%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD043-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:22:49 PM UTC 2026
% Result : Unsatisfiable 0.86s 0.73s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 39 ( 13 unt; 0 nHn; 39 RR)
% Number of literals : 95 ( 0 equ; 59 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 92 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity_1,axiom,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(product_3,negated_conjecture,
product(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_3) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(associativity_addition_2,axiom,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_sum_4,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
cnf(c_0_10,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[distributivity_1]) ).
cnf(c_0_11,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_12,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
c_0_10 ).
cnf(c_0_13,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_11 ).
cnf(c_0_14,plain,
( ~ defined(X5)
| ~ product(X5,X4,X2)
| ~ product(X5,X4,X3)
| ~ product(additive_identity,X4,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,negated_conjecture,
product(additive_identity,a,b),
product_3 ).
cnf(c_0_16,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_17,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_18,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_1]) ).
cnf(c_0_19,negated_conjecture,
( ~ product(additive_identity,a,X2)
| ~ product(additive_identity,a,X1)
| sum(X1,X2,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_20,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_2]) ).
cnf(c_0_21,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_17 ).
cnf(c_0_22,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_18 ).
cnf(c_0_23,negated_conjecture,
( ~ product(additive_identity,a,X1)
| sum(b,X1,b) ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_24,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
c_0_20 ).
cnf(c_0_25,plain,
( ~ defined(X1)
| sum(X1,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_26,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_27,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| ~ defined(X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_28,negated_conjecture,
sum(b,b,b),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_29,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_30,plain,
( ~ sum(X4,X3,X1)
| ~ sum(X4,X3,X2)
| ~ defined(X3)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_26 ).
cnf(c_0_32,negated_conjecture,
( ~ sum(X1,b,additive_identity)
| sum(X1,b,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_33,plain,
( ~ sum(additive_inverse(X2),X2,X1)
| ~ defined(X2)
| sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
sum(additive_inverse(b),b,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_31]),c_0_29])]) ).
cnf(c_0_35,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_4]) ).
cnf(c_0_36,negated_conjecture,
sum(b,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29])]) ).
cnf(c_0_37,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
c_0_35 ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD043-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 15:40:34 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.45 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
% 0.86/0.73 % Version: 3.5.1
% 0.86/0.73 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.86/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.86/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.86/0.73 % Starting new_bool_3 with 300s (1) cores
% 0.86/0.73 % Starting new_bool_1 with 300s (1) cores
% 0.86/0.73 % Starting sh5l with 300s (1) cores
% 0.86/0.73 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2929120 completed with status 0
% 0.86/0.73 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.86/0.73 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.86/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.86/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.86/0.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.86/0.73 % No SInE strategy applied
% 0.86/0.73 % Search class: FGUNF-FFMS21-SFFFFFNN
% 0.86/0.73 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.86/0.73 % Starting SubtermCWHack with 136s (1) cores
% 0.86/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.86/0.73 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.86/0.73 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.86/0.73 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.86/0.73 % G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with pid 2929126 completed with status 0
% 0.86/0.73 % Result found by G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c
% 0.86/0.73 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.86/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.86/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.86/0.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.86/0.73 % No SInE strategy applied
% 0.86/0.73 % Search class: FGUNF-FFMS21-SFFFFFNN
% 0.86/0.73 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.86/0.73 % Starting SubtermCWHack with 136s (1) cores
% 0.86/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.86/0.73 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.86/0.73 % Preprocessing time : 0.002 s
% 0.86/0.73 % Presaturation interreduction done
% 0.86/0.73
% 0.86/0.73 % Proof found!
% 0.86/0.73 % SZS status Unsatisfiable
% 0.86/0.73 % SZS output start CNFRefutation
% See solution above
% 0.86/0.73 % Parsed axioms : 30
% 0.86/0.73 % Removed by relevancy pruning/SinE : 0
% 0.86/0.73 % Initial clauses : 30
% 0.86/0.73 % Removed in clause preprocessing : 0
% 0.86/0.73 % Initial clauses in saturation : 30
% 0.86/0.73 % Processed clauses : 1080
% 0.86/0.73 % ...of these trivial : 105
% 0.86/0.73 % ...subsumed : 293
% 0.86/0.73 % ...remaining for further processing : 682
% 0.86/0.73 % Other redundant clauses eliminated : 0
% 0.86/0.73 % Clauses deleted for lack of memory : 0
% 0.86/0.73 % Backward-subsumed : 4
% 0.86/0.73 % Backward-rewritten : 19
% 0.86/0.73 % Generated clauses : 8151
% 1.91/0.73 % ...of the previous two non-redundant : 6499
% 1.91/0.73 % ...aggressively subsumed : 0
% 1.91/0.73 % Contextual simplify-reflections : 2
% 1.91/0.73 % Paramodulations : 8141
% 1.91/0.73 % Factorizations : 10
% 1.91/0.73 % NegExts : 0
% 1.91/0.73 % Equation resolutions : 0
% 1.91/0.73 % Disequality decompositions : 0
% 1.91/0.73 % Total rewrite steps : 4469
% 1.91/0.73 % ...of those cached : 4304
% 1.91/0.73 % Propositional unsat checks : 0
% 1.91/0.73 % Propositional check models : 0
% 1.91/0.73 % Propositional check unsatisfiable : 0
% 1.91/0.73 % Propositional clauses : 0
% 1.91/0.73 % Propositional clauses after purity: 0
% 1.91/0.73 % Propositional unsat core size : 0
% 1.91/0.73 % Propositional preprocessing time : 0.000
% 1.91/0.73 % Propositional encoding time : 0.000
% 1.91/0.73 % Propositional solver time : 0.000
% 1.91/0.73 % Success case prop preproc time : 0.000
% 1.91/0.73 % Success case prop encoding time : 0.000
% 1.91/0.73 % Success case prop solver time : 0.000
% 1.91/0.73 % Current number of processed clauses : 629
% 1.91/0.73 % Positive orientable unit clauses : 195
% 1.91/0.73 % Positive unorientable unit clauses: 0
% 1.91/0.73 % Negative unit clauses : 2
% 1.91/0.73 % Non-unit-clauses : 432
% 1.91/0.73 % Current number of unprocessed clauses: 5475
% 1.91/0.73 % ...number of literals in the above : 18167
% 1.91/0.73 % Current number of archived formulas : 0
% 1.91/0.73 % Current number of archived clauses : 53
% 1.91/0.73 % Clause-clause subsumption calls (NU) : 8948
% 1.91/0.73 % Rec. Clause-clause subsumption calls : 7346
% 1.91/0.73 % Non-unit clause-clause subsumptions : 297
% 1.91/0.73 % Unit Clause-clause subsumption calls : 258
% 1.91/0.73 % Rewrite failures with RHS unbound : 0
% 1.91/0.73 % BW rewrite match attempts : 126
% 1.91/0.73 % BW rewrite match successes : 20
% 1.91/0.73 % Condensation attempts : 0
% 1.91/0.73 % Condensation successes : 0
% 1.91/0.73 % Termbank termtop insertions : 126853
% 1.91/0.73 % Search garbage collected termcells : 116
% 1.91/0.73
% 1.91/0.73 % -------------------------------------------------
% 1.91/0.73 % User time : 0.237 s
% 1.91/0.73 % System time : 0.011 s
% 1.91/0.73 % Total time : 0.247 s
% 1.91/0.73 % Maximum resident set size: 3608 pages
% 1.91/0.73
% 1.91/0.73 % -------------------------------------------------
% 1.91/0.73 % User time : 1.025 s
% 1.91/0.73 % System time : 0.057 s
% 1.91/0.73 % Total time : 1.082 s
% 1.91/0.73 % Maximum resident set size: 4864 pages
% 1.91/0.73 % E exiting
%------------------------------------------------------------------------------