%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP012+5 : TPTP v9.2.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:23:34 PM UTC 2026
% Result : Theorem 1.39s 1.75s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 102 ( 33 ~; 30 |; 31 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 64 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_distribution,conjecture,
! [X1] :
( ( ! [X2,X3] :
? [X4] : product(X2,X3,X4)
& ! [X2,X3,X4,X5,X6,X7] :
( ( product(X2,X3,X5)
& product(X3,X4,X6)
& product(X5,X4,X7) )
=> product(X2,X6,X7) )
& ! [X2,X3,X4,X5,X6,X7] :
( ( product(X2,X3,X5)
& product(X3,X4,X6)
& product(X2,X6,X7) )
=> product(X5,X4,X7) )
& ! [X2] : product(X2,X1,X2)
& ! [X2] : product(X1,X2,X2)
& ! [X2] : product(X2,inverse(X2),X1)
& ! [X2] : product(inverse(X2),X2,X1) )
=> ! [X5,X6,X7,X2] :
( ( product(inverse(X5),inverse(X6),X7)
& product(X6,X5,X2) )
=> product(inverse(X7),inverse(X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distribution) ).
fof(c_0_1,negated_conjecture,
~ ! [X1] :
( ( ! [X2,X3] :
? [X4] : product(X2,X3,X4)
& ! [X2,X3,X4,X5,X6,X7] :
( ( product(X2,X3,X5)
& product(X3,X4,X6)
& product(X5,X4,X7) )
=> product(X2,X6,X7) )
& ! [X2,X3,X4,X5,X6,X7] :
( ( product(X2,X3,X5)
& product(X3,X4,X6)
& product(X2,X6,X7) )
=> product(X5,X4,X7) )
& ! [X2] : product(X2,X1,X2)
& ! [X2] : product(X1,X2,X2)
& ! [X2] : product(X2,inverse(X2),X1)
& ! [X2] : product(inverse(X2),X2,X1) )
=> ! [X5,X6,X7,X2] :
( ( product(inverse(X5),inverse(X6),X7)
& product(X6,X5,X2) )
=> product(inverse(X7),inverse(X2),X1) ) ),
inference(assume_negation,[status(cth)],[prove_distribution]) ).
fof(c_0_2,negated_conjecture,
! [X33,X34,X36,X37,X38,X39,X40,X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51] :
( product(X33,X34,esk2_2(X33,X34))
& ( ~ product(X36,X37,X39)
| ~ product(X37,X38,X40)
| ~ product(X39,X38,X41)
| product(X36,X40,X41) )
& ( ~ product(X42,X43,X45)
| ~ product(X43,X44,X46)
| ~ product(X42,X46,X47)
| product(X45,X44,X47) )
& product(X48,esk1_0,X48)
& product(esk1_0,X49,X49)
& product(X50,inverse(X50),esk1_0)
& product(inverse(X51),X51,esk1_0)
& product(inverse(esk3_0),inverse(esk4_0),esk5_0)
& product(esk4_0,esk3_0,esk6_0)
& ~ product(inverse(esk5_0),inverse(esk6_0),esk1_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])]) ).
cnf(c_0_3,negated_conjecture,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
product(X1,esk1_0,X1),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
product(inverse(X1),X1,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
( product(X1,esk1_0,X2)
| ~ product(X3,X4,X2)
| ~ product(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_7,negated_conjecture,
product(esk4_0,esk3_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_8,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X4,inverse(X2),X1)
| ~ product(X4,esk1_0,X3) ),
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_9,negated_conjecture,
product(inverse(esk3_0),inverse(esk4_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_11,negated_conjecture,
( product(X1,esk1_0,esk6_0)
| ~ product(esk4_0,esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_12,negated_conjecture,
product(X1,X2,esk2_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_13,negated_conjecture,
( product(esk5_0,esk4_0,X1)
| ~ product(inverse(esk3_0),esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X4,esk1_0,X2)
| ~ product(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_4]) ).
cnf(c_0_15,negated_conjecture,
product(esk2_2(esk4_0,esk3_0),esk1_0,esk6_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( product(X1,X2,esk1_0)
| ~ product(X1,X3,inverse(X4))
| ~ product(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_5]) ).
cnf(c_0_17,negated_conjecture,
product(esk5_0,esk4_0,inverse(esk3_0)),
inference(spm,[status(thm)],[c_0_13,c_0_4]) ).
cnf(c_0_18,negated_conjecture,
product(esk1_0,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_19,negated_conjecture,
( product(X1,esk6_0,X2)
| ~ product(X1,esk2_2(esk4_0,esk3_0),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( product(esk5_0,X1,esk1_0)
| ~ product(esk4_0,esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X1,X4,esk1_0)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
product(esk5_0,esk6_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_12])]) ).
cnf(c_0_23,negated_conjecture,
( product(X1,esk1_0,X2)
| ~ product(X2,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
cnf(c_0_24,negated_conjecture,
( product(esk5_0,X1,X2)
| ~ product(esk6_0,X2,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( product(X1,esk1_0,esk5_0)
| ~ product(esk6_0,X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
product(X1,inverse(X1),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_27,negated_conjecture,
product(inverse(esk6_0),esk1_0,esk5_0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,negated_conjecture,
~ product(inverse(esk5_0),inverse(esk6_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_29,negated_conjecture,
( product(inverse(X1),X2,X3)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_5]) ).
cnf(c_0_30,negated_conjecture,
product(esk5_0,esk1_0,inverse(esk6_0)),
inference(spm,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP012+5 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n022.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:17:21 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.39/1.75 % Version : CSE_E---1.7
% 1.39/1.75 % Problem : theBenchmark.p
% 1.39/1.75 % SZS status Theorem for theBenchmark.p
% 1.39/1.75 % SZS output start CNFRefutation
% See solution above
% 1.39/1.75 % Total time : 1.368s
%------------------------------------------------------------------------------