%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP130-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:42:36 PM UTC 2026
% Result : Unsatisfiable 0.16s 5.56s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of clauses : 51 ( 18 unt; 19 nHn; 51 RR)
% Number of literals : 119 ( 0 equ; 49 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 64 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(qg3_1,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X4,X2,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_1) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(qg3,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X1,X2,X3)
| product(X4,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
cnf(product_left_cancellation,axiom,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(product_total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
cnf(c_0_11,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_12,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_11 ).
cnf(c_0_13,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_14,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X4,X2,X1)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[qg3_1]) ).
cnf(c_0_15,plain,
( ~ group_element(X1)
| product(X1,e_3,e_1)
| product(X1,e_3,e_2)
| product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_17,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X4,X2,X1)
| product(X1,X2,X3) ),
c_0_14 ).
cnf(c_0_18,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X1,X2,X3)
| product(X4,X2,X1) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_20,negated_conjecture,
( ~ product(e_1,X1,e_1)
| product(e_1,e_3,X1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X1,X2,X3)
| product(X4,X2,X1) ),
c_0_19 ).
cnf(c_0_22,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ product(e_1,X1,e_3)
| product(e_3,X1,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_25,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_26,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_27,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_24 ).
cnf(c_0_28,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( ~ product(e_2,X1,e_1)
| product(e_2,e_3,X1)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_30,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_31,plain,
( ~ product(X1,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( product(e_3,e_3,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_33,plain,
~ equalish(e_3,e_2),
c_0_30 ).
cnf(c_0_34,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_35,negated_conjecture,
( ~ product(X1,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_36,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_37,plain,
~ equalish(e_2,e_1),
c_0_34 ).
cnf(c_0_38,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_39,negated_conjecture,
( ~ product(e_2,X1,e_3)
| product(e_3,X1,e_2)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_36]) ).
cnf(c_0_40,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_41,negated_conjecture,
( ~ product(X1,e_3,e_2)
| product(e_2,e_3,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_39,c_0_36]) ).
cnf(c_0_43,plain,
~ equalish(e_3,e_1),
c_0_40 ).
cnf(c_0_44,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_45,negated_conjecture,
product(e_2,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_46,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_44 ).
cnf(c_0_47,negated_conjecture,
( ~ product(e_2,X1,e_2)
| product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
( ~ product(e_2,e_3,X1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_46,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_47,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_48]),c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP130-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/5.38 % Computer : n011.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sun Sep 20 20:01:16 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.46 Running first-order theorem proving
% 0.16/5.46 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.16/5.56 % Version: 3.5.1
% 0.16/5.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.56 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.56 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.56 % Starting sh5l with 300s (1) cores
% 0.16/5.56 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 42638 completed with status 0
% 0.16/5.56 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/5.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.56 % No SInE strategy applied
% 0.16/5.56 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.16/5.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.56 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/5.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.16/5.56 % Starting new_bool_3 with 136s (1) cores
% 0.16/5.56 % Starting new_bool_1 with 136s (1) cores
% 0.16/5.56 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 42643 completed with status 0
% 0.16/5.56 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/5.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.56 % No SInE strategy applied
% 0.16/5.56 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.16/5.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.56 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/5.56 % Preprocessing time : 0.002 s
% 0.16/5.56 % Presaturation interreduction done
% 0.16/5.56
% 0.16/5.56 % Proof found!
% 0.16/5.56 % SZS status Unsatisfiable
% 0.16/5.56 % SZS output start CNFRefutation
% See solution above
% 0.16/5.56 % Parsed axioms : 18
% 0.16/5.56 % Removed by relevancy pruning/SinE : 0
% 0.16/5.56 % Initial clauses : 18
% 0.16/5.56 % Removed in clause preprocessing : 0
% 0.16/5.56 % Initial clauses in saturation : 18
% 0.16/5.56 % Processed clauses : 239
% 0.16/5.56 % ...of these trivial : 0
% 0.16/5.56 % ...subsumed : 33
% 0.16/5.56 % ...remaining for further processing : 206
% 0.16/5.56 % Other redundant clauses eliminated : 0
% 0.16/5.56 % Clauses deleted for lack of memory : 0
% 0.16/5.56 % Backward-subsumed : 34
% 0.16/5.56 % Backward-rewritten : 40
% 0.16/5.56 % Generated clauses : 832
% 0.16/5.56 % ...of the previous two non-redundant : 825
% 0.16/5.56 % ...aggressively subsumed : 0
% 0.16/5.56 % Contextual simplify-reflections : 0
% 0.16/5.56 % Paramodulations : 832
% 0.16/5.56 % Factorizations : 0
% 0.16/5.56 % NegExts : 0
% 0.16/5.56 % Equation resolutions : 0
% 0.16/5.56 % Disequality decompositions : 0
% 0.16/5.56 % Total rewrite steps : 43
% 0.16/5.56 % ...of those cached : 39
% 0.16/5.56 % Propositional unsat checks : 0
% 0.16/5.56 % Propositional check models : 0
% 0.16/5.56 % Propositional check unsatisfiable : 0
% 0.16/5.56 % Propositional clauses : 0
% 0.16/5.56 % Propositional clauses after purity: 0
% 0.16/5.56 % Propositional unsat core size : 0
% 0.16/5.56 % Propositional preprocessing time : 0.000
% 0.16/5.56 % Propositional encoding time : 0.000
% 0.16/5.56 % Propositional solver time : 0.000
% 0.16/5.56 % Success case prop preproc time : 0.000
% 0.16/5.56 % Success case prop encoding time : 0.000
% 0.16/5.56 % Success case prop solver time : 0.000
% 0.16/5.56 % Current number of processed clauses : 114
% 0.16/5.56 % Positive orientable unit clauses : 7
% 0.16/5.56 % Positive unorientable unit clauses: 0
% 0.16/5.56 % Negative unit clauses : 6
% 0.16/5.56 % Non-unit-clauses : 101
% 0.16/5.56 % Current number of unprocessed clauses: 617
% 0.16/5.56 % ...number of literals in the above : 2391
% 0.16/5.56 % Current number of archived formulas : 0
% 0.16/5.56 % Current number of archived clauses : 92
% 0.16/5.56 % Clause-clause subsumption calls (NU) : 1818
% 0.16/5.56 % Rec. Clause-clause subsumption calls : 911
% 0.16/5.56 % Non-unit clause-clause subsumptions : 62
% 0.16/5.56 % Unit Clause-clause subsumption calls : 201
% 0.16/5.56 % Rewrite failures with RHS unbound : 0
% 0.16/5.56 % BW rewrite match attempts : 16
% 0.16/5.56 % BW rewrite match successes : 4
% 0.16/5.56 % Condensation attempts : 0
% 0.16/5.56 % Condensation successes : 0
% 0.16/5.56 % Termbank termtop insertions : 12534
% 0.16/5.56 % Search garbage collected termcells : 48
% 0.16/5.56
% 0.16/5.56 % -------------------------------------------------
% 0.16/5.56 % User time : 0.034 s
% 0.16/5.56 % System time : 0.004 s
% 0.16/5.56 % Total time : 0.038 s
% 0.16/5.56 % Maximum resident set size: 3640 pages
% 0.16/5.56
% 0.16/5.56 % -------------------------------------------------
% 0.16/5.56 % User time : 0.131 s
% 0.16/5.56 % System time : 0.022 s
% 0.16/5.56 % Total time : 0.153 s
% 0.16/5.56 % Maximum resident set size: 4864 pages
% 0.16/5.56 % E exiting
%------------------------------------------------------------------------------