%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP748+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 : n003.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 12:45:03 PM UTC 2026
% Result : Theorem 0.59s 0.50s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 33 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 8 ~; 11 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
( ! [X13,X14,X15] : mult(mult(X15,X13),mult(X14,X15)) = mult(X15,mult(mult(X13,X14),X15))
| ! [X10,X11,X12] : mult(mult(X12,X10),mult(X11,X12)) = mult(mult(X12,mult(X10,X11)),X12)
| ! [X7,X8,X9] : mult(X7,mult(X9,mult(X8,X9))) = mult(mult(mult(X7,X9),X8),X9)
| ! [X4,X5,X6] : mult(X6,mult(X4,mult(X6,X5))) = mult(mult(mult(X6,X4),X6),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f07,axiom,
! [X3,X1,X2] : mult(mult(mult(X2,X1),X3),X1) = mult(X2,mult(mult(X1,X3),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f10,axiom,
! [X2] : mult(i(X2),X2) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
fof(f06,axiom,
! [X2] : mult(unit,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f08,axiom,
! [X1,X2] : mult(mult(X2,X1),i(X1)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(f09,axiom,
! [X2] : mult(X2,i(X2)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
fof(f11,axiom,
! [X1,X2] :
( mult(i(X2),mult(X2,X1)) = X1
| mult(X2,X1) = mult(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
fof(f05,axiom,
! [X2] : mult(X2,unit) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(c_0_9,negated_conjecture,
~ ( ! [X13,X14,X15] : mult(mult(X15,X13),mult(X14,X15)) = mult(X15,mult(mult(X13,X14),X15))
| ! [X10,X11,X12] : mult(mult(X12,X10),mult(X11,X12)) = mult(mult(X12,mult(X10,X11)),X12)
| ! [X7,X8,X9] : mult(X7,mult(X9,mult(X8,X9))) = mult(mult(mult(X7,X9),X8),X9)
| ! [X4,X5,X6] : mult(X6,mult(X4,mult(X6,X5))) = mult(mult(mult(X6,X4),X6),X5) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_10,plain,
! [X26,X27,X28] : mult(mult(mult(X28,X27),X26),X27) = mult(X28,mult(mult(X27,X26),X27)),
inference(variable_rename,[status(thm)],[f07]) ).
fof(c_0_11,plain,
! [X32] : mult(i(X32),X32) = unit,
inference(variable_rename,[status(thm)],[f10]) ).
fof(c_0_12,plain,
! [X25] : mult(unit,X25) = X25,
inference(variable_rename,[status(thm)],[f06]) ).
fof(c_0_13,plain,
! [X29,X30] : mult(mult(X30,X29),i(X29)) = X30,
inference(variable_rename,[status(thm)],[f08]) ).
fof(c_0_14,plain,
! [X31] : mult(X31,i(X31)) = unit,
inference(variable_rename,[status(thm)],[f09]) ).
fof(c_0_15,negated_conjecture,
( mult(mult(esk12_0,esk10_0),mult(esk11_0,esk12_0)) != mult(esk12_0,mult(mult(esk10_0,esk11_0),esk12_0))
& mult(mult(esk9_0,esk7_0),mult(esk8_0,esk9_0)) != mult(mult(esk9_0,mult(esk7_0,esk8_0)),esk9_0)
& mult(esk4_0,mult(esk6_0,mult(esk5_0,esk6_0))) != mult(mult(mult(esk4_0,esk6_0),esk5_0),esk6_0)
& mult(esk3_0,mult(esk1_0,mult(esk3_0,esk2_0))) != mult(mult(mult(esk3_0,esk1_0),esk3_0),esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_16,plain,
! [X33,X34] :
( mult(i(X34),mult(X34,X33)) = X33
| mult(X34,X33) = mult(X33,X34) ),
inference(variable_rename,[status(thm)],[f11]) ).
cnf(c_0_17,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
mult(i(X1),X1) = unit,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
mult(mult(X1,X2),i(X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
mult(X1,i(X1)) = unit,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_22,plain,
! [X24] : mult(X24,unit) = X24,
inference(variable_rename,[status(thm)],[f05]) ).
cnf(c_0_23,negated_conjecture,
mult(esk4_0,mult(esk6_0,mult(esk5_0,esk6_0))) != mult(mult(mult(esk4_0,esk6_0),esk5_0),esk6_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( mult(i(X1),mult(X1,X2)) = X2
| mult(X1,X2) = mult(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
mult(i(X1),mult(mult(X1,X2),X1)) = mult(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_26,plain,
i(i(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).
fof(c_0_27,plain,
! [X18,X19] : ld(X19,mult(X19,X18)) = X18,
inference(variable_rename,[status(thm)],[f02]) ).
cnf(c_0_28,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
mult(esk4_0,mult(mult(esk6_0,esk5_0),esk6_0)) != mult(esk4_0,mult(esk6_0,mult(esk5_0,esk6_0))),
inference(rw,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_30,plain,
( mult(X2,X1) = mult(X1,X2)
| mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_20]) ).
cnf(c_0_31,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_28]),c_0_28]) ).
cnf(c_0_33,negated_conjecture,
mult(esk5_0,esk6_0) = mult(esk6_0,esk5_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
ld(i(X1),mult(X2,X1)) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_35,negated_conjecture,
mult(mult(esk6_0,esk5_0),esk6_0) = mult(esk5_0,mult(esk6_0,esk6_0)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
( mult(X1,X2) = mult(X2,X1)
| ld(i(X1),X2) = mult(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_37,negated_conjecture,
ld(i(esk6_0),mult(esk6_0,esk5_0)) = mult(esk5_0,mult(esk6_0,esk6_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_33]),c_0_35]) ).
cnf(c_0_38,negated_conjecture,
mult(esk4_0,mult(esk5_0,mult(esk6_0,esk6_0))) != mult(esk4_0,mult(esk6_0,mult(esk6_0,esk5_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_35]),c_0_33]) ).
cnf(c_0_39,negated_conjecture,
mult(esk5_0,mult(esk6_0,esk6_0)) = mult(esk6_0,mult(esk6_0,esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_35])]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP748+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:39:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.59/0.50 % Version: 3.5.1
% 0.59/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.59/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.59/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.59/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.59/0.50 % Starting sh5l with 300s (1) cores
% 0.59/0.50 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2565622 completed with status 0
% 0.59/0.50 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.59/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.59/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.59/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.59/0.50 % No SInE strategy applied
% 0.59/0.50 % Search class: FGUPM-FFSF21-MFFFFFNN
% 0.59/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.59/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.59/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.59/0.50 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 136s (1) cores
% 0.59/0.50 % Starting new_bool_3 with 136s (1) cores
% 0.59/0.50 % Starting new_bool_1 with 136s (1) cores
% 0.59/0.50 % C12_02_nc_SAT001_MinMin_p005000_rr with pid 2565628 completed with status 0
% 0.59/0.50 % Result found by C12_02_nc_SAT001_MinMin_p005000_rr
% 0.59/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.59/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.59/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.59/0.50 % No SInE strategy applied
% 0.59/0.50 % Search class: FGUPM-FFSF21-MFFFFFNN
% 0.59/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.59/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.59/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.59/0.50 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 136s (1) cores
% 0.59/0.50 % Preprocessing time : 0.001 s
% 0.59/0.50 % Presaturation interreduction done
% 0.59/0.50
% 0.59/0.50 % Proof found!
% 0.59/0.50 % SZS status Theorem
% 0.59/0.50 % SZS output start CNFRefutation
% See solution above
% 0.59/0.50 % Parsed axioms : 12
% 0.59/0.50 % Removed by relevancy pruning/SinE : 0
% 0.59/0.50 % Initial clauses : 15
% 0.59/0.50 % Removed in clause preprocessing : 0
% 0.59/0.50 % Initial clauses in saturation : 15
% 0.59/0.50 % Processed clauses : 230
% 0.59/0.50 % ...of these trivial : 64
% 0.59/0.50 % ...subsumed : 39
% 0.59/0.50 % ...remaining for further processing : 127
% 0.59/0.50 % Other redundant clauses eliminated : 0
% 0.59/0.50 % Clauses deleted for lack of memory : 0
% 0.59/0.50 % Backward-subsumed : 0
% 0.59/0.50 % Backward-rewritten : 18
% 0.59/0.50 % Generated clauses : 4835
% 0.59/0.50 % ...of the previous two non-redundant : 3624
% 0.59/0.50 % ...aggressively subsumed : 0
% 0.59/0.50 % Contextual simplify-reflections : 0
% 0.59/0.50 % Paramodulations : 4835
% 0.59/0.50 % Factorizations : 0
% 0.59/0.50 % NegExts : 0
% 0.59/0.50 % Equation resolutions : 0
% 0.59/0.50 % Disequality decompositions : 0
% 0.59/0.50 % Total rewrite steps : 7034
% 0.59/0.50 % ...of those cached : 6513
% 0.59/0.50 % Propositional unsat checks : 0
% 0.59/0.50 % Propositional check models : 0
% 0.59/0.50 % Propositional check unsatisfiable : 0
% 0.59/0.50 % Propositional clauses : 0
% 0.59/0.50 % Propositional clauses after purity: 0
% 0.59/0.50 % Propositional unsat core size : 0
% 0.59/0.50 % Propositional preprocessing time : 0.000
% 0.59/0.50 % Propositional encoding time : 0.000
% 0.59/0.50 % Propositional solver time : 0.000
% 0.59/0.50 % Success case prop preproc time : 0.000
% 0.59/0.50 % Success case prop encoding time : 0.000
% 0.59/0.50 % Success case prop solver time : 0.000
% 0.59/0.50 % Current number of processed clauses : 94
% 0.59/0.50 % Positive orientable unit clauses : 68
% 0.59/0.50 % Positive unorientable unit clauses: 0
% 0.59/0.50 % Negative unit clauses : 3
% 0.59/0.50 % Non-unit-clauses : 23
% 0.59/0.50 % Current number of unprocessed clauses: 3411
% 0.59/0.50 % ...number of literals in the above : 5414
% 0.59/0.50 % Current number of archived formulas : 0
% 0.59/0.50 % Current number of archived clauses : 33
% 0.59/0.50 % Clause-clause subsumption calls (NU) : 614
% 0.59/0.50 % Rec. Clause-clause subsumption calls : 332
% 0.59/0.50 % Non-unit clause-clause subsumptions : 39
% 0.59/0.50 % Unit Clause-clause subsumption calls : 247
% 0.59/0.50 % Rewrite failures with RHS unbound : 0
% 0.59/0.50 % BW rewrite match attempts : 87
% 0.59/0.50 % BW rewrite match successes : 16
% 0.59/0.50 % Condensation attempts : 0
% 0.59/0.50 % Condensation successes : 0
% 0.59/0.50 % Termbank termtop insertions : 67524
% 0.59/0.50 % Search garbage collected termcells : 106
% 0.59/0.50
% 0.59/0.50 % -------------------------------------------------
% 0.59/0.50 % User time : 0.064 s
% 0.59/0.50 % System time : 0.008 s
% 0.59/0.50 % Total time : 0.073 s
% 0.59/0.50 % Maximum resident set size: 3388 pages
% 0.59/0.50
% 0.59/0.50 % -------------------------------------------------
% 0.59/0.50 % User time : 0.295 s
% 0.59/0.50 % System time : 0.032 s
% 0.59/0.50 % Total time : 0.328 s
% 0.59/0.50 % Maximum resident set size: 4608 pages
% 0.59/0.50 % E exiting
%------------------------------------------------------------------------------