%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP090-1 : 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 : n002.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 0.28s 0.62s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of clauses : 36 ( 33 unt; 0 nHn; 5 RR)
% Number of literals : 45 ( 44 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 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 : 70 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(single_axiom,axiom,
divide(divide(X1,divide(X2,X3)),divide(X1,X2)) = X3,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_4,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_5,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
multiply ).
cnf(c_0_6,axiom,
divide(divide(X1,divide(X2,X3)),divide(X1,X2)) = X3,
single_axiom ).
cnf(c_0_7,plain,
divide(inverse(divide(X1,X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_8,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_9,plain,
inverse(divide(divide(X1,X2),X1)) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_10,plain,
divide(inverse(multiply(inverse(X1),X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
multiply(divide(X1,X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_12,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_4]) ).
cnf(c_0_13,plain,
multiply(inverse(divide(X1,X2)),X1) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_10]),c_0_10]),c_0_8]) ).
cnf(c_0_14,plain,
multiply(divide(X1,X1),X2) = X2,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
multiply(X1,divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_16,plain,
divide(X1,divide(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
divide(X1,divide(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_16]) ).
cnf(c_0_18,plain,
multiply(divide(X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_19,plain,
divide(multiply(X1,X2),X1) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_16]),c_0_4]),c_0_8]) ).
cnf(c_0_20,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_22,plain,
divide(divide(X1,X2),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_23,plain,
multiply(inverse(X1),X2) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_25,plain,
divide(X1,divide(X2,X3)) = multiply(divide(X1,X2),X3),
inference(spm,[status(thm)],[c_0_15,c_0_6]) ).
cnf(c_0_26,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_27,plain,
multiply(X1,divide(X2,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_4]),c_0_12]) ).
cnf(c_0_28,plain,
multiply(divide(X1,X2),X3) = multiply(divide(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_29,plain,
multiply(divide(X1,X2),X3) = multiply(X1,divide(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_24]),c_0_25]) ).
cnf(c_0_30,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_26 ).
cnf(c_0_31,plain,
divide(X1,X1) = divide(X2,X2),
inference(spm,[status(thm)],[c_0_14,c_0_27]) ).
cnf(c_0_32,plain,
multiply(X1,divide(X2,X3)) = multiply(X2,divide(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
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(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_30,c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20])]),c_0_21]),c_0_21]),c_0_21]),c_0_27])]),c_0_31]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_8]),c_0_8]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP090-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n002.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 20 19:59:46 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.53 Running first-order theorem proving
% 0.28/0.53 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
% 0.28/0.61 % Version: 3.5.1
% 0.28/0.61 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.28/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.61 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.28/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.61 % Starting sh5l with 300s (1) cores
% 0.28/0.61 % new_bool_1 with pid 1571224 completed with status 0
% 0.28/0.61 % Result found by new_bool_1
% 0.28/0.61 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.28/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.61 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.28/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.61 % Search class: FUHPS-FFSF21-MFFFFFNN
% 0.28/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.28/0.61 % SubtermCWHack with pid 1571231 completed with status 0
% 0.28/0.61 % Result found by SubtermCWHack
% 0.28/0.62 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.28/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.62 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.28/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.62 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.62 % Search class: FUHPS-FFSF21-MFFFFFNN
% 0.28/0.62 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.62 % Starting SubtermCWHack with 31s (1) cores
% 0.28/0.62 % Preprocessing time : 0.002 s
% 0.28/0.62
% 0.28/0.62 % Proof found!
% 0.28/0.62 % SZS status Unsatisfiable
% 0.28/0.62 % SZS output start CNFRefutation
% See solution above
% 0.28/0.62 % Parsed axioms : 4
% 0.28/0.62 % Removed by relevancy pruning/SinE : 0
% 0.28/0.62 % Initial clauses : 4
% 0.28/0.62 % Removed in clause preprocessing : 0
% 0.28/0.62 % Initial clauses in saturation : 4
% 0.28/0.62 % Processed clauses : 196
% 0.28/0.62 % ...of these trivial : 54
% 0.28/0.62 % ...subsumed : 81
% 0.28/0.62 % ...remaining for further processing : 61
% 0.28/0.62 % Other redundant clauses eliminated : 0
% 0.28/0.62 % Clauses deleted for lack of memory : 0
% 0.28/0.62 % Backward-subsumed : 0
% 0.28/0.62 % Backward-rewritten : 34
% 0.28/0.62 % Generated clauses : 1400
% 0.28/0.62 % ...of the previous two non-redundant : 905
% 0.28/0.62 % ...aggressively subsumed : 0
% 0.28/0.62 % Contextual simplify-reflections : 0
% 0.28/0.62 % Paramodulations : 1400
% 0.28/0.62 % Factorizations : 0
% 0.28/0.62 % NegExts : 0
% 0.28/0.62 % Equation resolutions : 0
% 0.28/0.62 % Disequality decompositions : 0
% 0.28/0.62 % Total rewrite steps : 2035
% 0.28/0.62 % ...of those cached : 1377
% 0.28/0.62 % Propositional unsat checks : 0
% 0.28/0.62 % Propositional check models : 0
% 0.28/0.62 % Propositional check unsatisfiable : 0
% 0.28/0.62 % Propositional clauses : 0
% 0.28/0.62 % Propositional clauses after purity: 0
% 0.28/0.62 % Propositional unsat core size : 0
% 0.28/0.62 % Propositional preprocessing time : 0.000
% 0.28/0.62 % Propositional encoding time : 0.000
% 0.28/0.62 % Propositional solver time : 0.000
% 0.28/0.62 % Success case prop preproc time : 0.000
% 0.28/0.62 % Success case prop encoding time : 0.000
% 0.28/0.62 % Success case prop solver time : 0.000
% 0.28/0.62 % Current number of processed clauses : 27
% 0.28/0.62 % Positive orientable unit clauses : 22
% 0.28/0.62 % Positive unorientable unit clauses: 5
% 0.28/0.62 % Negative unit clauses : 0
% 0.28/0.62 % Non-unit-clauses : 0
% 0.28/0.62 % Current number of unprocessed clauses: 323
% 0.28/0.62 % ...number of literals in the above : 323
% 0.28/0.62 % Current number of archived formulas : 0
% 0.28/0.62 % Current number of archived clauses : 34
% 0.28/0.62 % Clause-clause subsumption calls (NU) : 0
% 0.28/0.62 % Rec. Clause-clause subsumption calls : 0
% 0.28/0.62 % Non-unit clause-clause subsumptions : 0
% 0.28/0.62 % Unit Clause-clause subsumption calls : 10
% 0.28/0.62 % Rewrite failures with RHS unbound : 52
% 0.28/0.62 % BW rewrite match attempts : 142
% 0.28/0.62 % BW rewrite match successes : 94
% 0.28/0.62 % Condensation attempts : 0
% 0.28/0.62 % Condensation successes : 0
% 0.28/0.62 % Termbank termtop insertions : 9420
% 0.28/0.62 % Search garbage collected termcells : 11
% 0.28/0.62
% 0.28/0.62 % -------------------------------------------------
% 0.28/0.62 % User time : 0.024 s
% 0.28/0.62 % System time : 0.003 s
% 0.28/0.62 % Total time : 0.027 s
% 0.28/0.62 % Maximum resident set size: 3632 pages
% 0.28/0.62
% 0.28/0.62 % -------------------------------------------------
% 0.28/0.62 % User time : 0.026 s
% 0.28/0.62 % System time : 0.010 s
% 0.28/0.62 % Total time : 0.036 s
% 0.28/0.62 % Maximum resident set size: 4864 pages
% 0.28/0.62 % E exiting
%------------------------------------------------------------------------------