%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP025-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:41:24 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of clauses : 73 ( 38 unt; 17 nHn; 73 RR)
% Number of literals : 118 ( 61 equ; 31 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-1 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_and_b_only_members_of_group1,hypothesis,
( ~ group_member(X1,g1)
| X1 = b
| X1 = a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_and_b_only_members_of_group1) ).
cnf(d2_member_of_group1,hypothesis,
group_member(d2,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_member_of_group1) ).
cnf(d1_member_of_group1,hypothesis,
group_member(d1,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_member_of_group1) ).
cnf(total_function2,axiom,
( ~ product(X1,X2,X3,X5)
| ~ product(X1,X2,X3,X4)
| X5 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP006-0.ax',total_function2) ).
cnf(d1_times_d2_is_d3,hypothesis,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_times_d2_is_d3) ).
cnf(prove_product_holds_in_group2,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_product_holds_in_group2) ).
cnf(d3_member_of_group1,hypothesis,
group_member(d3,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_member_of_group1) ).
cnf(b_times_b_is_a,hypothesis,
product(g1,b,b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_b_is_a) ).
cnf(a_maps_to_c,hypothesis,
an_isomorphism(a) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_maps_to_c) ).
cnf(b_maps_to_d,hypothesis,
an_isomorphism(b) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_maps_to_d) ).
cnf(a_times_a_is_a,hypothesis,
product(g1,a,a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_a_is_a) ).
cnf(c_times_c_is_c,hypothesis,
product(g2,c,c,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_c_is_c) ).
cnf(d_times_d_is_c,hypothesis,
product(g2,d,d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_d_is_c) ).
cnf(a_times_b_is_b,hypothesis,
product(g1,a,b,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_b) ).
cnf(c_times_d_is_d,hypothesis,
product(g2,c,d,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_d_is_d) ).
cnf(b_times_a_is_b,hypothesis,
product(g1,b,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_is_b) ).
cnf(d_times_c_is_d,hypothesis,
product(g2,d,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_c_is_d) ).
cnf(c_0_17,hypothesis,
( ~ group_member(X1,g1)
| X1 = b
| X1 = a ),
inference(fof_simplification,[status(thm)],[a_and_b_only_members_of_group1]) ).
cnf(c_0_18,hypothesis,
( ~ group_member(X1,g1)
| X1 = b
| X1 = a ),
c_0_17 ).
cnf(c_0_19,hypothesis,
group_member(d2,g1),
d2_member_of_group1 ).
cnf(c_0_20,hypothesis,
( d2 = b
| d2 = a ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,hypothesis,
group_member(d1,g1),
d1_member_of_group1 ).
cnf(c_0_22,plain,
( ~ product(X1,X2,X3,X5)
| ~ product(X1,X2,X3,X4)
| X5 = X4 ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_23,hypothesis,
product(g1,d1,d2,d3),
d1_times_d2_is_d3 ).
cnf(c_0_24,hypothesis,
( a != b
| d2 = b ),
inference(ef,[status(thm)],[c_0_20]) ).
cnf(c_0_25,hypothesis,
( d1 = b
| d1 = a ),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
inference(fof_simplification,[status(thm)],[prove_product_holds_in_group2]) ).
cnf(c_0_27,hypothesis,
group_member(d3,g1),
d3_member_of_group1 ).
cnf(c_0_28,plain,
( ~ product(X1,X2,X3,X5)
| ~ product(X1,X2,X3,X4)
| X5 = X4 ),
c_0_22 ).
cnf(c_0_29,hypothesis,
product(g1,b,b,a),
b_times_b_is_a ).
cnf(c_0_30,hypothesis,
( a != b
| product(g1,d1,b,d3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,hypothesis,
( a != b
| d1 = b ),
inference(ef,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
c_0_26 ).
cnf(c_0_33,hypothesis,
( d3 = b
| d3 = a ),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_34,hypothesis,
an_isomorphism(a) = c,
a_maps_to_c ).
cnf(c_0_35,hypothesis,
an_isomorphism(b) = d,
b_maps_to_d ).
cnf(c_0_36,hypothesis,
( ~ product(g1,b,b,X1)
| X1 = a ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,hypothesis,
( a != b
| product(g1,b,b,d3) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,hypothesis,
product(g1,a,a,a),
a_times_a_is_a ).
cnf(c_0_39,hypothesis,
( product(g1,d1,a,d3)
| d2 = b ),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_40,hypothesis,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),c)
| d3 = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_41,hypothesis,
( ~ product(g2,an_isomorphism(d1),d,an_isomorphism(d3))
| a != b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_35]) ).
cnf(c_0_42,hypothesis,
( a != b
| d3 = a ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,hypothesis,
( ~ product(g1,a,a,X1)
| X1 = a ),
inference(spm,[status(thm)],[c_0_28,c_0_38]) ).
cnf(c_0_44,hypothesis,
( product(g1,a,a,d3)
| d2 = b
| d1 = b ),
inference(spm,[status(thm)],[c_0_39,c_0_25]) ).
cnf(c_0_45,hypothesis,
( ~ product(g2,an_isomorphism(d1),c,c)
| d3 = b
| d2 = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_20]),c_0_34]) ).
cnf(c_0_46,hypothesis,
product(g2,c,c,c),
c_times_c_is_c ).
cnf(c_0_47,hypothesis,
( ~ product(g2,an_isomorphism(d1),d,c)
| a != b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_34]) ).
cnf(c_0_48,hypothesis,
product(g2,d,d,c),
d_times_d_is_c ).
cnf(c_0_49,hypothesis,
( d3 = a
| d1 = b
| d2 = b ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,hypothesis,
( d2 = b
| d3 = b
| d1 = b ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_25]),c_0_34]),c_0_46])]) ).
cnf(c_0_51,hypothesis,
a != b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_31]),c_0_35]),c_0_48])]) ).
cnf(c_0_52,hypothesis,
product(g1,a,b,b),
a_times_b_is_b ).
cnf(c_0_53,hypothesis,
( product(g1,a,d2,d3)
| d1 = b ),
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_54,hypothesis,
( d2 = b
| d1 = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_55,hypothesis,
( ~ product(g2,c,an_isomorphism(d2),an_isomorphism(d3))
| d1 = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_34]) ).
cnf(c_0_56,hypothesis,
( ~ product(g1,a,b,X1)
| X1 = b ),
inference(spm,[status(thm)],[c_0_28,c_0_52]) ).
cnf(c_0_57,hypothesis,
( product(g1,a,b,d3)
| d1 = b ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,hypothesis,
( ~ product(g2,c,d,an_isomorphism(d3))
| d1 = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_54]),c_0_35]) ).
cnf(c_0_59,hypothesis,
( d3 = b
| d1 = b ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,hypothesis,
product(g2,c,d,d),
c_times_d_is_d ).
cnf(c_0_61,hypothesis,
product(g1,b,a,b),
b_times_a_is_b ).
cnf(c_0_62,hypothesis,
d1 = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_35]),c_0_60])]) ).
cnf(c_0_63,hypothesis,
( ~ product(g1,b,a,X1)
| X1 = b ),
inference(spm,[status(thm)],[c_0_28,c_0_61]) ).
cnf(c_0_64,hypothesis,
( product(g1,b,a,d3)
| d2 = b ),
inference(rw,[status(thm)],[c_0_39,c_0_62]) ).
cnf(c_0_65,hypothesis,
( ~ product(g2,an_isomorphism(d1),c,an_isomorphism(d3))
| d2 = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_20]),c_0_34]) ).
cnf(c_0_66,hypothesis,
( d3 = b
| d2 = b ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,hypothesis,
product(g2,d,c,d),
d_times_c_is_d ).
cnf(c_0_68,hypothesis,
d2 = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_62]),c_0_35]),c_0_35]),c_0_67])]) ).
cnf(c_0_69,hypothesis,
product(g1,b,d2,d3),
inference(rw,[status(thm)],[c_0_23,c_0_62]) ).
cnf(c_0_70,hypothesis,
d3 = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_68]),c_0_62]),c_0_35]),c_0_35]),c_0_48])]) ).
cnf(c_0_71,hypothesis,
product(g1,b,b,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_68]),c_0_70]) ).
cnf(c_0_72,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_71]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP025-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 19:54:11 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.44 % Version: 3.5.1
% 0.12/0.44 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % Starting sh5l with 300s (1) cores
% 0.12/0.44 % new_bool_1 with pid 26312 completed with status 0
% 0.12/0.44 % Result found by new_bool_1
% 0.12/0.44 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.44 % Search class: FGUSF-FFSM11-SFFFFFNN
% 0.12/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.44 % SubtermCWHack with pid 26321 completed with status 0
% 0.12/0.44 % Result found by SubtermCWHack
% 0.12/0.44 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.44 % Search class: FGUSF-FFSM11-SFFFFFNN
% 0.12/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.44 % Preprocessing time : 0.001 s
% 0.12/0.44
% 0.12/0.44 % Proof found!
% 0.12/0.44 % SZS status Unsatisfiable
% 0.12/0.44 % SZS output start CNFRefutation
% See solution above
% 0.12/0.44 % Parsed axioms : 32
% 0.12/0.44 % Removed by relevancy pruning/SinE : 8
% 0.12/0.44 % Initial clauses : 24
% 0.12/0.44 % Removed in clause preprocessing : 0
% 0.12/0.44 % Initial clauses in saturation : 24
% 0.12/0.44 % Processed clauses : 130
% 0.12/0.44 % ...of these trivial : 0
% 0.12/0.44 % ...subsumed : 33
% 0.12/0.44 % ...remaining for further processing : 97
% 0.12/0.44 % Other redundant clauses eliminated : 0
% 0.12/0.44 % Clauses deleted for lack of memory : 0
% 0.12/0.44 % Backward-subsumed : 28
% 0.12/0.44 % Backward-rewritten : 30
% 0.12/0.44 % Generated clauses : 316
% 0.12/0.44 % ...of the previous two non-redundant : 292
% 0.12/0.44 % ...aggressively subsumed : 0
% 0.12/0.44 % Contextual simplify-reflections : 0
% 0.12/0.44 % Paramodulations : 313
% 0.12/0.44 % Factorizations : 3
% 0.12/0.44 % NegExts : 0
% 0.12/0.44 % Equation resolutions : 0
% 0.12/0.44 % Disequality decompositions : 0
% 0.12/0.44 % Total rewrite steps : 157
% 0.12/0.44 % ...of those cached : 142
% 0.12/0.44 % Propositional unsat checks : 0
% 0.12/0.44 % Propositional check models : 0
% 0.12/0.44 % Propositional check unsatisfiable : 0
% 0.12/0.44 % Propositional clauses : 0
% 0.12/0.44 % Propositional clauses after purity: 0
% 0.12/0.44 % Propositional unsat core size : 0
% 0.12/0.44 % Propositional preprocessing time : 0.000
% 0.12/0.44 % Propositional encoding time : 0.000
% 0.12/0.44 % Propositional solver time : 0.000
% 0.12/0.44 % Success case prop preproc time : 0.000
% 0.12/0.44 % Success case prop encoding time : 0.000
% 0.12/0.44 % Success case prop solver time : 0.000
% 0.12/0.44 % Current number of processed clauses : 39
% 0.12/0.44 % Positive orientable unit clauses : 18
% 0.12/0.44 % Positive unorientable unit clauses: 0
% 0.12/0.44 % Negative unit clauses : 3
% 0.12/0.44 % Non-unit-clauses : 18
% 0.12/0.44 % Current number of unprocessed clauses: 149
% 0.12/0.44 % ...number of literals in the above : 493
% 0.12/0.44 % Current number of archived formulas : 0
% 0.12/0.44 % Current number of archived clauses : 58
% 0.12/0.44 % Clause-clause subsumption calls (NU) : 356
% 0.12/0.44 % Rec. Clause-clause subsumption calls : 288
% 0.12/0.44 % Non-unit clause-clause subsumptions : 41
% 0.12/0.44 % Unit Clause-clause subsumption calls : 40
% 0.12/0.44 % Rewrite failures with RHS unbound : 0
% 0.12/0.44 % BW rewrite match attempts : 15
% 0.12/0.44 % BW rewrite match successes : 3
% 0.12/0.44 % Condensation attempts : 0
% 0.12/0.44 % Condensation successes : 0
% 0.12/0.44 % Termbank termtop insertions : 3815
% 0.12/0.44 % Search garbage collected termcells : 53
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.008 s
% 0.12/0.44 % System time : 0.003 s
% 0.12/0.44 % Total time : 0.011 s
% 0.12/0.44 % Maximum resident set size: 3652 pages
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.011 s
% 0.12/0.44 % System time : 0.007 s
% 0.12/0.44 % Total time : 0.018 s
% 0.12/0.44 % Maximum resident set size: 4864 pages
% 0.12/0.44 % E exiting
%------------------------------------------------------------------------------