%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP085-1 : 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 : n014.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 12:37:50 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of clauses : 27 ( 23 unt; 0 nHn; 7 RR)
% Number of literals : 37 ( 36 equ; 16 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3))) = X2,
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_2,axiom,
multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3))) = X2,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(multiply(X2,X1),inverse(multiply(X2,X3))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(multiply(X1,X2),inverse(multiply(multiply(multiply(X3,X1),X4),X2))) = inverse(multiply(X3,X4)),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_5,plain,
inverse(multiply(X1,multiply(X2,inverse(multiply(multiply(X1,X2),X3))))) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,plain,
multiply(multiply(X1,inverse(multiply(X2,X3))),inverse(X1)) = inverse(multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_2]) ).
cnf(c_0_7,plain,
inverse(multiply(multiply(X1,X2),inverse(multiply(X1,multiply(X2,X3))))) = X3,
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_8,plain,
multiply(multiply(X1,X2),inverse(X1)) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_10,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_11,plain,
multiply(multiply(inverse(X1),X2),X1) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_12,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_8]) ).
cnf(c_0_13,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_10]) ).
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,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_13]),c_0_13]) ).
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_14 ).
cnf(c_0_17,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_8]),c_0_10]) ).
cnf(c_0_18,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10]) ).
cnf(c_0_19,negated_conjecture,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)) ),
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)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]),c_0_17]),c_0_17]),c_0_17]),c_0_18]),c_0_17])]) ).
cnf(c_0_20,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_21,plain,
multiply(multiply(X1,X2),X3) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_2]),c_0_10]) ).
cnf(c_0_22,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_21]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP085-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n014.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 19:57:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.42 % Version: 3.5.1
% 0.14/0.42 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % Starting sh5l with 300s (1) cores
% 0.14/0.42 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 2216162 completed with status 0
% 0.14/0.42 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.14/0.42 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.14/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.42 % No SInE strategy applied
% 0.14/0.42 % Search class: FUHPF-FFSF21-MFFFFFNN
% 0.14/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.42 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.14/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.42 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 2216168 completed with status 0
% 0.14/0.42 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.14/0.42 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.14/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.42 % No SInE strategy applied
% 0.14/0.42 % Search class: FUHPF-FFSF21-MFFFFFNN
% 0.14/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.42 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.14/0.42 % Preprocessing time : 0.001 s
% 0.14/0.42
% 0.14/0.42 % Proof found!
% 0.14/0.42 % SZS status Unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation
% See solution above
% 0.14/0.42 % Parsed axioms : 2
% 0.14/0.42 % Removed by relevancy pruning/SinE : 0
% 0.14/0.42 % Initial clauses : 2
% 0.14/0.42 % Removed in clause preprocessing : 0
% 0.14/0.42 % Initial clauses in saturation : 2
% 0.14/0.42 % Processed clauses : 167
% 0.14/0.42 % ...of these trivial : 60
% 0.14/0.42 % ...subsumed : 72
% 0.14/0.42 % ...remaining for further processing : 35
% 0.14/0.42 % Other redundant clauses eliminated : 0
% 0.14/0.42 % Clauses deleted for lack of memory : 0
% 0.14/0.42 % Backward-subsumed : 0
% 0.14/0.42 % Backward-rewritten : 19
% 0.14/0.42 % Generated clauses : 993
% 0.14/0.42 % ...of the previous two non-redundant : 656
% 0.14/0.42 % ...aggressively subsumed : 0
% 0.14/0.42 % Contextual simplify-reflections : 0
% 0.14/0.42 % Paramodulations : 992
% 0.14/0.42 % Factorizations : 0
% 0.14/0.42 % NegExts : 0
% 0.14/0.42 % Equation resolutions : 0
% 0.14/0.42 % Disequality decompositions : 0
% 0.14/0.42 % Total rewrite steps : 766
% 0.14/0.42 % ...of those cached : 559
% 0.14/0.42 % Propositional unsat checks : 0
% 0.14/0.42 % Propositional check models : 0
% 0.14/0.42 % Propositional check unsatisfiable : 0
% 0.14/0.42 % Propositional clauses : 0
% 0.14/0.42 % Propositional clauses after purity: 0
% 0.14/0.42 % Propositional unsat core size : 0
% 0.14/0.42 % Propositional preprocessing time : 0.000
% 0.14/0.42 % Propositional encoding time : 0.000
% 0.14/0.42 % Propositional solver time : 0.000
% 0.14/0.42 % Success case prop preproc time : 0.000
% 0.14/0.42 % Success case prop encoding time : 0.000
% 0.14/0.42 % Success case prop solver time : 0.000
% 0.14/0.42 % Current number of processed clauses : 15
% 0.14/0.42 % Positive orientable unit clauses : 11
% 0.14/0.42 % Positive unorientable unit clauses: 4
% 0.14/0.42 % Negative unit clauses : 0
% 0.14/0.42 % Non-unit-clauses : 0
% 0.14/0.42 % Current number of unprocessed clauses: 437
% 0.14/0.42 % ...number of literals in the above : 437
% 0.14/0.42 % Current number of archived formulas : 0
% 0.14/0.42 % Current number of archived clauses : 20
% 0.14/0.42 % Clause-clause subsumption calls (NU) : 0
% 0.14/0.42 % Rec. Clause-clause subsumption calls : 0
% 0.14/0.42 % Non-unit clause-clause subsumptions : 0
% 0.14/0.42 % Unit Clause-clause subsumption calls : 26
% 0.14/0.42 % Rewrite failures with RHS unbound : 44
% 0.14/0.42 % BW rewrite match attempts : 194
% 0.14/0.42 % BW rewrite match successes : 119
% 0.14/0.42 % Condensation attempts : 0
% 0.14/0.42 % Condensation successes : 0
% 0.14/0.42 % Termbank termtop insertions : 7213
% 0.14/0.42 % Search garbage collected termcells : 11
% 0.14/0.42
% 0.14/0.42 % -------------------------------------------------
% 0.14/0.42 % User time : 0.013 s
% 0.14/0.42 % System time : 0.001 s
% 0.14/0.42 % Total time : 0.014 s
% 0.14/0.42 % Maximum resident set size: 3376 pages
% 0.14/0.42
% 0.14/0.42 % -------------------------------------------------
% 0.14/0.42 % User time : 0.041 s
% 0.14/0.42 % System time : 0.016 s
% 0.14/0.42 % Total time : 0.057 s
% 0.14/0.42 % Maximum resident set size: 4864 pages
% 0.14/0.42 % E exiting
%------------------------------------------------------------------------------