%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG210+1 : TPTP v9.2.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 04:08:14 PM UTC 2026
% Result : Theorem 2.18s 1.89s
% Output : CNFRefutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% Number of atoms : 84 ( 40 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 74 ( 34 ~; 30 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X2] :
( element(X2)
<=> ? [X3] :
( times(X2,X3) = X2
& times(X2,X2) = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(axiom_1,axiom,
! [X1,X2,X3] : times(times(X1,X2),X3) = times(X2,times(X3,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(conjecture_1,conjecture,
! [X1,X2] :
( ( element(X1)
& element(X2) )
=> element(times(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).
fof(c_0_3,plain,
! [X14,X16,X17] :
( ( times(X14,esk1_1(X14)) = X14
| ~ element(X14) )
& ( times(X14,X14) = esk1_1(X14)
| ~ element(X14) )
& ( times(X16,X17) != X16
| times(X16,X16) != X17
| element(X16) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_2])])])])])]) ).
fof(c_0_4,plain,
! [X11,X12,X13] : times(times(X11,X12),X13) = times(X12,times(X13,X11)),
inference(variable_rename,[status(thm)],[axiom_1]) ).
cnf(c_0_5,plain,
( times(X1,esk1_1(X1)) = X1
| ~ element(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,plain,
times(times(X1,X2),X3) = times(X2,times(X3,X1)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( times(X1,times(esk1_1(times(X2,X1)),X2)) = times(X2,X1)
| ~ element(times(X2,X1)) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
( times(X1,X1) = esk1_1(X1)
| ~ element(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,plain,
( times(esk1_1(X1),times(X2,X1)) = times(X1,X2)
| ~ element(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_10,plain,
times(X1,times(X2,times(X3,X4))) = times(X3,times(X4,times(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_6]),c_0_6]),c_0_6]),c_0_6]) ).
cnf(c_0_11,plain,
( times(esk1_1(X1),times(esk1_1(X1),X1)) = X1
| ~ element(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_5]) ).
cnf(c_0_12,plain,
( times(X1,times(X1,X1)) = X1
| ~ element(X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_13,plain,
( element(X1)
| times(X1,X2) != X1
| times(X1,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_14,plain,
( times(X1,times(X2,times(esk1_1(X1),X3))) = times(X1,times(X2,X3))
| ~ element(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_6]),c_0_10]) ).
cnf(c_0_15,plain,
( times(X1,times(esk1_1(X1),times(esk1_1(X1),X2))) = times(X1,X2)
| ~ element(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_11]),c_0_6]),c_0_6]) ).
cnf(c_0_16,plain,
( times(X1,times(X1,times(X2,X1))) = times(X2,X1)
| ~ element(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_17,plain,
( times(esk1_1(X1),X2) = times(X1,times(X2,X1))
| ~ element(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1,X2] :
( ( element(X1)
& element(X2) )
=> element(times(X1,X2)) ),
inference(assume_negation,[status(cth)],[conjecture_1]) ).
cnf(c_0_19,plain,
( element(X1)
| times(X1,times(X1,X1)) != X1 ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( times(esk1_1(X1),esk1_1(X1)) = times(X1,X1)
| ~ element(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_21,plain,
( times(X1,times(esk1_1(X1),X2)) = times(X1,X2)
| ~ element(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( times(X1,times(esk1_1(X1),X2)) = times(X2,X1)
| ~ element(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_23,negated_conjecture,
( element(esk2_0)
& element(esk3_0)
& ~ element(times(esk2_0,esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_24,plain,
( element(esk1_1(X1))
| times(esk1_1(X1),times(X1,X1)) != esk1_1(X1)
| ~ element(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( times(X1,X2) = times(X2,X1)
| ~ element(X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
element(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
( element(esk1_1(X1))
| ~ element(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_9]),c_0_8]) ).
cnf(c_0_28,plain,
( times(X1,times(X1,times(X1,X2))) = times(X1,X2)
| ~ element(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_12]),c_0_6]),c_0_6]) ).
cnf(c_0_29,negated_conjecture,
times(X1,esk3_0) = times(esk3_0,X1),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
element(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
( times(esk1_1(X1),times(X1,X1)) = esk1_1(X1)
| ~ element(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_20]),c_0_27]) ).
cnf(c_0_32,plain,
( element(times(X1,X2))
| times(X2,times(X1,times(X1,times(X2,times(X2,X1))))) != times(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]) ).
cnf(c_0_33,negated_conjecture,
times(esk3_0,times(esk3_0,times(X1,esk3_0))) = times(X1,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26])]) ).
cnf(c_0_34,negated_conjecture,
times(X1,esk2_0) = times(esk2_0,X1),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_35,plain,
( times(X1,times(X1,times(X1,X1))) = esk1_1(X1)
| ~ element(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_31]),c_0_6]) ).
cnf(c_0_36,negated_conjecture,
times(esk3_0,times(esk3_0,esk3_0)) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_29]),c_0_26])]) ).
cnf(c_0_37,negated_conjecture,
~ element(times(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_38,plain,
( element(times(X1,times(esk1_1(X1),X2)))
| times(esk1_1(X1),times(X1,times(X2,times(esk1_1(X1),times(X1,times(X2,times(X1,X2))))))) != times(X1,times(esk1_1(X1),X2))
| ~ element(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_9]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]) ).
cnf(c_0_39,negated_conjecture,
times(esk3_0,times(esk3_0,times(esk3_0,esk2_0))) = times(esk3_0,esk2_0),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
esk1_1(esk3_0) = times(esk3_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_26])]) ).
cnf(c_0_41,negated_conjecture,
~ element(times(esk3_0,esk2_0)),
inference(rw,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_42,negated_conjecture,
times(esk2_0,times(esk2_0,esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_34]),c_0_30])]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_36]),c_0_29]),c_0_39]),c_0_40]),c_0_40]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_29]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_36]),c_0_29]),c_0_6]),c_0_6]),c_0_29]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_36]),c_0_6]),c_0_6]),c_0_6]),c_0_29]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_29]),c_0_6]),c_0_6]),c_0_29]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_29]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_29]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_36]),c_0_29]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_29]),c_0_6]),c_0_6]),c_0_29]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_29]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_29]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_40]),c_0_6]),c_0_6]),c_0_6]),c_0_6]),c_0_36]),c_0_29]),c_0_39]),c_0_26])]),c_0_41]),c_0_10]),c_0_10]),c_0_29]),c_0_6]),c_0_6]),c_0_29]),c_0_10]),c_0_42]),c_0_39]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG210+1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n018.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 10:24:17 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.18/1.89 % Version : CSE_E---1.7
% 2.18/1.89 % Problem : theBenchmark.p
% 2.18/1.89 % SZS status Theorem for theBenchmark.p
% 2.18/1.89 % SZS output start CNFRefutation
% See solution above
% 2.18/1.89 % Total time : 1.372s
%------------------------------------------------------------------------------