%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP123-6.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:37:57 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of clauses : 50 ( 26 unt; 8 nHn; 46 RR)
% Number of literals : 99 ( 0 equ; 48 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 66 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product1_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product1(X1,X2,e_3)
| product1(X1,X2,e_2)
| product1(X1,X2,e_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).
cnf(product1_right_cancellation,axiom,
( ~ product1(X1,X4,X3)
| ~ product1(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(product1_left_cancellation,axiom,
( ~ product1(X4,X2,X3)
| ~ product1(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_left_cancellation) ).
cnf(product1_idempotence,axiom,
product1(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(product2_total_function2,axiom,
( ~ product2(X1,X2,X4)
| ~ product2(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).
cnf(qg1a,negated_conjecture,
( ~ product1(X3,X2,X4)
| ~ product1(X1,X2,X3)
| product2(X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1a) ).
cnf(product2_idempotence,axiom,
product2(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(c_0_14,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product1(X1,X2,e_3)
| product1(X1,X2,e_2)
| product1(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product1_total_function1]) ).
cnf(c_0_15,plain,
( ~ product1(X1,X4,X3)
| ~ product1(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product1_right_cancellation]) ).
cnf(c_0_16,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product1(X1,X2,e_3)
| product1(X1,X2,e_2)
| product1(X1,X2,e_1) ),
c_0_14 ).
cnf(c_0_17,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_18,plain,
( ~ product1(X4,X2,X3)
| ~ product1(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product1_left_cancellation]) ).
cnf(c_0_19,plain,
( ~ product1(X1,X4,X3)
| ~ product1(X1,X2,X3)
| equalish(X2,X4) ),
c_0_15 ).
cnf(c_0_20,axiom,
product1(X1,X1,X1),
product1_idempotence ).
cnf(c_0_21,plain,
( ~ group_element(X1)
| product1(X1,e_3,e_3)
| product1(X1,e_3,e_2)
| product1(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_23,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_24,plain,
( ~ product1(X4,X2,X3)
| ~ product1(X1,X2,X3)
| equalish(X1,X4) ),
c_0_18 ).
cnf(c_0_25,plain,
( ~ product1(X2,X1,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( product1(e_1,e_3,e_1)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
~ equalish(e_3,e_1),
c_0_23 ).
cnf(c_0_28,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_29,plain,
( ~ product2(X1,X2,X4)
| ~ product2(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product2_total_function2]) ).
cnf(c_0_30,negated_conjecture,
( ~ product1(X3,X2,X4)
| ~ product1(X1,X2,X3)
| product2(X4,X1,X2) ),
inference(fof_simplification,[status(thm)],[qg1a]) ).
cnf(c_0_31,plain,
( ~ product1(X1,X2,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_32,plain,
( product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_33,plain,
~ equalish(e_1,e_3),
c_0_28 ).
cnf(c_0_34,plain,
( ~ product2(X1,X2,X4)
| ~ product2(X1,X2,X3)
| equalish(X3,X4) ),
c_0_29 ).
cnf(c_0_35,axiom,
product2(X1,X1,X1),
product2_idempotence ).
cnf(c_0_36,negated_conjecture,
( ~ product1(X3,X2,X4)
| ~ product1(X1,X2,X3)
| product2(X4,X1,X2) ),
c_0_30 ).
cnf(c_0_37,plain,
product1(e_1,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_38,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_39,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_40,plain,
( ~ product2(X2,X2,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( ~ product1(X1,e_3,e_1)
| product2(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
~ equalish(e_3,e_2),
c_0_38 ).
cnf(c_0_43,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
~ product1(e_2,e_3,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_45,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_46,plain,
( product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,plain,
~ equalish(e_2,e_3),
c_0_45 ).
cnf(c_0_48,plain,
product1(e_2,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_46]),c_0_47]) ).
cnf(c_0_49,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_48]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-6.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 19:57:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.43 % Version: 3.5.1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % new_bool_3 with pid 3281189 completed with status 0
% 0.14/0.43 % Result found by new_bool_3
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.43 % Search class: FGUNS-FFSS00-SFFFFFNN
% 0.14/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.43 % SubtermCWHack with pid 3281192 completed with status 0
% 0.14/0.43 % Result found by SubtermCWHack
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.43 % Search class: FGUNS-FFSS00-SFFFFFNN
% 0.14/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.43 % Preprocessing time : 0.001 s
% 0.14/0.43
% 0.14/0.43 % Proof found!
% 0.14/0.43 % SZS status Unsatisfiable
% 0.14/0.43 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43 % Parsed axioms : 20
% 0.14/0.43 % Removed by relevancy pruning/SinE : 0
% 0.14/0.43 % Initial clauses : 20
% 0.14/0.43 % Removed in clause preprocessing : 0
% 0.14/0.43 % Initial clauses in saturation : 20
% 0.14/0.43 % Processed clauses : 68
% 0.14/0.43 % ...of these trivial : 0
% 0.14/0.43 % ...subsumed : 8
% 0.14/0.43 % ...remaining for further processing : 60
% 0.14/0.43 % Other redundant clauses eliminated : 0
% 0.14/0.43 % Clauses deleted for lack of memory : 0
% 0.14/0.43 % Backward-subsumed : 1
% 0.14/0.43 % Backward-rewritten : 2
% 0.14/0.43 % Generated clauses : 135
% 0.14/0.43 % ...of the previous two non-redundant : 98
% 0.14/0.43 % ...aggressively subsumed : 0
% 0.14/0.43 % Contextual simplify-reflections : 0
% 0.14/0.43 % Paramodulations : 134
% 0.14/0.43 % Factorizations : 0
% 0.14/0.43 % NegExts : 0
% 0.14/0.43 % Equation resolutions : 0
% 0.14/0.43 % Disequality decompositions : 0
% 0.14/0.43 % Total rewrite steps : 57
% 0.14/0.43 % ...of those cached : 43
% 0.14/0.43 % Propositional unsat checks : 0
% 0.14/0.43 % Propositional check models : 0
% 0.14/0.43 % Propositional check unsatisfiable : 0
% 0.14/0.43 % Propositional clauses : 0
% 0.14/0.43 % Propositional clauses after purity: 0
% 0.14/0.43 % Propositional unsat core size : 0
% 0.14/0.43 % Propositional preprocessing time : 0.000
% 0.14/0.43 % Propositional encoding time : 0.000
% 0.14/0.43 % Propositional solver time : 0.000
% 0.14/0.43 % Success case prop preproc time : 0.000
% 0.14/0.43 % Success case prop encoding time : 0.000
% 0.14/0.43 % Success case prop solver time : 0.000
% 0.14/0.43 % Current number of processed clauses : 56
% 0.14/0.43 % Positive orientable unit clauses : 9
% 0.14/0.43 % Positive unorientable unit clauses: 0
% 0.14/0.43 % Negative unit clauses : 10
% 0.14/0.43 % Non-unit-clauses : 37
% 0.14/0.43 % Current number of unprocessed clauses: 47
% 0.14/0.43 % ...number of literals in the above : 188
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 4
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 171
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 162
% 0.14/0.43 % Non-unit clause-clause subsumptions : 7
% 0.14/0.43 % Unit Clause-clause subsumption calls : 15
% 0.14/0.43 % Rewrite failures with RHS unbound : 0
% 0.14/0.43 % BW rewrite match attempts : 12
% 0.14/0.43 % BW rewrite match successes : 2
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 2052
% 0.14/0.43 % Search garbage collected termcells : 52
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.004 s
% 0.14/0.43 % System time : 0.002 s
% 0.14/0.43 % Total time : 0.007 s
% 0.14/0.43 % Maximum resident set size: 3640 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.006 s
% 0.14/0.43 % System time : 0.007 s
% 0.14/0.43 % Total time : 0.013 s
% 0.14/0.43 % Maximum resident set size: 4864 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------