%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP086-1 : 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 : n007.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 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of clauses : 26 ( 22 unt; 0 nHn; 7 RR)
% Number of literals : 36 ( 35 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 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 : 51 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,multiply(multiply(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(X1,multiply(multiply(X2,X3),inverse(multiply(X1,X3)))) = X2,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,multiply(multiply(X2,X3),inverse(multiply(X4,X3))))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_2]) ).
cnf(c_0_5,plain,
multiply(X1,multiply(X2,inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_4]),c_0_4]) ).
cnf(c_0_6,plain,
multiply(multiply(X1,X2),multiply(X3,inverse(multiply(X3,X2)))) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_7,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,multiply(X2,inverse(X3)))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_4]) ).
cnf(c_0_8,plain,
multiply(multiply(X1,X2),multiply(X3,inverse(X1))) = multiply(X3,X2),
inference(spm,[status(thm)],[c_0_3,c_0_6]) ).
cnf(c_0_9,plain,
multiply(X1,multiply(multiply(X2,X3),inverse(X2))) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_7,c_0_2]) ).
cnf(c_0_10,plain,
multiply(multiply(X1,X2),X3) = multiply(multiply(X1,X3),X2),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
multiply(X1,multiply(multiply(X2,inverse(X1)),X3)) = multiply(X2,X3),
inference(spm,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_12,plain,
multiply(X1,inverse(multiply(X1,inverse(X2)))) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_11]) ).
cnf(c_0_13,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_14,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_12]),c_0_10]) ).
cnf(c_0_15,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_13 ).
cnf(c_0_16,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_5,c_0_14]) ).
cnf(c_0_17,plain,
multiply(multiply(X1,X2),inverse(X1)) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_18,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_15,c_0_16]),c_0_16]),c_0_16]),c_0_16]),c_0_16]),c_0_4]),c_0_16])]) ).
cnf(c_0_19,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_20,plain,
multiply(multiply(X1,X2),X3) = multiply(X2,multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(sr,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_20]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_20]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP086-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.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 19:55:05 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.44 % Version: 3.5.1
% 0.11/0.44 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 3444819 completed with status 0
% 0.11/0.44 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.11/0.44 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.11/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.44 % No SInE strategy applied
% 0.11/0.44 % Search class: FUHPF-FFSF21-MFFFFFNN
% 0.11/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.44 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.11/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.44 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 3444825 completed with status 0
% 0.11/0.44 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.11/0.44 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.11/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.44 % No SInE strategy applied
% 0.11/0.44 % Search class: FUHPF-FFSF21-MFFFFFNN
% 0.11/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.44 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.11/0.44 % Preprocessing time : 0.001 s
% 0.11/0.44
% 0.11/0.44 % Proof found!
% 0.11/0.44 % SZS status Unsatisfiable
% 0.11/0.44 % SZS output start CNFRefutation
% See solution above
% 0.11/0.44 % Parsed axioms : 2
% 0.11/0.44 % Removed by relevancy pruning/SinE : 0
% 0.11/0.44 % Initial clauses : 2
% 0.11/0.44 % Removed in clause preprocessing : 0
% 0.11/0.44 % Initial clauses in saturation : 2
% 0.11/0.44 % Processed clauses : 182
% 0.11/0.44 % ...of these trivial : 59
% 0.11/0.44 % ...subsumed : 87
% 0.11/0.44 % ...remaining for further processing : 36
% 0.11/0.44 % Other redundant clauses eliminated : 0
% 0.11/0.44 % Clauses deleted for lack of memory : 0
% 0.11/0.44 % Backward-subsumed : 0
% 0.11/0.44 % Backward-rewritten : 19
% 0.11/0.44 % Generated clauses : 1081
% 0.11/0.44 % ...of the previous two non-redundant : 685
% 0.11/0.44 % ...aggressively subsumed : 0
% 0.11/0.44 % Contextual simplify-reflections : 0
% 0.11/0.44 % Paramodulations : 1080
% 0.11/0.44 % Factorizations : 0
% 0.11/0.44 % NegExts : 0
% 0.11/0.44 % Equation resolutions : 0
% 0.11/0.44 % Disequality decompositions : 0
% 0.11/0.44 % Total rewrite steps : 846
% 0.11/0.44 % ...of those cached : 587
% 0.11/0.44 % Propositional unsat checks : 0
% 0.11/0.44 % Propositional check models : 0
% 0.11/0.44 % Propositional check unsatisfiable : 0
% 0.11/0.44 % Propositional clauses : 0
% 0.11/0.44 % Propositional clauses after purity: 0
% 0.11/0.44 % Propositional unsat core size : 0
% 0.11/0.44 % Propositional preprocessing time : 0.000
% 0.11/0.44 % Propositional encoding time : 0.000
% 0.11/0.44 % Propositional solver time : 0.000
% 0.11/0.44 % Success case prop preproc time : 0.000
% 0.11/0.44 % Success case prop encoding time : 0.000
% 0.11/0.44 % Success case prop solver time : 0.000
% 0.11/0.44 % Current number of processed clauses : 16
% 0.11/0.44 % Positive orientable unit clauses : 12
% 0.11/0.44 % Positive unorientable unit clauses: 4
% 0.11/0.44 % Negative unit clauses : 0
% 0.11/0.44 % Non-unit-clauses : 0
% 0.11/0.44 % Current number of unprocessed clauses: 451
% 0.11/0.44 % ...number of literals in the above : 451
% 0.11/0.44 % Current number of archived formulas : 0
% 0.11/0.44 % Current number of archived clauses : 20
% 0.11/0.44 % Clause-clause subsumption calls (NU) : 0
% 0.11/0.44 % Rec. Clause-clause subsumption calls : 0
% 0.11/0.44 % Non-unit clause-clause subsumptions : 0
% 0.11/0.44 % Unit Clause-clause subsumption calls : 30
% 0.11/0.44 % Rewrite failures with RHS unbound : 40
% 0.11/0.44 % BW rewrite match attempts : 232
% 0.11/0.44 % BW rewrite match successes : 152
% 0.11/0.44 % Condensation attempts : 0
% 0.11/0.44 % Condensation successes : 0
% 0.11/0.44 % Termbank termtop insertions : 7693
% 0.11/0.44 % Search garbage collected termcells : 11
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.010 s
% 0.11/0.44 % System time : 0.004 s
% 0.11/0.44 % Total time : 0.014 s
% 0.11/0.44 % Maximum resident set size: 3632 pages
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.050 s
% 0.11/0.44 % System time : 0.016 s
% 0.11/0.44 % Total time : 0.066 s
% 0.11/0.44 % Maximum resident set size: 4864 pages
% 0.11/0.44 % E exiting
%------------------------------------------------------------------------------