%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP040-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:41:28 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.56s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of clauses : 75 ( 42 unt; 5 nHn; 54 RR)
% Number of literals : 138 ( 19 equ; 62 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 115 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity1,axiom,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(associativity2,axiom,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(a_times_c_is_d,hypothesis,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(d_in_subgroup,hypothesis,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_in_subgroup) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(a_in_subgroup,hypothesis,
~ subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_in_subgroup) ).
cnf(property_of_O2,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| product(X1,element_in_O2(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(prove_inverse_is_self_cancelling,negated_conjecture,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
cnf(b_times_a_inverse_is_c,hypothesis,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(closure_of_product_and_inverse,axiom,
( ~ product(X1,inverse(X2),X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| subgroup_member(element_in_O2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(b_is_in_subgroup,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(c_0_17,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_18,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_17 ).
cnf(c_0_19,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_20,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_21,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_22,plain,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_24,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_20 ).
cnf(c_0_25,hypothesis,
product(a,c,d),
a_times_c_is_d ).
cnf(c_0_26,hypothesis,
~ subgroup_member(d),
inference(fof_simplification,[status(thm)],[d_in_subgroup]) ).
cnf(c_0_27,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_21 ).
cnf(c_0_28,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_29,plain,
( ~ product(inverse(X1),X3,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,hypothesis,
( ~ product(X3,a,X1)
| ~ product(X3,d,X2)
| product(X1,c,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_32,hypothesis,
~ subgroup_member(a),
inference(fof_simplification,[status(thm)],[a_in_subgroup]) ).
cnf(c_0_33,hypothesis,
~ subgroup_member(d),
c_0_26 ).
cnf(c_0_34,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| product(X1,element_in_O2(X1,X2),X2) ),
property_of_O2 ).
cnf(c_0_35,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,plain,
product(X1,multiply(inverse(X1),X2),X2),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_37,hypothesis,
( ~ product(inverse(d),a,X1)
| product(X1,c,identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_39,hypothesis,
~ subgroup_member(a),
c_0_32 ).
cnf(c_0_40,hypothesis,
( product(d,element_in_O2(d,X1),X1)
| subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
inverse(inverse(X1)) = X1,
prove_inverse_is_self_cancelling ).
cnf(c_0_43,hypothesis,
product(multiply(inverse(d),a),c,identity),
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_44,plain,
( ~ product(X2,identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_45,hypothesis,
product(d,element_in_O2(d,a),a),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,hypothesis,
multiply(multiply(inverse(d),a),c) = identity,
inference(spm,[status(thm)],[c_0_35,c_0_43]) ).
cnf(c_0_48,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_28]) ).
cnf(c_0_49,hypothesis,
( ~ product(d,element_in_O2(d,a),X1)
| X1 = a ),
inference(spm,[status(thm)],[c_0_27,c_0_45]) ).
cnf(c_0_50,hypothesis,
inverse(multiply(inverse(d),a)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_51,hypothesis,
product(b,inverse(a),c),
b_times_a_inverse_is_c ).
cnf(c_0_52,plain,
( ~ product(X1,inverse(X2),X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
inference(fof_simplification,[status(thm)],[closure_of_product_and_inverse]) ).
cnf(c_0_53,hypothesis,
multiply(d,element_in_O2(d,a)) = a,
inference(spm,[status(thm)],[c_0_49,c_0_28]) ).
cnf(c_0_54,negated_conjecture,
multiply(inverse(d),a) = inverse(c),
inference(spm,[status(thm)],[c_0_42,c_0_50]) ).
cnf(c_0_55,hypothesis,
( ~ product(b,inverse(a),X1)
| X1 = c ),
inference(spm,[status(thm)],[c_0_27,c_0_51]) ).
cnf(c_0_56,plain,
( ~ product(X1,inverse(X2),X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
c_0_52 ).
cnf(c_0_57,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| subgroup_member(element_in_O2(X1,X2)) ),
an_element_in_O2 ).
cnf(c_0_58,hypothesis,
element_in_O2(d,a) = inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_53]),c_0_54]) ).
cnf(c_0_59,hypothesis,
multiply(b,inverse(a)) = c,
inference(spm,[status(thm)],[c_0_55,c_0_28]) ).
cnf(c_0_60,negated_conjecture,
( ~ product(X3,X2,X1)
| ~ subgroup_member(X3)
| ~ subgroup_member(inverse(X2))
| subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_42]) ).
cnf(c_0_61,hypothesis,
subgroup_member(inverse(c)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_39]),c_0_33]) ).
cnf(c_0_62,plain,
( ~ subgroup_member(X1)
| subgroup_member(identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_31]),c_0_42])]) ).
cnf(c_0_63,hypothesis,
subgroup_member(b),
b_is_in_subgroup ).
cnf(c_0_64,hypothesis,
multiply(inverse(b),c) = inverse(a),
inference(spm,[status(thm)],[c_0_46,c_0_59]) ).
cnf(c_0_65,negated_conjecture,
( ~ product(X2,c,X1)
| ~ subgroup_member(X2)
| subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,hypothesis,
( ~ product(identity,a,X1)
| product(X1,c,d) ),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_67,hypothesis,
subgroup_member(identity),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,hypothesis,
product(inverse(b),c,inverse(a)),
inference(spm,[status(thm)],[c_0_28,c_0_64]) ).
cnf(c_0_69,hypothesis,
( ~ product(identity,a,X1)
| ~ subgroup_member(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_33]) ).
cnf(c_0_70,plain,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_19]),c_0_67])]) ).
cnf(c_0_71,negated_conjecture,
( ~ subgroup_member(inverse(b))
| subgroup_member(inverse(a)) ),
inference(spm,[status(thm)],[c_0_65,c_0_68]) ).
cnf(c_0_72,hypothesis,
( ~ product(identity,a,inverse(X1))
| ~ subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_73,negated_conjecture,
subgroup_member(inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_70]),c_0_63])]) ).
cnf(c_0_74,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_42]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP040-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n013.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 20 19:55:06 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.50 Running first-order theorem proving
% 0.27/0.50 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
% 0.27/0.56 % Version: 3.5.1
% 0.27/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.56 % Starting sh5l with 300s (1) cores
% 0.27/0.56 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3274351 completed with status 0
% 0.27/0.56 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.27/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.56 % No SInE strategy applied
% 0.27/0.56 % Search class: FGUSM-FFSS21-SFFFFFNN
% 0.27/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.27/0.56 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 0.27/0.56 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.56 % Starting new_bool_1 with 136s (1) cores
% 0.27/0.56 % G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with pid 3274358 completed with status 0
% 0.27/0.56 % Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN
% 0.27/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.56 % No SInE strategy applied
% 0.27/0.56 % Search class: FGUSM-FFSS21-SFFFFFNN
% 0.27/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.27/0.56 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 0.27/0.56 % Preprocessing time : 0.001 s
% 0.27/0.56 % Presaturation interreduction done
% 0.27/0.56
% 0.27/0.56 % Proof found!
% 0.27/0.56 % SZS status Unsatisfiable
% 0.27/0.56 % SZS output start CNFRefutation
% See solution above
% 0.27/0.56 % Parsed axioms : 17
% 0.27/0.56 % Removed by relevancy pruning/SinE : 0
% 0.27/0.56 % Initial clauses : 17
% 0.27/0.56 % Removed in clause preprocessing : 0
% 0.27/0.56 % Initial clauses in saturation : 17
% 0.27/0.56 % Processed clauses : 416
% 0.27/0.56 % ...of these trivial : 10
% 0.27/0.56 % ...subsumed : 146
% 0.27/0.56 % ...remaining for further processing : 260
% 0.27/0.56 % Other redundant clauses eliminated : 0
% 0.27/0.56 % Clauses deleted for lack of memory : 0
% 0.27/0.56 % Backward-subsumed : 15
% 0.27/0.56 % Backward-rewritten : 39
% 0.27/0.56 % Generated clauses : 1209
% 0.27/0.56 % ...of the previous two non-redundant : 1012
% 0.27/0.56 % ...aggressively subsumed : 0
% 0.27/0.56 % Contextual simplify-reflections : 0
% 0.27/0.56 % Paramodulations : 1201
% 0.27/0.56 % Factorizations : 8
% 0.27/0.56 % NegExts : 0
% 0.27/0.56 % Equation resolutions : 0
% 0.27/0.56 % Disequality decompositions : 0
% 0.27/0.56 % Total rewrite steps : 395
% 0.27/0.56 % ...of those cached : 307
% 0.27/0.56 % Propositional unsat checks : 0
% 0.27/0.56 % Propositional check models : 0
% 0.27/0.56 % Propositional check unsatisfiable : 0
% 0.27/0.56 % Propositional clauses : 0
% 0.27/0.56 % Propositional clauses after purity: 0
% 0.27/0.56 % Propositional unsat core size : 0
% 0.27/0.56 % Propositional preprocessing time : 0.000
% 0.27/0.56 % Propositional encoding time : 0.000
% 0.27/0.56 % Propositional solver time : 0.000
% 0.27/0.56 % Success case prop preproc time : 0.000
% 0.27/0.56 % Success case prop encoding time : 0.000
% 0.27/0.56 % Success case prop solver time : 0.000
% 0.27/0.56 % Current number of processed clauses : 189
% 0.27/0.56 % Positive orientable unit clauses : 48
% 0.27/0.56 % Positive unorientable unit clauses: 0
% 0.27/0.56 % Negative unit clauses : 14
% 0.27/0.56 % Non-unit-clauses : 127
% 0.27/0.56 % Current number of unprocessed clauses: 619
% 0.27/0.56 % ...number of literals in the above : 1679
% 0.27/0.56 % Current number of archived formulas : 0
% 0.27/0.56 % Current number of archived clauses : 71
% 0.27/0.56 % Clause-clause subsumption calls (NU) : 2710
% 0.27/0.56 % Rec. Clause-clause subsumption calls : 2400
% 0.27/0.56 % Non-unit clause-clause subsumptions : 113
% 0.27/0.56 % Unit Clause-clause subsumption calls : 933
% 0.27/0.56 % Rewrite failures with RHS unbound : 0
% 0.27/0.56 % BW rewrite match attempts : 31
% 0.27/0.56 % BW rewrite match successes : 8
% 0.27/0.56 % Condensation attempts : 0
% 0.27/0.56 % Condensation successes : 0
% 0.27/0.56 % Termbank termtop insertions : 13870
% 0.27/0.56 % Search garbage collected termcells : 27
% 0.27/0.56
% 0.27/0.56 % -------------------------------------------------
% 0.27/0.56 % User time : 0.029 s
% 0.27/0.56 % System time : 0.003 s
% 0.27/0.56 % Total time : 0.033 s
% 0.27/0.56 % Maximum resident set size: 3592 pages
% 0.27/0.56
% 0.27/0.56 % -------------------------------------------------
% 0.27/0.56 % User time : 0.132 s
% 0.27/0.56 % System time : 0.029 s
% 0.27/0.56 % Total time : 0.161 s
% 0.27/0.56 % Maximum resident set size: 4864 pages
% 0.27/0.56 % E exiting
%------------------------------------------------------------------------------