%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP045-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:37:33 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.52s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 43 ( 19 unt; 0 nHn; 34 RR)
% Number of literals : 87 ( 0 equ; 47 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 100 ( 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/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity1) ).
cnf(total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function2) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_identity) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_inverse) ).
cnf(product_substitution3,axiom,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).
cnf(a_equals_b,hypothesis,
equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function1) ).
cnf(associativity2,axiom,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity2) ).
cnf(product_with_a,hypothesis,
product(c,a,result),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_with_a) ).
cnf(prove_product_with_b,negated_conjecture,
~ product(c,b,result),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_product_with_b) ).
cnf(c_0_10,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_11,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_12,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_10 ).
cnf(c_0_13,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_14,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_11 ).
cnf(c_0_15,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_16,plain,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
inference(fof_simplification,[status(thm)],[product_substitution3]) ).
cnf(c_0_18,plain,
( ~ product(inverse(X2),X2,X1)
| equalish(X1,identity) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( ~ product(X1,X3,X2)
| product(inverse(X1),X2,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_20,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
c_0_17 ).
cnf(c_0_21,plain,
( ~ product(X2,X1,X2)
| equalish(X1,identity) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( ~ equalish(X1,X2)
| product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_23,plain,
( ~ product(identity,X2,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_24,hypothesis,
equalish(a,b),
a_equals_b ).
cnf(c_0_25,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_26,plain,
( ~ product(X2,inverse(X2),X1)
| equalish(X1,identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_27,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_28,plain,
( ~ product(identity,X2,X1)
| product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,hypothesis,
product(identity,a,b),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_30,plain,
( ~ equalish(multiply(X1,X2),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_31,plain,
equalish(multiply(X1,inverse(X1)),identity),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_32,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_27 ).
cnf(c_0_33,hypothesis,
product(identity,b,a),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
product(X1,inverse(X1),identity),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,hypothesis,
( ~ product(X3,identity,X1)
| ~ product(X3,a,X2)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,hypothesis,
product(c,a,result),
product_with_a ).
cnf(c_0_37,plain,
( ~ product(inverse(X1),X3,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
~ product(c,b,result),
inference(fof_simplification,[status(thm)],[prove_product_with_b]) ).
cnf(c_0_39,hypothesis,
( ~ product(c,identity,X1)
| product(X1,b,result) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
product(X1,identity,X1),
inference(spm,[status(thm)],[c_0_37,c_0_15]) ).
cnf(c_0_41,negated_conjecture,
~ product(c,b,result),
c_0_38 ).
cnf(c_0_42,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP045-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 19:55:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.52 % Version: 3.5.1
% 0.13/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.52 % Starting sh5l with 300s (1) cores
% 0.13/0.52 % new_bool_3 with pid 1623757 completed with status 9
% 0.13/0.52 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1623756 completed with status 0
% 0.13/0.52 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.52 % No SInE strategy applied
% 0.13/0.52 % Search class: FHUNS-FFSF21-SFFFFFNN
% 0.13/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.52 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with 136s (1) cores
% 0.13/0.52 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.52 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.52 % G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with pid 1623764 completed with status 0
% 0.13/0.52 % Result found by G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y
% 0.13/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.52 % No SInE strategy applied
% 0.13/0.52 % Search class: FHUNS-FFSF21-SFFFFFNN
% 0.13/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.52 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with 136s (1) cores
% 0.13/0.52 % Preprocessing time : 0.002 s
% 0.13/0.52
% 0.13/0.52 % Proof found!
% 0.13/0.52 % SZS status Unsatisfiable
% 0.13/0.52 % SZS output start CNFRefutation
% See solution above
% 0.13/0.52 % Parsed axioms : 10
% 0.13/0.52 % Removed by relevancy pruning/SinE : 0
% 0.13/0.52 % Initial clauses : 10
% 0.13/0.52 % Removed in clause preprocessing : 0
% 0.13/0.52 % Initial clauses in saturation : 10
% 0.13/0.52 % Processed clauses : 499
% 0.13/0.52 % ...of these trivial : 12
% 0.13/0.52 % ...subsumed : 203
% 0.13/0.52 % ...remaining for further processing : 284
% 0.13/0.52 % Other redundant clauses eliminated : 0
% 0.13/0.52 % Clauses deleted for lack of memory : 0
% 0.13/0.52 % Backward-subsumed : 28
% 0.13/0.52 % Backward-rewritten : 6
% 0.13/0.52 % Generated clauses : 1847
% 0.13/0.52 % ...of the previous two non-redundant : 1555
% 0.13/0.52 % ...aggressively subsumed : 0
% 0.13/0.52 % Contextual simplify-reflections : 0
% 0.13/0.52 % Paramodulations : 1847
% 0.13/0.52 % Factorizations : 0
% 0.13/0.52 % NegExts : 0
% 0.13/0.52 % Equation resolutions : 0
% 0.13/0.52 % Disequality decompositions : 0
% 0.13/0.52 % Total rewrite steps : 349
% 0.13/0.52 % ...of those cached : 283
% 0.13/0.52 % Propositional unsat checks : 0
% 0.13/0.52 % Propositional check models : 0
% 0.13/0.52 % Propositional check unsatisfiable : 0
% 0.13/0.52 % Propositional clauses : 0
% 0.13/0.52 % Propositional clauses after purity: 0
% 0.13/0.52 % Propositional unsat core size : 0
% 0.13/0.52 % Propositional preprocessing time : 0.000
% 0.13/0.52 % Propositional encoding time : 0.000
% 0.13/0.52 % Propositional solver time : 0.000
% 0.13/0.52 % Success case prop preproc time : 0.000
% 0.13/0.52 % Success case prop encoding time : 0.000
% 0.13/0.52 % Success case prop solver time : 0.000
% 0.13/0.52 % Current number of processed clauses : 250
% 0.13/0.52 % Positive orientable unit clauses : 54
% 0.13/0.52 % Positive unorientable unit clauses: 0
% 0.13/0.52 % Negative unit clauses : 1
% 0.13/0.52 % Non-unit-clauses : 195
% 0.13/0.52 % Current number of unprocessed clauses: 1052
% 0.13/0.52 % ...number of literals in the above : 2833
% 0.13/0.52 % Current number of archived formulas : 0
% 0.13/0.52 % Current number of archived clauses : 34
% 0.13/0.52 % Clause-clause subsumption calls (NU) : 4744
% 0.13/0.52 % Rec. Clause-clause subsumption calls : 4458
% 0.13/0.52 % Non-unit clause-clause subsumptions : 231
% 0.13/0.52 % Unit Clause-clause subsumption calls : 109
% 0.13/0.52 % Rewrite failures with RHS unbound : 0
% 0.13/0.52 % BW rewrite match attempts : 114
% 0.13/0.52 % BW rewrite match successes : 6
% 0.13/0.52 % Condensation attempts : 0
% 0.13/0.52 % Condensation successes : 0
% 0.13/0.52 % Termbank termtop insertions : 19625
% 0.13/0.52 % Search garbage collected termcells : 24
% 0.13/0.52
% 0.13/0.52 % -------------------------------------------------
% 0.13/0.52 % User time : 0.067 s
% 0.13/0.52 % System time : 0.007 s
% 0.13/0.52 % Total time : 0.074 s
% 0.13/0.52 % Maximum resident set size: 3640 pages
% 0.13/0.52
% 0.13/0.52 % -------------------------------------------------
% 0.13/0.52 % User time : 0.348 s
% 0.13/0.52 % System time : 0.052 s
% 0.13/0.52 % Total time : 0.400 s
% 0.13/0.52 % Maximum resident set size: 4864 pages
% 0.13/0.52 % E exiting
%------------------------------------------------------------------------------