%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP088-1 : 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 : n015.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 12:37:51 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of clauses : 44 ( 35 unt; 0 nHn; 11 RR)
% Number of literals : 66 ( 65 equ; 32 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(single_axiom,axiom,
divide(X1,divide(X2,divide(X3,divide(X1,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(c_0_4,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
multiply ).
cnf(c_0_5,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_6,axiom,
divide(X1,divide(X2,divide(X3,divide(X1,X2)))) = X3,
single_axiom ).
cnf(c_0_7,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_8,plain,
inverse(divide(X1,multiply(X2,X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_5]),c_0_7]) ).
cnf(c_0_9,plain,
divide(X1,divide(divide(X2,divide(X3,X1)),X2)) = X3,
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_10,plain,
inverse(inverse(multiply(X1,divide(X2,X2)))) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_11,plain,
multiply(X1,divide(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_5]),c_0_7]) ).
cnf(c_0_12,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_13,plain,
divide(multiply(inverse(X1),X1),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_14,plain,
multiply(divide(X1,X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_15,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,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_12 ).
cnf(c_0_17,plain,
multiply(multiply(inverse(X1),X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_7,c_0_13]) ).
cnf(c_0_18,plain,
multiply(divide(X1,X1),X2) = X2,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( inverse(inverse(a2)) != a2
| multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
inverse(multiply(X1,inverse(X1))) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_17]),c_0_7]) ).
cnf(c_0_21,plain,
divide(X1,divide(divide(X2,divide(X3,divide(X1,X2))),divide(X4,X3))) = X4,
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_22,plain,
divide(X1,divide(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( multiply(divide(X1,X1),a2) != a2
| multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_24,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_20,c_0_20]) ).
cnf(c_0_25,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_5]),c_0_7]),c_0_11]) ).
cnf(c_0_26,negated_conjecture,
( multiply(divide(X1,X1),a2) != a2
| multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(sr,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
divide(inverse(divide(X1,X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_28,plain,
divide(X1,multiply(X1,X2)) = inverse(X2),
inference(spm,[status(thm)],[c_0_25,c_0_7]) ).
cnf(c_0_29,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_30,plain,
multiply(divide(X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(inverse(divide(X1,X1))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_28,c_0_11]) ).
cnf(c_0_33,plain,
multiply(inverse(X1),X2) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(inverse(multiply(inverse(X1),X1))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_31,c_0_7]) ).
cnf(c_0_35,plain,
divide(inverse(X1),X2) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_7]) ).
cnf(c_0_36,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_15]),c_0_7]) ).
cnf(c_0_37,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(spm,[status(thm)],[c_0_7,c_0_15]) ).
cnf(c_0_38,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_15]),c_0_17]),c_0_15])]) ).
cnf(c_0_39,plain,
multiply(X1,multiply(X2,divide(X3,multiply(X1,X2)))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_35]),c_0_36]),c_0_7]) ).
cnf(c_0_40,plain,
divide(multiply(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_30]),c_0_7]) ).
cnf(c_0_41,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_36]),c_0_36])]) ).
cnf(c_0_42,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP088-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:00:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.43 % Version: 3.5.1
% 0.13/0.43 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.13/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.43 % Starting sh5l with 300s (1) cores
% 0.13/0.43 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 3798016 completed with status 0
% 0.13/0.43 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.13/0.43 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.13/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.43 % No SInE strategy applied
% 0.13/0.43 % Search class: FUHPS-FFSF21-MFFFFFNN
% 0.13/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.43 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.43 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 3798023 completed with status 0
% 0.13/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.13/0.43 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.13/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.43 % No SInE strategy applied
% 0.13/0.43 % Search class: FUHPS-FFSF21-MFFFFFNN
% 0.13/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.43 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.43 % Preprocessing time : 0.001 s
% 0.13/0.43 % Presaturation interreduction done
% 0.13/0.43
% 0.13/0.43 % Proof found!
% 0.13/0.43 % SZS status Unsatisfiable
% 0.13/0.43 % SZS output start CNFRefutation
% See solution above
% 0.13/0.43 % Parsed axioms : 4
% 0.13/0.43 % Removed by relevancy pruning/SinE : 0
% 0.13/0.43 % Initial clauses : 4
% 0.13/0.43 % Removed in clause preprocessing : 0
% 0.13/0.43 % Initial clauses in saturation : 4
% 0.13/0.43 % Processed clauses : 145
% 0.13/0.43 % ...of these trivial : 32
% 0.13/0.43 % ...subsumed : 50
% 0.13/0.43 % ...remaining for further processing : 63
% 0.13/0.43 % Other redundant clauses eliminated : 0
% 0.13/0.43 % Clauses deleted for lack of memory : 0
% 0.13/0.43 % Backward-subsumed : 3
% 0.13/0.43 % Backward-rewritten : 32
% 0.13/0.43 % Generated clauses : 887
% 0.13/0.43 % ...of the previous two non-redundant : 599
% 0.13/0.43 % ...aggressively subsumed : 0
% 0.13/0.43 % Contextual simplify-reflections : 0
% 0.13/0.43 % Paramodulations : 885
% 0.13/0.43 % Factorizations : 0
% 0.13/0.43 % NegExts : 0
% 0.13/0.43 % Equation resolutions : 0
% 0.13/0.43 % Disequality decompositions : 0
% 0.13/0.43 % Total rewrite steps : 783
% 0.13/0.43 % ...of those cached : 543
% 0.13/0.43 % Propositional unsat checks : 0
% 0.13/0.43 % Propositional check models : 0
% 0.13/0.43 % Propositional check unsatisfiable : 0
% 0.13/0.43 % Propositional clauses : 0
% 0.13/0.43 % Propositional clauses after purity: 0
% 0.13/0.43 % Propositional unsat core size : 0
% 0.13/0.43 % Propositional preprocessing time : 0.000
% 0.13/0.43 % Propositional encoding time : 0.000
% 0.13/0.43 % Propositional solver time : 0.000
% 0.13/0.43 % Success case prop preproc time : 0.000
% 0.13/0.43 % Success case prop encoding time : 0.000
% 0.13/0.43 % Success case prop solver time : 0.000
% 0.13/0.43 % Current number of processed clauses : 22
% 0.13/0.43 % Positive orientable unit clauses : 19
% 0.13/0.43 % Positive unorientable unit clauses: 3
% 0.13/0.43 % Negative unit clauses : 0
% 0.13/0.43 % Non-unit-clauses : 0
% 0.13/0.43 % Current number of unprocessed clauses: 230
% 0.13/0.43 % ...number of literals in the above : 230
% 0.13/0.43 % Current number of archived formulas : 0
% 0.13/0.43 % Current number of archived clauses : 41
% 0.13/0.43 % Clause-clause subsumption calls (NU) : 57
% 0.13/0.43 % Rec. Clause-clause subsumption calls : 17
% 0.13/0.43 % Non-unit clause-clause subsumptions : 17
% 0.13/0.43 % Unit Clause-clause subsumption calls : 20
% 0.13/0.43 % Rewrite failures with RHS unbound : 88
% 0.13/0.43 % BW rewrite match attempts : 165
% 0.13/0.43 % BW rewrite match successes : 87
% 0.13/0.43 % Condensation attempts : 0
% 0.13/0.43 % Condensation successes : 0
% 0.13/0.43 % Termbank termtop insertions : 6769
% 0.13/0.43 % Search garbage collected termcells : 11
% 0.13/0.43
% 0.13/0.43 % -------------------------------------------------
% 0.13/0.43 % User time : 0.009 s
% 0.13/0.43 % System time : 0.001 s
% 0.13/0.43 % Total time : 0.010 s
% 0.13/0.43 % Maximum resident set size: 3636 pages
% 0.13/0.43
% 0.13/0.43 % -------------------------------------------------
% 0.13/0.43 % User time : 0.037 s
% 0.13/0.43 % System time : 0.012 s
% 0.13/0.43 % Total time : 0.049 s
% 0.13/0.43 % Maximum resident set size: 4864 pages
% 0.13/0.43 % E exiting
%------------------------------------------------------------------------------