%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP125-4.003 : 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 : n019.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 12:41:56 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 49 ( 27 unt; 8 nHn; 47 RR)
% Number of literals : 100 ( 0 equ; 51 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 : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
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(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(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(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
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(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(qg3_1,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X3,X4,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_1) ).
cnf(row_surjectivity,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
cnf(c_0_13,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_14,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_13 ).
cnf(c_0_15,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_16,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_17,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_18,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_19,plain,
( ~ product(X2,X1,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_16 ).
cnf(c_0_21,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_22,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_17 ).
cnf(c_0_23,plain,
~ equalish(e_3,e_1),
c_0_18 ).
cnf(c_0_24,plain,
( ~ group_element(X1)
| product(e_1,X1,e_3)
| product(e_1,X1,e_2)
| equalish(X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_25,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_26,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_27,plain,
( ~ product(X1,X2,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_28,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_29,plain,
~ equalish(e_1,e_3),
c_0_26 ).
cnf(c_0_30,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_31,plain,
product(e_1,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_32,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_33,plain,
~ equalish(e_2,e_3),
c_0_30 ).
cnf(c_0_34,plain,
( ~ product(e_1,X1,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_14,c_0_31]) ).
cnf(c_0_35,plain,
~ equalish(e_2,e_1),
c_0_32 ).
cnf(c_0_36,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_37,plain,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X3,X4,X1)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[qg3_1]) ).
cnf(c_0_39,plain,
product(e_1,e_2,e_3),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_24]),c_0_36])]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X3,X4,X1)
| product(X1,X2,X3) ),
c_0_38 ).
cnf(c_0_41,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
inference(fof_simplification,[status(thm)],[row_surjectivity]) ).
cnf(c_0_42,plain,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( ~ product(X1,e_2,e_3)
| product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_40,c_0_31]) ).
cnf(c_0_44,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
c_0_41 ).
cnf(c_0_45,plain,
~ product(e_3,e_2,e_3),
inference(spm,[status(thm)],[c_0_23,c_0_42]) ).
cnf(c_0_46,plain,
~ product(e_2,e_2,e_3),
inference(spm,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
product(e_2,e_1,e_1),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_25]),c_0_36])]),c_0_45]),c_0_46]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_47]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP125-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 19:59:52 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % new_bool_3 with pid 795964 completed with status 0
% 0.10/0.44 % Result found by new_bool_3
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % SubtermCWHack with pid 795967 completed with status 0
% 0.10/0.44 % Result found by SubtermCWHack
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % Preprocessing time : 0.001 s
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Unsatisfiable
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 19
% 0.10/0.44 % Removed by relevancy pruning/SinE : 0
% 0.10/0.44 % Initial clauses : 19
% 0.10/0.44 % Removed in clause preprocessing : 0
% 0.10/0.44 % Initial clauses in saturation : 19
% 0.10/0.44 % Processed clauses : 52
% 0.10/0.44 % ...of these trivial : 0
% 0.10/0.44 % ...subsumed : 2
% 0.10/0.44 % ...remaining for further processing : 50
% 0.10/0.44 % Other redundant clauses eliminated : 0
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 0
% 0.10/0.44 % Backward-rewritten : 1
% 0.10/0.44 % Generated clauses : 112
% 0.10/0.44 % ...of the previous two non-redundant : 92
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 0
% 0.10/0.44 % Paramodulations : 112
% 0.10/0.44 % Factorizations : 0
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 0
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 61
% 0.10/0.44 % ...of those cached : 51
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 49
% 0.10/0.44 % Positive orientable unit clauses : 8
% 0.10/0.44 % Positive unorientable unit clauses: 0
% 0.10/0.44 % Negative unit clauses : 16
% 0.10/0.44 % Non-unit-clauses : 25
% 0.10/0.44 % Current number of unprocessed clauses: 52
% 0.10/0.44 % ...number of literals in the above : 221
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 1
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 182
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 123
% 0.10/0.44 % Non-unit clause-clause subsumptions : 0
% 0.10/0.44 % Unit Clause-clause subsumption calls : 19
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 10
% 0.10/0.44 % BW rewrite match successes : 1
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 1712
% 0.10/0.44 % Search garbage collected termcells : 46
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.003 s
% 0.10/0.44 % System time : 0.003 s
% 0.10/0.44 % Total time : 0.007 s
% 0.10/0.44 % Maximum resident set size: 3640 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.004 s
% 0.10/0.44 % System time : 0.009 s
% 0.10/0.44 % Total time : 0.013 s
% 0.10/0.44 % Maximum resident set size: 4864 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------