%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP101-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:37:53 PM UTC 2026
% Result : Unsatisfiable 0.53s 0.59s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of clauses : 62 ( 57 unt; 0 nHn; 9 RR)
% Number of literals : 76 ( 75 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity,axiom,
identity = double_divide(X1,inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(inverse,axiom,
inverse(X1) = double_divide(X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(single_axiom,axiom,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_5,axiom,
identity = double_divide(X1,inverse(X1)),
identity ).
cnf(c_0_6,axiom,
inverse(X1) = double_divide(X1,identity),
inverse ).
cnf(c_0_7,axiom,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
single_axiom ).
cnf(c_0_8,plain,
double_divide(X1,double_divide(X1,identity)) = identity,
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),double_divide(identity,identity)) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_11,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_12,plain,
double_divide(identity,identity) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_10]),c_0_8]),c_0_10]) ).
cnf(c_0_13,plain,
double_divide(double_divide(X1,X2),multiply(X2,X1)) = identity,
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_14,plain,
multiply(double_divide(identity,double_divide(X1,identity)),identity) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_12]),c_0_11]) ).
cnf(c_0_15,plain,
multiply(double_divide(double_divide(X1,double_divide(X2,X3)),double_divide(X2,identity)),X3) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_12]),c_0_11]) ).
cnf(c_0_16,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),X1) = identity,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
multiply(multiply(double_divide(identity,X1),X2),X1) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_12]),c_0_11]) ).
cnf(c_0_18,plain,
multiply(double_divide(double_divide(X1,identity),X2),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_11]),c_0_14]) ).
cnf(c_0_19,plain,
multiply(X1,double_divide(X1,identity)) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_20,plain,
multiply(double_divide(identity,X1),X1) = identity,
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_21,plain,
multiply(multiply(X1,X2),double_divide(X2,X1)) = double_divide(identity,identity),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_22,plain,
multiply(identity,X1) = multiply(X1,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_11]) ).
cnf(c_0_23,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_24,plain,
multiply(multiply(X1,X2),double_divide(X2,X1)) = identity,
inference(rw,[status(thm)],[c_0_21,c_0_12]) ).
cnf(c_0_25,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
multiply(X1,double_divide(identity,X1)) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_26]),c_0_23]) ).
cnf(c_0_28,plain,
multiply(identity,double_divide(X1,X2)) = double_divide(multiply(X2,X1),identity),
inference(spm,[status(thm)],[c_0_11,c_0_11]) ).
cnf(c_0_29,plain,
double_divide(X1,identity) = double_divide(identity,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_27]),c_0_25]) ).
cnf(c_0_30,plain,
double_divide(X1,double_divide(identity,X1)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_27]),c_0_25]) ).
cnf(c_0_31,plain,
double_divide(identity,multiply(X1,X2)) = double_divide(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_23]),c_0_29]) ).
cnf(c_0_32,plain,
double_divide(multiply(X1,X2),double_divide(X2,X1)) = identity,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,plain,
double_divide(identity,double_divide(X1,X2)) = multiply(X2,X1),
inference(rw,[status(thm)],[c_0_11,c_0_29]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,X2),double_divide(identity,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_27]),c_0_12]),c_0_11]) ).
cnf(c_0_35,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_32]),c_0_33]),c_0_23]) ).
cnf(c_0_36,plain,
multiply(double_divide(identity,X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,plain,
multiply(double_divide(identity,X1),multiply(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_38,plain,
multiply(X1,multiply(double_divide(identity,X1),X2)) = X2,
inference(rw,[status(thm)],[c_0_17,c_0_35]) ).
cnf(c_0_39,plain,
multiply(X1,double_divide(X2,X1)) = double_divide(identity,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_37]),c_0_31]),c_0_35]) ).
cnf(c_0_40,plain,
double_divide(X1,X2) = double_divide(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_35]),c_0_31]) ).
cnf(c_0_41,plain,
multiply(multiply(double_divide(X1,identity),X2),X1) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_42,plain,
multiply(X1,multiply(X2,double_divide(identity,X1))) = X2,
inference(spm,[status(thm)],[c_0_38,c_0_35]) ).
cnf(c_0_43,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_39]),c_0_33]),c_0_25]),c_0_40]) ).
cnf(c_0_44,plain,
multiply(X1,multiply(double_divide(X1,identity),X2)) = X2,
inference(rw,[status(thm)],[c_0_41,c_0_35]) ).
cnf(c_0_45,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_46,plain,
multiply(multiply(X1,X2),multiply(X3,double_divide(X2,X1))) = X3,
inference(spm,[status(thm)],[c_0_42,c_0_31]) ).
cnf(c_0_47,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_43]),c_0_40]) ).
cnf(c_0_48,plain,
double_divide(X1,multiply(double_divide(X1,identity),X2)) = double_divide(identity,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_44]),c_0_40]) ).
cnf(c_0_49,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
c_0_45 ).
cnf(c_0_50,plain,
multiply(double_divide(X1,identity),X1) = double_divide(identity,identity),
inference(spm,[status(thm)],[c_0_11,c_0_8]) ).
cnf(c_0_51,plain,
multiply(multiply(X1,X2),multiply(X3,double_divide(X1,X2))) = X3,
inference(spm,[status(thm)],[c_0_46,c_0_40]) ).
cnf(c_0_52,plain,
multiply(X1,double_divide(double_divide(X2,identity),double_divide(X3,double_divide(X2,X1)))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_35]),c_0_40]) ).
cnf(c_0_53,plain,
multiply(double_divide(X1,identity),X2) = double_divide(X1,double_divide(identity,X2)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( double_divide(identity,identity) != identity
| multiply(identity,a2) != a2
| multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_6]),c_0_50]) ).
cnf(c_0_55,plain,
multiply(X1,double_divide(X2,multiply(double_divide(X2,X3),X1))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_33]),c_0_35]) ).
cnf(c_0_56,negated_conjecture,
( multiply(identity,a2) != a2
| multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_12])]) ).
cnf(c_0_57,plain,
multiply(X1,multiply(X2,multiply(double_divide(X2,X1),X3))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_55]),c_0_35]),c_0_35]) ).
cnf(c_0_58,plain,
multiply(double_divide(X1,X2),multiply(X3,multiply(X2,X1))) = X3,
inference(spm,[status(thm)],[c_0_42,c_0_33]) ).
cnf(c_0_59,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_23])]),c_0_35]),c_0_35])]) ).
cnf(c_0_60,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP101-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n014.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 19:57:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.53/0.59 % Version: 3.5.1
% 0.53/0.59 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.53/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.59 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.53/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.53/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.53/0.59 % Starting sh5l with 300s (1) cores
% 0.53/0.59 % new_bool_3 with pid 2216967 completed with status 0
% 0.53/0.59 % Result found by new_bool_3
% 0.53/0.59 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.53/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.59 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.53/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.53/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.53/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.53/0.59 % Search class: FUHPM-FFSF21-MFFFFFNN
% 0.53/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.53/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.53/0.59 % SubtermCWHack with pid 2216972 completed with status 0
% 0.53/0.59 % Result found by SubtermCWHack
% 0.53/0.59 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.53/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.59 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.53/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.53/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.53/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.53/0.59 % Search class: FUHPM-FFSF21-MFFFFFNN
% 0.53/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.53/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.53/0.59 % Preprocessing time : 0.001 s
% 0.53/0.59
% 0.53/0.59 % Proof found!
% 0.53/0.59 % SZS status Unsatisfiable
% 0.53/0.59 % SZS output start CNFRefutation
% See solution above
% 0.53/0.59 % Parsed axioms : 5
% 0.53/0.59 % Removed by relevancy pruning/SinE : 0
% 0.53/0.59 % Initial clauses : 5
% 0.53/0.59 % Removed in clause preprocessing : 0
% 0.53/0.59 % Initial clauses in saturation : 5
% 0.53/0.59 % Processed clauses : 1061
% 0.53/0.59 % ...of these trivial : 380
% 0.53/0.59 % ...subsumed : 521
% 0.53/0.59 % ...remaining for further processing : 160
% 0.53/0.59 % Other redundant clauses eliminated : 0
% 0.53/0.59 % Clauses deleted for lack of memory : 0
% 0.53/0.59 % Backward-subsumed : 1
% 0.53/0.59 % Backward-rewritten : 95
% 0.53/0.59 % Generated clauses : 10104
% 0.53/0.59 % ...of the previous two non-redundant : 6798
% 0.53/0.59 % ...aggressively subsumed : 0
% 0.53/0.59 % Contextual simplify-reflections : 0
% 0.53/0.59 % Paramodulations : 10104
% 0.53/0.59 % Factorizations : 0
% 0.53/0.59 % NegExts : 0
% 0.53/0.59 % Equation resolutions : 0
% 0.53/0.59 % Disequality decompositions : 0
% 0.53/0.59 % Total rewrite steps : 15436
% 0.53/0.59 % ...of those cached : 13110
% 0.53/0.59 % Propositional unsat checks : 0
% 0.53/0.59 % Propositional check models : 0
% 0.53/0.59 % Propositional check unsatisfiable : 0
% 0.53/0.59 % Propositional clauses : 0
% 0.53/0.59 % Propositional clauses after purity: 0
% 0.53/0.59 % Propositional unsat core size : 0
% 0.53/0.59 % Propositional preprocessing time : 0.000
% 0.53/0.59 % Propositional encoding time : 0.000
% 0.53/0.59 % Propositional solver time : 0.000
% 0.53/0.59 % Success case prop preproc time : 0.000
% 0.53/0.59 % Success case prop encoding time : 0.000
% 0.53/0.59 % Success case prop solver time : 0.000
% 0.53/0.59 % Current number of processed clauses : 64
% 0.53/0.59 % Positive orientable unit clauses : 58
% 0.53/0.59 % Positive unorientable unit clauses: 6
% 0.53/0.59 % Negative unit clauses : 0
% 0.53/0.59 % Non-unit-clauses : 0
% 0.53/0.59 % Current number of unprocessed clauses: 5091
% 0.53/0.59 % ...number of literals in the above : 5091
% 0.53/0.59 % Current number of archived formulas : 0
% 0.53/0.59 % Current number of archived clauses : 96
% 0.53/0.59 % Clause-clause subsumption calls (NU) : 0
% 0.53/0.59 % Rec. Clause-clause subsumption calls : 0
% 0.53/0.59 % Non-unit clause-clause subsumptions : 0
% 0.53/0.59 % Unit Clause-clause subsumption calls : 38
% 0.53/0.59 % Rewrite failures with RHS unbound : 0
% 0.53/0.59 % BW rewrite match attempts : 479
% 0.53/0.59 % BW rewrite match successes : 279
% 0.53/0.59 % Condensation attempts : 0
% 0.53/0.59 % Condensation successes : 0
% 0.53/0.59 % Termbank termtop insertions : 89078
% 0.53/0.59 % Search garbage collected termcells : 11
% 0.53/0.59
% 0.53/0.59 % -------------------------------------------------
% 0.53/0.59 % User time : 0.134 s
% 0.53/0.59 % System time : 0.012 s
% 0.53/0.59 % Total time : 0.147 s
% 0.53/0.59 % Maximum resident set size: 3380 pages
% 0.53/0.59
% 0.53/0.59 % -------------------------------------------------
% 0.53/0.59 % User time : 0.136 s
% 0.53/0.59 % System time : 0.017 s
% 0.53/0.59 % Total time : 0.153 s
% 0.53/0.59 % Maximum resident set size: 4608 pages
% 0.53/0.59 % E exiting
%------------------------------------------------------------------------------