%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP091-1 : 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 : n008.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 12:41:46 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of clauses : 48 ( 42 unt; 0 nHn; 9 RR)
% Number of literals : 63 ( 62 equ; 23 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 : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 81 ( 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(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(single_axiom,axiom,
divide(divide(X1,divide(divide(X1,X2),X3)),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(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox2/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,axiom,
divide(divide(X1,divide(divide(X1,X2),X3)),X2) = X3,
single_axiom ).
cnf(c_0_8,plain,
divide(X1,divide(identity,X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
divide(multiply(X1,X2),X1) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_8]) ).
cnf(c_0_10,plain,
multiply(divide(identity,X1),X1) = identity,
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_11,plain,
multiply(identity,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_8]) ).
cnf(c_0_12,plain,
divide(X1,identity) = multiply(X1,identity),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_13,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_11]),c_0_12]) ).
cnf(c_0_14,plain,
divide(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_14]),c_0_12]),c_0_13]) ).
cnf(c_0_16,plain,
divide(multiply(X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_17,plain,
multiply(multiply(X1,divide(identity,X2)),X2) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_16]) ).
cnf(c_0_18,plain,
multiply(multiply(divide(identity,X1),X2),X1) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_19,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_8]),c_0_11]) ).
cnf(c_0_20,plain,
divide(X1,multiply(identity,X2)) = multiply(X1,divide(identity,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_21,plain,
multiply(X1,multiply(X2,divide(identity,X1))) = X2,
inference(rw,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_22,plain,
multiply(X1,divide(identity,X2)) = divide(X1,X2),
inference(rw,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_23,plain,
divide(X1,multiply(X1,X2)) = divide(identity,X2),
inference(spm,[status(thm)],[c_0_15,c_0_8]) ).
cnf(c_0_24,plain,
multiply(X1,divide(X2,X1)) = X2,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
divide(identity,divide(X1,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
multiply(divide(X1,X2),divide(X2,X1)) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,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_28,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_29,plain,
multiply(multiply(X1,X2),divide(divide(identity,X2),X1)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_8]),c_0_19]) ).
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_27 ).
cnf(c_0_31,plain,
inverse(X1) = divide(identity,X1),
inference(rw,[status(thm)],[c_0_28,c_0_6]) ).
cnf(c_0_32,plain,
multiply(multiply(X1,X2),divide(divide(identity,X1),X2)) = identity,
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_33,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_30,c_0_31]),c_0_31]),c_0_31]) ).
cnf(c_0_34,plain,
divide(multiply(X1,X2),multiply(X2,X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_25]),c_0_8]),c_0_11]) ).
cnf(c_0_35,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_33,c_0_10]),c_0_10]),c_0_10])]) ).
cnf(c_0_36,plain,
divide(multiply(multiply(X1,X2),X3),multiply(X2,X1)) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_34]),c_0_8]) ).
cnf(c_0_37,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_35,c_0_11])]) ).
cnf(c_0_38,plain,
multiply(X1,divide(X2,divide(multiply(X2,X1),X3))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_7]),c_0_8]),c_0_19]) ).
cnf(c_0_39,plain,
divide(X1,multiply(X2,X1)) = divide(identity,X2),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_40,plain,
divide(multiply(X1,multiply(X2,X3)),multiply(X3,X2)) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_19]) ).
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_37,c_0_19]),c_0_19])]) ).
cnf(c_0_42,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_8]) ).
cnf(c_0_43,plain,
multiply(multiply(X1,X2),X3) = multiply(X3,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_40]) ).
cnf(c_0_44,plain,
multiply(multiply(X1,X2),X3) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_23]),c_0_8]) ).
cnf(c_0_45,negated_conjecture,
multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X1,X2)),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP091-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 19:57:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.15/0.45 % Version: 3.5.1
% 0.15/0.45 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.15/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.45 % Starting sh5l with 300s (1) cores
% 0.15/0.45 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 3478475 completed with status 0
% 0.15/0.45 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.15/0.45 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.15/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.45 % No SInE strategy applied
% 0.15/0.45 % Search class: FUHPM-FFSF21-MFFFFFNN
% 0.15/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.45 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.15/0.45 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.15/0.45 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 0.15/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.45 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 3478480 completed with status 0
% 0.15/0.45 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.15/0.45 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.15/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.45 % No SInE strategy applied
% 0.15/0.45 % Search class: FUHPM-FFSF21-MFFFFFNN
% 0.15/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.45 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.15/0.45 % Preprocessing time : 0.001 s
% 0.15/0.45
% 0.15/0.45 % Proof found!
% 0.15/0.45 % SZS status Unsatisfiable
% 0.15/0.45 % SZS output start CNFRefutation
% See solution above
% 0.15/0.45 % Parsed axioms : 5
% 0.15/0.45 % Removed by relevancy pruning/SinE : 0
% 0.15/0.45 % Initial clauses : 5
% 0.15/0.45 % Removed in clause preprocessing : 0
% 0.15/0.45 % Initial clauses in saturation : 5
% 0.15/0.45 % Processed clauses : 144
% 0.15/0.45 % ...of these trivial : 39
% 0.15/0.45 % ...subsumed : 53
% 0.15/0.45 % ...remaining for further processing : 52
% 0.15/0.45 % Other redundant clauses eliminated : 0
% 0.15/0.45 % Clauses deleted for lack of memory : 0
% 0.15/0.45 % Backward-subsumed : 0
% 0.15/0.45 % Backward-rewritten : 26
% 0.15/0.45 % Generated clauses : 802
% 0.15/0.45 % ...of the previous two non-redundant : 389
% 0.15/0.45 % ...aggressively subsumed : 0
% 0.15/0.45 % Contextual simplify-reflections : 0
% 0.15/0.45 % Paramodulations : 802
% 0.15/0.45 % Factorizations : 0
% 0.15/0.45 % NegExts : 0
% 0.15/0.45 % Equation resolutions : 0
% 0.15/0.45 % Disequality decompositions : 0
% 0.15/0.45 % Total rewrite steps : 1018
% 0.15/0.45 % ...of those cached : 799
% 0.15/0.45 % Propositional unsat checks : 0
% 0.15/0.45 % Propositional check models : 0
% 0.15/0.45 % Propositional check unsatisfiable : 0
% 0.15/0.45 % Propositional clauses : 0
% 0.15/0.45 % Propositional clauses after purity: 0
% 0.15/0.45 % Propositional unsat core size : 0
% 0.15/0.45 % Propositional preprocessing time : 0.000
% 0.15/0.45 % Propositional encoding time : 0.000
% 0.15/0.45 % Propositional solver time : 0.000
% 0.15/0.45 % Success case prop preproc time : 0.000
% 0.15/0.45 % Success case prop encoding time : 0.000
% 0.15/0.45 % Success case prop solver time : 0.000
% 0.15/0.45 % Current number of processed clauses : 26
% 0.15/0.45 % Positive orientable unit clauses : 23
% 0.15/0.45 % Positive unorientable unit clauses: 3
% 0.15/0.45 % Negative unit clauses : 0
% 0.15/0.45 % Non-unit-clauses : 0
% 0.15/0.45 % Current number of unprocessed clauses: 212
% 0.15/0.45 % ...number of literals in the above : 212
% 0.15/0.45 % Current number of archived formulas : 0
% 0.15/0.45 % Current number of archived clauses : 26
% 0.15/0.45 % Clause-clause subsumption calls (NU) : 0
% 0.15/0.45 % Rec. Clause-clause subsumption calls : 0
% 0.15/0.45 % Non-unit clause-clause subsumptions : 0
% 0.15/0.45 % Unit Clause-clause subsumption calls : 3
% 0.15/0.45 % Rewrite failures with RHS unbound : 0
% 0.15/0.45 % BW rewrite match attempts : 89
% 0.15/0.45 % BW rewrite match successes : 80
% 0.15/0.45 % Condensation attempts : 0
% 0.15/0.45 % Condensation successes : 0
% 0.15/0.45 % Termbank termtop insertions : 5467
% 0.15/0.45 % Search garbage collected termcells : 11
% 0.15/0.45
% 0.15/0.45 % -------------------------------------------------
% 0.15/0.45 % User time : 0.008 s
% 0.15/0.45 % System time : 0.004 s
% 0.15/0.45 % Total time : 0.012 s
% 0.15/0.45 % Maximum resident set size: 3636 pages
% 0.15/0.45
% 0.15/0.45 % -------------------------------------------------
% 0.15/0.45 % User time : 0.045 s
% 0.15/0.45 % System time : 0.013 s
% 0.15/0.45 % Total time : 0.059 s
% 0.15/0.45 % Maximum resident set size: 4864 pages
% 0.15/0.45 % E exiting
%------------------------------------------------------------------------------