%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP083-1 : 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 : n010.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 12:37:49 PM UTC 2026
% Result : Unsatisfiable 4.51s 1.11s
% Output : CNFRefutation 4.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of clauses : 49 ( 45 unt; 0 nHn; 5 RR)
% Number of literals : 57 ( 56 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 156 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X1,inverse(double_divide(X2,X3))),double_divide(inverse(X2),inverse(double_divide(X4,double_divide(X1,X4))))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( 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,inverse(double_divide(X2,X3))),double_divide(inverse(X2),inverse(double_divide(X4,double_divide(X1,X4))))) = X3,
single_axiom ).
cnf(c_0_4,plain,
double_divide(double_divide(X1,inverse(X2)),double_divide(inverse(double_divide(X3,inverse(double_divide(X4,X2)))),inverse(double_divide(X5,double_divide(X1,X5))))) = double_divide(inverse(X4),inverse(double_divide(X6,double_divide(X3,X6)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
double_divide(inverse(X1),inverse(double_divide(X2,double_divide(X3,X2)))) = double_divide(inverse(X1),inverse(double_divide(X4,double_divide(X3,X4)))),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_6,plain,
inverse(double_divide(X1,double_divide(X2,X1))) = inverse(double_divide(X3,double_divide(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_5]),c_0_3]) ).
cnf(c_0_7,plain,
double_divide(double_divide(X1,inverse(double_divide(X2,double_divide(X3,X2)))),double_divide(inverse(X4),inverse(double_divide(X5,double_divide(X1,X5))))) = double_divide(X3,X4),
inference(spm,[status(thm)],[c_0_3,c_0_6]) ).
cnf(c_0_8,plain,
double_divide(X1,double_divide(X2,inverse(double_divide(X3,double_divide(X4,double_divide(X1,X4)))))) = double_divide(inverse(X3),inverse(double_divide(X5,double_divide(X2,X5)))),
inference(spm,[status(thm)],[c_0_4,c_0_7]) ).
cnf(c_0_9,plain,
double_divide(inverse(double_divide(double_divide(X1,inverse(double_divide(X2,X3))),X1)),inverse(double_divide(X4,double_divide(inverse(X2),X4)))) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_8]) ).
cnf(c_0_10,plain,
double_divide(double_divide(inverse(X1),inverse(double_divide(double_divide(double_divide(X2,inverse(double_divide(X1,X3))),X2),X4))),X3) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_9]) ).
cnf(c_0_11,plain,
double_divide(inverse(X1),inverse(double_divide(X2,double_divide(inverse(double_divide(double_divide(X3,inverse(double_divide(X4,inverse(X4)))),X3)),X2)))) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
double_divide(double_divide(X1,inverse(double_divide(double_divide(double_divide(X2,inverse(double_divide(X3,inverse(X3)))),X2),X4))),X1) = X4,
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_13,plain,
double_divide(X1,double_divide(X2,double_divide(X3,X2))) = double_divide(X1,double_divide(X4,double_divide(X3,X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_7]) ).
cnf(c_0_14,plain,
double_divide(double_divide(double_divide(X1,inverse(double_divide(X2,X3))),inverse(double_divide(X4,X5))),double_divide(inverse(X4),inverse(double_divide(double_divide(inverse(X2),inverse(double_divide(X6,double_divide(X1,X6)))),X3)))) = X5,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_15,plain,
double_divide(double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X2,inverse(double_divide(X3,inverse(X3)))),X2)),X4))),X1) = X4,
inference(spm,[status(thm)],[c_0_12,c_0_12]) ).
cnf(c_0_16,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(X3,double_divide(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_13]),c_0_3]) ).
cnf(c_0_17,plain,
double_divide(X1,double_divide(inverse(X2),inverse(double_divide(inverse(double_divide(X2,X3)),X1)))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_9]) ).
cnf(c_0_18,plain,
double_divide(double_divide(X1,inverse(inverse(X2))),X1) = inverse(double_divide(X3,double_divide(inverse(X2),X3))),
inference(spm,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_19,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(double_divide(inverse(X3),inverse(double_divide(inverse(double_divide(X3,X4)),X2))),X4),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
double_divide(inverse(double_divide(double_divide(X1,inverse(double_divide(X2,X3))),X1)),double_divide(double_divide(X4,inverse(inverse(X2))),X4)) = X3,
inference(spm,[status(thm)],[c_0_9,c_0_18]) ).
cnf(c_0_21,plain,
double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X2,double_divide(inverse(X3),X2))),inverse(X3)))) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_22,plain,
double_divide(inverse(double_divide(X1,double_divide(X2,X1))),inverse(double_divide(X3,double_divide(inverse(inverse(double_divide(X4,inverse(X4)))),X3)))) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_19]) ).
cnf(c_0_23,plain,
double_divide(inverse(double_divide(X1,double_divide(inverse(X2),X1))),double_divide(inverse(double_divide(X3,inverse(double_divide(X2,X4)))),inverse(X4))) = X3,
inference(spm,[status(thm)],[c_0_17,c_0_9]) ).
cnf(c_0_24,plain,
double_divide(X1,double_divide(double_divide(inverse(double_divide(double_divide(X2,inverse(double_divide(X3,X4))),X2)),inverse(inverse(X3))),X1)) = X4,
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_25,plain,
double_divide(inverse(X1),inverse(inverse(double_divide(X2,double_divide(inverse(inverse(double_divide(X3,inverse(X3)))),X2))))) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
double_divide(double_divide(X1,inverse(double_divide(double_divide(X2,double_divide(inverse(inverse(double_divide(X3,inverse(X3)))),X2)),X4))),X1) = X4,
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_27,plain,
double_divide(X1,double_divide(inverse(double_divide(X2,inverse(double_divide(X3,double_divide(X4,double_divide(inverse(X3),X4)))))),X1)) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_28,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_29,plain,
inverse(double_divide(X1,inverse(double_divide(X2,inverse(X2))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
cnf(c_0_30,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(double_divide(X3,X2),double_divide(X4,double_divide(X3,X4))),
inference(spm,[status(thm)],[c_0_16,c_0_16]) ).
cnf(c_0_31,plain,
inverse(double_divide(X1,double_divide(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_29]) ).
cnf(c_0_32,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_28]),c_0_28]) ).
cnf(c_0_33,plain,
double_divide(double_divide(X1,inverse(X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
( 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_35,plain,
double_divide(double_divide(double_divide(X1,inverse(X2)),double_divide(inverse(double_divide(X3,inverse(double_divide(X4,X2)))),inverse(double_divide(X5,double_divide(X1,X5))))),double_divide(inverse(double_divide(X6,inverse(double_divide(X7,double_divide(X8,double_divide(X3,X8)))))),inverse(double_divide(X9,double_divide(inverse(X4),X9))))) = double_divide(inverse(X7),inverse(double_divide(X10,double_divide(X6,X10)))),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_36,plain,
double_divide(double_divide(double_divide(X1,inverse(X2)),double_divide(inverse(double_divide(X3,inverse(double_divide(X4,X2)))),inverse(double_divide(X5,double_divide(X1,X5))))),double_divide(inverse(X6),inverse(double_divide(X7,double_divide(inverse(X4),X7))))) = double_divide(X3,X6),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_37,plain,
double_divide(inverse(X1),inverse(X2)) = inverse(double_divide(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_33]),c_0_33]),c_0_31]),c_0_28]) ).
cnf(c_0_38,plain,
inverse(double_divide(inverse(double_divide(X1,inverse(X1))),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_32]),c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( 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_34 ).
cnf(c_0_40,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_41,plain,
double_divide(X1,double_divide(X2,inverse(double_divide(X3,X1)))) = inverse(double_divide(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_28]),c_0_28]),c_0_37]) ).
cnf(c_0_42,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_29]),c_0_33]) ).
cnf(c_0_43,plain,
double_divide(inverse(X1),double_divide(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_31]),c_0_28]),c_0_29]) ).
cnf(c_0_44,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 ),
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_39,c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]) ).
cnf(c_0_45,plain,
double_divide(inverse(double_divide(X1,X2)),X3) = double_divide(X1,inverse(double_divide(X2,X3))),
inference(spm,[status(thm)],[c_0_32,c_0_41]) ).
cnf(c_0_46,plain,
inverse(double_divide(X1,inverse(X2))) = double_divide(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_37,c_0_42]) ).
cnf(c_0_47,plain,
double_divide(X1,inverse(X1)) = double_divide(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_32,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_29])]),c_0_45]),c_0_46]),c_0_46]),c_0_46]),c_0_46])]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP083-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 19:57:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 4.51/1.11 % Version: 3.5.1
% 4.51/1.11 % Preprocessing class: FSSSSMSSSSSNFFN.
% 4.51/1.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.51/1.11 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 4.51/1.11 % Starting new_bool_3 with 300s (1) cores
% 4.51/1.11 % Starting new_bool_1 with 300s (1) cores
% 4.51/1.11 % Starting sh5l with 300s (1) cores
% 4.51/1.11 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3382306 completed with status 0
% 4.51/1.11 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 4.51/1.11 % Preprocessing class: FSSSSMSSSSSNFFN.
% 4.51/1.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.51/1.11 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 4.51/1.11 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.51/1.11 % No SInE strategy applied
% 4.51/1.11 % Search class: FUHPF-FFSF21-MFFFFFNN
% 4.51/1.11 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.51/1.11 % Starting SubtermCWHack with 136s (1) cores
% 4.51/1.11 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 4.51/1.11 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 4.51/1.11 % Starting new_bool_3 with 136s (1) cores
% 4.51/1.11 % Starting new_bool_1 with 136s (1) cores
% 4.51/1.11 % SubtermCWHack with pid 3382307 completed with status 0
% 4.51/1.11 % Result found by SubtermCWHack
% 4.51/1.11 % Preprocessing class: FSSSSMSSSSSNFFN.
% 4.51/1.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.51/1.11 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 4.51/1.11 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.51/1.11 % No SInE strategy applied
% 4.51/1.11 % Search class: FUHPF-FFSF21-MFFFFFNN
% 4.51/1.11 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.51/1.11 % Starting SubtermCWHack with 136s (1) cores
% 4.51/1.11 % Preprocessing time : 0.002 s
% 4.51/1.11
% 4.51/1.11 % Proof found!
% 4.51/1.11 % SZS status Unsatisfiable
% 4.51/1.11 % SZS output start CNFRefutation
% See solution above
% 4.51/1.11 % Parsed axioms : 3
% 4.51/1.11 % Removed by relevancy pruning/SinE : 0
% 4.51/1.11 % Initial clauses : 3
% 4.51/1.11 % Removed in clause preprocessing : 1
% 4.51/1.11 % Initial clauses in saturation : 2
% 4.51/1.11 % Processed clauses : 550
% 4.51/1.11 % ...of these trivial : 51
% 4.51/1.11 % ...subsumed : 384
% 4.51/1.11 % ...remaining for further processing : 114
% 4.51/1.11 % Other redundant clauses eliminated : 0
% 4.51/1.11 % Clauses deleted for lack of memory : 0
% 4.51/1.11 % Backward-subsumed : 3
% 4.51/1.11 % Backward-rewritten : 95
% 4.51/1.11 % Generated clauses : 28608
% 4.51/1.11 % ...of the previous two non-redundant : 27765
% 4.51/1.11 % ...aggressively subsumed : 0
% 4.51/1.11 % Contextual simplify-reflections : 0
% 4.51/1.11 % Paramodulations : 28608
% 4.51/1.11 % Factorizations : 0
% 4.51/1.11 % NegExts : 0
% 4.51/1.11 % Equation resolutions : 0
% 4.51/1.11 % Disequality decompositions : 0
% 4.51/1.11 % Total rewrite steps : 28290
% 4.51/1.11 % ...of those cached : 24553
% 4.51/1.11 % Propositional unsat checks : 0
% 4.51/1.11 % Propositional check models : 0
% 4.51/1.11 % Propositional check unsatisfiable : 0
% 4.51/1.11 % Propositional clauses : 0
% 4.51/1.11 % Propositional clauses after purity: 0
% 4.51/1.11 % Propositional unsat core size : 0
% 4.51/1.11 % Propositional preprocessing time : 0.000
% 4.51/1.11 % Propositional encoding time : 0.000
% 4.51/1.11 % Propositional solver time : 0.000
% 4.51/1.11 % Success case prop preproc time : 0.000
% 4.51/1.11 % Success case prop encoding time : 0.000
% 4.51/1.11 % Success case prop solver time : 0.000
% 4.51/1.11 % Current number of processed clauses : 16
% 4.51/1.11 % Positive orientable unit clauses : 13
% 4.51/1.11 % Positive unorientable unit clauses: 3
% 4.51/1.11 % Negative unit clauses : 0
% 4.51/1.11 % Non-unit-clauses : 0
% 4.51/1.11 % Current number of unprocessed clauses: 9206
% 4.51/1.11 % ...number of literals in the above : 9206
% 4.51/1.11 % Current number of archived formulas : 0
% 4.51/1.11 % Current number of archived clauses : 99
% 4.51/1.11 % Clause-clause subsumption calls (NU) : 0
% 4.51/1.11 % Rec. Clause-clause subsumption calls : 0
% 4.51/1.11 % Non-unit clause-clause subsumptions : 0
% 4.51/1.11 % Unit Clause-clause subsumption calls : 431
% 4.51/1.11 % Rewrite failures with RHS unbound : 2252
% 4.51/1.11 % BW rewrite match attempts : 2123
% 4.51/1.11 % BW rewrite match successes : 327
% 4.51/1.11 % Condensation attempts : 0
% 4.51/1.11 % Condensation successes : 0
% 4.51/1.11 % Termbank termtop insertions : 874729
% 4.51/1.11 % Search garbage collected termcells : 8
% 4.51/1.11
% 4.51/1.11 % -------------------------------------------------
% 4.51/1.11 % User time : 0.563 s
% 4.51/1.11 % System time : 0.037 s
% 4.51/1.11 % Total time : 0.600 s
% 4.51/1.11 % Maximum resident set size: 3380 pages
% 4.51/1.11
% 4.51/1.11 % -------------------------------------------------
% 4.51/1.11 % User time : 2.784 s
% 4.51/1.11 % System time : 0.157 s
% 4.51/1.11 % Total time : 2.941 s
% 4.51/1.11 % Maximum resident set size: 4608 pages
% 4.51/1.11 % E exiting
%------------------------------------------------------------------------------