%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP078-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:37:48 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 23 unt; 0 nHn; 14 RR)
% Number of literals : 42 ( 41 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_these_axioms,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(identity,axiom,
identity = double_divide(X1,inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(inverse,axiom,
inverse(X1) = double_divide(X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(single_axiom,axiom,
double_divide(double_divide(identity,X1),double_divide(identity,double_divide(double_divide(double_divide(X1,X2),identity),double_divide(X3,X2)))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c_0_5,plain,
double_divide(double_divide(identity,X1),double_divide(identity,identity)) = double_divide(double_divide(X1,identity),identity) ).
cnf(c_0_6,plain,
double_divide(identity,double_divide(X1,double_divide(identity,X2))) = double_divide(X2,double_divide(X1,identity)) ).
cnf(c_0_7,plain,
double_divide(identity,double_divide(double_divide(identity,X1),X2)) = double_divide(double_divide(identity,X2),X1) ).
cnf(c_0_8,plain,
double_divide(double_divide(identity,X1),double_divide(X2,X3)) = double_divide(double_divide(X3,X1),double_divide(identity,X2)) ).
cnf(c_0_9,negated_conjecture,
( 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_10,axiom,
identity = double_divide(X1,inverse(X1)),
identity ).
cnf(c_0_11,axiom,
inverse(X1) = double_divide(X1,identity),
inverse ).
cnf(c_0_12,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
c_0_9 ).
cnf(c_0_13,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_14,plain,
identity = double_divide(X1,double_divide(X1,identity)),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity)
| double_divide(double_divide(a1,double_divide(a1,identity)),identity) != identity
| double_divide(double_divide(a2,identity),identity) != a2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11]),c_0_13]),c_0_13]),c_0_13]),c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_16,plain,
double_divide(double_divide(double_divide(identity,identity),identity),identity) = identity,
inference(rw,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
double_divide(double_divide(identity,identity),identity) = double_divide(identity,identity),
inference(rw,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( double_divide(identity,identity) != identity
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_19,plain,
double_divide(identity,identity) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]) ).
cnf(c_0_20,axiom,
double_divide(double_divide(identity,X1),double_divide(identity,double_divide(double_divide(double_divide(X1,X2),identity),double_divide(X3,X2)))) = X3,
single_axiom ).
cnf(c_0_21,negated_conjecture,
( double_divide(double_divide(a2,identity),identity) != a2
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_22,plain,
double_divide(double_divide(identity,X1),identity) = double_divide(double_divide(X1,identity),identity),
inference(rw,[status(thm)],[c_0_5,c_0_19]) ).
cnf(c_0_23,plain,
double_divide(X1,identity) = double_divide(identity,X1),
inference(rw,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( double_divide(identity,double_divide(identity,a2)) != a2
| double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_25,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19]),c_0_23]) ).
cnf(c_0_26,negated_conjecture,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_27,negated_conjecture,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_6]),c_0_23]) ).
cnf(c_0_28,negated_conjecture,
double_divide(double_divide(b3,a3),double_divide(identity,c3)) != double_divide(double_divide(identity,a3),double_divide(c3,b3)),
inference(rw,[status(thm)],[c_0_27,c_0_7]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_8])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP078-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.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 19:59:22 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52 % Version: 3.5.1
% 0.19/0.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.19/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.19/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.52 % Starting sh5l with 300s (1) cores
% 0.19/0.52 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 464994 completed with status 0
% 0.19/0.52 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.19/0.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.19/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.19/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.52 % No SInE strategy applied
% 0.19/0.52 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.19/0.52 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.19/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.19/0.52 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.19/0.52 % Starting new_bool_3 with 136s (1) cores
% 0.19/0.52 % Starting new_bool_1 with 136s (1) cores
% 0.19/0.52 % G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with pid 465002 completed with status 0
% 0.19/0.52 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni
% 0.19/0.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.19/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.19/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.52 % No SInE strategy applied
% 0.19/0.52 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.19/0.52 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.19/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.19/0.52 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.19/0.52 % Preprocessing time : 0.001 s
% 0.19/0.52 % Presaturation interreduction done
% 0.19/0.52
% 0.19/0.52 % Proof found!
% 0.19/0.52 % SZS status Unsatisfiable
% 0.19/0.52 % SZS output start CNFRefutation
% See solution above
% 0.19/0.52 % Parsed axioms : 5
% 0.19/0.52 % Removed by relevancy pruning/SinE : 0
% 0.19/0.52 % Initial clauses : 5
% 0.19/0.52 % Removed in clause preprocessing : 2
% 0.19/0.52 % Initial clauses in saturation : 3
% 0.19/0.52 % Processed clauses : 887
% 0.19/0.52 % ...of these trivial : 429
% 0.19/0.52 % ...subsumed : 377
% 0.19/0.52 % ...remaining for further processing : 81
% 0.19/0.52 % Other redundant clauses eliminated : 0
% 0.19/0.52 % Clauses deleted for lack of memory : 0
% 0.19/0.52 % Backward-subsumed : 0
% 0.19/0.52 % Backward-rewritten : 36
% 0.19/0.52 % Generated clauses : 5565
% 0.19/0.52 % ...of the previous two non-redundant : 2837
% 0.19/0.52 % ...aggressively subsumed : 0
% 0.19/0.52 % Contextual simplify-reflections : 0
% 0.19/0.52 % Paramodulations : 5565
% 0.19/0.52 % Factorizations : 0
% 0.19/0.52 % NegExts : 0
% 0.19/0.52 % Equation resolutions : 0
% 0.19/0.52 % Disequality decompositions : 0
% 0.19/0.52 % Total rewrite steps : 15353
% 0.19/0.52 % ...of those cached : 11803
% 0.19/0.52 % Propositional unsat checks : 0
% 0.19/0.52 % Propositional check models : 0
% 0.19/0.52 % Propositional check unsatisfiable : 0
% 0.19/0.52 % Propositional clauses : 0
% 0.19/0.52 % Propositional clauses after purity: 0
% 0.19/0.52 % Propositional unsat core size : 0
% 0.19/0.52 % Propositional preprocessing time : 0.000
% 0.19/0.52 % Propositional encoding time : 0.000
% 0.19/0.52 % Propositional solver time : 0.000
% 0.19/0.52 % Success case prop preproc time : 0.000
% 0.19/0.52 % Success case prop encoding time : 0.000
% 0.19/0.52 % Success case prop solver time : 0.000
% 0.19/0.52 % Current number of processed clauses : 42
% 0.19/0.52 % Positive orientable unit clauses : 37
% 0.19/0.52 % Positive unorientable unit clauses: 5
% 0.19/0.52 % Negative unit clauses : 0
% 0.19/0.52 % Non-unit-clauses : 0
% 0.19/0.52 % Current number of unprocessed clauses: 1956
% 0.19/0.52 % ...number of literals in the above : 1956
% 0.19/0.52 % Current number of archived formulas : 0
% 0.19/0.52 % Current number of archived clauses : 41
% 0.19/0.52 % Clause-clause subsumption calls (NU) : 0
% 0.19/0.52 % Rec. Clause-clause subsumption calls : 0
% 0.19/0.52 % Non-unit clause-clause subsumptions : 0
% 0.19/0.52 % Unit Clause-clause subsumption calls : 60
% 0.19/0.52 % Rewrite failures with RHS unbound : 0
% 0.19/0.52 % BW rewrite match attempts : 4933
% 0.19/0.52 % BW rewrite match successes : 68
% 0.19/0.52 % Condensation attempts : 0
% 0.19/0.52 % Condensation successes : 0
% 0.19/0.52 % Termbank termtop insertions : 93501
% 0.19/0.52 % Search garbage collected termcells : 8
% 0.19/0.52
% 0.19/0.52 % -------------------------------------------------
% 0.19/0.52 % User time : 0.069 s
% 0.19/0.52 % System time : 0.006 s
% 0.19/0.52 % Total time : 0.075 s
% 0.19/0.52 % Maximum resident set size: 3636 pages
% 0.19/0.52
% 0.19/0.52 % -------------------------------------------------
% 0.19/0.52 % User time : 0.287 s
% 0.19/0.52 % System time : 0.031 s
% 0.19/0.52 % Total time : 0.318 s
% 0.19/0.52 % Maximum resident set size: 4608 pages
% 0.19/0.52 % E exiting
%------------------------------------------------------------------------------