0.42 % Removed by relevancy pruning/SinE : 0
% 0.09/0.42 % Initial clauses : 8
% 0.09/0.42 % Removed in clause preprocessing : 0
% 0.09/0.42 % Initial clauses in saturation : 8
% 0.09/0.42 % Processed clauses : 67
% 0.09/0.42 % ...of these trivial : 0
% 0.09/0.42 % ...subsumed : 7
% 0.09/0.42 % ...remaining for further processing : 60
% 0.09/0.42 % Other redundant clauses eliminated : 0
% 0.09/0.42 % Clauses deleted for lack of memory : 0
% 0.09/0.42 % Backward-subsumed : 1
% 0.09/0.42 % Backward-rewritten : 2
% 0.09/0.42 % Generated clauses : 301
% 0.09/0.42 % ...of the previous two non-redundant : 219
% 0.09/0.42 % ...aggressively subsumed : 0
% 0.09/0.42 % Contextual simplify-reflections : 0
% 0.09/0.42 % Paramodulations : 301
% 0.09/0.42 % Factorizations : 0
% 0.09/0.42 % NegExts : 0
% 0.09/0.42 % Equation resolutions : 0
% 0.09/0.42 % Disequality decompositions : 0
% 0.09/0.42 % Total rewrite steps : 73
% 0.09/0.42 % ...of those cached : 48
% 0.09/0.42 % Propositional unsat checks : 0
% 0.09/0.42 % Propositional check models : 0
% 0.09/0.42 % Propositional check unsatisfiable : 0
% 0.09/0.42 % Propositional clauses : 0
% 0.09/0.42 % Propositional clauses after purity: 0
% 0.09/0.42 % Propositional unsat core size : 0
% 0.09/0.42 % Propositional preprocessing time : 0.000
% 0.09/0.42 % Propositional encoding time : 0.000
% 0.09/0.42 % Propositional solver time : 0.000
% 0.09/0.42 % Success case prop preproc time : 0.000
% 0.09/0.42 % Success case prop encoding time : 0.000
% 0.09/0.42 % Success case prop solver time : 0.000
% 0.09/0.42 % Current number of processed clauses : 57
% 0.09/0.42 % Positive orientable unit clauses : 22
% 0.09/0.42 % Positive unorientable unit clauses: 0
% 0.09/0.42 % Negative unit clauses : 0
% 0.09/0.42 % Non-unit-clauses : 35
% 0.09/0.42 % Current number of unprocessed clauses: 159
% 0.09/0.42 % ...number of literals in the above : 376
% 0.09/0.42 % Current number of archived formulas : 0
% 0.09/0.42 % Current number of archived clauses : 3
% 0.09/0.42 % Clause-clause subsumption calls (NU) : 137
% 0.09/0.42 % Rec. Clause-clause subsumption calls : 114
% 0.09/0.42 % Non-unit clause-clause subsumptions : 8
% 0.09/0.42 % Unit Clause-clause subsumption calls : 15
% 0.09/0.42 % Rewrite failures with RHS unbound : 0
% 0.09/0.42 % BW rewrite match attempts : 40
% 0.09/0.42 % BW rewrite match successes : 2
% 0.09/0.42 % Condensation attempts : 0
% 0.09/0.42 % Condensation successes : 0
% 0.09/0.42 % Termbank termtop insertions : 3270
% 0.09/0.42 % Search garbage collected termcells : 24
% 0.09/0.42
% 0.09/0.42 % -------------------------------------------------
% 0.09/0.42 % User time : 0.007 s
% 0.09/0.42 % System time : 0.005 s
% 0.09/0.42 % Total time : 0.011 s
% 0.09/0.42 % Maximum resident set size: 3332 pages
% 0.09/0.42
% 0.09/0.42 % -------------------------------------------------
% 0.09/0.42 % User time : 0.033 s
% 0.09/0.42 % System time : 0.016 s
% 0.09/0.42 % Total time : 0.049 s
% 0.09/0.42 % Maximum resident set size: 4608 pages
% 0.09/0.42 % E exiting
%------------------------------------------------------------------------------