%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : KLE027+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:59:09 PM UTC 2026
% Result : Theorem 0.12s 0.51s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 30 unt; 0 def)
% Number of atoms : 95 ( 54 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 73 ( 30 ~; 26 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 95 ( 3 sgn 50 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( addition(X4,X5) = one
& multiplication(X5,X4) = zero
& multiplication(X4,X5) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(goals,conjecture,
! [X4,X5,X6,X7,X8] :
( ( test(X8)
& test(X7) )
=> addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6)) = addition(multiplication(X7,X4),multiplication(c(X7),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(c_0_11,plain,
! [X35,X36] :
( ( complement(X36,X35)
| addition(X35,X36) != one
| multiplication(X36,X35) != zero
| multiplication(X35,X36) != zero )
& ( ~ complement(X36,X35)
| addition(X35,X36) = one )
& ( ~ complement(X36,X35)
| multiplication(X36,X35) = zero )
& ( ~ complement(X36,X35)
| multiplication(X35,X36) = zero ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])])]) ).
fof(c_0_12,plain,
! [X31,X33,X34] :
( ( test(X33)
| ~ complement(X34,X33) )
& ( complement(esk1_1(X31),X31)
| ~ test(X31) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])])]) ).
fof(c_0_13,plain,
! [X37,X38] :
( ( ~ test(X37)
| c(X37) = X38
| ~ complement(X37,X38) )
& ( ~ test(X37)
| complement(X37,X38)
| c(X37) != X38 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
fof(c_0_14,plain,
! [X21,X22,X23] : multiplication(X21,addition(X22,X23)) = addition(multiplication(X21,X22),multiplication(X21,X23)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_15,plain,
( ~ complement(X2,X1)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ test(X1)
| complement(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X14] : addition(X14,zero) = X14,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_18,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ test(X1)
| multiplication(X1,esk1_1(X1)) = zero ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_23,plain,
! [X19] : multiplication(X19,one) = X19,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_24,negated_conjecture,
~ ! [X4,X5,X6,X7,X8] :
( ( test(X8)
& test(X7) )
=> addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6)) = addition(multiplication(X7,X4),multiplication(c(X7),X6)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_25,plain,
! [X16,X17,X18] : multiplication(X16,multiplication(X17,X18)) = multiplication(multiplication(X16,X17),X18),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_26,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_18]) ).
fof(c_0_28,plain,
! [X28] : multiplication(zero,X28) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_29,plain,
( ~ test(X1)
| multiplication(X1,addition(X2,esk1_1(X1))) = multiplication(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_30,plain,
( ~ test(X1)
| addition(X1,esk1_1(X1)) = one ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_31,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_32,negated_conjecture,
( addition(multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0))),multiplication(c(esk5_0),esk4_0)) != addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0))
& test(esk6_0)
& test(esk5_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_33,plain,
! [X9,X10] : addition(X9,X10) = addition(X10,X9),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_34,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( ~ test(X1)
| multiplication(X1,c(X1)) = zero ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_36,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
( ~ test(X1)
| multiplication(X1,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_38,negated_conjecture,
test(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_39,plain,
! [X11,X12,X13] : addition(X13,addition(X12,X11)) = addition(addition(X13,X12),X11),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_40,negated_conjecture,
addition(multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0))),multiplication(c(esk5_0),esk4_0)) != addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
( ~ test(X1)
| multiplication(X1,multiplication(c(X1),X2)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_43,negated_conjecture,
multiplication(esk5_0,esk5_0) = esk5_0,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,negated_conjecture,
addition(multiplication(c(esk5_0),esk4_0),multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0)))) != addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
( ~ test(X1)
| multiplication(X1,addition(X2,multiplication(c(X1),X3))) = multiplication(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_42]),c_0_21]) ).
cnf(c_0_47,negated_conjecture,
multiplication(esk5_0,multiplication(esk5_0,X1)) = multiplication(esk5_0,X1),
inference(spm,[status(thm)],[c_0_34,c_0_43]) ).
cnf(c_0_48,plain,
addition(X1,X2) = addition(X2,X1),
c_0_41 ).
cnf(c_0_49,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
c_0_44 ).
cnf(c_0_50,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
c_0_34 ).
cnf(c_0_51,negated_conjecture,
$false,
inference(ar,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_38])]),c_0_48,c_0_49,c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE027+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 22:39:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 0.12/0.51 % Version: 3.5.1
% 0.12/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.51 % Starting sh5l with 300s (1) cores
% 0.12/0.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1646193 completed with status 0
% 0.12/0.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.51 % No SInE strategy applied
% 0.12/0.51 % Search class: FGUSM-FFMF21-MFFFFFNN
% 0.12/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.51 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 0.12/0.51 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.51 % Starting new_bool_1 with 136s (1) cores
% 0.12/0.51 % SubtermCWHack with pid 1646198 completed with status 0
% 0.12/0.51 % Result found by SubtermCWHack
% 0.12/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.51 % No SInE strategy applied
% 0.12/0.51 % Search class: FGUSM-FFMF21-MFFFFFNN
% 0.12/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.51 % Preprocessing time : 0.001 s
% 0.12/0.51
% 0.12/0.51 % Proof found!
% 0.12/0.51 % SZS status Theorem
% 0.12/0.51 % SZS output start CNFRefutation
% See solution above
% 0.12/0.51 % Parsed axioms : 19
% 0.12/0.51 % Removed by relevancy pruning/SinE : 0
% 0.12/0.51 % Initial clauses : 27
% 0.12/0.51 % Removed in clause preprocessing : 0
% 0.12/0.51 % Initial clauses in saturation : 27
% 0.12/0.51 % Processed clauses : 1342
% 0.12/0.51 % ...of these trivial : 106
% 0.12/0.51 % ...subsumed : 867
% 0.12/0.51 % ...remaining for further processing : 369
% 0.12/0.51 % Other redundant clauses eliminated : 20
% 0.12/0.51 % Clauses deleted for lack of memory : 0
% 0.12/0.51 % Backward-subsumed : 17
% 0.12/0.51 % Backward-rewritten : 72
% 0.12/0.51 % Generated clauses : 15916
% 0.12/0.51 % ...of the previous two non-redundant : 10619
% 0.12/0.51 % ...aggressively subsumed : 0
% 0.12/0.51 % Contextual simplify-reflections : 12
% 0.12/0.51 % Paramodulations : 15893
% 0.12/0.51 % Factorizations : 3
% 0.12/0.51 % NegExts : 0
% 0.12/0.51 % Equation resolutions : 20
% 0.12/0.51 % Disequality decompositions : 0
% 0.12/0.51 % Total rewrite steps : 20104
% 0.12/0.51 % ...of those cached : 17458
% 0.12/0.51 % Propositional unsat checks : 0
% 0.12/0.51 % Propositional check models : 0
% 0.12/0.51 % Propositional check unsatisfiable : 0
% 0.12/0.51 % Propositional clauses : 0
% 0.12/0.51 % Propositional clauses after purity: 0
% 0.12/0.51 % Propositional unsat core size : 0
% 0.12/0.51 % Propositional preprocessing time : 0.000
% 0.12/0.51 % Propositional encoding time : 0.000
% 0.12/0.51 % Propositional solver time : 0.000
% 0.12/0.51 % Success case prop preproc time : 0.000
% 0.12/0.51 % Success case prop encoding time : 0.000
% 0.12/0.51 % Success case prop solver time : 0.000
% 0.12/0.51 % Current number of processed clauses : 279
% 0.12/0.51 % Positive orientable unit clauses : 102
% 0.12/0.51 % Positive unorientable unit clauses: 4
% 0.12/0.51 % Negative unit clauses : 1
% 0.12/0.51 % Non-unit-clauses : 172
% 0.12/0.51 % Current number of unprocessed clauses: 9235
% 0.12/0.51 % ...number of literals in the above : 25753
% 0.12/0.51 % Current number of archived formulas : 0
% 0.12/0.51 % Current number of archived clauses : 89
% 0.12/0.51 % Clause-clause subsumption calls (NU) : 10459
% 0.12/0.51 % Rec. Clause-clause subsumption calls : 8269
% 0.12/0.51 % Non-unit clause-clause subsumptions : 757
% 0.12/0.51 % Unit Clause-clause subsumption calls : 548
% 0.12/0.51 % Rewrite failures with RHS unbound : 0
% 0.12/0.51 % BW rewrite match attempts : 142
% 0.12/0.51 % BW rewrite match successes : 112
% 0.12/0.51 % Condensation attempts : 0
% 0.12/0.51 % Condensation successes : 0
% 0.12/0.51 % Termbank termtop insertions : 194976
% 0.12/0.51 % Search garbage collected termcells : 219
% 0.12/0.51
% 0.12/0.51 % -------------------------------------------------
% 0.12/0.51 % User time : 0.093 s
% 0.12/0.51 % System time : 0.009 s
% 0.12/0.51 % Total time : 0.101 s
% 0.12/0.51 % Maximum resident set size: 3652 pages
% 0.12/0.51
% 0.12/0.51 % -------------------------------------------------
% 0.12/0.51 % User time : 0.455 s
% 0.12/0.51 % System time : 0.050 s
% 0.12/0.51 % Total time : 0.505 s
% 0.12/0.51 % Maximum resident set size: 4864 pages
% 0.12/0.51 % E exiting
%------------------------------------------------------------------------------