%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP046-2 : 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 : n001.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 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 25 ( 12 unt; 0 nHn; 20 RR)
% Number of literals : 51 ( 0 equ; 30 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(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(prove_multiply_substitution1,negated_conjecture,
~ equalish(multiply(a,c),multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_substitution1) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',left_identity) ).
cnf(a_equals_b,hypothesis,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).
cnf(c_0_7,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_8,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_9,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
inference(fof_simplification,[status(thm)],[product_substitution3]) ).
cnf(c_0_10,negated_conjecture,
~ equalish(multiply(a,c),multiply(b,c)),
inference(fof_simplification,[status(thm)],[prove_multiply_substitution1]) ).
cnf(c_0_11,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_7 ).
cnf(c_0_12,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_13,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_8 ).
cnf(c_0_14,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
c_0_9 ).
cnf(c_0_15,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_16,negated_conjecture,
~ equalish(multiply(a,c),multiply(b,c)),
c_0_10 ).
cnf(c_0_17,plain,
( ~ product(X2,X3,X1)
| equalish(X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
( ~ product(X4,X5,X1)
| ~ product(X4,multiply(X5,X2),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_19,plain,
( ~ equalish(X1,X2)
| product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,hypothesis,
equalish(a,b),
a_equals_b ).
cnf(c_0_21,negated_conjecture,
~ product(b,c,multiply(a,c)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( ~ product(identity,X3,X1)
| product(X1,X2,multiply(X3,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_23,hypothesis,
product(identity,a,b),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP046-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % 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 20:00:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1265040 completed with status 0
% 0.14/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FHUNS-FFSF21-SFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.44 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with 136s (1) cores
% 0.14/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.44 % G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with pid 1265047 completed with status 0
% 0.14/0.44 % Result found by G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FHUNS-FFSF21-SFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.44 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with 136s (1) cores
% 0.14/0.44 % Preprocessing time : 0.001 s
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Unsatisfiable
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 9
% 0.14/0.44 % Removed by relevancy pruning/SinE : 0
% 0.14/0.44 % Initial clauses : 9
% 0.14/0.44 % Removed in clause preprocessing : 0
% 0.14/0.44 % Initial clauses in saturation : 9
% 0.14/0.44 % Processed clauses : 66
% 0.14/0.44 % ...of these trivial : 1
% 0.14/0.44 % ...subsumed : 6
% 0.14/0.44 % ...remaining for further processing : 59
% 0.14/0.44 % Other redundant clauses eliminated : 0
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 0
% 0.14/0.44 % Backward-rewritten : 0
% 0.14/0.44 % Generated clauses : 217
% 0.14/0.44 % ...of the previous two non-redundant : 169
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 0
% 0.14/0.44 % Paramodulations : 217
% 0.14/0.44 % Factorizations : 0
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 0
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 38
% 0.14/0.44 % ...of those cached : 24
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 59
% 0.14/0.44 % Positive orientable unit clauses : 16
% 0.14/0.44 % Positive unorientable unit clauses: 0
% 0.14/0.44 % Negative unit clauses : 4
% 0.14/0.44 % Non-unit-clauses : 39
% 0.14/0.44 % Current number of unprocessed clauses: 112
% 0.14/0.44 % ...number of literals in the above : 286
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 0
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 85
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 80
% 0.14/0.44 % Non-unit clause-clause subsumptions : 6
% 0.14/0.44 % Unit Clause-clause subsumption calls : 2
% 0.14/0.44 % Rewrite failures with RHS unbound : 0
% 0.14/0.44 % BW rewrite match attempts : 24
% 0.14/0.44 % BW rewrite match successes : 0
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 2575
% 0.14/0.44 % Search garbage collected termcells : 24
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.008 s
% 0.14/0.44 % System time : 0.002 s
% 0.14/0.44 % Total time : 0.010 s
% 0.14/0.44 % Maximum resident set size: 3640 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.037 s
% 0.14/0.44 % System time : 0.013 s
% 0.14/0.44 % Total time : 0.050 s
% 0.14/0.44 % Maximum resident set size: 4608 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------