%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP106-1 : 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 : n001.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 0.11s 0.47s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of clauses : 38 ( 35 unt; 0 nHn; 4 RR)
% Number of literals : 47 ( 46 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 87 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(X3,X2)))))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
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(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_3,axiom,
inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(X3,X2)))))) = X3,
single_axiom ).
cnf(c_0_4,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_5,plain,
multiply(multiply(multiply(X1,X2),X3),double_divide(X3,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_3,c_0_4]),c_0_4]),c_0_4]) ).
cnf(c_0_6,plain,
multiply(X1,double_divide(double_divide(X2,X3),multiply(X3,X1))) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_7,plain,
multiply(multiply(X1,X2),double_divide(X2,multiply(multiply(X3,X1),X4))) = double_divide(X4,X3),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_8,plain,
double_divide(multiply(X1,double_divide(X2,multiply(X3,X1))),X3) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
double_divide(double_divide(multiply(X1,X2),X3),multiply(X3,X1)) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_10,plain,
multiply(multiply(X1,X2),double_divide(multiply(X2,X3),X1)) = inverse(X3),
inference(spm,[status(thm)],[c_0_4,c_0_9]) ).
cnf(c_0_11,plain,
multiply(inverse(X1),double_divide(double_divide(multiply(X2,X1),X3),X3)) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_12,plain,
double_divide(multiply(X1,X2),multiply(X3,inverse(X2))) = double_divide(X1,X3),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_13,plain,
double_divide(multiply(inverse(X1),double_divide(X2,X3)),X3) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_14,plain,
multiply(double_divide(multiply(X1,X2),X3),X2) = double_divide(X1,X3),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_15,plain,
multiply(X1,double_divide(X1,multiply(X2,X3))) = double_divide(X3,X2),
inference(spm,[status(thm)],[c_0_14,c_0_8]) ).
cnf(c_0_16,plain,
double_divide(X1,X2) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
cnf(c_0_17,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_15]) ).
cnf(c_0_18,plain,
inverse(inverse(multiply(X1,X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_4,c_0_16]) ).
cnf(c_0_19,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(rw,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_20,plain,
multiply(X1,multiply(X2,double_divide(X3,multiply(X1,X2)))) = inverse(X3),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_21,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_23,plain,
inverse(multiply(X1,inverse(multiply(X1,X2)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_16]),c_0_16]) ).
cnf(c_0_24,plain,
multiply(multiply(X1,inverse(X2)),multiply(X3,X2)) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_11]),c_0_4]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(X2,inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_26,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_21]) ).
cnf(c_0_27,plain,
multiply(multiply(X1,inverse(X2)),multiply(multiply(X3,X2),inverse(multiply(multiply(X1,X3),X4)))) = inverse(X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_24]),c_0_16]) ).
cnf(c_0_28,plain,
multiply(X1,inverse(multiply(X1,inverse(X2)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_25]),c_0_26]) ).
cnf(c_0_29,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_30,plain,
multiply(X1,inverse(multiply(X1,X2))) = inverse(X2),
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_31,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,X1)))) = inverse(multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_16]),c_0_16]),c_0_26]) ).
cnf(c_0_32,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_21]) ).
cnf(c_0_33,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_29 ).
cnf(c_0_34,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_21]),c_0_21]) ).
cnf(c_0_35,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_36,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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(rw,[status(thm)],[c_0_33,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26])]),c_0_34]),c_0_35])]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP106-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 20:03:14 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 0.11/0.47 % Version: 3.5.1
% 0.11/0.47 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.11/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.47 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.11/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.47 % Starting sh5l with 300s (1) cores
% 0.11/0.47 % new_bool_3 with pid 1271512 completed with status 0
% 0.11/0.47 % Result found by new_bool_3
% 0.11/0.47 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.11/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.47 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.11/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.47 % Search class: FUHPS-FFSF21-DFFFFFNN
% 0.11/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.47 % SubtermCWHack with pid 1271517 completed with status 0
% 0.11/0.47 % Result found by SubtermCWHack
% 0.11/0.47 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.11/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.47 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.11/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.47 % Search class: FUHPS-FFSF21-DFFFFFNN
% 0.11/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.47 % Preprocessing time : 0.001 s
% 0.11/0.47
% 0.11/0.47 % Proof found!
% 0.11/0.47 % SZS status Unsatisfiable
% 0.11/0.47 % SZS output start CNFRefutation
% See solution above
% 0.11/0.47 % Parsed axioms : 3
% 0.11/0.47 % Removed by relevancy pruning/SinE : 0
% 0.11/0.47 % Initial clauses : 3
% 0.11/0.47 % Removed in clause preprocessing : 0
% 0.11/0.47 % Initial clauses in saturation : 3
% 0.11/0.47 % Processed clauses : 220
% 0.11/0.47 % ...of these trivial : 63
% 0.11/0.47 % ...subsumed : 98
% 0.11/0.47 % ...remaining for further processing : 58
% 0.11/0.47 % Other redundant clauses eliminated : 0
% 0.11/0.47 % Clauses deleted for lack of memory : 0
% 0.11/0.47 % Backward-subsumed : 0
% 0.11/0.47 % Backward-rewritten : 36
% 0.11/0.47 % Generated clauses : 2352
% 0.11/0.47 % ...of the previous two non-redundant : 1946
% 0.11/0.47 % ...aggressively subsumed : 0
% 0.11/0.47 % Contextual simplify-reflections : 0
% 0.11/0.47 % Paramodulations : 2352
% 0.11/0.47 % Factorizations : 0
% 0.11/0.47 % NegExts : 0
% 0.11/0.47 % Equation resolutions : 0
% 0.11/0.47 % Disequality decompositions : 0
% 0.11/0.47 % Total rewrite steps : 2168
% 0.11/0.47 % ...of those cached : 1521
% 0.11/0.47 % Propositional unsat checks : 0
% 0.11/0.47 % Propositional check models : 0
% 0.11/0.47 % Propositional check unsatisfiable : 0
% 0.11/0.47 % Propositional clauses : 0
% 0.11/0.47 % Propositional clauses after purity: 0
% 0.11/0.47 % Propositional unsat core size : 0
% 0.11/0.47 % Propositional preprocessing time : 0.000
% 0.11/0.47 % Propositional encoding time : 0.000
% 0.11/0.47 % Propositional solver time : 0.000
% 0.11/0.47 % Success case prop preproc time : 0.000
% 0.11/0.47 % Success case prop encoding time : 0.000
% 0.11/0.47 % Success case prop solver time : 0.000
% 0.11/0.47 % Current number of processed clauses : 22
% 0.11/0.47 % Positive orientable unit clauses : 17
% 0.11/0.47 % Positive unorientable unit clauses: 5
% 0.11/0.47 % Negative unit clauses : 0
% 0.11/0.47 % Non-unit-clauses : 0
% 0.11/0.47 % Current number of unprocessed clauses: 1443
% 0.11/0.47 % ...number of literals in the above : 1443
% 0.11/0.47 % Current number of archived formulas : 0
% 0.11/0.47 % Current number of archived clauses : 36
% 0.11/0.47 % Clause-clause subsumption calls (NU) : 0
% 0.11/0.47 % Rec. Clause-clause subsumption calls : 0
% 0.11/0.47 % Non-unit clause-clause subsumptions : 0
% 0.11/0.47 % Unit Clause-clause subsumption calls : 35
% 0.11/0.47 % Rewrite failures with RHS unbound : 28
% 0.11/0.47 % BW rewrite match attempts : 279
% 0.11/0.47 % BW rewrite match successes : 161
% 0.11/0.47 % Condensation attempts : 0
% 0.11/0.47 % Condensation successes : 0
% 0.11/0.47 % Termbank termtop insertions : 21810
% 0.11/0.47 % Search garbage collected termcells : 11
% 0.11/0.47
% 0.11/0.47 % -------------------------------------------------
% 0.11/0.47 % User time : 0.016 s
% 0.11/0.47 % System time : 0.001 s
% 0.11/0.47 % Total time : 0.016 s
% 0.11/0.47 % Maximum resident set size: 3356 pages
% 0.11/0.47
% 0.11/0.47 % -------------------------------------------------
% 0.11/0.47 % User time : 0.017 s
% 0.11/0.47 % System time : 0.005 s
% 0.11/0.47 % Total time : 0.022 s
% 0.11/0.47 % Maximum resident set size: 4864 pages
% 0.11/0.47 % E exiting
%------------------------------------------------------------------------------