%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : FLD043-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 12:23:17 PM UTC 2026
% Result : Unsatisfiable 1.39s 0.81s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 44 ( 16 unt; 4 nHn; 44 RR)
% Number of literals : 105 ( 0 equ; 60 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 83 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(totality_of_order_relation,axiom,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
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/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_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/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(product_3,negated_conjecture,
product(additive_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_3) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(not_sum_4,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_4) ).
cnf(c_0_11,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[totality_of_order_relation]) ).
cnf(c_0_12,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_11 ).
cnf(c_0_13,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_14,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
inference(fof_simplification,[status(thm)],[antisymmetry_of_order_relation]) ).
cnf(c_0_15,plain,
( ~ defined(X1)
| less_or_equal(multiplicative_identity,X1)
| less_or_equal(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,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_17,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_18,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_19,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
c_0_14 ).
cnf(c_0_20,plain,
less_or_equal(multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_21,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
c_0_16 ).
cnf(c_0_22,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_17 ).
cnf(c_0_23,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_18 ).
cnf(c_0_24,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_20])]) ).
cnf(c_0_25,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_26,plain,
( ~ sum(X5,X4,multiplicative_identity)
| ~ defined(X3)
| ~ product(X5,X3,X1)
| ~ product(X4,X3,X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,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_29,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_25 ).
cnf(c_0_30,plain,
( ~ defined(X3)
| ~ product(multiplicative_identity,X3,X1)
| ~ product(additive_identity,X3,X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
product(additive_identity,a,b),
product_3 ).
cnf(c_0_32,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_33,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_28 ).
cnf(c_0_34,plain,
( ~ defined(X1)
| sum(X1,additive_inverse(X1),additive_identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( ~ product(multiplicative_identity,a,X1)
| sum(X1,b,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_36,plain,
( ~ sum(X1,X4,X3)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ defined(X3)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
sum(a,b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_22]),c_0_32])]) ).
cnf(c_0_38,plain,
( ~ sum(X1,X2,X2)
| ~ defined(X2)
| sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
sum(b,a,a),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_4]) ).
cnf(c_0_41,negated_conjecture,
sum(b,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_32])]) ).
cnf(c_0_42,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
c_0_40 ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD043-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n009.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 15:40:27 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.51 Running first-order theorem proving
% 0.27/0.51 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
% 1.39/0.81 % Version: 3.5.1
% 1.39/0.81 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.39/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.39/0.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.39/0.81 % Starting new_bool_3 with 300s (1) cores
% 1.39/0.81 % Starting new_bool_1 with 300s (1) cores
% 1.39/0.81 % Starting sh5l with 300s (1) cores
% 1.39/0.81 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2120517 completed with status 0
% 1.39/0.81 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.39/0.81 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.39/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.39/0.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.39/0.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.39/0.81 % No SInE strategy applied
% 1.39/0.81 % Search class: FGUNF-FFMS21-SFFFFFNN
% 1.39/0.81 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 1.39/0.81 % Starting SubtermCWHack with 136s (1) cores
% 1.39/0.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.39/0.81 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 1.39/0.81 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.39/0.81 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.39/0.81 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2120524 completed with status 0
% 1.39/0.81 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.39/0.81 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.39/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.39/0.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.39/0.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.39/0.81 % No SInE strategy applied
% 1.39/0.81 % Search class: FGUNF-FFMS21-SFFFFFNN
% 1.39/0.81 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 1.39/0.81 % Starting SubtermCWHack with 136s (1) cores
% 1.39/0.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.39/0.81 % Preprocessing time : 0.002 s
% 1.39/0.81 % Presaturation interreduction done
% 1.39/0.81
% 1.39/0.81 % Proof found!
% 1.39/0.81 % SZS status Unsatisfiable
% 1.39/0.81 % SZS output start CNFRefutation
% See solution above
% 1.39/0.81 % Parsed axioms : 30
% 1.39/0.81 % Removed by relevancy pruning/SinE : 0
% 1.39/0.81 % Initial clauses : 30
% 1.39/0.81 % Removed in clause preprocessing : 0
% 1.39/0.81 % Initial clauses in saturation : 30
% 1.39/0.81 % Processed clauses : 1335
% 1.39/0.81 % ...of these trivial : 28
% 1.39/0.81 % ...subsumed : 433
% 1.39/0.81 % ...remaining for further processing : 874
% 1.39/0.81 % Other redundant clauses eliminated : 0
% 1.39/0.81 % Clauses deleted for lack of memory : 0
% 1.39/0.81 % Backward-subsumed : 15
% 1.39/0.81 % Backward-rewritten : 6
% 1.39/0.81 % Generated clauses : 4945
% 1.39/0.81 % ...of the previous two non-redundant : 4167
% 1.39/0.81 % ...aggressively subsumed : 0
% 1.39/0.81 % Contextual simplify-reflections : 0
% 1.39/0.81 % Paramodulations : 4945
% 1.39/0.81 % Factorizations : 0
% 1.39/0.81 % NegExts : 0
% 1.39/0.81 % Equation resolutions : 0
% 1.39/0.81 % Disequality decompositions : 0
% 1.39/0.81 % Total rewrite steps : 2001
% 1.39/0.81 % ...of those cached : 1921
% 1.39/0.81 % Propositional unsat checks : 0
% 1.39/0.81 % Propositional check models : 0
% 1.39/0.81 % Propositional check unsatisfiable : 0
% 1.39/0.81 % Propositional clauses : 0
% 1.39/0.81 % Propositional clauses after purity: 0
% 1.39/0.81 % Propositional unsat core size : 0
% 1.39/0.81 % Propositional preprocessing time : 0.000
% 1.39/0.81 % Propositional encoding time : 0.000
% 1.39/0.81 % Propositional solver time : 0.000
% 1.39/0.81 % Success case prop preproc time : 0.000
% 1.39/0.81 % Success case prop encoding time : 0.000
% 1.39/0.81 % Success case prop solver time : 0.000
% 1.39/0.81 % Current number of processed clauses : 823
% 1.39/0.81 % Positive orientable unit clauses : 97
% 1.39/0.81 % Positive unorientable unit clauses: 0
% 1.39/0.81 % Negative unit clauses : 2
% 1.39/0.81 % Non-unit-clauses : 724
% 1.39/0.81 % Current number of unprocessed clauses: 2874
% 1.39/0.81 % ...number of literals in the above : 10404
% 1.39/0.81 % Current number of archived formulas : 0
% 1.39/0.81 % Current number of archived clauses : 51
% 1.39/0.81 % Clause-clause subsumption calls (NU) : 26943
% 1.39/0.81 % Rec. Clause-clause subsumption calls : 22772
% 1.39/0.81 % Non-unit clause-clause subsumptions : 446
% 1.39/0.81 % Unit Clause-clause subsumption calls : 641
% 1.39/0.81 % Rewrite failures with RHS unbound : 0
% 1.39/0.81 % BW rewrite match attempts : 24
% 1.39/0.81 % BW rewrite match successes : 5
% 1.39/0.81 % Condensation attempts : 0
% 1.39/0.81 % Condensation successes : 0
% 1.39/0.81 % Termbank termtop insertions : 73644
% 1.39/0.81 % Search garbage collected termcells : 116
% 1.39/0.81
% 1.39/0.81 % -------------------------------------------------
% 1.39/0.81 % User time : 0.216 s
% 1.39/0.81 % System time : 0.007 s
% 1.39/0.81 % Total time : 0.224 s
% 1.39/0.81 % Maximum resident set size: 3660 pages
% 1.39/0.81
% 1.39/0.81 % -------------------------------------------------
% 1.39/0.81 % User time : 0.719 s
% 1.39/0.81 % System time : 0.049 s
% 1.39/0.81 % Total time : 0.767 s
% 1.39/0.81 % Maximum resident set size: 4608 pages
% 1.39/0.81 % E exiting
%------------------------------------------------------------------------------