%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD029-3 : 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 12:22:45 PM UTC 2026
% Result : Unsatisfiable 2.15s 0.76s
% Output : CNFRefutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of clauses : 58 ( 24 unt; 6 nHn; 58 RR)
% Number of literals : 124 ( 0 equ; 66 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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_7,negated_conjecture,
product(a,v,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_7) ).
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(not_sum_5,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_5) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
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_6,negated_conjecture,
product(a,u,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_6) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
cnf(v_is_defined,hypothesis,
defined(v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_is_defined) ).
cnf(not_product_8,negated_conjecture,
~ product(multiplicative_identity,u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_8) ).
cnf(c_0_15,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_16,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_15 ).
cnf(c_0_17,negated_conjecture,
product(a,v,b),
product_7 ).
cnf(c_0_18,negated_conjecture,
( ~ product(X1,X3,a)
| ~ product(X3,v,X2)
| product(X1,X2,b) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
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(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_21,negated_conjecture,
( ~ product(X1,a,a)
| product(X1,b,b) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_22,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_19 ).
cnf(c_0_23,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_24,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_20 ).
cnf(c_0_25,negated_conjecture,
product(multiplicative_identity,b,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_26,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_27,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_5]) ).
cnf(c_0_28,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_29,negated_conjecture,
( ~ product(X3,multiplicative_identity,X1)
| ~ product(X3,b,X2)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_26 ).
cnf(c_0_31,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_32,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
c_0_27 ).
cnf(c_0_33,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_28 ).
cnf(c_0_34,negated_conjecture,
( ~ product(multiplicative_inverse(b),multiplicative_identity,X1)
| product(X1,b,multiplicative_identity) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_35,plain,
( ~ defined(X1)
| product(X1,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_36,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_37,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_multiplication]) ).
cnf(c_0_38,negated_conjecture,
( ~ defined(multiplicative_inverse(b))
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_36 ).
cnf(c_0_40,negated_conjecture,
( ~ product(X3,a,X1)
| ~ product(X3,b,X2)
| product(X1,v,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_41,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
c_0_37 ).
cnf(c_0_42,negated_conjecture,
product(a,u,b),
product_6 ).
cnf(c_0_43,plain,
( ~ defined(X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,multiplicative_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_44,negated_conjecture,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_31])]),c_0_32]) ).
cnf(c_0_45,negated_conjecture,
( ~ defined(X2)
| ~ product(X2,a,X1)
| product(X1,v,multiply(X2,b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_31])]) ).
cnf(c_0_46,negated_conjecture,
product(u,a,b),
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
cnf(c_0_47,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_48,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X2,X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_41]) ).
cnf(c_0_49,negated_conjecture,
( ~ defined(X2)
| ~ product(b,X2,X1)
| product(multiplicative_inverse(b),X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
product(b,v,multiply(u,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_51,hypothesis,
defined(v),
v_is_defined ).
cnf(c_0_52,plain,
( ~ defined(X2)
| ~ defined(X5)
| ~ product(X4,X5,X1)
| ~ product(X4,multiply(X2,X5),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
product(multiplicative_inverse(b),multiply(u,b),v),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_54,negated_conjecture,
~ product(multiplicative_identity,u,v),
inference(fof_simplification,[status(thm)],[not_product_8]) ).
cnf(c_0_55,negated_conjecture,
( ~ product(multiplicative_inverse(b),b,X1)
| product(X1,u,v) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_31]),c_0_47])]) ).
cnf(c_0_56,negated_conjecture,
~ product(multiplicative_identity,u,v),
c_0_54 ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_30]),c_0_31])]),c_0_56]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD029-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 15:41:17 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 2.15/0.76 % Version: 3.5.1
% 2.15/0.76 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.15/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.15/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.15/0.76 % Starting new_bool_3 with 300s (1) cores
% 2.15/0.76 % Starting new_bool_1 with 300s (1) cores
% 2.15/0.76 % Starting sh5l with 300s (1) cores
% 2.15/0.76 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3628699 completed with status 0
% 2.15/0.76 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.15/0.76 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.15/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.15/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.15/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.15/0.76 % No SInE strategy applied
% 2.15/0.76 % Search class: FGUNF-FFMM21-SFFFFFNN
% 2.15/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.15/0.76 % Starting SubtermCWHack with 136s (1) cores
% 2.15/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.15/0.76 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 2.15/0.76 % Starting new_bool_3 with 269s (1) cores
% 2.15/0.76 % Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 136s (1) cores
% 2.15/0.76 % H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 3628707 completed with status 0
% 2.15/0.76 % Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 2.15/0.76 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.15/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.15/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.15/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.15/0.76 % No SInE strategy applied
% 2.15/0.76 % Search class: FGUNF-FFMM21-SFFFFFNN
% 2.15/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.15/0.76 % Starting SubtermCWHack with 136s (1) cores
% 2.15/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.15/0.76 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 2.15/0.76 % Preprocessing time : 0.002 s
% 2.15/0.76 % Presaturation interreduction done
% 2.15/0.76
% 2.15/0.76 % Proof found!
% 2.15/0.76 % SZS status Unsatisfiable
% 2.15/0.76 % SZS output start CNFRefutation
% See solution above
% 2.15/0.76 % Parsed axioms : 34
% 2.15/0.76 % Removed by relevancy pruning/SinE : 0
% 2.15/0.76 % Initial clauses : 34
% 2.15/0.76 % Removed in clause preprocessing : 0
% 2.15/0.76 % Initial clauses in saturation : 34
% 2.15/0.76 % Processed clauses : 2294
% 2.15/0.76 % ...of these trivial : 146
% 2.15/0.76 % ...subsumed : 862
% 2.15/0.76 % ...remaining for further processing : 1286
% 2.15/0.76 % Other redundant clauses eliminated : 0
% 2.15/0.76 % Clauses deleted for lack of memory : 0
% 2.15/0.76 % Backward-subsumed : 5
% 2.15/0.76 % Backward-rewritten : 38
% 2.15/0.76 % Generated clauses : 22363
% 2.15/0.76 % ...of the previous two non-redundant : 17425
% 2.15/0.76 % ...aggressively subsumed : 0
% 2.15/0.76 % Contextual simplify-reflections : 7
% 2.15/0.76 % Paramodulations : 22343
% 2.15/0.76 % Factorizations : 20
% 2.15/0.76 % NegExts : 0
% 2.15/0.76 % Equation resolutions : 0
% 2.15/0.76 % Disequality decompositions : 0
% 2.15/0.76 % Total rewrite steps : 13931
% 2.15/0.76 % ...of those cached : 13605
% 2.15/0.76 % Propositional unsat checks : 0
% 2.15/0.76 % Propositional check models : 0
% 2.15/0.76 % Propositional check unsatisfiable : 0
% 2.15/0.76 % Propositional clauses : 0
% 2.15/0.76 % Propositional clauses after purity: 0
% 2.15/0.76 % Propositional unsat core size : 0
% 2.15/0.76 % Propositional preprocessing time : 0.000
% 2.15/0.76 % Propositional encoding time : 0.000
% 2.15/0.76 % Propositional solver time : 0.000
% 2.15/0.76 % Success case prop preproc time : 0.000
% 2.15/0.76 % Success case prop encoding time : 0.000
% 2.15/0.76 % Success case prop solver time : 0.000
% 2.15/0.76 % Current number of processed clauses : 1209
% 2.15/0.76 % Positive orientable unit clauses : 395
% 2.15/0.76 % Positive unorientable unit clauses: 0
% 2.15/0.76 % Negative unit clauses : 3
% 2.15/0.76 % Non-unit-clauses : 811
% 2.15/0.76 % Current number of unprocessed clauses: 15197
% 2.15/0.76 % ...number of literals in the above : 47998
% 2.15/0.76 % Current number of archived formulas : 0
% 2.15/0.76 % Current number of archived clauses : 77
% 2.15/0.76 % Clause-clause subsumption calls (NU) : 32578
% 2.15/0.76 % Rec. Clause-clause subsumption calls : 24925
% 2.15/0.76 % Non-unit clause-clause subsumptions : 874
% 2.15/0.76 % Unit Clause-clause subsumption calls : 2059
% 2.15/0.76 % Rewrite failures with RHS unbound : 0
% 2.15/0.76 % BW rewrite match attempts : 248
% 2.15/0.76 % BW rewrite match successes : 37
% 2.15/0.76 % Condensation attempts : 0
% 2.15/0.76 % Condensation successes : 0
% 2.15/0.76 % Termbank termtop insertions : 331958
% 2.15/0.76 % Search garbage collected termcells : 118
% 2.15/0.76
% 2.15/0.76 % -------------------------------------------------
% 2.15/0.76 % User time : 0.315 s
% 2.15/0.76 % System time : 0.014 s
% 2.15/0.76 % Total time : 0.329 s
% 2.15/0.76 % Maximum resident set size: 3660 pages
% 2.15/0.76
% 2.15/0.76 % -------------------------------------------------
% 2.15/0.76 % User time : 1.465 s
% 2.15/0.76 % System time : 0.063 s
% 2.15/0.76 % Total time : 1.528 s
% 2.15/0.76 % Maximum resident set size: 4608 pages
% 2.15/0.76 % E exiting
%------------------------------------------------------------------------------