%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : BOO017-1 : 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 : n007.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 12:07:15 PM UTC 2026
% Result : Unsatisfiable 0.43s 0.47s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of clauses : 70 ( 33 unt; 0 nHn; 44 RR)
% Number of literals : 149 ( 17 equ; 82 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 189 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity8,axiom,
( ~ product(X3,X5,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| sum(X6,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity8) ).
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(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
cnf(addition_is_well_defined,axiom,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
cnf(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
cnf(distributivity1,axiom,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity1) ).
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(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(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(x_plus_y,hypothesis,
sum(x,y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y) ).
cnf(prove_product,negated_conjecture,
~ product(x,z,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_product) ).
cnf(c_0_16,plain,
( ~ product(X3,X5,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| sum(X6,X2,X7) ),
inference(fof_simplification,[status(thm)],[distributivity8]) ).
cnf(c_0_17,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_18,plain,
( ~ product(X3,X5,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| sum(X6,X2,X7) ),
c_0_16 ).
cnf(c_0_19,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1 ).
cnf(c_0_20,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_21,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_17 ).
cnf(c_0_22,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_23,plain,
( ~ sum(X5,X2,X3)
| ~ sum(X4,X2,multiplicative_identity)
| ~ product(X4,X5,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
cnf(c_0_25,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_20 ).
cnf(c_0_26,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( ~ sum(X4,X2,X3)
| ~ product(inverse(X2),X4,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2 ).
cnf(c_0_29,plain,
( ~ sum(inverse(X2),X2,X1)
| X1 = multiplicative_identity ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_30,plain,
( ~ sum(X3,X2,X1)
| X1 = add(X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( ~ sum(multiplicative_identity,X1,X2)
| sum(inverse(X1),X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_33,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity1]) ).
cnf(c_0_34,plain,
( ~ sum(multiplicative_identity,X2,X1)
| X1 = multiplicative_identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_35,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_36,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_multiplication]) ).
cnf(c_0_37,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_33 ).
cnf(c_0_38,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_39,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_35 ).
cnf(c_0_40,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
c_0_36 ).
cnf(c_0_41,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_42,plain,
( ~ sum(X5,X4,multiplicative_identity)
| ~ product(X3,X5,X1)
| ~ product(X3,X4,X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_43,plain,
sum(multiplicative_identity,X1,multiplicative_identity),
inference(spm,[status(thm)],[c_0_22,c_0_38]) ).
cnf(c_0_44,plain,
( ~ product(multiplicative_identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_39,c_0_19]) ).
cnf(c_0_45,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
( ~ product(X3,X4,X2)
| ~ product(X3,multiplicative_identity,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
multiply(X1,multiplicative_identity) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,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_49,plain,
( ~ product(X1,X3,X2)
| sum(X1,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_41]),c_0_47]) ).
cnf(c_0_50,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1 ).
cnf(c_0_51,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_52,plain,
( ~ sum(X6,X2,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| product(X3,X5,X7) ),
c_0_48 ).
cnf(c_0_53,plain,
sum(X1,multiply(X1,X2),X1),
inference(spm,[status(thm)],[c_0_49,c_0_41]) ).
cnf(c_0_54,plain,
( ~ sum(X1,X1,X2)
| sum(additive_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_50]) ).
cnf(c_0_55,plain,
( ~ sum(additive_identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_25,c_0_51]) ).
cnf(c_0_56,plain,
( ~ sum(X4,X6,X1)
| ~ sum(X5,X6,X2)
| ~ sum(multiply(X4,X5),X6,X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_52,c_0_41]) ).
cnf(c_0_57,plain,
sum(multiply(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_21,c_0_53]) ).
cnf(c_0_58,hypothesis,
sum(x,y,z),
x_plus_y ).
cnf(c_0_59,plain,
( ~ sum(X2,X3,X1)
| X1 = add(X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_60,plain,
sum(additive_identity,X1,add(X1,X1)),
inference(spm,[status(thm)],[c_0_54,c_0_22]) ).
cnf(c_0_61,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_55,c_0_22]) ).
cnf(c_0_62,negated_conjecture,
~ product(x,z,x),
inference(fof_simplification,[status(thm)],[prove_product]) ).
cnf(c_0_63,plain,
( ~ sum(X3,X3,X1)
| ~ sum(X4,X3,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,hypothesis,
sum(y,x,z),
inference(spm,[status(thm)],[c_0_21,c_0_58]) ).
cnf(c_0_65,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_66,negated_conjecture,
~ product(x,z,x),
c_0_62 ).
cnf(c_0_67,hypothesis,
( ~ sum(x,x,X1)
| product(X1,z,x) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,plain,
sum(X1,X1,X1),
inference(spm,[status(thm)],[c_0_22,c_0_65]) ).
cnf(c_0_69,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO017-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 13:46:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.43/0.47 % Version: 3.5.1
% 0.43/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.43/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.43/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.43/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.43/0.47 % Starting sh5l with 300s (1) cores
% 0.43/0.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1245485 completed with status 0
% 0.43/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.43/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.43/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.43/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.43/0.47 % No SInE strategy applied
% 0.43/0.47 % Search class: FHUSM-FFMF21-SFFFFFNN
% 0.43/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.43/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.43/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.43/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.43/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.43/0.47 % Starting new_bool_1 with 136s (1) cores
% 0.43/0.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1245491 completed with status 0
% 0.43/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.43/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.43/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.43/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.43/0.47 % No SInE strategy applied
% 0.43/0.47 % Search class: FHUSM-FFMF21-SFFFFFNN
% 0.43/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.43/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.43/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.43/0.47 % Preprocessing time : 0.001 s
% 0.43/0.47 % Presaturation interreduction done
% 0.43/0.47
% 0.43/0.47 % Proof found!
% 0.43/0.47 % SZS status Unsatisfiable
% 0.43/0.47 % SZS output start CNFRefutation
% See solution above
% 0.43/0.47 % Parsed axioms : 24
% 0.43/0.47 % Removed by relevancy pruning/SinE : 0
% 0.43/0.47 % Initial clauses : 24
% 0.43/0.47 % Removed in clause preprocessing : 0
% 0.43/0.47 % Initial clauses in saturation : 24
% 0.43/0.47 % Processed clauses : 903
% 0.43/0.47 % ...of these trivial : 46
% 0.43/0.47 % ...subsumed : 566
% 0.43/0.47 % ...remaining for further processing : 291
% 0.43/0.47 % Other redundant clauses eliminated : 0
% 0.43/0.47 % Clauses deleted for lack of memory : 0
% 0.43/0.47 % Backward-subsumed : 16
% 0.43/0.47 % Backward-rewritten : 6
% 0.43/0.47 % Generated clauses : 3183
% 0.43/0.47 % ...of the previous two non-redundant : 2505
% 0.43/0.47 % ...aggressively subsumed : 0
% 0.43/0.47 % Contextual simplify-reflections : 0
% 0.43/0.47 % Paramodulations : 3183
% 0.43/0.47 % Factorizations : 0
% 0.43/0.47 % NegExts : 0
% 0.43/0.47 % Equation resolutions : 0
% 0.43/0.47 % Disequality decompositions : 0
% 0.43/0.47 % Total rewrite steps : 1372
% 0.43/0.47 % ...of those cached : 1253
% 0.43/0.47 % Propositional unsat checks : 0
% 0.43/0.47 % Propositional check models : 0
% 0.43/0.47 % Propositional check unsatisfiable : 0
% 0.43/0.47 % Propositional clauses : 0
% 0.43/0.47 % Propositional clauses after purity: 0
% 0.43/0.47 % Propositional unsat core size : 0
% 0.43/0.47 % Propositional preprocessing time : 0.000
% 0.43/0.47 % Propositional encoding time : 0.000
% 0.43/0.47 % Propositional solver time : 0.000
% 0.43/0.47 % Success case prop preproc time : 0.000
% 0.43/0.47 % Success case prop encoding time : 0.000
% 0.43/0.47 % Success case prop solver time : 0.000
% 0.43/0.47 % Current number of processed clauses : 245
% 0.43/0.47 % Positive orientable unit clauses : 45
% 0.43/0.47 % Positive unorientable unit clauses: 2
% 0.43/0.47 % Negative unit clauses : 2
% 0.43/0.47 % Non-unit-clauses : 196
% 0.43/0.47 % Current number of unprocessed clauses: 1622
% 0.43/0.47 % ...number of literals in the above : 5614
% 0.43/0.47 % Current number of archived formulas : 0
% 0.43/0.47 % Current number of archived clauses : 46
% 0.43/0.47 % Clause-clause subsumption calls (NU) : 15281
% 0.43/0.47 % Rec. Clause-clause subsumption calls : 11763
% 0.43/0.47 % Non-unit clause-clause subsumptions : 580
% 0.43/0.47 % Unit Clause-clause subsumption calls : 41
% 0.43/0.47 % Rewrite failures with RHS unbound : 0
% 0.43/0.47 % BW rewrite match attempts : 187
% 0.43/0.47 % BW rewrite match successes : 35
% 0.43/0.47 % Condensation attempts : 0
% 0.43/0.47 % Condensation successes : 0
% 0.43/0.47 % Termbank termtop insertions : 32189
% 0.43/0.47 % Search garbage collected termcells : 68
% 0.43/0.47
% 0.43/0.47 % -------------------------------------------------
% 0.43/0.47 % User time : 0.040 s
% 0.43/0.47 % System time : 0.004 s
% 0.43/0.47 % Total time : 0.044 s
% 0.43/0.47 % Maximum resident set size: 3396 pages
% 0.43/0.47
% 0.43/0.47 % -------------------------------------------------
% 0.43/0.47 % User time : 0.182 s
% 0.43/0.47 % System time : 0.018 s
% 0.43/0.47 % Total time : 0.200 s
% 0.43/0.47 % Maximum resident set size: 4608 pages
% 0.43/0.47 % E exiting
%------------------------------------------------------------------------------