%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP001-1 : 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 : n008.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 12:37:23 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 38 ( 24 unt; 0 nHn; 24 RR)
% Number of literals : 63 ( 10 equ; 28 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(square_element,hypothesis,
product(X1,X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_element) ).
cnf(a_times_b_is_c,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
cnf(c_0_9,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_10,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_11,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_9 ).
cnf(c_0_12,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_13,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_10 ).
cnf(c_0_14,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_15,plain,
( ~ product(X2,identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_17,plain,
( ~ product(X4,identity,X3)
| ~ product(X4,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_20,plain,
( ~ product(X3,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_18]) ).
cnf(c_0_21,hypothesis,
product(X1,X1,identity),
square_element ).
cnf(c_0_22,plain,
( ~ product(identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_11,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
product(a,b,c),
a_times_b_is_c ).
cnf(c_0_24,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_25,hypothesis,
product(identity,X1,inverse(X1)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_27,negated_conjecture,
( ~ product(X3,a,X1)
| ~ product(X3,c,X2)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_28,hypothesis,
inverse(X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_29,hypothesis,
( ~ product(c,a,X1)
| product(X1,b,identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_30,plain,
( ~ product(X3,X2,X1)
| product(X1,X2,X3) ),
inference(rw,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_31,hypothesis,
product(multiply(c,a),b,identity),
inference(spm,[status(thm)],[c_0_29,c_0_16]) ).
cnf(c_0_32,hypothesis,
product(identity,b,multiply(c,a)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,hypothesis,
multiply(c,a) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_32]),c_0_26]) ).
cnf(c_0_34,negated_conjecture,
~ product(b,a,c),
inference(fof_simplification,[status(thm)],[prove_b_times_a_is_c]) ).
cnf(c_0_35,hypothesis,
product(c,a,b),
inference(spm,[status(thm)],[c_0_16,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
~ product(b,a,c),
c_0_34 ).
cnf(c_0_37,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 19:53:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.45 % Version: 3.5.1
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3469497 completed with status 0
% 0.11/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.45 % No SInE strategy applied
% 0.11/0.45 % Search class: FHUSM-FFSF21-SFFFFFNN
% 0.11/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 136s (1) cores
% 0.11/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.45 % new_bool_1 with pid 3469505 completed with status 0
% 0.11/0.45 % Result found by new_bool_1
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.45 % No SInE strategy applied
% 0.11/0.45 % Search class: FHUSM-FFSF21-SFFFFFNN
% 0.11/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 136s (1) cores
% 0.11/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.45 % Preprocessing time : 0.001 s
% 0.11/0.45 % Presaturation interreduction done
% 0.11/0.45
% 0.11/0.45 % Proof found!
% 0.11/0.45 % SZS status Unsatisfiable
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.45 % Parsed axioms : 11
% 0.11/0.45 % Removed by relevancy pruning/SinE : 0
% 0.11/0.45 % Initial clauses : 11
% 0.11/0.45 % Removed in clause preprocessing : 0
% 0.11/0.45 % Initial clauses in saturation : 11
% 0.11/0.45 % Processed clauses : 69
% 0.11/0.45 % ...of these trivial : 4
% 0.11/0.45 % ...subsumed : 7
% 0.11/0.45 % ...remaining for further processing : 58
% 0.11/0.45 % Other redundant clauses eliminated : 0
% 0.11/0.45 % Clauses deleted for lack of memory : 0
% 0.11/0.45 % Backward-subsumed : 1
% 0.11/0.45 % Backward-rewritten : 15
% 0.11/0.45 % Generated clauses : 139
% 0.11/0.45 % ...of the previous two non-redundant : 101
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 0
% 0.11/0.45 % Paramodulations : 139
% 0.11/0.45 % Factorizations : 0
% 0.11/0.45 % NegExts : 0
% 0.11/0.45 % Equation resolutions : 0
% 0.11/0.45 % Disequality decompositions : 0
% 0.11/0.45 % Total rewrite steps : 81
% 0.11/0.45 % ...of those cached : 51
% 0.11/0.45 % Propositional unsat checks : 0
% 0.11/0.45 % Propositional check models : 0
% 0.11/0.45 % Propositional check unsatisfiable : 0
% 0.11/0.45 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 31
% 0.11/0.45 % Positive orientable unit clauses : 15
% 0.11/0.45 % Positive unorientable unit clauses: 0
% 0.11/0.45 % Negative unit clauses : 1
% 0.11/0.45 % Non-unit-clauses : 15
% 0.11/0.45 % Current number of unprocessed clauses: 42
% 0.11/0.45 % ...number of literals in the above : 98
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 27
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 152
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 133
% 0.11/0.45 % Non-unit clause-clause subsumptions : 8
% 0.11/0.45 % Unit Clause-clause subsumption calls : 0
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 30
% 0.11/0.45 % BW rewrite match successes : 5
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 1619
% 0.11/0.45 % Search garbage collected termcells : 18
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.006 s
% 0.11/0.45 % System time : 0.001 s
% 0.11/0.45 % Total time : 0.007 s
% 0.11/0.45 % Maximum resident set size: 3588 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.027 s
% 0.11/0.45 % System time : 0.011 s
% 0.11/0.45 % Total time : 0.038 s
% 0.11/0.45 % Maximum resident set size: 4864 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------