%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM432+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:20:01 PM UTC 2026
% Result : Theorem 36.02s 8.51s
% Output : Proof 36.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 39 unt; 1 def)
% Number of atoms : 139 ( 63 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 121 ( 47 ~; 33 |; 37 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 47 ( 2 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,conjecture,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc))
& aInteger0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f26_neg,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc))
& aInteger0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f26_nnf,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xc,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
& ! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc))
| ~ aInteger0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f26_neg]) ).
fof(f26_sk,plain,
! [W0] :
( ~ sdteqdtlpzmzozddtrp0(xa,xc,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
& ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc))
| ~ aInteger0(W0) ) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c50,plain,
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xc))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(t241,plain,
ifeq(aInteger0(X1),true,ifeq(sdtasdt0(xq,X1),sdtpldt0(xa,smndt0(xc)),false,true),true) = true,
inference(equality_encoding,[status(esa)],[c50]) ).
cnf(t579,plain,
ifeq(aInteger0(X1),true,ifeq(sdtasdt0(xq,X1),sdtpldt0(xa,smndt0(xc)),false,true),true) = true,
inference(orient,[status(thm)],[t241]) ).
fof(f4,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
fof(f4_nnf,plain,
! [W0,W1] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [W0,W1] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t239,plain,
ifeq(aInteger0(X1),true,ifeq(aInteger0(X2),true,aInteger0(sdtpldt0(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t699,plain,
ifeq(aInteger0(X1),true,ifeq(aInteger0(X2),true,aInteger0(sdtpldt0(X1,X2)),true),true) = true,
inference(orient,[status(thm)],[t239]) ).
fof(f7,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f7_nnf,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi6,axiom,
ifeq(aInteger0(X0),true,ifeq(aInteger0(X1),true,sdtpldt0(X0,X1),sdtpldt0(X1,X0)),sdtpldt0(X1,X0)) = sdtpldt0(X1,X0),
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f23,hypothesis,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__876) ).
fof(f23_nnf,plain,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c45,plain,
aInteger0(xn),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi42,axiom,
aInteger0(xn) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
fof(f24,hypothesis,
( sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc))
& aInteger0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__899) ).
fof(f24_nnf,plain,
( sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc))
& aInteger0(xm) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
( sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc))
& aInteger0(xm) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c47,plain,
aInteger0(xm),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi44,axiom,
aInteger0(xm) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t174,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(hyper_resolution,[status(thm)],[hi6,hi42,hi44]) ).
cnf(t4477,plain,
sdtpldt0(xm,xn) = sdtpldt0(xn,xm),
inference(orient,[status(thm)],[t174]) ).
cnf(t4478,plain,
true = ifeq(aInteger0(xm),true,ifeq(aInteger0(xn),true,aInteger0(sdtpldt0(xn,xm)),true),true),
inference(cp,[status(thm)],[t699,t4477]) ).
cnf(t7,plain,
aInteger0(xm) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t541,plain,
aInteger0(xm) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t6199,plain,
true = ifeq(true,true,ifeq(aInteger0(xn),true,aInteger0(sdtpldt0(xn,xm)),true),true),
inference(step,[status(thm)],[t4478,t541]) ).
cnf(t134,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t134]) ).
cnf(t6200,plain,
true = ifeq(aInteger0(xn),true,aInteger0(sdtpldt0(xn,xm)),true),
inference(step,[status(thm)],[t6199,t256]) ).
cnf(t8,plain,
aInteger0(xn) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t533,plain,
aInteger0(xn) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t6201,plain,
true = ifeq(true,true,aInteger0(sdtpldt0(xn,xm)),true),
inference(step,[status(thm)],[t6200,t533]) ).
cnf(t6202,plain,
true = aInteger0(sdtpldt0(xn,xm)),
inference(step,[status(thm)],[t6201,t256]) ).
cnf(t6034,plain,
aInteger0(sdtpldt0(xn,xm)) = true,
inference(orient,[status(thm)],[t6202]) ).
cnf(t6062,plain,
true = ifeq(true,true,ifeq(sdtasdt0(xq,sdtpldt0(xn,xm)),sdtpldt0(xa,smndt0(xc)),false,true),true),
inference(cp,[status(thm)],[t579,t6034]) ).
cnf(t6203,plain,
true = ifeq(sdtasdt0(xq,sdtpldt0(xn,xm)),sdtpldt0(xa,smndt0(xc)),false,true),
inference(step,[status(thm)],[t6062,t256]) ).
fof(f25,hypothesis,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__924) ).
fof(f25_nnf,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c49,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(t226,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(t2245,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(orient,[status(thm)],[t226]) ).
cnf(t6204,plain,
true = ifeq(sdtpldt0(xa,smndt0(xc)),sdtpldt0(xa,smndt0(xc)),false,true),
inference(step,[status(thm)],[t6203,t2245]) ).
cnf(t6205,plain,
true = false,
inference(step,[status(thm)],[t6204,t256]) ).
cnf(t6090,plain,
false = true,
inference(orient,[status(thm)],[t6205]) ).
fof(f17,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(f17_nnf,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [W0,W1,W2] :
( ( ( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2)
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ( ( sdtasdt0(W1,sk0(W0,W1)) = W0
& aInteger0(sk0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f17_nnf]) ).
cnf(c24,plain,
( X1 != sz00
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f21,hypothesis,
( aInteger0(xc)
& xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__818) ).
fof(f21_nnf,plain,
( aInteger0(xc)
& xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
( aInteger0(xc)
& xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c35,plain,
xq != sz00,
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(c51,plain,
~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc))),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(c52,plain,
~ sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c24,c35,c50,c51,c52]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t6090]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM432+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 03:52:16 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 36.02/8.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.02/8.51 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------