%------------------------------------------------------------------------------
% File : E-SAT---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 : n001.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 12:41:21 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 37 ( 17 unt; 0 nHn; 29 RR)
% Number of literals : 76 ( 9 equ; 42 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 82 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
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(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
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(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
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,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity2]) ).
cnf(c_0_11,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_10 ).
cnf(c_0_12,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_13,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_14,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_15,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_16,plain,
( ~ product(X4,identity,X3)
| ~ product(X4,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,hypothesis,
product(inverse(b),inverse(a),d),
inverse_b_multiply_inverse_a_is_d ).
cnf(c_0_18,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_13 ).
cnf(c_0_19,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_20,plain,
( ~ product(X4,X2,X1)
| ~ product(X4,identity,X3)
| product(X1,inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_21,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_22,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_15 ).
cnf(c_0_23,hypothesis,
( ~ product(inverse(b),identity,X1)
| product(d,a,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
( ~ product(identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( ~ product(X3,X2,X1)
| product(X1,inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( ~ product(X3,X4,X2)
| ~ product(X1,X3,inverse(X4))
| product(X1,X2,identity) ),
inference(spm,[status(thm)],[c_0_22,c_0_12]) ).
cnf(c_0_27,hypothesis,
product(d,a,inverse(b)),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_28,hypothesis,
product(a,b,c),
a_multiply_b_is_c ).
cnf(c_0_29,plain,
( ~ product(X1,X2,identity)
| X1 = inverse(X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,hypothesis,
( ~ product(a,b,X1)
| product(d,X1,identity) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,hypothesis,
( ~ product(X1,X3,a)
| ~ product(X3,b,X2)
| product(X1,X2,c) ),
inference(spm,[status(thm)],[c_0_22,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
inverse(c) != d,
inference(fof_simplification,[status(thm)],[prove_c_inverse_equals_d]) ).
cnf(c_0_33,hypothesis,
( ~ product(a,b,X1)
| inverse(X1) = d ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,hypothesis,
( ~ product(X1,identity,a)
| product(X1,b,c) ),
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_35,negated_conjecture,
inverse(c) != d,
c_0_32 ).
cnf(c_0_36,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_21])]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.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 19:59:14 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.43 % Version: 3.5.1
% 0.13/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.43 % Starting sh5l with 300s (1) cores
% 0.13/0.43 % new_bool_3 with pid 1261340 completed with status 0
% 0.13/0.43 % Result found by new_bool_3
% 0.13/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.43 % Search class: FHUSM-FFSF11-SFFFFFNN
% 0.13/0.43 % partial match(1): FHUSM-FFSF21-SFFFFFNN
% 0.13/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.43 % SubtermCWHack with pid 1261346 completed with status 0
% 0.13/0.43 % Result found by SubtermCWHack
% 0.13/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.43 % Search class: FHUSM-FFSF11-SFFFFFNN
% 0.13/0.43 % partial match(1): FHUSM-FFSF21-SFFFFFNN
% 0.13/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.43 % Preprocessing time : 0.001 s
% 0.13/0.43
% 0.13/0.43 % Proof found!
% 0.13/0.43 % SZS status Unsatisfiable
% 0.13/0.43 % SZS output start CNFRefutation
% See solution above
% 0.13/0.43 % Parsed axioms : 11
% 0.13/0.43 % Removed by relevancy pruning/SinE : 1
% 0.13/0.43 % Initial clauses : 10
% 0.13/0.43 % Removed in clause preprocessing : 0
% 0.13/0.43 % Initial clauses in saturation : 10
% 0.13/0.43 % Processed clauses : 115
% 0.13/0.43 % ...of these trivial : 0
% 0.13/0.43 % ...subsumed : 40
% 0.13/0.43 % ...remaining for further processing : 75
% 0.13/0.43 % Other redundant clauses eliminated : 0
% 0.13/0.43 % Clauses deleted for lack of memory : 0
% 0.13/0.43 % Backward-subsumed : 4
% 0.13/0.43 % Backward-rewritten : 0
% 0.13/0.43 % Generated clauses : 337
% 0.13/0.43 % ...of the previous two non-redundant : 286
% 0.13/0.43 % ...aggressively subsumed : 0
% 0.13/0.43 % Contextual simplify-reflections : 0
% 0.13/0.43 % Paramodulations : 337
% 0.13/0.43 % Factorizations : 0
% 0.13/0.43 % NegExts : 0
% 0.13/0.43 % Equation resolutions : 0
% 0.13/0.43 % Disequality decompositions : 0
% 0.13/0.43 % Total rewrite steps : 77
% 0.13/0.43 % ...of those cached : 60
% 0.13/0.43 % Propositional unsat checks : 0
% 0.13/0.43 % Propositional check models : 0
% 0.13/0.43 % Propositional check unsatisfiable : 0
% 0.13/0.43 % Propositional clauses : 0
% 0.13/0.43 % Propositional clauses after purity: 0
% 0.13/0.43 % Propositional unsat core size : 0
% 0.13/0.43 % Propositional preprocessing time : 0.000
% 0.13/0.43 % Propositional encoding time : 0.000
% 0.13/0.43 % Propositional solver time : 0.000
% 0.13/0.43 % Success case prop preproc time : 0.000
% 0.13/0.43 % Success case prop encoding time : 0.000
% 0.13/0.43 % Success case prop solver time : 0.000
% 0.13/0.43 % Current number of processed clauses : 71
% 0.13/0.43 % Positive orientable unit clauses : 9
% 0.13/0.43 % Positive unorientable unit clauses: 0
% 0.13/0.43 % Negative unit clauses : 1
% 0.13/0.43 % Non-unit-clauses : 61
% 0.13/0.43 % Current number of unprocessed clauses: 180
% 0.13/0.43 % ...number of literals in the above : 517
% 0.13/0.43 % Current number of archived formulas : 0
% 0.13/0.43 % Current number of archived clauses : 4
% 0.13/0.43 % Clause-clause subsumption calls (NU) : 733
% 0.13/0.43 % Rec. Clause-clause subsumption calls : 722
% 0.13/0.43 % Non-unit clause-clause subsumptions : 44
% 0.13/0.43 % Unit Clause-clause subsumption calls : 0
% 0.13/0.43 % Rewrite failures with RHS unbound : 0
% 0.13/0.43 % BW rewrite match attempts : 1
% 0.13/0.43 % BW rewrite match successes : 0
% 0.13/0.43 % Condensation attempts : 0
% 0.13/0.43 % Condensation successes : 0
% 0.13/0.43 % Termbank termtop insertions : 3638
% 0.13/0.43 % Search garbage collected termcells : 21
% 0.13/0.43
% 0.13/0.43 % -------------------------------------------------
% 0.13/0.43 % User time : 0.006 s
% 0.13/0.43 % System time : 0.002 s
% 0.13/0.43 % Total time : 0.008 s
% 0.13/0.43 % Maximum resident set size: 3640 pages
% 0.13/0.43
% 0.13/0.43 % -------------------------------------------------
% 0.13/0.43 % User time : 0.008 s
% 0.13/0.43 % System time : 0.006 s
% 0.13/0.43 % Total time : 0.014 s
% 0.13/0.43 % Maximum resident set size: 4864 pages
% 0.13/0.43 % E exiting
%------------------------------------------------------------------------------