%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO009-1 : 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 : n009.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 12:06:56 PM UTC 2026
% Result : Unsatisfiable 0.72s 0.65s
% Output : CNFRefutation 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 45 ( 23 unt; 0 nHn; 26 RR)
% Number of literals : 93 ( 8 equ; 51 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 123 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity4,axiom,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
cnf(multiplication_is_well_defined,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
cnf(commutativity_of_multiplication,axiom,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(distributivity7,axiom,
( ~ sum(X6,X2,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| product(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity7) ).
cnf(commutativity_of_addition,axiom,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(prove_equations,negated_conjecture,
~ product(x,add(x,y),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equations) ).
cnf(c_0_11,plain,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
inference(fof_simplification,[status(thm)],[distributivity4]) ).
cnf(c_0_12,plain,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
c_0_11 ).
cnf(c_0_13,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_14,plain,
( ~ sum(X4,X5,X1)
| ~ product(X5,X2,X3)
| ~ product(X4,X2,additive_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_16,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_17,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_multiplication]) ).
cnf(c_0_18,plain,
( ~ product(additive_identity,X2,X3)
| ~ product(X1,X2,additive_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1 ).
cnf(c_0_20,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_16 ).
cnf(c_0_21,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_22,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
c_0_17 ).
cnf(c_0_23,plain,
( ~ product(additive_identity,X1,X2)
| product(inverse(X1),X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_26,plain,
( ~ product(inverse(X2),X2,X1)
| X1 = additive_identity ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_27,plain,
( ~ sum(X6,X2,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| product(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity7]) ).
cnf(c_0_28,plain,
product(inverse(X1),X1,multiply(additive_identity,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_29,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_31,plain,
( ~ sum(X6,X2,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| product(X3,X5,X7) ),
c_0_27 ).
cnf(c_0_32,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_28]),c_0_29]),c_0_30]) ).
cnf(c_0_33,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_34,plain,
( ~ sum(X4,X3,X1)
| ~ sum(X5,X3,X2)
| ~ product(X4,X5,additive_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_13]) ).
cnf(c_0_35,plain,
product(X1,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_36,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_33 ).
cnf(c_0_37,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_38,plain,
( ~ sum(X3,X2,X1)
| product(X1,X2,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_13]),c_0_35])]) ).
cnf(c_0_39,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
~ product(x,add(x,y),x),
inference(fof_simplification,[status(thm)],[prove_equations]) ).
cnf(c_0_41,plain,
product(add(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
~ product(x,add(x,y),x),
c_0_40 ).
cnf(c_0_43,plain,
product(X1,add(X1,X2),X1),
inference(spm,[status(thm)],[c_0_22,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 % Computer : n009.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Mon Sep 21 13:47:27 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.55 Running first-order theorem proving
% 0.27/0.55 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
% 0.72/0.65 % Version: 3.5.1
% 0.72/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.72/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.72/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.72/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.72/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.72/0.65 % Starting sh5l with 300s (1) cores
% 0.72/0.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1914833 completed with status 0
% 0.72/0.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.72/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.72/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.72/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.72/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.72/0.65 % No SInE strategy applied
% 0.72/0.65 % Search class: FHUSM-FFMF21-SFFFFFNN
% 0.72/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.72/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.72/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.72/0.65 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.72/0.65 % Starting new_bool_3 with 136s (1) cores
% 0.72/0.65 % Starting new_bool_1 with 136s (1) cores
% 0.72/0.65 % new_bool_1 with pid 1914841 completed with status 0
% 0.72/0.65 % Result found by new_bool_1
% 0.72/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.72/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.72/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.72/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.72/0.65 % No SInE strategy applied
% 0.72/0.65 % Search class: FHUSM-FFMF21-SFFFFFNN
% 0.72/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.72/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.72/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.72/0.65 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.72/0.65 % Starting new_bool_3 with 136s (1) cores
% 0.72/0.65 % Starting new_bool_1 with 136s (1) cores
% 0.72/0.65 % Preprocessing time : 0.002 s
% 0.72/0.65 % Presaturation interreduction done
% 0.72/0.65
% 0.72/0.65 % Proof found!
% 0.72/0.65 % SZS status Unsatisfiable
% 0.72/0.65 % SZS output start CNFRefutation
% See solution above
% 0.72/0.65 % Parsed axioms : 23
% 0.72/0.65 % Removed by relevancy pruning/SinE : 0
% 0.72/0.65 % Initial clauses : 23
% 0.72/0.65 % Removed in clause preprocessing : 0
% 0.72/0.65 % Initial clauses in saturation : 23
% 0.72/0.65 % Processed clauses : 511
% 0.72/0.65 % ...of these trivial : 29
% 0.72/0.65 % ...subsumed : 249
% 0.72/0.65 % ...remaining for further processing : 233
% 0.72/0.65 % Other redundant clauses eliminated : 0
% 0.72/0.65 % Clauses deleted for lack of memory : 0
% 0.72/0.65 % Backward-subsumed : 10
% 0.72/0.65 % Backward-rewritten : 16
% 0.72/0.65 % Generated clauses : 1616
% 0.72/0.65 % ...of the previous two non-redundant : 938
% 0.72/0.65 % ...aggressively subsumed : 0
% 0.72/0.65 % Contextual simplify-reflections : 0
% 0.72/0.65 % Paramodulations : 1616
% 0.72/0.65 % Factorizations : 0
% 0.72/0.65 % NegExts : 0
% 0.72/0.65 % Equation resolutions : 0
% 0.72/0.65 % Disequality decompositions : 0
% 0.72/0.65 % Total rewrite steps : 1251
% 0.72/0.65 % ...of those cached : 1132
% 0.72/0.65 % Propositional unsat checks : 0
% 0.72/0.65 % Propositional check models : 0
% 0.72/0.65 % Propositional check unsatisfiable : 0
% 0.72/0.65 % Propositional clauses : 0
% 0.72/0.65 % Propositional clauses after purity: 0
% 0.72/0.65 % Propositional unsat core size : 0
% 0.72/0.65 % Propositional preprocessing time : 0.000
% 0.72/0.65 % Propositional encoding time : 0.000
% 0.72/0.65 % Propositional solver time : 0.000
% 0.72/0.65 % Success case prop preproc time : 0.000
% 0.72/0.65 % Success case prop encoding time : 0.000
% 0.72/0.65 % Success case prop solver time : 0.000
% 0.72/0.65 % Current number of processed clauses : 184
% 0.72/0.65 % Positive orientable unit clauses : 39
% 0.72/0.65 % Positive unorientable unit clauses: 2
% 0.72/0.65 % Negative unit clauses : 0
% 0.72/0.65 % Non-unit-clauses : 143
% 0.72/0.65 % Current number of unprocessed clauses: 438
% 0.72/0.65 % ...number of literals in the above : 1288
% 0.72/0.65 % Current number of archived formulas : 0
% 0.72/0.65 % Current number of archived clauses : 49
% 0.72/0.65 % Clause-clause subsumption calls (NU) : 7676
% 0.72/0.65 % Rec. Clause-clause subsumption calls : 6142
% 0.72/0.65 % Non-unit clause-clause subsumptions : 245
% 0.72/0.65 % Unit Clause-clause subsumption calls : 45
% 0.72/0.65 % Rewrite failures with RHS unbound : 0
% 0.72/0.65 % BW rewrite match attempts : 218
% 0.72/0.65 % BW rewrite match successes : 39
% 0.72/0.65 % Condensation attempts : 0
% 0.72/0.65 % Condensation successes : 0
% 0.72/0.65 % Termbank termtop insertions : 16936
% 0.72/0.65 % Search garbage collected termcells : 68
% 0.72/0.65
% 0.72/0.65 % -------------------------------------------------
% 0.72/0.65 % User time : 0.053 s
% 0.72/0.65 % System time : 0.007 s
% 0.72/0.65 % Total time : 0.060 s
% 0.72/0.65 % Maximum resident set size: 3652 pages
% 0.72/0.65
% 0.72/0.65 % -------------------------------------------------
% 0.72/0.65 % User time : 0.215 s
% 0.72/0.65 % System time : 0.031 s
% 0.72/0.65 % Total time : 0.246 s
% 0.72/0.65 % Maximum resident set size: 4608 pages
% 0.72/0.65 % E exiting
%------------------------------------------------------------------------------