%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:37:26 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.64s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 44 ( 26 unt; 0 nHn; 31 RR)
% Number of literals : 79 ( 15 equ; 38 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(associativity2,axiom,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(associativity1,axiom,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity1) ).
cnf(inverse_b_multiply_inverse_a_is_d,hypothesis,
product(inverse(b),inverse(a),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_b_multiply_inverse_a_is_d) ).
cnf(a_multiply_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_multiply_b_is_c) ).
cnf(prove_c_inverse_equals_d,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_inverse_equals_d) ).
cnf(c_0_10,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_11,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity2]) ).
cnf(c_0_12,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_10 ).
cnf(c_0_13,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_14,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_11 ).
cnf(c_0_15,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_16,plain,
( ~ product(X2,identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_18,plain,
( ~ product(X4,identity,X3)
| ~ product(X4,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_21,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity1]) ).
cnf(c_0_22,plain,
( ~ product(X3,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_19]) ).
cnf(c_0_23,plain,
( ~ product(identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_24,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_21 ).
cnf(c_0_25,hypothesis,
product(inverse(b),inverse(a),d),
inverse_b_multiply_inverse_a_is_d ).
cnf(c_0_26,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_27,plain,
product(identity,X1,inverse(inverse(X1))),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_28,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_29,plain,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_30,hypothesis,
product(d,a,inverse(b)),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_31,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_32,hypothesis,
( ~ product(X1,d,identity)
| product(X1,inverse(b),a) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
product(multiply(X1,inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_34,hypothesis,
product(a,b,c),
a_multiply_b_is_c ).
cnf(c_0_35,plain,
( ~ product(X3,X2,X1)
| product(X1,inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_31]) ).
cnf(c_0_36,hypothesis,
product(inverse(d),inverse(b),a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_28]) ).
cnf(c_0_37,hypothesis,
( ~ product(a,b,X1)
| X1 = c ),
inference(spm,[status(thm)],[c_0_12,c_0_34]) ).
cnf(c_0_38,hypothesis,
product(a,b,inverse(d)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_31]) ).
cnf(c_0_39,hypothesis,
multiply(a,b) = c,
inference(spm,[status(thm)],[c_0_37,c_0_17]) ).
cnf(c_0_40,negated_conjecture,
inverse(c) != d,
inference(fof_simplification,[status(thm)],[prove_c_inverse_equals_d]) ).
cnf(c_0_41,hypothesis,
inverse(d) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_38]),c_0_39]) ).
cnf(c_0_42,negated_conjecture,
inverse(c) != d,
c_0_40 ).
cnf(c_0_43,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.57 % Computer : n026.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Sun Sep 20 19:56:24 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.62 Running first-order theorem proving
% 0.10/0.62 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
% 0.14/0.64 % Version: 3.5.1
% 0.14/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.64 % Starting sh5l with 300s (1) cores
% 0.14/0.64 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 458337 completed with status 0
% 0.14/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.64 % No SInE strategy applied
% 0.14/0.64 % Search class: FHUSM-FFSF21-SFFFFFNN
% 0.14/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 136s (1) cores
% 0.14/0.64 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.64 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.64 % new_bool_1 with pid 458345 completed with status 0
% 0.14/0.64 % Result found by new_bool_1
% 0.14/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.64 % No SInE strategy applied
% 0.14/0.64 % Search class: FHUSM-FFSF21-SFFFFFNN
% 0.14/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 136s (1) cores
% 0.14/0.64 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.64 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.64 % Preprocessing time : 0.001 s
% 0.14/0.64 % Presaturation interreduction done
% 0.14/0.64
% 0.14/0.64 % Proof found!
% 0.14/0.64 % SZS status Unsatisfiable
% 0.14/0.64 % SZS output start CNFRefutation
% See solution above
% 0.14/0.64 % Parsed axioms : 11
% 0.14/0.64 % Removed by relevancy pruning/SinE : 0
% 0.14/0.64 % Initial clauses : 11
% 0.14/0.64 % Removed in clause preprocessing : 0
% 0.14/0.64 % Initial clauses in saturation : 11
% 0.14/0.64 % Processed clauses : 101
% 0.14/0.64 % ...of these trivial : 2
% 0.14/0.64 % ...subsumed : 11
% 0.14/0.64 % ...remaining for further processing : 88
% 0.14/0.64 % Other redundant clauses eliminated : 0
% 0.14/0.64 % Clauses deleted for lack of memory : 0
% 0.14/0.64 % Backward-subsumed : 0
% 0.14/0.64 % Backward-rewritten : 4
% 0.14/0.64 % Generated clauses : 327
% 0.14/0.64 % ...of the previous two non-redundant : 207
% 0.14/0.64 % ...aggressively subsumed : 0
% 0.14/0.64 % Contextual simplify-reflections : 0
% 0.14/0.64 % Paramodulations : 327
% 0.14/0.64 % Factorizations : 0
% 0.14/0.64 % NegExts : 0
% 0.14/0.64 % Equation resolutions : 0
% 0.14/0.64 % Disequality decompositions : 0
% 0.14/0.64 % Total rewrite steps : 200
% 0.14/0.64 % ...of those cached : 152
% 0.14/0.64 % Propositional unsat checks : 0
% 0.14/0.64 % Propositional check models : 0
% 0.14/0.64 % Propositional check unsatisfiable : 0
% 0.14/0.64 % Propositional clauses : 0
% 0.14/0.64 % Propositional clauses after purity: 0
% 0.14/0.64 % Propositional unsat core size : 0
% 0.14/0.64 % Propositional preprocessing time : 0.000
% 0.14/0.64 % Propositional encoding time : 0.000
% 0.14/0.64 % Propositional solver time : 0.000
% 0.14/0.64 % Success case prop preproc time : 0.000
% 0.14/0.64 % Success case prop encoding time : 0.000
% 0.14/0.64 % Success case prop solver time : 0.000
% 0.14/0.64 % Current number of processed clauses : 73
% 0.14/0.64 % Positive orientable unit clauses : 27
% 0.14/0.64 % Positive unorientable unit clauses: 0
% 0.14/0.64 % Negative unit clauses : 1
% 0.14/0.64 % Non-unit-clauses : 45
% 0.14/0.64 % Current number of unprocessed clauses: 113
% 0.14/0.64 % ...number of literals in the above : 240
% 0.14/0.64 % Current number of archived formulas : 0
% 0.14/0.64 % Current number of archived clauses : 15
% 0.14/0.64 % Clause-clause subsumption calls (NU) : 401
% 0.14/0.64 % Rec. Clause-clause subsumption calls : 378
% 0.14/0.64 % Non-unit clause-clause subsumptions : 11
% 0.14/0.64 % Unit Clause-clause subsumption calls : 0
% 0.14/0.64 % Rewrite failures with RHS unbound : 0
% 0.14/0.64 % BW rewrite match attempts : 26
% 0.14/0.64 % BW rewrite match successes : 2
% 0.14/0.64 % Condensation attempts : 0
% 0.14/0.64 % Condensation successes : 0
% 0.14/0.64 % Termbank termtop insertions : 3548
% 0.14/0.64 % Search garbage collected termcells : 18
% 0.14/0.64
% 0.14/0.64 % -------------------------------------------------
% 0.14/0.64 % User time : 0.006 s
% 0.14/0.64 % System time : 0.001 s
% 0.14/0.64 % Total time : 0.007 s
% 0.14/0.64 % Maximum resident set size: 3640 pages
% 0.14/0.64
% 0.14/0.64 % -------------------------------------------------
% 0.14/0.64 % User time : 0.030 s
% 0.14/0.64 % System time : 0.011 s
% 0.14/0.64 % Total time : 0.041 s
% 0.14/0.64 % Maximum resident set size: 4864 pages
% 0.14/0.64 % E exiting
%------------------------------------------------------------------------------