TSTP Solution File: ALG019+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG019+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n015.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 : Wed Aug 30 16:00:07 EDT 2023
% Result : Theorem 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 33 ( 4 unt; 8 typ; 0 def)
% Number of atoms : 92 ( 23 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 105 ( 38 ~; 28 |; 17 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 7 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 48 ( 1 sgn; 32 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
sorti1: $i > $o ).
tff(decl_23,type,
op1: ( $i * $i ) > $i ).
tff(decl_24,type,
sorti2: $i > $o ).
tff(decl_25,type,
op2: ( $i * $i ) > $i ).
tff(decl_26,type,
h: $i > $i ).
tff(decl_27,type,
j: $i > $i ).
tff(decl_28,type,
esk1_1: $i > $i ).
tff(decl_29,type,
esk2_0: $i ).
fof(co1,conjecture,
( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax4,axiom,
~ ~ ? [X1] :
( sorti2(X1)
& ! [X2] :
( sorti2(X2)
=> op2(X2,X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(ax1,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> sorti1(op1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(ax3,axiom,
~ ? [X1] :
( sorti1(X1)
& ! [X2] :
( sorti1(X2)
=> op1(X2,X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(c_0_4,negated_conjecture,
~ ( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_5,plain,
! [X16] :
( sorti2(esk2_0)
& ( ~ sorti2(X16)
| op2(X16,X16) = esk2_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])]) ).
fof(c_0_6,negated_conjecture,
! [X17,X18,X19,X20,X21,X22,X23,X24] :
( ( ~ sorti1(X17)
| sorti2(h(X17)) )
& ( ~ sorti2(X18)
| sorti1(j(X18)) )
& ( ~ sorti1(X19)
| ~ sorti1(X20)
| h(op1(X19,X20)) = op2(h(X19),h(X20)) )
& ( ~ sorti2(X21)
| ~ sorti2(X22)
| j(op2(X21,X22)) = op1(j(X21),j(X22)) )
& ( ~ sorti2(X23)
| h(j(X23)) = X23 )
& ( ~ sorti1(X24)
| j(h(X24)) = X24 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_7,plain,
( op2(X1,X1) = esk2_0
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( h(op1(X1,X2)) = op2(h(X1),h(X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( sorti2(h(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( j(h(X1)) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
( h(op1(X1,X1)) = esk2_0
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
fof(c_0_12,plain,
! [X9,X10] :
( ~ sorti1(X9)
| ~ sorti1(X10)
| sorti1(op1(X9,X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])]) ).
cnf(c_0_13,negated_conjecture,
( op1(X1,X1) = j(esk2_0)
| ~ sorti1(op1(X1,X1))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( sorti1(op1(X1,X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X13] :
( ( sorti1(esk1_1(X13))
| ~ sorti1(X13) )
& ( op1(esk1_1(X13),esk1_1(X13)) != X13
| ~ sorti1(X13) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])]) ).
cnf(c_0_16,negated_conjecture,
( op1(X1,X1) = j(esk2_0)
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( op1(esk1_1(X1),esk1_1(X1)) != X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( sorti1(j(esk2_0))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
~ sorti1(esk1_1(j(esk2_0))),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16])]),c_0_18]) ).
cnf(c_0_20,plain,
( sorti1(esk1_1(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
~ sorti1(j(esk2_0)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,plain,
sorti2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ALG019+1 : TPTP v8.1.2. Released v2.7.0.
% 0.10/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 05:12:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.57 % Version : CSE_E---1.5
% 0.19/0.57 % Problem : theBenchmark.p
% 0.19/0.57 % Proof found
% 0.19/0.57 % SZS status Theorem for theBenchmark.p
% 0.19/0.57 % SZS output start Proof
% See solution above
% 0.19/0.57 % Total time : 0.006000 s
% 0.19/0.57 % SZS output end Proof
% 0.19/0.57 % Total time : 0.008000 s
%------------------------------------------------------------------------------