%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG090+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 : Sun Sep 27 08:26:36 AM UTC 2026
% Result : Theorem 25.78s 5.00s
% Output : CNFRefutation 25.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 144 ( 85 unt; 0 def)
% Number of atoms : 243 ( 113 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 175 ( 76 ~; 71 |; 17 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mAddComm,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('theBenchmark.p',mAddComm) ).
fof(mAddAsso,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
file('theBenchmark.p',mAddAsso) ).
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mDefSSum,axiom,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSSum) ).
fof(mDefIdeal,axiom,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('theBenchmark.p',mDefIdeal) ).
fof(m__870,axiom,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('theBenchmark.p',m__870) ).
fof(m__901,axiom,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElementOf0(xx,sdtpldt1(xI,xJ)) ),
file('theBenchmark.p',m__901) ).
fof(m__934,axiom,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('theBenchmark.p',m__934) ).
fof(m__967,axiom,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
file('theBenchmark.p',m__967) ).
fof(m__994,axiom,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('theBenchmark.p',m__994) ).
fof(m__,conjecture,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_32,plain,
( aSet0(A)
| ~ aIdeal0(A) ),
inference(clausify,[status(thm)],[mDefIdeal]) ).
cnf(c_37,plain,
aIdeal0(xI),
inference(clausify,[status(thm)],[m__870]) ).
cnf(c_38,plain,
aIdeal0(xJ),
inference(clausify,[status(thm)],[m__870]) ).
cnf(c_39,plain,
aSet0(xJ),
inference(resolve,[status(thm)],[c_38,c_32]) ).
cnf(c_42,plain,
aSet0(xI),
inference(resolve,[status(thm)],[c_37,c_32]) ).
cnf(c_55,negated_conjecture,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) != sdtpldt0(xx,xy),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_59,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(clausify,[status(thm)],[m__994]) ).
cnf(c_60,plain,
sdtpldt0(xm,xn) = xy,
inference(clausify,[status(thm)],[m__967]) ).
cnf(c_61,plain,
xy = sdtpldt0(xm,xn),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_62,plain,
aElementOf0(xn,xJ),
inference(clausify,[status(thm)],[m__967]) ).
cnf(c_63,plain,
aElementOf0(xm,xI),
inference(clausify,[status(thm)],[m__967]) ).
cnf(c_64,plain,
sdtpldt0(xk,xl) = xx,
inference(clausify,[status(thm)],[m__934]) ).
cnf(c_65,plain,
xx = sdtpldt0(xk,xl),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_66,plain,
aElementOf0(xl,xJ),
inference(clausify,[status(thm)],[m__934]) ).
cnf(c_67,plain,
aElementOf0(xk,xI),
inference(clausify,[status(thm)],[m__934]) ).
cnf(c_71,plain,
aElementOf0(xx,sdtpldt1(xI,xJ)),
inference(clausify,[status(thm)],[m__901]) ).
cnf(c_72,plain,
aElementOf0(sdtpldt0(xk,xl),sdtpldt1(xI,xJ)),
inference(paramod,[status(thm)],[c_65,c_71]) ).
cnf(c_89,plain,
( aSet0(C)
| sdtpldt1(A,B) != C
| ~ aSet0(B)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSSum]) ).
cnf(c_94,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_114,plain,
( sdtpldt0(sdtpldt0(A,B),C) = sdtpldt0(A,sdtpldt0(B,C))
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAddAsso]) ).
cnf(c_115,plain,
( sdtpldt0(B,A) = sdtpldt0(A,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAddComm]) ).
cnf(c_17591,negated_conjecture,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) != sdtpldt0(sdtpldt0(xk,xl),xy),
inference(paramod,[status(thm)],[c_65,c_55]) ).
cnf(c_140,negated_conjecture,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) != sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)),
inference(paramod,[status(thm)],[c_61,c_17591]) ).
cnf(c_17592,plain,
( aSet0(B)
| sdtpldt1(xI,A) != B
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_89,c_42]) ).
cnf(c_17593,plain,
( aSet0(A)
| sdtpldt1(xI,xJ) != A ),
inference(resolve,[status(thm)],[c_17592,c_39]) ).
cnf(c_900,plain,
aSet0(sdtpldt1(xI,xJ)),
inference(xxres,[status(thm)],[c_17593]) ).
cnf(c_17594,plain,
( aElement0(sdtpldt0(xk,xl))
| ~ aSet0(sdtpldt1(xI,xJ)) ),
inference(resolve,[status(thm)],[c_94,c_72]) ).
cnf(c_997,plain,
aElement0(sdtpldt0(xk,xl)),
inference(resolve,[status(thm)],[c_900,c_17594]) ).
cnf(c_17595,plain,
( aElement0(xk)
| ~ aSet0(xI) ),
inference(resolve,[status(thm)],[c_94,c_67]) ).
cnf(c_999,plain,
aElement0(xk),
inference(resolve,[status(thm)],[c_42,c_17595]) ).
cnf(c_17596,plain,
( aElement0(xl)
| ~ aSet0(xJ) ),
inference(resolve,[status(thm)],[c_94,c_66]) ).
cnf(c_1000,plain,
aElement0(xl),
inference(resolve,[status(thm)],[c_39,c_17596]) ).
cnf(c_17597,plain,
( aElement0(xm)
| ~ aSet0(xI) ),
inference(resolve,[status(thm)],[c_94,c_63]) ).
cnf(c_1001,plain,
aElement0(xm),
inference(resolve,[status(thm)],[c_42,c_17597]) ).
cnf(c_17598,plain,
( aElement0(xn)
| ~ aSet0(xJ) ),
inference(resolve,[status(thm)],[c_94,c_62]) ).
cnf(c_1002,plain,
aElement0(xn),
inference(resolve,[status(thm)],[c_39,c_17598]) ).
cnf(c_17599,plain,
( aElement0(sdtpldt0(xk,xm))
| ~ aSet0(xI) ),
inference(resolve,[status(thm)],[c_94,c_59]) ).
cnf(c_1003,plain,
aElement0(sdtpldt0(xk,xm)),
inference(resolve,[status(thm)],[c_42,c_17599]) ).
cnf(c_17600,plain,
( sdtpldt0(A,xk) = sdtpldt0(xk,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_115,c_999]) ).
cnf(c_1814,plain,
sdtpldt0(xl,xk) = sdtpldt0(xk,xl),
inference(resolve,[status(thm)],[c_17600,c_1000]) ).
cnf(c_17601,plain,
( sdtpldt0(A,xl) = sdtpldt0(xl,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_115,c_1000]) ).
cnf(c_2183,plain,
sdtpldt0(xm,xl) = sdtpldt0(xl,xm),
inference(resolve,[status(thm)],[c_17601,c_1001]) ).
cnf(c_17602,plain,
( sdtpldt0(A,xk) = sdtpldt0(xk,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_115,c_999]) ).
cnf(c_2184,plain,
sdtpldt0(xm,xk) = sdtpldt0(xk,xm),
inference(resolve,[status(thm)],[c_17602,c_1001]) ).
cnf(c_17603,plain,
( sdtpldt0(sdtpldt0(xl,A),B) = sdtpldt0(xl,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_1000]) ).
cnf(c_17604,plain,
( sdtpldt0(sdtpldt0(xl,xk),A) = sdtpldt0(xl,sdtpldt0(xk,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17603,c_999]) ).
cnf(c_17605,plain,
sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)),
inference(resolve,[status(thm)],[c_17604,c_1001]) ).
cnf(c_2190,plain,
sdtpldt0(sdtpldt0(xk,xl),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)),
inference(paramod,[status(thm)],[c_1814,c_17605]) ).
cnf(c_17606,plain,
( sdtpldt0(sdtpldt0(xk,A),B) = sdtpldt0(xk,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_999]) ).
cnf(c_17607,plain,
( sdtpldt0(sdtpldt0(xk,xl),A) = sdtpldt0(xk,sdtpldt0(xl,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17606,c_1000]) ).
cnf(c_17608,plain,
sdtpldt0(sdtpldt0(xk,xl),xm) = sdtpldt0(xk,sdtpldt0(xl,xm)),
inference(resolve,[status(thm)],[c_17607,c_1001]) ).
cnf(c_2193,plain,
sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(xk,sdtpldt0(xl,xm)),
inference(paramod,[status(thm)],[c_2190,c_17608]) ).
cnf(c_17609,plain,
( sdtpldt0(sdtpldt0(xl,A),B) = sdtpldt0(xl,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_1000]) ).
cnf(c_17610,plain,
( sdtpldt0(sdtpldt0(xl,xm),A) = sdtpldt0(xl,sdtpldt0(xm,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17609,c_1001]) ).
cnf(c_17611,plain,
sdtpldt0(sdtpldt0(xl,xm),xk) = sdtpldt0(xl,sdtpldt0(xm,xk)),
inference(resolve,[status(thm)],[c_17610,c_999]) ).
cnf(c_17612,plain,
sdtpldt0(sdtpldt0(xl,xm),xk) = sdtpldt0(xl,sdtpldt0(xk,xm)),
inference(paramod,[status(thm)],[c_2184,c_17611]) ).
cnf(c_2207,plain,
sdtpldt0(sdtpldt0(xl,xm),xk) = sdtpldt0(xk,sdtpldt0(xl,xm)),
inference(paramod,[status(thm)],[c_2193,c_17612]) ).
cnf(c_17613,plain,
( sdtpldt0(sdtpldt0(xk,A),B) = sdtpldt0(xk,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_999]) ).
cnf(c_17614,plain,
( sdtpldt0(sdtpldt0(xk,xm),A) = sdtpldt0(xk,sdtpldt0(xm,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17613,c_1001]) ).
cnf(c_17615,plain,
sdtpldt0(sdtpldt0(xk,xm),xl) = sdtpldt0(xk,sdtpldt0(xm,xl)),
inference(resolve,[status(thm)],[c_17614,c_1000]) ).
cnf(c_2211,plain,
sdtpldt0(sdtpldt0(xk,xm),xl) = sdtpldt0(xk,sdtpldt0(xl,xm)),
inference(paramod,[status(thm)],[c_2183,c_17615]) ).
cnf(c_17616,plain,
( sdtpldt0(sdtpldt0(xm,A),B) = sdtpldt0(xm,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_1001]) ).
cnf(c_17617,plain,
( sdtpldt0(sdtpldt0(xm,xl),A) = sdtpldt0(xm,sdtpldt0(xl,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17616,c_1000]) ).
cnf(c_17618,plain,
sdtpldt0(sdtpldt0(xm,xl),xk) = sdtpldt0(xm,sdtpldt0(xl,xk)),
inference(resolve,[status(thm)],[c_17617,c_999]) ).
cnf(c_17619,plain,
sdtpldt0(sdtpldt0(xl,xm),xk) = sdtpldt0(xm,sdtpldt0(xl,xk)),
inference(paramod,[status(thm)],[c_2183,c_17618]) ).
cnf(c_17620,plain,
sdtpldt0(xk,sdtpldt0(xl,xm)) = sdtpldt0(xm,sdtpldt0(xl,xk)),
inference(paramod,[status(thm)],[c_2207,c_17619]) ).
cnf(c_17621,plain,
sdtpldt0(xk,sdtpldt0(xl,xm)) = sdtpldt0(xm,sdtpldt0(xk,xl)),
inference(paramod,[status(thm)],[c_1814,c_17620]) ).
cnf(c_2225,plain,
sdtpldt0(xm,sdtpldt0(xk,xl)) = sdtpldt0(xk,sdtpldt0(xl,xm)),
inference(copy,[status(thm)],[c_17621]) ).
cnf(c_2376,plain,
sdtpldt0(sdtpldt0(xk,xl),xm) = sdtpldt0(xk,sdtpldt0(xl,xm)),
inference(paramod,[status(thm)],[c_2193,c_2190]) ).
cnf(c_17622,plain,
( sdtpldt0(A,xm) = sdtpldt0(xm,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_115,c_1001]) ).
cnf(c_2599,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(resolve,[status(thm)],[c_17622,c_1002]) ).
cnf(c_17623,plain,
( sdtpldt0(A,xl) = sdtpldt0(xl,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_115,c_1000]) ).
cnf(c_2600,plain,
sdtpldt0(xn,xl) = sdtpldt0(xl,xn),
inference(resolve,[status(thm)],[c_17623,c_1002]) ).
cnf(c_17624,plain,
( sdtpldt0(A,xk) = sdtpldt0(xk,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_115,c_999]) ).
cnf(c_2601,plain,
sdtpldt0(xn,xk) = sdtpldt0(xk,xn),
inference(resolve,[status(thm)],[c_17624,c_1002]) ).
cnf(c_17625,plain,
( sdtpldt0(sdtpldt0(xl,A),B) = sdtpldt0(xl,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_1000]) ).
cnf(c_17626,plain,
( sdtpldt0(sdtpldt0(xl,xk),A) = sdtpldt0(xl,sdtpldt0(xk,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17625,c_999]) ).
cnf(c_17627,plain,
sdtpldt0(sdtpldt0(xl,xk),xn) = sdtpldt0(xl,sdtpldt0(xk,xn)),
inference(resolve,[status(thm)],[c_17626,c_1002]) ).
cnf(c_2613,plain,
sdtpldt0(sdtpldt0(xk,xl),xn) = sdtpldt0(xl,sdtpldt0(xk,xn)),
inference(paramod,[status(thm)],[c_1814,c_17627]) ).
cnf(c_17628,plain,
( sdtpldt0(sdtpldt0(xk,A),B) = sdtpldt0(xk,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_999]) ).
cnf(c_17629,plain,
( sdtpldt0(sdtpldt0(xk,xl),A) = sdtpldt0(xk,sdtpldt0(xl,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17628,c_1000]) ).
cnf(c_17630,plain,
sdtpldt0(sdtpldt0(xk,xl),xn) = sdtpldt0(xk,sdtpldt0(xl,xn)),
inference(resolve,[status(thm)],[c_17629,c_1002]) ).
cnf(c_2617,plain,
sdtpldt0(xl,sdtpldt0(xk,xn)) = sdtpldt0(xk,sdtpldt0(xl,xn)),
inference(paramod,[status(thm)],[c_2613,c_17630]) ).
cnf(c_17631,plain,
( sdtpldt0(sdtpldt0(xl,A),B) = sdtpldt0(xl,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_1000]) ).
cnf(c_17632,plain,
( sdtpldt0(sdtpldt0(xl,xn),A) = sdtpldt0(xl,sdtpldt0(xn,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17631,c_1002]) ).
cnf(c_17633,plain,
sdtpldt0(sdtpldt0(xl,xn),xk) = sdtpldt0(xl,sdtpldt0(xn,xk)),
inference(resolve,[status(thm)],[c_17632,c_999]) ).
cnf(c_17634,plain,
sdtpldt0(sdtpldt0(xl,xn),xk) = sdtpldt0(xl,sdtpldt0(xk,xn)),
inference(paramod,[status(thm)],[c_2601,c_17633]) ).
cnf(c_2640,plain,
sdtpldt0(sdtpldt0(xl,xn),xk) = sdtpldt0(xk,sdtpldt0(xl,xn)),
inference(paramod,[status(thm)],[c_2617,c_17634]) ).
cnf(c_17635,plain,
( sdtpldt0(sdtpldt0(xn,A),B) = sdtpldt0(xn,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_1002]) ).
cnf(c_17636,plain,
( sdtpldt0(sdtpldt0(xn,xl),A) = sdtpldt0(xn,sdtpldt0(xl,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17635,c_1000]) ).
cnf(c_17637,plain,
sdtpldt0(sdtpldt0(xn,xl),xk) = sdtpldt0(xn,sdtpldt0(xl,xk)),
inference(resolve,[status(thm)],[c_17636,c_999]) ).
cnf(c_17638,plain,
sdtpldt0(sdtpldt0(xl,xn),xk) = sdtpldt0(xn,sdtpldt0(xl,xk)),
inference(paramod,[status(thm)],[c_2600,c_17637]) ).
cnf(c_17639,plain,
sdtpldt0(xk,sdtpldt0(xl,xn)) = sdtpldt0(xn,sdtpldt0(xl,xk)),
inference(paramod,[status(thm)],[c_2640,c_17638]) ).
cnf(c_17640,plain,
sdtpldt0(xk,sdtpldt0(xl,xn)) = sdtpldt0(xn,sdtpldt0(xk,xl)),
inference(paramod,[status(thm)],[c_1814,c_17639]) ).
cnf(c_2666,plain,
sdtpldt0(xn,sdtpldt0(xk,xl)) = sdtpldt0(xk,sdtpldt0(xl,xn)),
inference(copy,[status(thm)],[c_17640]) ).
cnf(c_2890,plain,
sdtpldt0(sdtpldt0(xk,xl),xn) = sdtpldt0(xk,sdtpldt0(xl,xn)),
inference(paramod,[status(thm)],[c_2617,c_2613]) ).
cnf(c_17641,plain,
( sdtpldt0(sdtpldt0(xn,A),B) = sdtpldt0(xn,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_1002]) ).
cnf(c_17642,plain,
( sdtpldt0(sdtpldt0(xn,xm),A) = sdtpldt0(xn,sdtpldt0(xm,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17641,c_1001]) ).
cnf(c_17643,plain,
sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(xk,xl)) = sdtpldt0(xn,sdtpldt0(xm,sdtpldt0(xk,xl))),
inference(resolve,[status(thm)],[c_17642,c_997]) ).
cnf(c_17644,plain,
sdtpldt0(sdtpldt0(xm,xn),sdtpldt0(xk,xl)) = sdtpldt0(xn,sdtpldt0(xm,sdtpldt0(xk,xl))),
inference(paramod,[status(thm)],[c_2599,c_17643]) ).
cnf(c_15270,plain,
sdtpldt0(sdtpldt0(xm,xn),sdtpldt0(xk,xl)) = sdtpldt0(xn,sdtpldt0(xk,sdtpldt0(xl,xm))),
inference(paramod,[status(thm)],[c_2225,c_17644]) ).
cnf(c_17645,plain,
( sdtpldt0(sdtpldt0(xm,A),B) = sdtpldt0(xm,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_1001]) ).
cnf(c_17646,plain,
( sdtpldt0(sdtpldt0(xm,xn),A) = sdtpldt0(xm,sdtpldt0(xn,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17645,c_1002]) ).
cnf(c_17647,plain,
sdtpldt0(sdtpldt0(xm,xn),sdtpldt0(xk,xl)) = sdtpldt0(xm,sdtpldt0(xn,sdtpldt0(xk,xl))),
inference(resolve,[status(thm)],[c_17646,c_997]) ).
cnf(c_17648,plain,
sdtpldt0(xn,sdtpldt0(xk,sdtpldt0(xl,xm))) = sdtpldt0(xm,sdtpldt0(xn,sdtpldt0(xk,xl))),
inference(paramod,[status(thm)],[c_15270,c_17647]) ).
cnf(c_15281,plain,
sdtpldt0(xn,sdtpldt0(xk,sdtpldt0(xl,xm))) = sdtpldt0(xm,sdtpldt0(xk,sdtpldt0(xl,xn))),
inference(paramod,[status(thm)],[c_2666,c_17648]) ).
cnf(c_17649,plain,
( sdtpldt0(sdtpldt0(xn,A),B) = sdtpldt0(xn,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_1002]) ).
cnf(c_17650,plain,
( sdtpldt0(sdtpldt0(xn,sdtpldt0(xk,xl)),A) = sdtpldt0(xn,sdtpldt0(sdtpldt0(xk,xl),A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17649,c_997]) ).
cnf(c_17651,plain,
sdtpldt0(sdtpldt0(xn,sdtpldt0(xk,xl)),xm) = sdtpldt0(xn,sdtpldt0(sdtpldt0(xk,xl),xm)),
inference(resolve,[status(thm)],[c_17650,c_1001]) ).
cnf(c_17652,plain,
sdtpldt0(sdtpldt0(xk,sdtpldt0(xl,xn)),xm) = sdtpldt0(xn,sdtpldt0(sdtpldt0(xk,xl),xm)),
inference(paramod,[status(thm)],[c_2666,c_17651]) ).
cnf(c_17653,plain,
sdtpldt0(sdtpldt0(xk,sdtpldt0(xl,xn)),xm) = sdtpldt0(xn,sdtpldt0(xk,sdtpldt0(xl,xm))),
inference(paramod,[status(thm)],[c_2376,c_17652]) ).
cnf(c_15386,plain,
sdtpldt0(sdtpldt0(xk,sdtpldt0(xl,xn)),xm) = sdtpldt0(xm,sdtpldt0(xk,sdtpldt0(xl,xn))),
inference(paramod,[status(thm)],[c_15281,c_17653]) ).
cnf(c_17654,plain,
( sdtpldt0(sdtpldt0(xm,A),B) = sdtpldt0(xm,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_1001]) ).
cnf(c_17655,plain,
( sdtpldt0(sdtpldt0(xm,sdtpldt0(xk,xl)),A) = sdtpldt0(xm,sdtpldt0(sdtpldt0(xk,xl),A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17654,c_997]) ).
cnf(c_17656,plain,
sdtpldt0(sdtpldt0(xm,sdtpldt0(xk,xl)),xn) = sdtpldt0(xm,sdtpldt0(sdtpldt0(xk,xl),xn)),
inference(resolve,[status(thm)],[c_17655,c_1002]) ).
cnf(c_17657,plain,
sdtpldt0(sdtpldt0(xk,sdtpldt0(xl,xm)),xn) = sdtpldt0(xm,sdtpldt0(sdtpldt0(xk,xl),xn)),
inference(paramod,[status(thm)],[c_2225,c_17656]) ).
cnf(c_15398,plain,
sdtpldt0(sdtpldt0(xk,sdtpldt0(xl,xm)),xn) = sdtpldt0(xm,sdtpldt0(xk,sdtpldt0(xl,xn))),
inference(paramod,[status(thm)],[c_2890,c_17657]) ).
cnf(c_17658,plain,
( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),A),B) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_997]) ).
cnf(c_17659,plain,
( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xn),A) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xn,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17658,c_1002]) ).
cnf(c_17660,plain,
sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xn),xm) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xn,xm)),
inference(resolve,[status(thm)],[c_17659,c_1001]) ).
cnf(c_17661,plain,
sdtpldt0(sdtpldt0(xk,sdtpldt0(xl,xn)),xm) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xn,xm)),
inference(paramod,[status(thm)],[c_2890,c_17660]) ).
cnf(c_17662,plain,
sdtpldt0(xm,sdtpldt0(xk,sdtpldt0(xl,xn))) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xn,xm)),
inference(paramod,[status(thm)],[c_15386,c_17661]) ).
cnf(c_17663,plain,
sdtpldt0(xm,sdtpldt0(xk,sdtpldt0(xl,xn))) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)),
inference(paramod,[status(thm)],[c_2599,c_17662]) ).
cnf(c_15492,plain,
sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) = sdtpldt0(xm,sdtpldt0(xk,sdtpldt0(xl,xn))),
inference(copy,[status(thm)],[c_17663]) ).
cnf(c_16635,negated_conjecture,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) != sdtpldt0(xm,sdtpldt0(xk,sdtpldt0(xl,xn))),
inference(paramod,[status(thm)],[c_15492,c_140]) ).
cnf(c_17664,plain,
( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),A),B) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_114,c_1003]) ).
cnf(c_17665,plain,
( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),A) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_17664,c_1000]) ).
cnf(c_17666,plain,
sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(resolve,[status(thm)],[c_17665,c_1002]) ).
cnf(c_17667,plain,
sdtpldt0(sdtpldt0(xk,sdtpldt0(xl,xm)),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(paramod,[status(thm)],[c_2211,c_17666]) ).
cnf(c_17668,plain,
sdtpldt0(xm,sdtpldt0(xk,sdtpldt0(xl,xn))) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(paramod,[status(thm)],[c_15398,c_17667]) ).
cnf(c_17669,plain,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xm,sdtpldt0(xk,sdtpldt0(xl,xn))),
inference(copy,[status(thm)],[c_17668]) ).
cnf(c_17590,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_16635,c_17669]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG090+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.35 % Computer : n017.cluster.edu
% 0.05/0.35 % Model : x86_64 x86_64
% 0.05/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.35 % Memory : 8046.5625MB
% 0.05/0.35 % OS : Linux 6.8.0-71-generic
% 0.05/0.35 % CPULimit : 300
% 0.05/0.35 % WCLimit : 300
% 0.05/0.35 % DateTime : Sat Sep 26 05:57:32 UTC 2026
% 0.05/0.35 % CPUTime :
% 0.05/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.36 % Process 8936 was started by sandbox on n017,
% 0.05/0.36 % Sat Sep 26 05:57:32 2026
% 0.05/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/0.36
% 0.05/0.36 % From the command line: assign(max_seconds, 300).
% 25.78/5.00
% 25.78/5.00 % SZS status Theorem for theBenchmark
% 25.78/5.00
% 25.78/5.00 % Proof 1 at 2.98 (+ 0.69) seconds.
% 25.78/5.00 % Length of proof is 64.
% 25.78/5.00 % Level of proof is 14.
% 25.78/5.00 % Maximum clause weight is 55.000.
% 25.78/5.00 % Given clauses 185.
% 25.78/5.00
% 25.78/5.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------