%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE055+1 : 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 : n009.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 12:58:44 PM UTC 2026
% Result : Theorem 0.28s 0.81s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 30 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4] :
( addition(X4,one) = one
=> addition(X4,domain(X4)) = domain(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(domain3,axiom,
! [X4] : addition(domain(X4),one) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(domain1,axiom,
! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(c_0_8,negated_conjecture,
~ ! [X4] :
( addition(X4,one) = one
=> addition(X4,domain(X4)) = domain(X4) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_9,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_10,plain,
! [X25] : multiplication(X25,one) = X25,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_11,negated_conjecture,
( addition(esk1_0,domain(esk1_0)) != domain(esk1_0)
& addition(esk1_0,one) = one ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_12,plain,
! [X13,X14] : addition(X13,X14) = addition(X14,X13),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_13,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_14,plain,
! [X26] : multiplication(one,X26) = X26,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_15,plain,
! [X10] : addition(domain(X10),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
cnf(c_0_16,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
addition(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X7] : addition(X7,multiplication(domain(X7),X7)) = multiplication(domain(X7),X7),
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_21,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
addition(one,esk1_0) = one,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_19]) ).
cnf(c_0_28,plain,
addition(one,domain(X1)) = one,
inference(rw,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_29,negated_conjecture,
addition(X1,multiplication(X1,esk1_0)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_17]) ).
cnf(c_0_30,plain,
multiplication(domain(X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]),c_0_28]),c_0_22]) ).
cnf(c_0_31,negated_conjecture,
addition(esk1_0,domain(esk1_0)) != domain(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_19]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE055+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.64 % Computer : n009.cluster.edu
% 0.17/0.64 % Model : x86_64 x86_64
% 0.17/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.64 % Memory : 8046.5625MB
% 0.17/0.64 % OS : Linux 6.8.0-71-generic
% 0.17/0.64 % CPULimit : 300
% 0.17/0.64 % WCLimit : 300
% 0.17/0.64 % DateTime : Sun Sep 20 22:41:43 UTC 2026
% 0.17/0.65 % CPUTime :
% 0.17/0.65 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.72 Running first-order theorem proving
% 0.26/0.72 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
% 0.28/0.81 % Version: 3.5.1
% 0.28/0.81 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.81 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.81 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.81 % Starting sh5l with 300s (1) cores
% 0.28/0.81 % new_bool_3 with pid 208146 completed with status 0
% 0.28/0.81 % Result found by new_bool_3
% 0.28/0.81 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.81 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.81 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.81 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.81 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.28/0.81 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.81 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.81 % SubtermCWHack with pid 208152 completed with status 0
% 0.28/0.81 % Result found by SubtermCWHack
% 0.28/0.81 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.81 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.81 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.81 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.81 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.28/0.81 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.81 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.81 % Preprocessing time : 0.002 s
% 0.28/0.81
% 0.28/0.81 % Proof found!
% 0.28/0.81 % SZS status Theorem
% 0.28/0.81 % SZS output start CNFRefutation
% See solution above
% 0.28/0.81 % Parsed axioms : 18
% 0.28/0.81 % Removed by relevancy pruning/SinE : 1
% 0.28/0.81 % Initial clauses : 18
% 0.28/0.81 % Removed in clause preprocessing : 0
% 0.28/0.81 % Initial clauses in saturation : 18
% 0.28/0.81 % Processed clauses : 197
% 0.28/0.81 % ...of these trivial : 59
% 0.28/0.81 % ...subsumed : 52
% 0.28/0.81 % ...remaining for further processing : 85
% 0.28/0.81 % Other redundant clauses eliminated : 0
% 0.28/0.81 % Clauses deleted for lack of memory : 0
% 0.28/0.81 % Backward-subsumed : 0
% 0.28/0.81 % Backward-rewritten : 17
% 0.28/0.81 % Generated clauses : 2690
% 0.28/0.81 % ...of the previous two non-redundant : 1143
% 0.28/0.81 % ...aggressively subsumed : 0
% 0.28/0.81 % Contextual simplify-reflections : 0
% 0.28/0.81 % Paramodulations : 2690
% 0.28/0.81 % Factorizations : 0
% 0.28/0.81 % NegExts : 0
% 0.28/0.81 % Equation resolutions : 0
% 0.28/0.81 % Disequality decompositions : 0
% 0.28/0.81 % Total rewrite steps : 3996
% 0.28/0.81 % ...of those cached : 3140
% 0.28/0.81 % Propositional unsat checks : 0
% 0.28/0.81 % Propositional check models : 0
% 0.28/0.81 % Propositional check unsatisfiable : 0
% 0.28/0.81 % Propositional clauses : 0
% 0.28/0.81 % Propositional clauses after purity: 0
% 0.28/0.81 % Propositional unsat core size : 0
% 0.28/0.81 % Propositional preprocessing time : 0.000
% 0.28/0.81 % Propositional encoding time : 0.000
% 0.28/0.81 % Propositional solver time : 0.000
% 0.28/0.81 % Success case prop preproc time : 0.000
% 0.28/0.81 % Success case prop encoding time : 0.000
% 0.28/0.81 % Success case prop solver time : 0.000
% 0.28/0.81 % Current number of processed clauses : 68
% 0.28/0.81 % Positive orientable unit clauses : 61
% 0.28/0.81 % Positive unorientable unit clauses: 6
% 0.28/0.81 % Negative unit clauses : 1
% 0.28/0.81 % Non-unit-clauses : 0
% 0.28/0.81 % Current number of unprocessed clauses: 953
% 0.28/0.81 % ...number of literals in the above : 953
% 0.28/0.81 % Current number of archived formulas : 0
% 0.28/0.81 % Current number of archived clauses : 17
% 0.28/0.81 % Clause-clause subsumption calls (NU) : 0
% 0.28/0.81 % Rec. Clause-clause subsumption calls : 0
% 0.28/0.81 % Non-unit clause-clause subsumptions : 0
% 0.28/0.81 % Unit Clause-clause subsumption calls : 6
% 0.28/0.81 % Rewrite failures with RHS unbound : 0
% 0.28/0.81 % BW rewrite match attempts : 169
% 0.28/0.81 % BW rewrite match successes : 77
% 0.28/0.81 % Condensation attempts : 0
% 0.28/0.81 % Condensation successes : 0
% 0.28/0.81 % Termbank termtop insertions : 24880
% 0.28/0.81 % Search garbage collected termcells : 29
% 0.28/0.81
% 0.28/0.81 % -------------------------------------------------
% 0.28/0.81 % User time : 0.039 s
% 0.28/0.81 % System time : 0.004 s
% 0.28/0.81 % Total time : 0.043 s
% 0.28/0.81 % Maximum resident set size: 3648 pages
% 0.28/0.81
% 0.28/0.81 % -------------------------------------------------
% 0.28/0.81 % User time : 0.042 s
% 0.28/0.81 % System time : 0.010 s
% 0.28/0.81 % Total time : 0.052 s
% 0.28/0.81 % Maximum resident set size: 4864 pages
% 0.28/0.81 % E exiting
%------------------------------------------------------------------------------