%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP704+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 : n015.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 12:41:00 PM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 21 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 4 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [X1,X2] : mult(X2,ld(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f10,axiom,
! [X1,X2] : mult(X2,mult(op_c,X1)) = mult(mult(X2,op_c),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
fof(f13,axiom,
! [X1,X2] : op_f = mult(X2,mult(X1,ld(mult(X2,X1),op_c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f13) ).
fof(goals,conjecture,
! [X4,X5] :
( mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5)
& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)
& mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f08,axiom,
! [X1,X2] : mult(op_c,mult(X2,X1)) = mult(mult(op_c,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(f09,axiom,
! [X1,X2] : mult(X2,mult(X1,op_c)) = mult(mult(X2,X1),op_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
fof(c_0_6,plain,
! [X13,X14] : mult(X14,ld(X14,X13)) = X13,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_7,plain,
! [X21,X22] : mult(X22,mult(op_c,X21)) = mult(mult(X22,op_c),X21),
inference(variable_rename,[status(thm)],[f10]) ).
fof(c_0_8,plain,
! [X11,X12] : op_f = mult(X12,mult(X11,ld(mult(X12,X11),op_c))),
inference(variable_rename,[status(thm)],[f13]) ).
cnf(c_0_9,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
mult(X1,mult(op_c,X2)) = mult(mult(X1,op_c),X2),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
~ ! [X4,X5] :
( mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5)
& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)
& mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_12,plain,
! [X17,X18] : mult(op_c,mult(X18,X17)) = mult(mult(op_c,X18),X17),
inference(variable_rename,[status(thm)],[f08]) ).
cnf(c_0_13,plain,
op_f = mult(X1,mult(X2,ld(mult(X1,X2),op_c))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
mult(X1,mult(op_c,ld(mult(X1,op_c),X2))) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_15,plain,
! [X19,X20] : mult(X20,mult(X19,op_c)) = mult(mult(X20,X19),op_c),
inference(variable_rename,[status(thm)],[f09]) ).
fof(c_0_16,negated_conjecture,
( mult(esk1_0,mult(op_f,esk2_0)) != mult(mult(esk1_0,op_f),esk2_0)
| mult(esk1_0,mult(esk2_0,op_f)) != mult(mult(esk1_0,esk2_0),op_f)
| mult(op_f,mult(esk1_0,esk2_0)) != mult(mult(op_f,esk1_0),esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_17,plain,
mult(op_c,mult(X1,X2)) = mult(mult(op_c,X1),X2),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
op_c = op_f,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
mult(X1,mult(X2,op_c)) = mult(mult(X1,X2),op_c),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( mult(esk1_0,mult(op_f,esk2_0)) != mult(mult(esk1_0,op_f),esk2_0)
| mult(esk1_0,mult(esk2_0,op_f)) != mult(mult(esk1_0,esk2_0),op_f)
| mult(op_f,mult(esk1_0,esk2_0)) != mult(mult(op_f,esk1_0),esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
mult(mult(op_f,X1),X2) = mult(op_f,mult(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
cnf(c_0_22,plain,
mult(mult(X1,op_f),X2) = mult(X1,mult(op_f,X2)),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_23,plain,
mult(mult(X1,X2),op_f) = mult(X1,mult(X2,op_f)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_18]),c_0_18]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP704+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 20:37:36 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.44 % Version: 3.5.1
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % Starting sh5l with 300s (1) cores
% 0.12/0.44 % new_bool_3 with pid 3893578 completed with status 0
% 0.12/0.44 % Result found by new_bool_3
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.44 % Search class: FUHPM-FFSF22-MFFFFFNN
% 0.12/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.44 % SubtermCWHack with pid 3893585 completed with status 0
% 0.12/0.44 % Result found by SubtermCWHack
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.44 % Search class: FUHPM-FFSF22-MFFFFFNN
% 0.12/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.44 % Preprocessing time : 0.001 s
% 0.12/0.44
% 0.12/0.44 % Proof found!
% 0.12/0.44 % SZS status Theorem
% 0.12/0.44 % SZS output start CNFRefutation
% See solution above
% 0.12/0.44 % Parsed axioms : 14
% 0.12/0.44 % Removed by relevancy pruning/SinE : 6
% 0.12/0.44 % Initial clauses : 8
% 0.12/0.44 % Removed in clause preprocessing : 0
% 0.12/0.44 % Initial clauses in saturation : 8
% 0.12/0.44 % Processed clauses : 22
% 0.12/0.44 % ...of these trivial : 3
% 0.12/0.44 % ...subsumed : 0
% 0.12/0.44 % ...remaining for further processing : 18
% 0.12/0.44 % Other redundant clauses eliminated : 0
% 0.12/0.44 % Clauses deleted for lack of memory : 0
% 0.12/0.44 % Backward-subsumed : 0
% 0.12/0.44 % Backward-rewritten : 3
% 0.12/0.44 % Generated clauses : 182
% 0.12/0.44 % ...of the previous two non-redundant : 163
% 0.12/0.44 % ...aggressively subsumed : 0
% 0.12/0.44 % Contextual simplify-reflections : 0
% 0.12/0.44 % Paramodulations : 182
% 0.12/0.44 % Factorizations : 0
% 0.12/0.44 % NegExts : 0
% 0.12/0.44 % Equation resolutions : 0
% 0.12/0.44 % Disequality decompositions : 0
% 0.12/0.44 % Total rewrite steps : 222
% 0.12/0.44 % ...of those cached : 144
% 0.12/0.44 % Propositional unsat checks : 0
% 0.12/0.44 % Propositional check models : 0
% 0.12/0.44 % Propositional check unsatisfiable : 0
% 0.12/0.44 % Propositional clauses : 0
% 0.12/0.44 % Propositional clauses after purity: 0
% 0.12/0.44 % Propositional unsat core size : 0
% 0.12/0.44 % Propositional preprocessing time : 0.000
% 0.12/0.44 % Propositional encoding time : 0.000
% 0.12/0.44 % Propositional solver time : 0.000
% 0.12/0.44 % Success case prop preproc time : 0.000
% 0.12/0.44 % Success case prop encoding time : 0.000
% 0.12/0.44 % Success case prop solver time : 0.000
% 0.12/0.44 % Current number of processed clauses : 15
% 0.12/0.44 % Positive orientable unit clauses : 15
% 0.12/0.44 % Positive unorientable unit clauses: 0
% 0.12/0.44 % Negative unit clauses : 0
% 0.12/0.44 % Non-unit-clauses : 0
% 0.12/0.44 % Current number of unprocessed clauses: 144
% 0.12/0.44 % ...number of literals in the above : 144
% 0.12/0.44 % Current number of archived formulas : 0
% 0.12/0.44 % Current number of archived clauses : 3
% 0.12/0.44 % Clause-clause subsumption calls (NU) : 0
% 0.12/0.44 % Rec. Clause-clause subsumption calls : 0
% 0.12/0.44 % Non-unit clause-clause subsumptions : 0
% 0.12/0.44 % Unit Clause-clause subsumption calls : 0
% 0.12/0.44 % Rewrite failures with RHS unbound : 0
% 0.12/0.44 % BW rewrite match attempts : 2
% 0.12/0.44 % BW rewrite match successes : 2
% 0.12/0.44 % Condensation attempts : 0
% 0.12/0.44 % Condensation successes : 0
% 0.12/0.44 % Termbank termtop insertions : 2926
% 0.12/0.44 % Search garbage collected termcells : 70
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.005 s
% 0.12/0.44 % System time : 0.003 s
% 0.12/0.44 % Total time : 0.008 s
% 0.12/0.44 % Maximum resident set size: 3644 pages
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.006 s
% 0.12/0.44 % System time : 0.008 s
% 0.12/0.44 % Total time : 0.014 s
% 0.12/0.44 % Maximum resident set size: 4864 pages
% 0.12/0.44 % E exiting
%------------------------------------------------------------------------------