%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO003-1 : 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 : n011.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 12:06:53 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 40 ( 22 unt; 0 nHn; 22 RR)
% Number of literals : 76 ( 12 equ; 39 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 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 : 94 ( 0 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/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
cnf(addition_is_well_defined,axiom,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(commutativity_of_addition,axiom,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
cnf(multiplication_is_well_defined,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(prove_both_equalities,negated_conjecture,
~ product(x,x,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_both_equalities) ).
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(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_13,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_14,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_15,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1 ).
cnf(c_0_16,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_12 ).
cnf(c_0_17,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_18,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_13 ).
cnf(c_0_19,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_20,plain,
( ~ sum(X5,additive_identity,X3)
| ~ sum(X4,inverse(X2),X1)
| ~ product(X4,X2,X5)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,axiom,
sum(X1,inverse(X1),multiplicative_identity),
additive_inverse2 ).
cnf(c_0_22,plain,
( ~ sum(additive_identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_25,plain,
( ~ sum(X3,additive_identity,X2)
| ~ product(X1,X1,X3)
| product(multiplicative_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_24 ).
cnf(c_0_28,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1 ).
cnf(c_0_29,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_30,plain,
( ~ product(X1,X1,X2)
| product(multiplicative_identity,X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_26]) ).
cnf(c_0_31,plain,
( ~ product(multiplicative_identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_29]) ).
cnf(c_0_33,plain,
product(multiplicative_identity,X1,multiply(X1,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_34,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
~ product(x,x,x),
inference(fof_simplification,[status(thm)],[prove_both_equalities]) ).
cnf(c_0_36,plain,
multiply(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_37,negated_conjecture,
~ product(x,x,x),
c_0_35 ).
cnf(c_0_38,plain,
product(X1,X1,X1),
inference(spm,[status(thm)],[c_0_29,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 13:46:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.09/0.44 % Version: 3.5.1
% 0.09/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.44 % Starting sh5l with 300s (1) cores
% 0.09/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2066149 completed with status 0
% 0.09/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.09/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.44 % No SInE strategy applied
% 0.09/0.44 % Search class: FHUSM-FFMF21-SFFFFFNN
% 0.09/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.09/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.09/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.09/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.09/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2066155 completed with status 0
% 0.09/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.09/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.44 % No SInE strategy applied
% 0.09/0.44 % Search class: FHUSM-FFMF21-SFFFFFNN
% 0.09/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.09/0.44 % Preprocessing time : 0.001 s
% 0.09/0.44 % Presaturation interreduction done
% 0.09/0.44
% 0.09/0.44 % Proof found!
% 0.09/0.44 % SZS status Unsatisfiable
% 0.09/0.44 % SZS output start CNFRefutation
% See solution above
% 0.09/0.44 % Parsed axioms : 23
% 0.09/0.44 % Removed by relevancy pruning/SinE : 0
% 0.09/0.44 % Initial clauses : 23
% 0.09/0.44 % Removed in clause preprocessing : 0
% 0.09/0.44 % Initial clauses in saturation : 23
% 0.09/0.44 % Processed clauses : 96
% 0.09/0.44 % ...of these trivial : 5
% 0.09/0.44 % ...subsumed : 10
% 0.09/0.44 % ...remaining for further processing : 81
% 0.09/0.44 % Other redundant clauses eliminated : 0
% 0.09/0.44 % Clauses deleted for lack of memory : 0
% 0.09/0.44 % Backward-subsumed : 0
% 0.09/0.44 % Backward-rewritten : 5
% 0.09/0.44 % Generated clauses : 245
% 0.09/0.44 % ...of the previous two non-redundant : 133
% 0.09/0.44 % ...aggressively subsumed : 0
% 0.09/0.44 % Contextual simplify-reflections : 0
% 0.09/0.44 % Paramodulations : 245
% 0.09/0.44 % Factorizations : 0
% 0.09/0.44 % NegExts : 0
% 0.09/0.44 % Equation resolutions : 0
% 0.09/0.44 % Disequality decompositions : 0
% 0.09/0.44 % Total rewrite steps : 120
% 0.09/0.44 % ...of those cached : 78
% 0.09/0.44 % Propositional unsat checks : 0
% 0.09/0.44 % Propositional check models : 0
% 0.09/0.44 % Propositional check unsatisfiable : 0
% 0.09/0.44 % Propositional clauses : 0
% 0.09/0.44 % Propositional clauses after purity: 0
% 0.09/0.44 % Propositional unsat core size : 0
% 0.09/0.44 % Propositional preprocessing time : 0.000
% 0.09/0.44 % Propositional encoding time : 0.000
% 0.09/0.44 % Propositional solver time : 0.000
% 0.09/0.44 % Success case prop preproc time : 0.000
% 0.09/0.44 % Success case prop encoding time : 0.000
% 0.09/0.44 % Success case prop solver time : 0.000
% 0.09/0.44 % Current number of processed clauses : 53
% 0.09/0.44 % Positive orientable unit clauses : 23
% 0.09/0.44 % Positive unorientable unit clauses: 1
% 0.09/0.44 % Negative unit clauses : 0
% 0.09/0.44 % Non-unit-clauses : 29
% 0.09/0.44 % Current number of unprocessed clauses: 83
% 0.09/0.44 % ...number of literals in the above : 294
% 0.09/0.44 % Current number of archived formulas : 0
% 0.09/0.44 % Current number of archived clauses : 28
% 0.09/0.44 % Clause-clause subsumption calls (NU) : 440
% 0.09/0.44 % Rec. Clause-clause subsumption calls : 256
% 0.09/0.44 % Non-unit clause-clause subsumptions : 10
% 0.09/0.44 % Unit Clause-clause subsumption calls : 11
% 0.09/0.44 % Rewrite failures with RHS unbound : 0
% 0.09/0.44 % BW rewrite match attempts : 98
% 0.09/0.44 % BW rewrite match successes : 18
% 0.09/0.44 % Condensation attempts : 0
% 0.09/0.44 % Condensation successes : 0
% 0.09/0.44 % Termbank termtop insertions : 3025
% 0.09/0.44 % Search garbage collected termcells : 68
% 0.09/0.44
% 0.09/0.44 % -------------------------------------------------
% 0.09/0.44 % User time : 0.006 s
% 0.09/0.44 % System time : 0.002 s
% 0.09/0.44 % Total time : 0.008 s
% 0.09/0.44 % Maximum resident set size: 3652 pages
% 0.09/0.44
% 0.09/0.44 % -------------------------------------------------
% 0.09/0.44 % User time : 0.028 s
% 0.09/0.44 % System time : 0.013 s
% 0.09/0.44 % Total time : 0.040 s
% 0.09/0.44 % Maximum resident set size: 4608 pages
% 0.09/0.44 % E exiting
%------------------------------------------------------------------------------