%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : FLD068-4 : 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 : n019.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 12:23:25 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 15 unt; 0 nHn; 35 RR)
% Number of literals : 70 ( 0 equ; 38 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 : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(existence_of_identity_addition,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(sum_4,negated_conjecture,
sum(b,additive_inverse(a),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_4) ).
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(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(less_or_equal_5,negated_conjecture,
less_or_equal(additive_identity,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_5) ).
cnf(not_less_or_equal_6,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_6) ).
cnf(c_0_10,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_11,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_12,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_13,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_10 ).
cnf(c_0_14,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_11 ).
cnf(c_0_15,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_12 ).
cnf(c_0_16,negated_conjecture,
sum(b,additive_inverse(a),u),
sum_4 ).
cnf(c_0_17,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_18,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| ~ defined(X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
sum(additive_inverse(a),b,u),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_21,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_17 ).
cnf(c_0_22,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
cnf(c_0_23,negated_conjecture,
( ~ sum(X1,additive_inverse(a),additive_identity)
| sum(X1,u,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_24,plain,
( ~ defined(X1)
| sum(X1,additive_inverse(X1),additive_identity) ),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_25,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_26,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
c_0_22 ).
cnf(c_0_27,negated_conjecture,
less_or_equal(additive_identity,u),
less_or_equal_5 ).
cnf(c_0_28,negated_conjecture,
sum(a,u,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
( ~ sum(additive_identity,X3,X1)
| ~ sum(u,X3,X2)
| less_or_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
sum(u,a,b),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
~ less_or_equal(a,b),
inference(fof_simplification,[status(thm)],[not_less_or_equal_6]) ).
cnf(c_0_32,negated_conjecture,
( ~ sum(additive_identity,a,X1)
| less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
~ less_or_equal(a,b),
c_0_31 ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_14]),c_0_25])]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD068-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 15:45:04 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 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
% 0.15/0.51 % Version: 3.5.1
% 0.15/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.51 % Starting sh5l with 300s (1) cores
% 0.15/0.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2936109 completed with status 0
% 0.15/0.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.51 % No SInE strategy applied
% 0.15/0.51 % Search class: FGUNF-FFMM21-SFFFFFNN
% 0.15/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.51 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 0.15/0.51 % Starting new_bool_3 with 269s (1) cores
% 0.15/0.51 % Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 136s (1) cores
% 0.15/0.51 % new_bool_3 with pid 2936117 completed with status 0
% 0.15/0.51 % Result found by new_bool_3
% 0.15/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.51 % No SInE strategy applied
% 0.15/0.51 % Search class: FGUNF-FFMM21-SFFFFFNN
% 0.15/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.51 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 0.15/0.51 % Starting new_bool_3 with 269s (1) cores
% 0.15/0.51 % Preprocessing time : 0.001 s
% 0.15/0.51 % Presaturation interreduction done
% 0.15/0.51
% 0.15/0.51 % Proof found!
% 0.15/0.51 % SZS status Unsatisfiable
% 0.15/0.51 % SZS output start CNFRefutation
% See solution above
% 0.15/0.51 % Parsed axioms : 32
% 0.15/0.51 % Removed by relevancy pruning/SinE : 0
% 0.15/0.51 % Initial clauses : 32
% 0.15/0.51 % Removed in clause preprocessing : 0
% 0.15/0.51 % Initial clauses in saturation : 32
% 0.15/0.51 % Processed clauses : 319
% 0.15/0.51 % ...of these trivial : 6
% 0.15/0.51 % ...subsumed : 37
% 0.15/0.51 % ...remaining for further processing : 276
% 0.15/0.51 % Other redundant clauses eliminated : 0
% 0.15/0.51 % Clauses deleted for lack of memory : 0
% 0.15/0.51 % Backward-subsumed : 0
% 0.15/0.51 % Backward-rewritten : 18
% 0.15/0.51 % Generated clauses : 1157
% 0.15/0.51 % ...of the previous two non-redundant : 962
% 0.15/0.51 % ...aggressively subsumed : 0
% 0.15/0.51 % Contextual simplify-reflections : 0
% 0.15/0.51 % Paramodulations : 1155
% 0.15/0.51 % Factorizations : 2
% 0.15/0.51 % NegExts : 0
% 0.15/0.51 % Equation resolutions : 0
% 0.15/0.51 % Disequality decompositions : 0
% 0.15/0.51 % Total rewrite steps : 634
% 0.15/0.51 % ...of those cached : 568
% 0.15/0.51 % Propositional unsat checks : 0
% 0.15/0.51 % Propositional check models : 0
% 0.15/0.51 % Propositional check unsatisfiable : 0
% 0.15/0.51 % Propositional clauses : 0
% 0.15/0.51 % Propositional clauses after purity: 0
% 0.15/0.51 % Propositional unsat core size : 0
% 0.15/0.51 % Propositional preprocessing time : 0.000
% 0.15/0.51 % Propositional encoding time : 0.000
% 0.15/0.51 % Propositional solver time : 0.000
% 0.15/0.51 % Success case prop preproc time : 0.000
% 0.15/0.51 % Success case prop encoding time : 0.000
% 0.15/0.51 % Success case prop solver time : 0.000
% 0.15/0.51 % Current number of processed clauses : 226
% 0.15/0.51 % Positive orientable unit clauses : 86
% 0.15/0.51 % Positive unorientable unit clauses: 0
% 0.15/0.51 % Negative unit clauses : 2
% 0.15/0.51 % Non-unit-clauses : 138
% 0.15/0.51 % Current number of unprocessed clauses: 705
% 0.15/0.51 % ...number of literals in the above : 2090
% 0.15/0.51 % Current number of archived formulas : 0
% 0.15/0.51 % Current number of archived clauses : 50
% 0.15/0.51 % Clause-clause subsumption calls (NU) : 858
% 0.15/0.51 % Rec. Clause-clause subsumption calls : 625
% 0.15/0.51 % Non-unit clause-clause subsumptions : 37
% 0.15/0.51 % Unit Clause-clause subsumption calls : 30
% 0.15/0.51 % Rewrite failures with RHS unbound : 0
% 0.15/0.51 % BW rewrite match attempts : 39
% 0.15/0.51 % BW rewrite match successes : 17
% 0.15/0.51 % Condensation attempts : 0
% 0.15/0.51 % Condensation successes : 0
% 0.15/0.51 % Termbank termtop insertions : 16301
% 0.15/0.51 % Search garbage collected termcells : 116
% 0.15/0.51
% 0.15/0.51 % -------------------------------------------------
% 0.15/0.51 % User time : 0.027 s
% 0.15/0.51 % System time : 0.006 s
% 0.15/0.51 % Total time : 0.033 s
% 0.15/0.51 % Maximum resident set size: 3660 pages
% 0.15/0.51
% 0.15/0.51 % -------------------------------------------------
% 0.15/0.51 % User time : 0.105 s
% 0.15/0.51 % System time : 0.027 s
% 0.15/0.51 % Total time : 0.132 s
% 0.15/0.51 % Maximum resident set size: 4864 pages
% 0.15/0.51 % E exiting
%------------------------------------------------------------------------------