%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP092-1 : 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 : n016.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 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of clauses : 38 ( 32 unt; 0 nHn; 8 RR)
% Number of literals : 53 ( 52 equ; 22 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(single_axiom,axiom,
divide(divide(X1,X2),divide(divide(X1,X3),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(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(c_0_5,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
multiply ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,plain,
divide(X1,divide(identity,X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,axiom,
divide(divide(X1,X2),divide(divide(X1,X3),X2)) = X3,
single_axiom ).
cnf(c_0_9,plain,
divide(X1,identity) = multiply(X1,identity),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_10,plain,
multiply(divide(X1,divide(X1,X2)),identity) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_6]),c_0_9]) ).
cnf(c_0_11,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_12,plain,
multiply(divide(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_6]),c_0_7]) ).
cnf(c_0_13,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,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_15,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_16,plain,
multiply(X1,divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,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_14 ).
cnf(c_0_18,plain,
inverse(X1) = divide(identity,X1),
inference(rw,[status(thm)],[c_0_15,c_0_6]) ).
cnf(c_0_19,plain,
multiply(divide(identity,X1),multiply(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_7]) ).
cnf(c_0_20,plain,
multiply(multiply(X1,X2),divide(identity,X2)) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_21,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_6]) ).
cnf(c_0_22,plain,
divide(X1,multiply(identity,X2)) = multiply(X1,divide(identity,X2)),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_23,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(divide(identity,b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(divide(identity,a1),a1) != multiply(divide(identity,b1),b1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_24,plain,
multiply(divide(identity,X1),X1) = identity,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_25,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_7]),c_0_21]) ).
cnf(c_0_26,plain,
divide(multiply(X1,X2),multiply(divide(X1,X3),X2)) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_7]),c_0_7]) ).
cnf(c_0_27,plain,
multiply(X1,divide(identity,X2)) = divide(X1,X2),
inference(rw,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( multiply(identity,a2) != a2
| 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_23,c_0_24]),c_0_24]),c_0_24])]) ).
cnf(c_0_29,plain,
multiply(multiply(X1,X2),divide(identity,X1)) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_30,plain,
multiply(X1,multiply(divide(X2,X1),X3)) = multiply(X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_26]),c_0_25]) ).
cnf(c_0_31,plain,
divide(multiply(X1,X2),X2) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_27]) ).
cnf(c_0_32,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)],[c_0_28,c_0_21])]) ).
cnf(c_0_33,plain,
divide(multiply(X1,X2),X1) = X2,
inference(rw,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,X2),X3) = multiply(X2,multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,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_32,c_0_25]),c_0_25])]) ).
cnf(c_0_36,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_33]),c_0_34]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP092-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:01:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.43 % Version: 3.5.1
% 0.14/0.43 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 667398 completed with status 0
% 0.14/0.43 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.14/0.43 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.14/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.43 % No SInE strategy applied
% 0.14/0.43 % Search class: FUHPM-FFSF21-MFFFFFNN
% 0.14/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.43 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.14/0.43 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.14/0.43 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 0.14/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.43 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 667403 completed with status 0
% 0.14/0.43 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.14/0.43 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.14/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.43 % No SInE strategy applied
% 0.14/0.43 % Search class: FUHPM-FFSF21-MFFFFFNN
% 0.14/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.43 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.14/0.43 % Preprocessing time : 0.001 s
% 0.14/0.43
% 0.14/0.43 % Proof found!
% 0.14/0.43 % SZS status Unsatisfiable
% 0.14/0.43 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43 % Parsed axioms : 5
% 0.14/0.43 % Removed by relevancy pruning/SinE : 0
% 0.14/0.43 % Initial clauses : 5
% 0.14/0.43 % Removed in clause preprocessing : 0
% 0.14/0.43 % Initial clauses in saturation : 5
% 0.14/0.43 % Processed clauses : 110
% 0.14/0.43 % ...of these trivial : 38
% 0.14/0.43 % ...subsumed : 20
% 0.14/0.43 % ...remaining for further processing : 52
% 0.14/0.43 % Other redundant clauses eliminated : 0
% 0.14/0.43 % Clauses deleted for lack of memory : 0
% 0.14/0.43 % Backward-subsumed : 0
% 0.14/0.43 % Backward-rewritten : 27
% 0.14/0.43 % Generated clauses : 662
% 0.14/0.43 % ...of the previous two non-redundant : 301
% 0.14/0.43 % ...aggressively subsumed : 0
% 0.14/0.43 % Contextual simplify-reflections : 0
% 0.14/0.43 % Paramodulations : 662
% 0.14/0.43 % Factorizations : 0
% 0.14/0.43 % NegExts : 0
% 0.14/0.43 % Equation resolutions : 0
% 0.14/0.43 % Disequality decompositions : 0
% 0.14/0.43 % Total rewrite steps : 827
% 0.14/0.43 % ...of those cached : 652
% 0.14/0.43 % Propositional unsat checks : 0
% 0.14/0.43 % Propositional check models : 0
% 0.14/0.43 % Propositional check unsatisfiable : 0
% 0.14/0.43 % Propositional clauses : 0
% 0.14/0.43 % Propositional clauses after purity: 0
% 0.14/0.43 % Propositional unsat core size : 0
% 0.14/0.43 % Propositional preprocessing time : 0.000
% 0.14/0.43 % Propositional encoding time : 0.000
% 0.14/0.43 % Propositional solver time : 0.000
% 0.14/0.43 % Success case prop preproc time : 0.000
% 0.14/0.43 % Success case prop encoding time : 0.000
% 0.14/0.43 % Success case prop solver time : 0.000
% 0.14/0.43 % Current number of processed clauses : 25
% 0.14/0.43 % Positive orientable unit clauses : 23
% 0.14/0.43 % Positive unorientable unit clauses: 2
% 0.14/0.43 % Negative unit clauses : 0
% 0.14/0.43 % Non-unit-clauses : 0
% 0.14/0.43 % Current number of unprocessed clauses: 156
% 0.14/0.43 % ...number of literals in the above : 156
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 27
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 0
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 0
% 0.14/0.43 % Non-unit clause-clause subsumptions : 0
% 0.14/0.43 % Unit Clause-clause subsumption calls : 3
% 0.14/0.43 % Rewrite failures with RHS unbound : 0
% 0.14/0.43 % BW rewrite match attempts : 78
% 0.14/0.43 % BW rewrite match successes : 67
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 4527
% 0.14/0.43 % Search garbage collected termcells : 11
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.008 s
% 0.14/0.43 % System time : 0.003 s
% 0.14/0.43 % Total time : 0.011 s
% 0.14/0.43 % Maximum resident set size: 3380 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.041 s
% 0.14/0.43 % System time : 0.013 s
% 0.14/0.43 % Total time : 0.054 s
% 0.14/0.43 % Maximum resident set size: 4608 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------