%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP047-2 : 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 : n010.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 12:37:34 PM UTC 2026
% Result : Unsatisfiable 0.68s 0.57s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 38 ( 18 unt; 0 nHn; 27 RR)
% Number of literals : 79 ( 0 equ; 44 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity1,axiom,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',associativity1) ).
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/GRP005-0.ax',associativity2) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',left_identity) ).
cnf(product_substitution3,axiom,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',left_inverse) ).
cnf(a_equals_b,hypothesis,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function1) ).
cnf(total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function2) ).
cnf(prove_multiply_substitution2,negated_conjecture,
~ equalish(multiply(c,a),multiply(c,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_substitution2) ).
cnf(c_0_9,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity1]) ).
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(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_9 ).
cnf(c_0_12,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_13,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
inference(fof_simplification,[status(thm)],[product_substitution3]) ).
cnf(c_0_14,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_10 ).
cnf(c_0_15,plain,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_17,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
c_0_13 ).
cnf(c_0_18,hypothesis,
equalish(a,b),
a_equals_b ).
cnf(c_0_19,plain,
( ~ product(X4,X2,X3)
| ~ product(X4,identity,X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_20,plain,
( ~ product(X1,inverse(X2),identity)
| product(X1,identity,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_22,hypothesis,
( ~ product(X1,X2,a)
| product(X1,X2,b) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( ~ product(inverse(X2),identity,X1)
| product(X1,X2,identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_24,plain,
product(inverse(inverse(X1)),identity,X1),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_25,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_26,plain,
( ~ product(X1,X5,X3)
| ~ product(X5,X4,X2)
| product(X1,X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_27,hypothesis,
product(identity,a,b),
inference(spm,[status(thm)],[c_0_22,c_0_12]) ).
cnf(c_0_28,plain,
product(X1,inverse(X1),identity),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_25 ).
cnf(c_0_30,hypothesis,
( ~ product(X1,identity,X2)
| product(X1,b,multiply(X2,a)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
product(X1,identity,X1),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
~ equalish(multiply(c,a),multiply(c,b)),
inference(fof_simplification,[status(thm)],[prove_multiply_substitution2]) ).
cnf(c_0_33,plain,
( ~ product(X2,X3,X1)
| equalish(X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_34,hypothesis,
product(X1,b,multiply(X1,a)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
~ equalish(multiply(c,a),multiply(c,b)),
c_0_32 ).
cnf(c_0_36,hypothesis,
equalish(multiply(X1,a),multiply(X1,b)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP047-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 19:56:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.68/0.57 % Version: 3.5.1
% 0.68/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.68/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.68/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.68/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.68/0.57 % Starting sh5l with 300s (1) cores
% 0.68/0.57 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3378650 completed with status 0
% 0.68/0.57 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.68/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.68/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.68/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.68/0.57 % No SInE strategy applied
% 0.68/0.57 % Search class: FHUNS-FFSF21-SFFFFFNN
% 0.68/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.68/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.68/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.68/0.57 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with 136s (1) cores
% 0.68/0.57 % Starting new_bool_3 with 136s (1) cores
% 0.68/0.57 % Starting new_bool_1 with 136s (1) cores
% 0.68/0.57 % new_bool_3 with pid 3378659 completed with status 0
% 0.68/0.57 % Result found by new_bool_3
% 0.68/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.68/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.68/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.68/0.57 % No SInE strategy applied
% 0.68/0.57 % Search class: FHUNS-FFSF21-SFFFFFNN
% 0.68/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.68/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.68/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.68/0.57 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with 136s (1) cores
% 0.68/0.57 % Starting new_bool_3 with 136s (1) cores
% 0.68/0.57 % Preprocessing time : 0.001 s
% 0.68/0.57 % Presaturation interreduction done
% 0.68/0.57
% 0.68/0.57 % Proof found!
% 0.68/0.57 % SZS status Unsatisfiable
% 0.68/0.57 % SZS output start CNFRefutation
% See solution above
% 0.68/0.57 % Parsed axioms : 9
% 0.68/0.57 % Removed by relevancy pruning/SinE : 0
% 0.68/0.57 % Initial clauses : 9
% 0.68/0.57 % Removed in clause preprocessing : 0
% 0.68/0.57 % Initial clauses in saturation : 9
% 0.68/0.57 % Processed clauses : 1215
% 0.68/0.57 % ...of these trivial : 128
% 0.68/0.57 % ...subsumed : 86
% 0.68/0.57 % ...remaining for further processing : 1001
% 0.68/0.57 % Other redundant clauses eliminated : 0
% 0.68/0.57 % Clauses deleted for lack of memory : 0
% 0.68/0.57 % Backward-subsumed : 43
% 0.68/0.57 % Backward-rewritten : 42
% 0.68/0.57 % Generated clauses : 9593
% 0.68/0.57 % ...of the previous two non-redundant : 7840
% 0.68/0.57 % ...aggressively subsumed : 0
% 0.68/0.57 % Contextual simplify-reflections : 0
% 0.68/0.57 % Paramodulations : 9593
% 0.68/0.57 % Factorizations : 0
% 0.68/0.57 % NegExts : 0
% 0.68/0.57 % Equation resolutions : 0
% 0.68/0.57 % Disequality decompositions : 0
% 0.68/0.57 % Total rewrite steps : 1897
% 0.68/0.57 % ...of those cached : 1391
% 0.68/0.57 % Propositional unsat checks : 0
% 0.68/0.57 % Propositional check models : 0
% 0.68/0.57 % Propositional check unsatisfiable : 0
% 0.68/0.57 % Propositional clauses : 0
% 0.68/0.57 % Propositional clauses after purity: 0
% 0.68/0.57 % Propositional unsat core size : 0
% 0.68/0.57 % Propositional preprocessing time : 0.000
% 0.68/0.57 % Propositional encoding time : 0.000
% 0.68/0.57 % Propositional solver time : 0.000
% 0.68/0.57 % Success case prop preproc time : 0.000
% 0.68/0.57 % Success case prop encoding time : 0.000
% 0.68/0.57 % Success case prop solver time : 0.000
% 0.68/0.57 % Current number of processed clauses : 907
% 0.68/0.57 % Positive orientable unit clauses : 474
% 0.68/0.57 % Positive unorientable unit clauses: 0
% 0.68/0.57 % Negative unit clauses : 0
% 0.68/0.57 % Non-unit-clauses : 433
% 0.68/0.57 % Current number of unprocessed clauses: 6607
% 0.68/0.57 % ...number of literals in the above : 10261
% 0.68/0.57 % Current number of archived formulas : 0
% 0.68/0.57 % Current number of archived clauses : 94
% 0.68/0.57 % Clause-clause subsumption calls (NU) : 17152
% 0.68/0.57 % Rec. Clause-clause subsumption calls : 15969
% 0.68/0.57 % Non-unit clause-clause subsumptions : 129
% 0.68/0.57 % Unit Clause-clause subsumption calls : 255
% 0.68/0.57 % Rewrite failures with RHS unbound : 0
% 0.68/0.57 % BW rewrite match attempts : 1476
% 0.68/0.57 % BW rewrite match successes : 42
% 0.68/0.57 % Condensation attempts : 0
% 0.68/0.57 % Condensation successes : 0
% 0.68/0.57 % Termbank termtop insertions : 113691
% 0.68/0.57 % Search garbage collected termcells : 24
% 0.68/0.57
% 0.68/0.57 % -------------------------------------------------
% 0.68/0.57 % User time : 0.131 s
% 0.68/0.57 % System time : 0.008 s
% 0.68/0.57 % Total time : 0.140 s
% 0.68/0.57 % Maximum resident set size: 3640 pages
% 0.68/0.57
% 0.68/0.57 % -------------------------------------------------
% 0.68/0.57 % User time : 0.580 s
% 0.68/0.57 % System time : 0.035 s
% 0.68/0.57 % Total time : 0.615 s
% 0.68/0.57 % Maximum resident set size: 4864 pages
% 0.68/0.57 % E exiting
%------------------------------------------------------------------------------