%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD025-3 : 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 : n002.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 12:22:43 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.56s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 40 ( 15 unt; 0 nHn; 40 RR)
% Number of literals : 90 ( 0 equ; 54 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(product_6,negated_conjecture,
product(multiplicative_identity,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_6) ).
cnf(totality_of_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(product_5,negated_conjecture,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_5) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
cnf(not_product_7,negated_conjecture,
~ product(d,b,multiply(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_7) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(well_definedness_of_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).
cnf(c_0_11,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_12,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_13,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_14,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_15,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_11 ).
cnf(c_0_16,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_12 ).
cnf(c_0_17,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_13 ).
cnf(c_0_18,negated_conjecture,
product(multiplicative_identity,c,d),
product_6 ).
cnf(c_0_19,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_multiplication]) ).
cnf(c_0_20,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_14 ).
cnf(c_0_21,plain,
( ~ defined(X1)
| product(X1,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
product(multiplicative_identity,a,b),
product_5 ).
cnf(c_0_23,plain,
( ~ defined(X2)
| ~ product(X4,X2,X3)
| ~ product(X4,multiplicative_identity,X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_24,negated_conjecture,
product(c,multiplicative_identity,d),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_25,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
c_0_19 ).
cnf(c_0_26,plain,
( ~ defined(X3)
| ~ product(X1,X4,X3)
| ~ product(X4,multiplicative_identity,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
product(a,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( ~ defined(X1)
| ~ product(c,X1,X2)
| product(d,X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X2,X1)) ),
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_30,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_31,negated_conjecture,
~ product(d,b,multiply(a,c)),
inference(fof_simplification,[status(thm)],[not_product_7]) ).
cnf(c_0_32,negated_conjecture,
( ~ defined(X2)
| ~ product(X1,a,X2)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( ~ defined(X1)
| product(d,X1,multiply(X1,c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_34,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_35,negated_conjecture,
~ product(d,b,multiply(a,c)),
c_0_31 ).
cnf(c_0_36,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_multiplication]) ).
cnf(c_0_37,negated_conjecture,
~ defined(multiply(a,c)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_38,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
c_0_36 ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_30]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD025-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 15:41:34 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 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
% 0.21/0.56 % Version: 3.5.1
% 0.21/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.56 % Starting sh5l with 300s (1) cores
% 0.21/0.56 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3629541 completed with status 0
% 0.21/0.56 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.21/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.56 % No SInE strategy applied
% 0.21/0.56 % Search class: FGUNF-FFMM21-SFFFFFNN
% 0.21/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.21/0.56 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 0.21/0.56 % Starting new_bool_3 with 269s (1) cores
% 0.21/0.56 % Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 136s (1) cores
% 0.21/0.56 % H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 3629549 completed with status 0
% 0.21/0.56 % Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 0.21/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.56 % No SInE strategy applied
% 0.21/0.56 % Search class: FGUNF-FFMM21-SFFFFFNN
% 0.21/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.21/0.56 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 0.21/0.56 % Preprocessing time : 0.002 s
% 0.21/0.56 % Presaturation interreduction done
% 0.21/0.56
% 0.21/0.56 % Proof found!
% 0.21/0.56 % SZS status Unsatisfiable
% 0.21/0.56 % SZS output start CNFRefutation
% See solution above
% 0.21/0.56 % Parsed axioms : 33
% 0.21/0.56 % Removed by relevancy pruning/SinE : 0
% 0.21/0.56 % Initial clauses : 33
% 0.21/0.56 % Removed in clause preprocessing : 0
% 0.21/0.56 % Initial clauses in saturation : 33
% 0.21/0.56 % Processed clauses : 498
% 0.21/0.56 % ...of these trivial : 25
% 0.21/0.56 % ...subsumed : 112
% 0.21/0.56 % ...remaining for further processing : 361
% 0.21/0.56 % Other redundant clauses eliminated : 0
% 0.21/0.56 % Clauses deleted for lack of memory : 0
% 0.21/0.56 % Backward-subsumed : 1
% 0.21/0.56 % Backward-rewritten : 9
% 0.21/0.56 % Generated clauses : 2360
% 0.21/0.56 % ...of the previous two non-redundant : 1862
% 0.21/0.56 % ...aggressively subsumed : 0
% 0.21/0.56 % Contextual simplify-reflections : 1
% 0.21/0.56 % Paramodulations : 2356
% 0.21/0.56 % Factorizations : 4
% 0.21/0.56 % NegExts : 0
% 0.21/0.56 % Equation resolutions : 0
% 0.21/0.56 % Disequality decompositions : 0
% 0.21/0.56 % Total rewrite steps : 1413
% 0.21/0.56 % ...of those cached : 1323
% 0.21/0.56 % Propositional unsat checks : 0
% 0.21/0.56 % Propositional check models : 0
% 0.21/0.56 % Propositional check unsatisfiable : 0
% 0.21/0.56 % Propositional clauses : 0
% 0.21/0.56 % Propositional clauses after purity: 0
% 0.21/0.56 % Propositional unsat core size : 0
% 0.21/0.56 % Propositional preprocessing time : 0.000
% 0.21/0.56 % Propositional encoding time : 0.000
% 0.21/0.56 % Propositional solver time : 0.000
% 0.21/0.56 % Success case prop preproc time : 0.000
% 0.21/0.56 % Success case prop encoding time : 0.000
% 0.21/0.56 % Success case prop solver time : 0.000
% 0.21/0.56 % Current number of processed clauses : 318
% 0.21/0.56 % Positive orientable unit clauses : 103
% 0.21/0.56 % Positive unorientable unit clauses: 0
% 0.21/0.56 % Negative unit clauses : 3
% 0.21/0.56 % Non-unit-clauses : 212
% 0.21/0.56 % Current number of unprocessed clauses: 1430
% 0.21/0.56 % ...number of literals in the above : 4603
% 0.21/0.56 % Current number of archived formulas : 0
% 0.21/0.56 % Current number of archived clauses : 43
% 0.21/0.56 % Clause-clause subsumption calls (NU) : 2700
% 0.21/0.56 % Rec. Clause-clause subsumption calls : 2243
% 0.21/0.56 % Non-unit clause-clause subsumptions : 114
% 0.21/0.56 % Unit Clause-clause subsumption calls : 307
% 0.21/0.56 % Rewrite failures with RHS unbound : 0
% 0.21/0.56 % BW rewrite match attempts : 50
% 0.21/0.56 % BW rewrite match successes : 9
% 0.21/0.56 % Condensation attempts : 0
% 0.21/0.56 % Condensation successes : 0
% 0.21/0.56 % Termbank termtop insertions : 32497
% 0.21/0.56 % Search garbage collected termcells : 116
% 0.21/0.56
% 0.21/0.56 % -------------------------------------------------
% 0.21/0.56 % User time : 0.080 s
% 0.21/0.56 % System time : 0.004 s
% 0.21/0.56 % Total time : 0.084 s
% 0.21/0.56 % Maximum resident set size: 3660 pages
% 0.21/0.56
% 0.21/0.56 % -------------------------------------------------
% 0.21/0.56 % User time : 0.309 s
% 0.21/0.56 % System time : 0.029 s
% 0.21/0.56 % Total time : 0.338 s
% 0.21/0.56 % Maximum resident set size: 4608 pages
% 0.21/0.56 % E exiting
%------------------------------------------------------------------------------