%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD016-5 : 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 : 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 12:22:41 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.60s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of clauses : 57 ( 26 unt; 3 nHn; 57 RR)
% Number of literals : 115 ( 0 equ; 58 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 : 79 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
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(sum_8,negated_conjecture,
sum(additive_identity,q,r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_8) ).
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(sum_6,negated_conjecture,
sum(a,u,q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
cnf(totality_of_order_relation,axiom,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
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(sum_7,negated_conjecture,
sum(a,v,r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_7) ).
cnf(v_is_defined,hypothesis,
defined(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_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(r_is_defined,hypothesis,
defined(r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r_is_defined) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(not_sum_9,negated_conjecture,
~ sum(additive_identity,u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_9) ).
cnf(c_0_15,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_16,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_17,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_15 ).
cnf(c_0_18,negated_conjecture,
sum(additive_identity,q,r),
sum_8 ).
cnf(c_0_19,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_20,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_16 ).
cnf(c_0_21,negated_conjecture,
sum(q,additive_identity,r),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_19 ).
cnf(c_0_23,negated_conjecture,
( ~ sum(X1,X3,q)
| ~ sum(X3,additive_identity,X2)
| sum(X1,X2,r) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( ~ defined(X1)
| sum(X1,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( ~ sum(X1,X2,q)
| ~ defined(X2)
| sum(X1,X2,r) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
sum(a,u,q),
sum_6 ).
cnf(c_0_27,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_28,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[totality_of_order_relation]) ).
cnf(c_0_29,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| ~ defined(X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_30,negated_conjecture,
sum(a,u,r),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_31,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_32,negated_conjecture,
sum(a,v,r),
sum_7 ).
cnf(c_0_33,hypothesis,
defined(v),
v_is_defined ).
cnf(c_0_34,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_35,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_28 ).
cnf(c_0_36,negated_conjecture,
( ~ sum(X1,a,additive_identity)
| sum(X1,r,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27])]) ).
cnf(c_0_37,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_31 ).
cnf(c_0_38,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_39,negated_conjecture,
( ~ sum(X1,a,additive_identity)
| sum(X1,r,v) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_33])]) ).
cnf(c_0_40,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
c_0_34 ).
cnf(c_0_41,plain,
( ~ defined(X1)
| less_or_equal(X1,X1) ),
inference(ef,[status(thm)],[c_0_35]) ).
cnf(c_0_42,negated_conjecture,
sum(additive_inverse(a),r,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_43,negated_conjecture,
sum(additive_inverse(a),r,v),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_37]),c_0_38])]) ).
cnf(c_0_44,plain,
( ~ sum(X3,X4,X1)
| ~ sum(X3,X4,X2)
| ~ defined(X3)
| less_or_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
sum(r,additive_inverse(a),u),
inference(spm,[status(thm)],[c_0_17,c_0_42]) ).
cnf(c_0_46,hypothesis,
defined(r),
r_is_defined ).
cnf(c_0_47,negated_conjecture,
sum(r,additive_inverse(a),v),
inference(spm,[status(thm)],[c_0_17,c_0_43]) ).
cnf(c_0_48,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
inference(fof_simplification,[status(thm)],[antisymmetry_of_order_relation]) ).
cnf(c_0_49,negated_conjecture,
( ~ sum(r,additive_inverse(a),X1)
| less_or_equal(X1,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_50,negated_conjecture,
( ~ sum(r,additive_inverse(a),X1)
| less_or_equal(X1,v) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_47]),c_0_46])]) ).
cnf(c_0_51,negated_conjecture,
~ sum(additive_identity,u,v),
inference(fof_simplification,[status(thm)],[not_sum_9]) ).
cnf(c_0_52,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
c_0_48 ).
cnf(c_0_53,negated_conjecture,
less_or_equal(v,u),
inference(spm,[status(thm)],[c_0_49,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
less_or_equal(u,v),
inference(spm,[status(thm)],[c_0_50,c_0_45]) ).
cnf(c_0_55,negated_conjecture,
~ sum(additive_identity,u,v),
c_0_51 ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD016-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n002.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 15:39:47 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.52 Running first-order theorem proving
% 0.27/0.52 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
% 0.27/0.60 % Version: 3.5.1
% 0.27/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.60 % Starting sh5l with 300s (1) cores
% 0.27/0.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3626261 completed with status 0
% 0.27/0.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.27/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.60 % No SInE strategy applied
% 0.27/0.60 % Search class: FGUNF-FFMM21-SFFFFFNN
% 0.27/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.27/0.60 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 0.27/0.60 % Starting new_bool_3 with 269s (1) cores
% 0.27/0.60 % Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 136s (1) cores
% 0.27/0.60 % new_bool_3 with pid 3626270 completed with status 0
% 0.27/0.60 % Result found by new_bool_3
% 0.27/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.60 % No SInE strategy applied
% 0.27/0.60 % Search class: FGUNF-FFMM21-SFFFFFNN
% 0.27/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.27/0.60 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 0.27/0.60 % Starting new_bool_3 with 269s (1) cores
% 0.27/0.60 % Preprocessing time : 0.002 s
% 0.27/0.60 % Presaturation interreduction done
% 0.27/0.60
% 0.27/0.60 % Proof found!
% 0.27/0.60 % SZS status Unsatisfiable
% 0.27/0.60 % SZS output start CNFRefutation
% See solution above
% 0.27/0.60 % Parsed axioms : 35
% 0.27/0.60 % Removed by relevancy pruning/SinE : 0
% 0.27/0.60 % Initial clauses : 35
% 0.27/0.60 % Removed in clause preprocessing : 0
% 0.27/0.60 % Initial clauses in saturation : 35
% 0.27/0.60 % Processed clauses : 320
% 0.27/0.60 % ...of these trivial : 22
% 0.27/0.60 % ...subsumed : 14
% 0.27/0.60 % ...remaining for further processing : 284
% 0.27/0.60 % Other redundant clauses eliminated : 0
% 0.27/0.60 % Clauses deleted for lack of memory : 0
% 0.27/0.60 % Backward-subsumed : 0
% 0.27/0.60 % Backward-rewritten : 5
% 0.27/0.60 % Generated clauses : 1225
% 0.27/0.60 % ...of the previous two non-redundant : 981
% 0.27/0.60 % ...aggressively subsumed : 0
% 0.27/0.60 % Contextual simplify-reflections : 0
% 0.27/0.60 % Paramodulations : 1223
% 0.27/0.60 % Factorizations : 2
% 0.27/0.60 % NegExts : 0
% 0.27/0.60 % Equation resolutions : 0
% 0.27/0.60 % Disequality decompositions : 0
% 0.27/0.60 % Total rewrite steps : 847
% 0.27/0.60 % ...of those cached : 775
% 0.27/0.60 % Propositional unsat checks : 0
% 0.27/0.60 % Propositional check models : 0
% 0.27/0.60 % Propositional check unsatisfiable : 0
% 0.27/0.60 % Propositional clauses : 0
% 0.27/0.60 % Propositional clauses after purity: 0
% 0.27/0.60 % Propositional unsat core size : 0
% 0.27/0.60 % Propositional preprocessing time : 0.000
% 0.27/0.60 % Propositional encoding time : 0.000
% 0.27/0.60 % Propositional solver time : 0.000
% 0.27/0.60 % Success case prop preproc time : 0.000
% 0.27/0.60 % Success case prop encoding time : 0.000
% 0.27/0.60 % Success case prop solver time : 0.000
% 0.27/0.60 % Current number of processed clauses : 244
% 0.27/0.60 % Positive orientable unit clauses : 92
% 0.27/0.60 % Positive unorientable unit clauses: 0
% 0.27/0.60 % Negative unit clauses : 2
% 0.27/0.60 % Non-unit-clauses : 150
% 0.27/0.60 % Current number of unprocessed clauses: 731
% 0.27/0.60 % ...number of literals in the above : 2156
% 0.27/0.60 % Current number of archived formulas : 0
% 0.27/0.60 % Current number of archived clauses : 40
% 0.27/0.60 % Clause-clause subsumption calls (NU) : 1059
% 0.27/0.60 % Rec. Clause-clause subsumption calls : 826
% 0.27/0.60 % Non-unit clause-clause subsumptions : 14
% 0.27/0.60 % Unit Clause-clause subsumption calls : 516
% 0.27/0.60 % Rewrite failures with RHS unbound : 0
% 0.27/0.60 % BW rewrite match attempts : 23
% 0.27/0.60 % BW rewrite match successes : 4
% 0.27/0.60 % Condensation attempts : 0
% 0.27/0.60 % Condensation successes : 0
% 0.27/0.60 % Termbank termtop insertions : 16710
% 0.27/0.60 % Search garbage collected termcells : 116
% 0.27/0.60
% 0.27/0.60 % -------------------------------------------------
% 0.27/0.60 % User time : 0.047 s
% 0.27/0.60 % System time : 0.005 s
% 0.27/0.60 % Total time : 0.051 s
% 0.27/0.60 % Maximum resident set size: 3660 pages
% 0.27/0.60
% 0.27/0.60 % -------------------------------------------------
% 0.27/0.60 % User time : 0.220 s
% 0.27/0.60 % System time : 0.021 s
% 0.27/0.60 % Total time : 0.241 s
% 0.27/0.60 % Maximum resident set size: 4864 pages
% 0.27/0.60 % E exiting
%------------------------------------------------------------------------------