%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP009-1 : 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 : n014.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 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 34 ( 21 unt; 0 nHn; 26 RR)
% Number of literals : 59 ( 11 equ; 28 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 56 ( 0 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/GRP003-0.ax',associativity2) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(c_is_an_inverse_of_b,hypothesis,
product(c,b,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_an_inverse_of_b) ).
cnf(a_is_an_inverse_of_b,hypothesis,
product(a,b,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_an_inverse_of_b) ).
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(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(prove_a_equals_c,negated_conjecture,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_equals_c) ).
cnf(c_0_8,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_9,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_8 ).
cnf(c_0_10,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_11,hypothesis,
product(c,b,identity),
c_is_an_inverse_of_b ).
cnf(c_0_12,hypothesis,
product(a,b,identity),
a_is_an_inverse_of_b ).
cnf(c_0_13,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_14,plain,
( ~ product(X4,identity,X3)
| ~ product(X4,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,hypothesis,
( ~ product(X3,c,X1)
| ~ product(X3,identity,X2)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_16,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_17,hypothesis,
( ~ product(X3,a,X1)
| ~ product(X3,identity,X2)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_18,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_13 ).
cnf(c_0_19,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_20,plain,
( ~ product(inverse(inverse(X1)),identity,X2)
| product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_21,hypothesis,
( ~ product(X2,c,X1)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,hypothesis,
( ~ product(X2,a,X1)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_23,plain,
( ~ product(identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
product(identity,X1,inverse(inverse(X1))),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_25,hypothesis,
product(identity,b,inverse(c)),
inference(spm,[status(thm)],[c_0_21,c_0_10]) ).
cnf(c_0_26,hypothesis,
product(identity,b,inverse(a)),
inference(spm,[status(thm)],[c_0_22,c_0_10]) ).
cnf(c_0_27,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,hypothesis,
inverse(c) = b,
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
a != c,
inference(fof_simplification,[status(thm)],[prove_a_equals_c]) ).
cnf(c_0_30,hypothesis,
inverse(a) = b,
inference(spm,[status(thm)],[c_0_23,c_0_26]) ).
cnf(c_0_31,hypothesis,
inverse(b) = c,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
a != c,
c_0_29 ).
cnf(c_0_33,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_30]),c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 19:53:21 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 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
% 0.14/0.42 % Version: 3.5.1
% 0.14/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % Starting sh5l with 300s (1) cores
% 0.14/0.42 % sh5l with pid 2206916 completed with status 0
% 0.14/0.42 % Result found by sh5l
% 0.14/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % Starting sh5l with 300s (1) cores
% 0.14/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.42 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.42 % Search class: FHUSM-FFSF11-SFFFFFNN
% 0.14/0.42 % partial match(1): FHUSM-FFSF21-SFFFFFNN
% 0.14/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.42 % SubtermCWHack with pid 2206922 completed with status 0
% 0.14/0.42 % Result found by SubtermCWHack
% 0.14/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % Starting sh5l with 300s (1) cores
% 0.14/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.42 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.42 % Search class: FHUSM-FFSF11-SFFFFFNN
% 0.14/0.42 % partial match(1): FHUSM-FFSF21-SFFFFFNN
% 0.14/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.42 % Preprocessing time : 0.001 s
% 0.14/0.42
% 0.14/0.42 % Proof found!
% 0.14/0.42 % SZS status Unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation
% See solution above
% 0.14/0.42 % Parsed axioms : 11
% 0.14/0.42 % Removed by relevancy pruning/SinE : 1
% 0.14/0.42 % Initial clauses : 10
% 0.14/0.42 % Removed in clause preprocessing : 0
% 0.14/0.42 % Initial clauses in saturation : 10
% 0.14/0.42 % Processed clauses : 59
% 0.14/0.42 % ...of these trivial : 0
% 0.14/0.42 % ...subsumed : 15
% 0.14/0.42 % ...remaining for further processing : 43
% 0.14/0.42 % Other redundant clauses eliminated : 0
% 0.14/0.42 % Clauses deleted for lack of memory : 0
% 0.14/0.42 % Backward-subsumed : 2
% 0.14/0.42 % Backward-rewritten : 4
% 0.14/0.42 % Generated clauses : 143
% 0.14/0.42 % ...of the previous two non-redundant : 106
% 0.14/0.42 % ...aggressively subsumed : 0
% 0.14/0.42 % Contextual simplify-reflections : 0
% 0.14/0.42 % Paramodulations : 143
% 0.14/0.42 % Factorizations : 0
% 0.14/0.42 % NegExts : 0
% 0.14/0.42 % Equation resolutions : 0
% 0.14/0.42 % Disequality decompositions : 0
% 0.14/0.42 % Total rewrite steps : 71
% 0.14/0.42 % ...of those cached : 57
% 0.14/0.42 % Propositional unsat checks : 0
% 0.14/0.42 % Propositional check models : 0
% 0.14/0.42 % Propositional check unsatisfiable : 0
% 0.14/0.42 % Propositional clauses : 0
% 0.14/0.42 % Propositional clauses after purity: 0
% 0.14/0.42 % Propositional unsat core size : 0
% 0.14/0.42 % Propositional preprocessing time : 0.000
% 0.14/0.42 % Propositional encoding time : 0.000
% 0.14/0.42 % Propositional solver time : 0.000
% 0.14/0.42 % Success case prop preproc time : 0.000
% 0.14/0.42 % Success case prop encoding time : 0.000
% 0.14/0.42 % Success case prop solver time : 0.000
% 0.14/0.42 % Current number of processed clauses : 37
% 0.14/0.42 % Positive orientable unit clauses : 13
% 0.14/0.42 % Positive unorientable unit clauses: 0
% 0.14/0.42 % Negative unit clauses : 1
% 0.14/0.42 % Non-unit-clauses : 23
% 0.14/0.42 % Current number of unprocessed clauses: 55
% 0.14/0.42 % ...number of literals in the above : 150
% 0.14/0.42 % Current number of archived formulas : 0
% 0.14/0.42 % Current number of archived clauses : 6
% 0.14/0.42 % Clause-clause subsumption calls (NU) : 200
% 0.14/0.42 % Rec. Clause-clause subsumption calls : 188
% 0.14/0.42 % Non-unit clause-clause subsumptions : 17
% 0.14/0.42 % Unit Clause-clause subsumption calls : 0
% 0.14/0.42 % Rewrite failures with RHS unbound : 0
% 0.14/0.42 % BW rewrite match attempts : 8
% 0.14/0.42 % BW rewrite match successes : 3
% 0.14/0.42 % Condensation attempts : 0
% 0.14/0.42 % Condensation successes : 0
% 0.14/0.42 % Termbank termtop insertions : 1632
% 0.14/0.42 % Search garbage collected termcells : 21
% 0.14/0.42
% 0.14/0.42 % -------------------------------------------------
% 0.14/0.42 % User time : 0.004 s
% 0.14/0.42 % System time : 0.003 s
% 0.14/0.42 % Total time : 0.008 s
% 0.14/0.42 % Maximum resident set size: 3640 pages
% 0.14/0.42
% 0.14/0.42 % -------------------------------------------------
% 0.14/0.42 % User time : 0.004 s
% 0.14/0.42 % System time : 0.007 s
% 0.14/0.42 % Total time : 0.011 s
% 0.14/0.42 % Maximum resident set size: 4864 pages
% 0.14/0.42 % E exiting
%------------------------------------------------------------------------------