%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD028-3 : 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 : n007.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 12:22:44 PM UTC 2026
% Result : Unsatisfiable 0.30s 0.74s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 51 ( 22 unt; 6 nHn; 51 RR)
% Number of literals : 104 ( 0 equ; 53 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 74 ( 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(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(product_7,negated_conjecture,
product(a,v,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_7) ).
cnf(v_is_defined,hypothesis,
defined(v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_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,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_5) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
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(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(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
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(not_product_8,negated_conjecture,
~ product(multiplicative_identity,u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_8) ).
cnf(c_0_13,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_14,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_15,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_13 ).
cnf(c_0_16,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_14 ).
cnf(c_0_17,plain,
( ~ defined(X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,multiplicative_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,negated_conjecture,
product(a,v,b),
product_7 ).
cnf(c_0_19,hypothesis,
defined(v),
v_is_defined ).
cnf(c_0_20,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_21,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_5]) ).
cnf(c_0_22,negated_conjecture,
( ~ product(X1,a,multiplicative_identity)
| product(X1,b,v) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_23,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_20 ).
cnf(c_0_24,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_25,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
c_0_21 ).
cnf(c_0_26,negated_conjecture,
product(multiplicative_inverse(a),b,v),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_27,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_28,negated_conjecture,
product(a,u,b),
product_6 ).
cnf(c_0_29,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_30,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_31,negated_conjecture,
( ~ product(X3,b,X2)
| ~ product(X1,X3,multiplicative_inverse(a))
| product(X1,X2,v) ),
inference(spm,[status(thm)],[c_0_15,c_0_26]) ).
cnf(c_0_32,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_27 ).
cnf(c_0_33,negated_conjecture,
( ~ product(X1,a,multiplicative_identity)
| product(X1,b,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_28]),c_0_29])]) ).
cnf(c_0_34,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_30 ).
cnf(c_0_35,negated_conjecture,
( ~ product(X1,multiplicative_inverse(a),multiplicative_inverse(a))
| product(X1,v,v) ),
inference(spm,[status(thm)],[c_0_31,c_0_26]) ).
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,negated_conjecture,
( ~ product(X3,a,X1)
| ~ product(X3,b,X2)
| product(X1,v,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_38,negated_conjecture,
product(multiplicative_inverse(a),b,u),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_39,plain,
( ~ defined(X1)
| product(X1,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_40,negated_conjecture,
( ~ defined(multiplicative_inverse(a))
| product(multiplicative_identity,v,v) ),
inference(spm,[status(thm)],[c_0_35,c_0_16]) ).
cnf(c_0_41,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_36 ).
cnf(c_0_42,negated_conjecture,
( ~ product(multiplicative_inverse(a),a,X1)
| product(X1,v,u) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( ~ defined(X3)
| ~ product(X1,X4,X3)
| ~ product(X4,multiplicative_identity,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
product(multiplicative_identity,v,v),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_24])]),c_0_25]) ).
cnf(c_0_45,negated_conjecture,
product(multiplicative_identity,v,u),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_46,negated_conjecture,
~ product(multiplicative_identity,u,v),
inference(fof_simplification,[status(thm)],[not_product_8]) ).
cnf(c_0_47,negated_conjecture,
( ~ product(v,multiplicative_identity,X1)
| product(multiplicative_identity,X1,v) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_19])]) ).
cnf(c_0_48,negated_conjecture,
product(v,multiplicative_identity,u),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
~ product(multiplicative_identity,u,v),
c_0_46 ).
cnf(c_0_50,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD028-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.53 % Computer : n007.cluster.edu
% 0.20/0.53 % Model : x86_64 x86_64
% 0.20/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.53 % Memory : 8046.5625MB
% 0.20/0.53 % OS : Linux 6.8.0-71-generic
% 0.20/0.53 % CPULimit : 300
% 0.20/0.53 % WCLimit : 300
% 0.20/0.53 % DateTime : Mon Sep 21 15:36:36 UTC 2026
% 0.20/0.54 % CPUTime :
% 0.20/0.54 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.61 Running first-order theorem proving
% 0.20/0.61 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
% 0.30/0.74 % Version: 3.5.1
% 0.30/0.74 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.30/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.30/0.74 % Starting new_bool_3 with 300s (1) cores
% 0.30/0.74 % Starting new_bool_1 with 300s (1) cores
% 0.30/0.74 % Starting sh5l with 300s (1) cores
% 0.30/0.74 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1441595 completed with status 0
% 0.30/0.74 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.30/0.74 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.30/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.30/0.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.30/0.74 % No SInE strategy applied
% 0.30/0.74 % Search class: FGUNF-FFMM21-SFFFFFNN
% 0.30/0.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.30/0.74 % Starting SubtermCWHack with 136s (1) cores
% 0.30/0.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.30/0.74 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 0.30/0.74 % Starting new_bool_3 with 269s (1) cores
% 0.30/0.74 % Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 136s (1) cores
% 0.30/0.74 % new_bool_3 with pid 1441605 completed with status 0
% 0.30/0.74 % Result found by new_bool_3
% 0.30/0.74 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.30/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.30/0.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.30/0.74 % No SInE strategy applied
% 0.30/0.74 % Search class: FGUNF-FFMM21-SFFFFFNN
% 0.30/0.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.30/0.74 % Starting SubtermCWHack with 136s (1) cores
% 0.30/0.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.30/0.74 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 0.30/0.74 % Starting new_bool_3 with 269s (1) cores
% 0.30/0.74 % Preprocessing time : 0.002 s
% 0.30/0.74 % Presaturation interreduction done
% 0.30/0.74
% 0.30/0.74 % Proof found!
% 0.30/0.74 % SZS status Unsatisfiable
% 0.30/0.74 % SZS output start CNFRefutation
% See solution above
% 0.30/0.74 % Parsed axioms : 34
% 0.30/0.74 % Removed by relevancy pruning/SinE : 0
% 0.30/0.74 % Initial clauses : 34
% 0.30/0.74 % Removed in clause preprocessing : 0
% 0.30/0.74 % Initial clauses in saturation : 34
% 0.30/0.74 % Processed clauses : 429
% 0.30/0.74 % ...of these trivial : 21
% 0.30/0.74 % ...subsumed : 71
% 0.30/0.74 % ...remaining for further processing : 337
% 0.30/0.74 % Other redundant clauses eliminated : 0
% 0.30/0.74 % Clauses deleted for lack of memory : 0
% 0.30/0.74 % Backward-subsumed : 0
% 0.30/0.74 % Backward-rewritten : 15
% 0.30/0.74 % Generated clauses : 1795
% 0.30/0.74 % ...of the previous two non-redundant : 1406
% 0.30/0.74 % ...aggressively subsumed : 0
% 0.30/0.74 % Contextual simplify-reflections : 0
% 0.30/0.74 % Paramodulations : 1793
% 0.30/0.74 % Factorizations : 2
% 0.30/0.74 % NegExts : 0
% 0.30/0.74 % Equation resolutions : 0
% 0.30/0.74 % Disequality decompositions : 0
% 0.30/0.74 % Total rewrite steps : 1045
% 0.30/0.74 % ...of those cached : 972
% 0.30/0.74 % Propositional unsat checks : 0
% 0.30/0.74 % Propositional check models : 0
% 0.30/0.74 % Propositional check unsatisfiable : 0
% 0.30/0.74 % Propositional clauses : 0
% 0.30/0.74 % Propositional clauses after purity: 0
% 0.30/0.74 % Propositional unsat core size : 0
% 0.30/0.74 % Propositional preprocessing time : 0.000
% 0.30/0.74 % Propositional encoding time : 0.000
% 0.30/0.74 % Propositional solver time : 0.000
% 0.30/0.74 % Success case prop preproc time : 0.000
% 0.30/0.74 % Success case prop encoding time : 0.000
% 0.30/0.74 % Success case prop solver time : 0.000
% 0.30/0.74 % Current number of processed clauses : 288
% 0.30/0.74 % Positive orientable unit clauses : 89
% 0.30/0.74 % Positive unorientable unit clauses: 0
% 0.30/0.74 % Negative unit clauses : 3
% 0.30/0.74 % Non-unit-clauses : 196
% 0.30/0.74 % Current number of unprocessed clauses: 1037
% 0.30/0.74 % ...number of literals in the above : 3230
% 0.30/0.74 % Current number of archived formulas : 0
% 0.30/0.74 % Current number of archived clauses : 49
% 0.30/0.74 % Clause-clause subsumption calls (NU) : 2670
% 0.30/0.74 % Rec. Clause-clause subsumption calls : 2063
% 0.30/0.74 % Non-unit clause-clause subsumptions : 71
% 0.30/0.74 % Unit Clause-clause subsumption calls : 128
% 0.30/0.74 % Rewrite failures with RHS unbound : 0
% 0.30/0.74 % BW rewrite match attempts : 48
% 0.30/0.74 % BW rewrite match successes : 13
% 0.30/0.74 % Condensation attempts : 0
% 0.30/0.74 % Condensation successes : 0
% 0.30/0.74 % Termbank termtop insertions : 26164
% 0.30/0.74 % Search garbage collected termcells : 118
% 0.30/0.74
% 0.30/0.74 % -------------------------------------------------
% 0.30/0.74 % User time : 0.063 s
% 0.30/0.74 % System time : 0.009 s
% 0.30/0.74 % Total time : 0.072 s
% 0.30/0.74 % Maximum resident set size: 3660 pages
% 0.30/0.74
% 0.30/0.74 % -------------------------------------------------
% 0.30/0.74 % User time : 0.380 s
% 0.30/0.74 % System time : 0.042 s
% 0.30/0.74 % Total time : 0.422 s
% 0.30/0.74 % Maximum resident set size: 4608 pages
% 0.30/0.74 % E exiting
%------------------------------------------------------------------------------