%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : FLD049-3 : 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 : n015.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 12:23:18 PM UTC 2026
% Result : Unsatisfiable 8.65s 1.85s
% Output : CNFRefutation 8.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 59 ( 27 unt; 6 nHn; 59 RR)
% Number of literals : 123 ( 0 equ; 68 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(not_sum_5,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_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_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_sum_6,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_6) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(totality_of_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(product_7,negated_conjecture,
product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_7) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(not_product_8,negated_conjecture,
~ product(a,d,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_8) ).
cnf(well_definedness_of_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).
cnf(c_0_16,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_multiplication]) ).
cnf(c_0_17,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_5]) ).
cnf(c_0_18,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_1]) ).
cnf(c_0_19,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_20,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_21,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_16 ).
cnf(c_0_22,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_23,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
c_0_17 ).
cnf(c_0_24,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_18 ).
cnf(c_0_25,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_19 ).
cnf(c_0_26,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_20 ).
cnf(c_0_27,hypothesis,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_28,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_6]) ).
cnf(c_0_29,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_2]) ).
cnf(c_0_30,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_multiplication]) ).
cnf(c_0_31,plain,
( ~ defined(X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,multiplicative_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,hypothesis,
product(b,multiplicative_inverse(b),multiplicative_identity),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))),
product_7 ).
cnf(c_0_34,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c_0_35,hypothesis,
defined(d),
d_is_defined ).
cnf(c_0_36,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
c_0_28 ).
cnf(c_0_37,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_29 ).
cnf(c_0_38,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
c_0_30 ).
cnf(c_0_39,hypothesis,
( ~ defined(X2)
| ~ product(multiplicative_inverse(b),X2,X1)
| product(b,X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
product(multiplicative_inverse(b),a,multiply(c,multiplicative_inverse(d))),
inference(spm,[status(thm)],[c_0_26,c_0_33]) ).
cnf(c_0_41,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_42,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_34 ).
cnf(c_0_43,hypothesis,
product(multiplicative_inverse(d),d,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_35]),c_0_36]) ).
cnf(c_0_44,plain,
( ~ defined(X5)
| ~ defined(X2)
| ~ product(X4,X5,X1)
| ~ product(X4,multiply(X5,X2),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
product(b,multiply(c,multiplicative_inverse(d)),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_46,hypothesis,
defined(multiplicative_inverse(d)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_35]),c_0_36]) ).
cnf(c_0_47,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_48,hypothesis,
( ~ product(X3,multiplicative_identity,X2)
| ~ product(X3,multiplicative_inverse(d),X1)
| product(X1,d,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( ~ product(b,c,X1)
| product(X1,multiplicative_inverse(d),a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_50,hypothesis,
( ~ product(X2,multiplicative_identity,X1)
| ~ product(b,c,X2)
| product(a,d,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_51,negated_conjecture,
~ product(a,d,multiply(b,c)),
inference(fof_simplification,[status(thm)],[not_product_8]) ).
cnf(c_0_52,hypothesis,
( ~ product(multiply(b,c),multiplicative_identity,X1)
| product(a,d,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_38]),c_0_47]),c_0_22])]) ).
cnf(c_0_53,plain,
( ~ defined(X1)
| product(X1,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_54,negated_conjecture,
~ product(a,d,multiply(b,c)),
c_0_51 ).
cnf(c_0_55,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_multiplication]) ).
cnf(c_0_56,hypothesis,
~ defined(multiply(b,c)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_57,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
c_0_55 ).
cnf(c_0_58,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_47]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD049-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n015.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 15:44:51 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.55 Running first-order theorem proving
% 0.24/0.55 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
% 8.65/1.85 % Version: 3.5.1
% 8.65/1.85 % Preprocessing class: FSMSSMSSSSSNFFN.
% 8.65/1.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.65/1.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.65/1.85 % Starting new_bool_3 with 300s (1) cores
% 8.65/1.85 % Starting new_bool_1 with 300s (1) cores
% 8.65/1.85 % Starting sh5l with 300s (1) cores
% 8.65/1.85 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1817782 completed with status 0
% 8.65/1.85 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 8.65/1.85 % Preprocessing class: FSMSSMSSSSSNFFN.
% 8.65/1.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.65/1.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.65/1.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.65/1.85 % No SInE strategy applied
% 8.65/1.85 % Search class: FGUNF-FFMM21-SFFFFFNN
% 8.65/1.85 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.65/1.85 % Starting SubtermCWHack with 136s (1) cores
% 8.65/1.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.65/1.85 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 8.65/1.85 % Starting new_bool_3 with 269s (1) cores
% 8.65/1.85 % Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 136s (1) cores
% 8.65/1.85 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1817789 completed with status 0
% 8.65/1.85 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 8.65/1.85 % Preprocessing class: FSMSSMSSSSSNFFN.
% 8.65/1.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.65/1.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.65/1.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.65/1.85 % No SInE strategy applied
% 8.65/1.85 % Search class: FGUNF-FFMM21-SFFFFFNN
% 8.65/1.85 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.65/1.85 % Starting SubtermCWHack with 136s (1) cores
% 8.65/1.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.65/1.85 % Preprocessing time : 0.002 s
% 8.65/1.85 % Presaturation interreduction done
% 8.65/1.85
% 8.65/1.85 % Proof found!
% 8.65/1.85 % SZS status Unsatisfiable
% 8.65/1.85 % SZS output start CNFRefutation
% See solution above
% 8.65/1.85 % Parsed axioms : 34
% 8.65/1.85 % Removed by relevancy pruning/SinE : 0
% 8.65/1.85 % Initial clauses : 34
% 8.65/1.85 % Removed in clause preprocessing : 0
% 8.65/1.85 % Initial clauses in saturation : 34
% 8.65/1.85 % Processed clauses : 4653
% 8.65/1.85 % ...of these trivial : 35
% 8.65/1.85 % ...subsumed : 1860
% 8.65/1.85 % ...remaining for further processing : 2758
% 8.65/1.85 % Other redundant clauses eliminated : 0
% 8.65/1.85 % Clauses deleted for lack of memory : 0
% 8.65/1.85 % Backward-subsumed : 27
% 8.65/1.85 % Backward-rewritten : 13
% 8.65/1.85 % Generated clauses : 28243
% 8.65/1.85 % ...of the previous two non-redundant : 25392
% 8.65/1.85 % ...aggressively subsumed : 0
% 8.65/1.85 % Contextual simplify-reflections : 10
% 8.65/1.85 % Paramodulations : 28243
% 8.65/1.85 % Factorizations : 0
% 8.65/1.85 % NegExts : 0
% 8.65/1.85 % Equation resolutions : 0
% 8.65/1.85 % Disequality decompositions : 0
% 8.65/1.85 % Total rewrite steps : 6455
% 8.65/1.85 % ...of those cached : 6207
% 8.65/1.85 % Propositional unsat checks : 0
% 8.65/1.85 % Propositional check models : 0
% 8.65/1.85 % Propositional check unsatisfiable : 0
% 8.65/1.85 % Propositional clauses : 0
% 8.65/1.85 % Propositional clauses after purity: 0
% 8.65/1.85 % Propositional unsat core size : 0
% 8.65/1.85 % Propositional preprocessing time : 0.000
% 8.65/1.85 % Propositional encoding time : 0.000
% 8.65/1.85 % Propositional solver time : 0.000
% 8.65/1.85 % Success case prop preproc time : 0.000
% 8.65/1.85 % Success case prop encoding time : 0.000
% 8.65/1.85 % Success case prop solver time : 0.000
% 8.65/1.85 % Current number of processed clauses : 2684
% 8.65/1.85 % Positive orientable unit clauses : 272
% 8.65/1.85 % Positive unorientable unit clauses: 0
% 8.65/1.85 % Negative unit clauses : 5
% 8.65/1.85 % Non-unit-clauses : 2407
% 8.65/1.85 % Current number of unprocessed clauses: 20759
% 8.65/1.85 % ...number of literals in the above : 83461
% 8.65/1.85 % Current number of archived formulas : 0
% 8.65/1.85 % Current number of archived clauses : 74
% 8.65/1.85 % Clause-clause subsumption calls (NU) : 548210
% 8.65/1.85 % Rec. Clause-clause subsumption calls : 363921
% 8.65/1.85 % Non-unit clause-clause subsumptions : 1895
% 8.65/1.85 % Unit Clause-clause subsumption calls : 6263
% 8.65/1.85 % Rewrite failures with RHS unbound : 0
% 8.65/1.85 % BW rewrite match attempts : 32
% 8.65/1.85 % BW rewrite match successes : 9
% 8.65/1.85 % Condensation attempts : 0
% 8.65/1.85 % Condensation successes : 0
% 8.65/1.85 % Termbank termtop insertions : 510466
% 8.65/1.85 % Search garbage collected termcells : 120
% 8.65/1.85
% 8.65/1.85 % -------------------------------------------------
% 8.65/1.85 % User time : 1.182 s
% 8.65/1.85 % System time : 0.054 s
% 8.65/1.85 % Total time : 1.236 s
% 8.65/1.85 % Maximum resident set size: 3352 pages
% 8.65/1.85
% 8.65/1.85 % -------------------------------------------------
% 8.65/1.85 % User time : 5.823 s
% 8.65/1.85 % System time : 0.261 s
% 8.65/1.85 % Total time : 6.084 s
% 8.65/1.85 % Maximum resident set size: 4608 pages
% 8.65/1.85 % E exiting
%------------------------------------------------------------------------------