%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : BOO016-1 : 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 : n003.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 0.14s 0.61s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 40 ( 21 unt; 0 nHn; 26 RR)
% Number of literals : 85 ( 8 equ; 48 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; 4 con; 0-2 aty)
% Number of variables : 104 ( 3 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/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity8) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
cnf(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
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(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
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/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity1) ).
cnf(x_times_y,hypothesis,
product(x,y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times_y) ).
cnf(prove_sum,negated_conjecture,
~ sum(x,z,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sum) ).
cnf(c_0_10,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_11,plain,
( ~ product(X3,X5,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| sum(X6,X2,X7) ),
c_0_10 ).
cnf(c_0_12,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1 ).
cnf(c_0_13,plain,
( ~ sum(X5,X2,X3)
| ~ sum(X4,X2,multiplicative_identity)
| ~ product(X4,X5,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2 ).
cnf(c_0_15,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_16,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_17,plain,
( ~ sum(multiplicative_identity,X2,X3)
| ~ sum(X1,X2,multiplicative_identity)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
cnf(c_0_19,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_15 ).
cnf(c_0_20,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_21,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_16 ).
cnf(c_0_22,plain,
( ~ sum(multiplicative_identity,X1,X2)
| sum(inverse(X1),X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( ~ sum(X2,X3,X1)
| X1 = add(X2,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_25,plain,
( ~ sum(inverse(X2),X2,X1)
| X1 = multiplicative_identity ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_26,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_27,plain,
sum(inverse(X1),X1,add(multiplicative_identity,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_28,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_30,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_26 ).
cnf(c_0_31,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_27]),c_0_28]),c_0_29]) ).
cnf(c_0_32,plain,
( ~ sum(X5,X4,multiplicative_identity)
| ~ product(X3,X5,X1)
| ~ product(X3,X4,X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_14]) ).
cnf(c_0_33,plain,
sum(X1,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_24,c_0_31]) ).
cnf(c_0_34,plain,
( ~ product(X2,X3,X1)
| sum(X1,X2,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_14]),c_0_33])]) ).
cnf(c_0_35,hypothesis,
product(x,y,z),
x_times_y ).
cnf(c_0_36,negated_conjecture,
~ sum(x,z,x),
inference(fof_simplification,[status(thm)],[prove_sum]) ).
cnf(c_0_37,hypothesis,
sum(z,x,x),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
~ sum(x,z,x),
c_0_36 ).
cnf(c_0_39,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_37]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.53 % Computer : n003.cluster.edu
% 0.08/0.53 % Model : x86_64 x86_64
% 0.08/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.53 % Memory : 8046.5625MB
% 0.08/0.53 % OS : Linux 6.8.0-71-generic
% 0.08/0.53 % CPULimit : 300
% 0.08/0.53 % WCLimit : 300
% 0.08/0.53 % DateTime : Mon Sep 21 13:50:01 UTC 2026
% 0.08/0.53 % CPUTime :
% 0.08/0.53 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.58 Running first-order theorem proving
% 0.14/0.58 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
% 0.14/0.61 % Version: 3.5.1
% 0.14/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.61 % Starting sh5l with 300s (1) cores
% 0.14/0.61 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 267610 completed with status 0
% 0.14/0.61 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.61 % No SInE strategy applied
% 0.14/0.61 % Search class: FHUSM-FFMF21-SFFFFFNN
% 0.14/0.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.61 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.14/0.61 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.61 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.61 % G-E--_208_C18_F1_SE_CS_SP_PS_S4d with pid 267617 completed with status 0
% 0.14/0.61 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4d
% 0.14/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.61 % No SInE strategy applied
% 0.14/0.61 % Search class: FHUSM-FFMF21-SFFFFFNN
% 0.14/0.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.61 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.14/0.61 % Preprocessing time : 0.001 s
% 0.14/0.61 % Presaturation interreduction done
% 0.14/0.61
% 0.14/0.61 % Proof found!
% 0.14/0.61 % SZS status Unsatisfiable
% 0.14/0.61 % SZS output start CNFRefutation
% See solution above
% 0.14/0.61 % Parsed axioms : 24
% 0.14/0.61 % Removed by relevancy pruning/SinE : 0
% 0.14/0.61 % Initial clauses : 24
% 0.14/0.61 % Removed in clause preprocessing : 0
% 0.14/0.61 % Initial clauses in saturation : 24
% 0.14/0.61 % Processed clauses : 386
% 0.14/0.61 % ...of these trivial : 29
% 0.14/0.61 % ...subsumed : 105
% 0.14/0.61 % ...remaining for further processing : 252
% 0.14/0.61 % Other redundant clauses eliminated : 0
% 0.14/0.61 % Clauses deleted for lack of memory : 0
% 0.14/0.61 % Backward-subsumed : 4
% 0.14/0.61 % Backward-rewritten : 10
% 0.14/0.61 % Generated clauses : 1020
% 0.14/0.61 % ...of the previous two non-redundant : 651
% 0.14/0.61 % ...aggressively subsumed : 0
% 0.14/0.61 % Contextual simplify-reflections : 0
% 0.14/0.61 % Paramodulations : 1020
% 0.14/0.61 % Factorizations : 0
% 0.14/0.61 % NegExts : 0
% 0.14/0.61 % Equation resolutions : 0
% 0.14/0.61 % Disequality decompositions : 0
% 0.14/0.61 % Total rewrite steps : 588
% 0.14/0.61 % ...of those cached : 483
% 0.14/0.61 % Propositional unsat checks : 0
% 0.14/0.61 % Propositional check models : 0
% 0.14/0.61 % Propositional check unsatisfiable : 0
% 0.14/0.61 % Propositional clauses : 0
% 0.14/0.61 % Propositional clauses after purity: 0
% 0.14/0.61 % Propositional unsat core size : 0
% 0.14/0.61 % Propositional preprocessing time : 0.000
% 0.14/0.61 % Propositional encoding time : 0.000
% 0.14/0.61 % Propositional solver time : 0.000
% 0.14/0.61 % Success case prop preproc time : 0.000
% 0.14/0.61 % Success case prop encoding time : 0.000
% 0.14/0.61 % Success case prop solver time : 0.000
% 0.14/0.61 % Current number of processed clauses : 214
% 0.14/0.61 % Positive orientable unit clauses : 38
% 0.14/0.61 % Positive unorientable unit clauses: 2
% 0.14/0.61 % Negative unit clauses : 2
% 0.14/0.61 % Non-unit-clauses : 172
% 0.14/0.61 % Current number of unprocessed clauses: 298
% 0.14/0.61 % ...number of literals in the above : 835
% 0.14/0.61 % Current number of archived formulas : 0
% 0.14/0.61 % Current number of archived clauses : 38
% 0.14/0.61 % Clause-clause subsumption calls (NU) : 4480
% 0.14/0.61 % Rec. Clause-clause subsumption calls : 3703
% 0.14/0.61 % Non-unit clause-clause subsumptions : 107
% 0.14/0.61 % Unit Clause-clause subsumption calls : 175
% 0.14/0.61 % Rewrite failures with RHS unbound : 0
% 0.14/0.61 % BW rewrite match attempts : 377
% 0.14/0.61 % BW rewrite match successes : 40
% 0.14/0.61 % Condensation attempts : 0
% 0.14/0.61 % Condensation successes : 0
% 0.14/0.61 % Termbank termtop insertions : 12905
% 0.14/0.61 % Search garbage collected termcells : 68
% 0.14/0.61
% 0.14/0.61 % -------------------------------------------------
% 0.14/0.61 % User time : 0.017 s
% 0.14/0.61 % System time : 0.002 s
% 0.14/0.61 % Total time : 0.019 s
% 0.14/0.61 % Maximum resident set size: 3652 pages
% 0.14/0.61
% 0.14/0.61 % -------------------------------------------------
% 0.14/0.61 % User time : 0.079 s
% 0.14/0.61 % System time : 0.015 s
% 0.14/0.61 % Total time : 0.094 s
% 0.14/0.61 % Maximum resident set size: 4864 pages
% 0.14/0.61 % E exiting
%------------------------------------------------------------------------------