%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP107-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 0.20s 0.53s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of clauses : 33 ( 29 unt; 0 nHn; 6 RR)
% Number of literals : 45 ( 44 equ; 17 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(inverse(X3),X2))))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(multiply,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_3,axiom,
double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(inverse(X3),X2))))) = X3,
single_axiom ).
cnf(c_0_4,plain,
double_divide(X1,inverse(double_divide(double_divide(X2,X3),inverse(double_divide(inverse(X4),inverse(double_divide(X2,inverse(double_divide(inverse(X1),X3))))))))) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
double_divide(X1,inverse(double_divide(inverse(X2),inverse(X1)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_4]),c_0_3]) ).
cnf(c_0_6,plain,
double_divide(double_divide(X1,inverse(X1)),inverse(X2)) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_7,plain,
double_divide(inverse(X1),inverse(double_divide(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
double_divide(double_divide(double_divide(inverse(X1),X2),inverse(double_divide(inverse(X3),X2))),inverse(X3)) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_9,plain,
double_divide(X1,inverse(double_divide(inverse(X1),inverse(X2)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_7]),c_0_7]) ).
cnf(c_0_10,plain,
double_divide(double_divide(X1,inverse(X2)),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_7]),c_0_7]) ).
cnf(c_0_11,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_10]) ).
cnf(c_0_12,plain,
double_divide(double_divide(inverse(X1),X1),inverse(X2)) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_11]) ).
cnf(c_0_13,plain,
double_divide(double_divide(inverse(X1),X2),inverse(X1)) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_14,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_16,plain,
double_divide(X1,X2) = double_divide(X2,X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
double_divide(inverse(X1),inverse(double_divide(X1,inverse(X2)))) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_19,plain,
inverse(double_divide(X1,inverse(X2))) = double_divide(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_21,plain,
double_divide(double_divide(X1,X2),double_divide(inverse(X1),double_divide(inverse(X3),X2))) = X3,
inference(rw,[status(thm)],[c_0_3,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
c_0_20 ).
cnf(c_0_23,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_24,plain,
double_divide(double_divide(X1,inverse(X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_6,c_0_11]) ).
cnf(c_0_25,plain,
double_divide(inverse(X1),double_divide(inverse(X2),X3)) = double_divide(double_divide(X1,X3),X2),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1)))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) ),
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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_27,plain,
double_divide(X1,inverse(X1)) = double_divide(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_10,c_0_6]) ).
cnf(c_0_28,plain,
double_divide(X1,double_divide(X2,inverse(X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_29,plain,
double_divide(inverse(X1),double_divide(double_divide(X1,X2),X3)) = double_divide(inverse(X3),X2),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
double_divide(inverse(a3),double_divide(c3,b3)) != double_divide(inverse(c3),double_divide(b3,a3)),
inference(cn,[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)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_16]),c_0_16])]),c_0_27]),c_0_19]),c_0_19]),c_0_19]),c_0_16]),c_0_28]),c_0_11])]) ).
cnf(c_0_31,plain,
double_divide(inverse(X1),double_divide(X2,X3)) = double_divide(inverse(X3),double_divide(X1,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_17]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP107-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 19:55:37 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.45 Running first-order theorem proving
% 0.09/0.45 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
% 0.20/0.53 % Version: 3.5.1
% 0.20/0.53 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.20/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.20/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.53 % Starting sh5l with 300s (1) cores
% 0.20/0.53 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 3446460 completed with status 0
% 0.20/0.53 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.20/0.53 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.20/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.20/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.53 % No SInE strategy applied
% 0.20/0.53 % Search class: FUHPF-FFSF21-DFFFFFNN
% 0.20/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.53 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.20/0.53 % Starting G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.20/0.53 % Starting new_bool_3 with 136s (1) cores
% 0.20/0.53 % Starting new_bool_1 with 136s (1) cores
% 0.20/0.53 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 3446463 completed with status 0
% 0.20/0.53 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.20/0.53 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.20/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.20/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.53 % No SInE strategy applied
% 0.20/0.53 % Search class: FUHPF-FFSF21-DFFFFFNN
% 0.20/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.53 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.20/0.53 % Preprocessing time : 0.002 s
% 0.20/0.53
% 0.20/0.53 % Proof found!
% 0.20/0.53 % SZS status Unsatisfiable
% 0.20/0.53 % SZS output start CNFRefutation
% See solution above
% 0.20/0.53 % Parsed axioms : 3
% 0.20/0.53 % Removed by relevancy pruning/SinE : 0
% 0.20/0.53 % Initial clauses : 3
% 0.20/0.53 % Removed in clause preprocessing : 1
% 0.20/0.53 % Initial clauses in saturation : 2
% 0.20/0.53 % Processed clauses : 233
% 0.20/0.53 % ...of these trivial : 54
% 0.20/0.53 % ...subsumed : 129
% 0.20/0.53 % ...remaining for further processing : 50
% 0.20/0.53 % Other redundant clauses eliminated : 0
% 0.20/0.53 % Clauses deleted for lack of memory : 0
% 0.20/0.53 % Backward-subsumed : 0
% 0.20/0.53 % Backward-rewritten : 29
% 0.20/0.53 % Generated clauses : 1443
% 0.20/0.53 % ...of the previous two non-redundant : 983
% 0.20/0.53 % ...aggressively subsumed : 0
% 0.20/0.53 % Contextual simplify-reflections : 0
% 0.20/0.53 % Paramodulations : 1443
% 0.20/0.53 % Factorizations : 0
% 0.20/0.53 % NegExts : 0
% 0.20/0.53 % Equation resolutions : 0
% 0.20/0.53 % Disequality decompositions : 0
% 0.20/0.53 % Total rewrite steps : 1851
% 0.20/0.53 % ...of those cached : 1348
% 0.20/0.53 % Propositional unsat checks : 0
% 0.20/0.53 % Propositional check models : 0
% 0.20/0.53 % Propositional check unsatisfiable : 0
% 0.20/0.53 % Propositional clauses : 0
% 0.20/0.53 % Propositional clauses after purity: 0
% 0.20/0.53 % Propositional unsat core size : 0
% 0.20/0.53 % Propositional preprocessing time : 0.000
% 0.20/0.53 % Propositional encoding time : 0.000
% 0.20/0.53 % Propositional solver time : 0.000
% 0.20/0.53 % Success case prop preproc time : 0.000
% 0.20/0.53 % Success case prop encoding time : 0.000
% 0.20/0.53 % Success case prop solver time : 0.000
% 0.20/0.53 % Current number of processed clauses : 21
% 0.20/0.53 % Positive orientable unit clauses : 17
% 0.20/0.53 % Positive unorientable unit clauses: 4
% 0.20/0.53 % Negative unit clauses : 0
% 0.20/0.53 % Non-unit-clauses : 0
% 0.20/0.53 % Current number of unprocessed clauses: 602
% 0.20/0.53 % ...number of literals in the above : 606
% 0.20/0.53 % Current number of archived formulas : 0
% 0.20/0.53 % Current number of archived clauses : 30
% 0.20/0.53 % Clause-clause subsumption calls (NU) : 0
% 0.20/0.53 % Rec. Clause-clause subsumption calls : 0
% 0.20/0.53 % Non-unit clause-clause subsumptions : 0
% 0.20/0.53 % Unit Clause-clause subsumption calls : 44
% 0.20/0.53 % Rewrite failures with RHS unbound : 62
% 0.20/0.53 % BW rewrite match attempts : 215
% 0.20/0.53 % BW rewrite match successes : 106
% 0.20/0.53 % Condensation attempts : 0
% 0.20/0.53 % Condensation successes : 0
% 0.20/0.53 % Termbank termtop insertions : 13553
% 0.20/0.53 % Search garbage collected termcells : 11
% 0.20/0.53
% 0.20/0.53 % -------------------------------------------------
% 0.20/0.53 % User time : 0.028 s
% 0.20/0.53 % System time : 0.006 s
% 0.20/0.53 % Total time : 0.034 s
% 0.20/0.53 % Maximum resident set size: 3380 pages
% 0.20/0.53
% 0.20/0.53 % -------------------------------------------------
% 0.20/0.53 % User time : 0.103 s
% 0.20/0.53 % System time : 0.025 s
% 0.20/0.53 % Total time : 0.129 s
% 0.20/0.53 % Maximum resident set size: 4864 pages
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------