%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP665+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 : n018.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 12:40:41 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 20 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 4 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( mult(mult(X4,X5),op_c) = mult(X4,mult(X5,op_c))
& mult(mult(X4,op_c),X5) = mult(X4,mult(op_c,X5))
& mult(op_c,mult(X4,X5)) = mult(mult(op_c,X4),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f07,axiom,
! [X3,X1,X2] : mult(X2,mult(X1,X3)) = mult(rd(mult(X2,X1),X2),mult(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f09,axiom,
! [X2] : mult(op_c,X2) = mult(X2,op_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f08,axiom,
! [X3,X1,X2] : mult(mult(X2,X1),X3) = mult(mult(X2,X3),ld(X3,mult(X1,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(c_0_6,negated_conjecture,
~ ! [X4,X5] :
( mult(mult(X4,X5),op_c) = mult(X4,mult(X5,op_c))
& mult(mult(X4,op_c),X5) = mult(X4,mult(op_c,X5))
& mult(op_c,mult(X4,X5)) = mult(mult(op_c,X4),X5) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_7,plain,
! [X16,X17,X18] : mult(X18,mult(X17,X16)) = mult(rd(mult(X18,X17),X18),mult(X18,X16)),
inference(variable_rename,[status(thm)],[f07]) ).
fof(c_0_8,plain,
! [X22] : mult(op_c,X22) = mult(X22,op_c),
inference(variable_rename,[status(thm)],[f09]) ).
fof(c_0_9,plain,
! [X12,X13] : rd(mult(X13,X12),X12) = X13,
inference(variable_rename,[status(thm)],[f04]) ).
fof(c_0_10,plain,
! [X8,X9] : ld(X9,mult(X9,X8)) = X8,
inference(variable_rename,[status(thm)],[f02]) ).
fof(c_0_11,negated_conjecture,
( mult(mult(esk1_0,esk2_0),op_c) != mult(esk1_0,mult(esk2_0,op_c))
| mult(mult(esk1_0,op_c),esk2_0) != mult(esk1_0,mult(op_c,esk2_0))
| mult(op_c,mult(esk1_0,esk2_0)) != mult(mult(op_c,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_6])])])]) ).
cnf(c_0_12,plain,
mult(X1,mult(X2,X3)) = mult(rd(mult(X1,X2),X1),mult(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
mult(op_c,X1) = mult(X1,op_c),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,plain,
! [X19,X20,X21] : mult(mult(X21,X20),X19) = mult(mult(X21,X19),ld(X19,mult(X20,X19))),
inference(variable_rename,[status(thm)],[f08]) ).
cnf(c_0_16,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( mult(mult(esk1_0,esk2_0),op_c) != mult(esk1_0,mult(esk2_0,op_c))
| mult(mult(esk1_0,op_c),esk2_0) != mult(esk1_0,mult(op_c,esk2_0))
| mult(op_c,mult(esk1_0,esk2_0)) != mult(mult(op_c,esk1_0),esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
mult(X1,mult(op_c,X2)) = mult(op_c,mult(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_19,plain,
mult(mult(X1,X2),X3) = mult(mult(X1,X3),ld(X3,mult(X2,X3))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
ld(op_c,mult(X1,op_c)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
mult(mult(op_c,esk1_0),esk2_0) != mult(op_c,mult(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_13]),c_0_18]),c_0_13]),c_0_13]),c_0_18])]) ).
cnf(c_0_22,plain,
mult(mult(op_c,X1),X2) = mult(op_c,mult(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_13]),c_0_20]),c_0_13]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP665+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:32:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43 % Version: 3.5.1
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.43 % Starting sh5l with 300s (1) cores
% 0.11/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 145348 completed with status 0
% 0.11/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.43 % No SInE strategy applied
% 0.11/0.43 % Search class: FUHPM-FFSF22-MFFFFFNN
% 0.11/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.43 % Starting H----_102_C18_F1_PI_AE_Q4_CS_SP_PS_S5PRR_S2S with 136s (1) cores
% 0.11/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.44 % SubtermCWHack with pid 145352 completed with status 0
% 0.11/0.44 % Result found by SubtermCWHack
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.44 % No SInE strategy applied
% 0.11/0.44 % Search class: FUHPM-FFSF22-MFFFFFNN
% 0.11/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.44 % Preprocessing time : 0.001 s
% 0.11/0.44
% 0.11/0.44 % Proof found!
% 0.11/0.44 % SZS status Theorem
% 0.11/0.44 % SZS output start CNFRefutation
% See solution above
% 0.11/0.44 % Parsed axioms : 10
% 0.11/0.44 % Removed by relevancy pruning/SinE : 0
% 0.11/0.44 % Initial clauses : 10
% 0.11/0.44 % Removed in clause preprocessing : 0
% 0.11/0.44 % Initial clauses in saturation : 10
% 0.11/0.44 % Processed clauses : 43
% 0.11/0.44 % ...of these trivial : 8
% 0.11/0.44 % ...subsumed : 9
% 0.11/0.44 % ...remaining for further processing : 26
% 0.11/0.44 % Other redundant clauses eliminated : 0
% 0.11/0.44 % Clauses deleted for lack of memory : 0
% 0.11/0.44 % Backward-subsumed : 0
% 0.11/0.44 % Backward-rewritten : 3
% 0.11/0.44 % Generated clauses : 181
% 0.11/0.44 % ...of the previous two non-redundant : 100
% 0.11/0.44 % ...aggressively subsumed : 0
% 0.11/0.44 % Contextual simplify-reflections : 0
% 0.11/0.44 % Paramodulations : 181
% 0.11/0.44 % Factorizations : 0
% 0.11/0.44 % NegExts : 0
% 0.11/0.44 % Equation resolutions : 0
% 0.11/0.44 % Disequality decompositions : 0
% 0.11/0.44 % Total rewrite steps : 127
% 0.11/0.44 % ...of those cached : 70
% 0.11/0.44 % Propositional unsat checks : 0
% 0.11/0.44 % Propositional check models : 0
% 0.11/0.44 % Propositional check unsatisfiable : 0
% 0.11/0.44 % Propositional clauses : 0
% 0.11/0.44 % Propositional clauses after purity: 0
% 0.11/0.44 % Propositional unsat core size : 0
% 0.11/0.44 % Propositional preprocessing time : 0.000
% 0.11/0.44 % Propositional encoding time : 0.000
% 0.11/0.44 % Propositional solver time : 0.000
% 0.11/0.44 % Success case prop preproc time : 0.000
% 0.11/0.44 % Success case prop encoding time : 0.000
% 0.11/0.44 % Success case prop solver time : 0.000
% 0.11/0.44 % Current number of processed clauses : 23
% 0.11/0.44 % Positive orientable unit clauses : 21
% 0.11/0.44 % Positive unorientable unit clauses: 2
% 0.11/0.44 % Negative unit clauses : 0
% 0.11/0.44 % Non-unit-clauses : 0
% 0.11/0.44 % Current number of unprocessed clauses: 60
% 0.11/0.44 % ...number of literals in the above : 60
% 0.11/0.44 % Current number of archived formulas : 0
% 0.11/0.44 % Current number of archived clauses : 3
% 0.11/0.44 % Clause-clause subsumption calls (NU) : 0
% 0.11/0.44 % Rec. Clause-clause subsumption calls : 0
% 0.11/0.44 % Non-unit clause-clause subsumptions : 0
% 0.11/0.44 % Unit Clause-clause subsumption calls : 0
% 0.11/0.44 % Rewrite failures with RHS unbound : 0
% 0.11/0.44 % BW rewrite match attempts : 9
% 0.11/0.44 % BW rewrite match successes : 3
% 0.11/0.44 % Condensation attempts : 0
% 0.11/0.44 % Condensation successes : 0
% 0.11/0.44 % Termbank termtop insertions : 2018
% 0.11/0.44 % Search garbage collected termcells : 43
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.003 s
% 0.11/0.44 % System time : 0.004 s
% 0.11/0.44 % Total time : 0.007 s
% 0.11/0.44 % Maximum resident set size: 3636 pages
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.021 s
% 0.11/0.44 % System time : 0.012 s
% 0.11/0.44 % Total time : 0.034 s
% 0.11/0.44 % Maximum resident set size: 4608 pages
% 0.11/0.44 % E exiting
%------------------------------------------------------------------------------