%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM435+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 78.65s 10.69s
% Output : Proof 78.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 73 ( 52 unt; 1 def)
% Number of atoms : 150 ( 82 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 126 ( 49 ~; 29 |; 44 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 50 ( 2 sgn 23 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,conjecture,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f25_neg,negated_conjecture,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f25_nnf,plain,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(nnf_transformation,[status(thm)],[f25_neg]) ).
fof(f25_sk,plain,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c46,plain,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(t228,plain,
eq(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xq,sdtasdt0(xp,xm))) = false,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t4397,plain,
eq(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xq,sdtasdt0(xp,xm))) = false,
inference(orient,[status(thm)],[t228]) ).
fof(f10,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(f10_nnf,plain,
! [W0,W1,W2] :
( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [W0,W1,W2] :
( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c12,plain,
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t251,plain,
ifeq(aInteger0(X1),true,ifeq(aInteger0(X2),true,ifeq(aInteger0(X3),true,sdtasdt0(X1,sdtasdt0(X2,X3)),sdtasdt0(sdtasdt0(X1,X2),X3)),sdtasdt0(sdtasdt0(X1,X2),X3)),sdtasdt0(sdtasdt0(X1,X2),X3)) = sdtasdt0(sdtasdt0(X1,X2),X3),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t2025,plain,
ifeq(aInteger0(X1),true,ifeq(aInteger0(X2),true,ifeq(aInteger0(X3),true,sdtasdt0(X1,sdtasdt0(X2,X3)),sdtasdt0(sdtasdt0(X1,X2),X3)),sdtasdt0(sdtasdt0(X1,X2),X3)),sdtasdt0(sdtasdt0(X1,X2),X3)) = sdtasdt0(sdtasdt0(X1,X2),X3),
inference(orient,[status(thm)],[t251]) ).
fof(f24,hypothesis,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1032) ).
fof(f24_nnf,plain,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c45,plain,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t224,plain,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)),
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t2270,plain,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)),
inference(orient,[status(thm)],[t224]) ).
fof(f11,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f11_nnf,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c13,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi12,axiom,
ifeq(aInteger0(X0),true,ifeq(aInteger0(X1),true,sdtasdt0(X0,X1),sdtasdt0(X1,X0)),sdtasdt0(X1,X0)) = sdtasdt0(X1,X0),
inference(equality_encoding,[status(esa)],[c13]) ).
fof(f22,hypothesis,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__979) ).
fof(f22_nnf,plain,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c35,plain,
aInteger0(xp),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi33,axiom,
aInteger0(xp) = true,
inference(equality_encoding,[status(esa)],[c35]) ).
cnf(c37,plain,
aInteger0(xq),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi34,axiom,
aInteger0(xq) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t154,plain,
sdtasdt0(xq,xp) = sdtasdt0(xp,xq),
inference(hyper_resolution,[status(thm)],[hi12,hi33,hi34]) ).
cnf(t2597,plain,
sdtasdt0(xp,xq) = sdtasdt0(xq,xp),
inference(orient,[status(thm)],[t154]) ).
cnf(t17865,plain,
sdtasdt0(sdtasdt0(xq,xp),xm) = sdtpldt0(xa,smndt0(xb)),
inference(step,[status(thm)],[t2270,t2597]) ).
cnf(t2605,plain,
sdtasdt0(sdtasdt0(xq,xp),xm) = sdtpldt0(xa,smndt0(xb)),
inference(rw,[status(thm)],[t17865]) ).
cnf(t17733,plain,
sdtasdt0(sdtasdt0(xq,xp),xm) = sdtpldt0(xa,smndt0(xb)),
inference(orient,[status(thm)],[t2605]) ).
cnf(t17751,plain,
sdtasdt0(sdtasdt0(xq,xp),xm) = ifeq(aInteger0(xq),true,ifeq(aInteger0(xp),true,ifeq(aInteger0(xm),true,sdtasdt0(xq,sdtasdt0(xp,xm)),sdtpldt0(xa,smndt0(xb))),sdtasdt0(sdtasdt0(xq,xp),xm)),sdtasdt0(sdtasdt0(xq,xp),xm)),
inference(cp,[status(thm)],[t2025,t17733]) ).
cnf(t18546,plain,
sdtpldt0(xa,smndt0(xb)) = ifeq(aInteger0(xq),true,ifeq(aInteger0(xp),true,ifeq(aInteger0(xm),true,sdtasdt0(xq,sdtasdt0(xp,xm)),sdtpldt0(xa,smndt0(xb))),sdtasdt0(sdtasdt0(xq,xp),xm)),sdtasdt0(sdtasdt0(xq,xp),xm)),
inference(step,[status(thm)],[t17751,t17733]) ).
cnf(t7,plain,
aInteger0(xq) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t539,plain,
aInteger0(xq) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t18547,plain,
sdtpldt0(xa,smndt0(xb)) = ifeq(true,true,ifeq(aInteger0(xp),true,ifeq(aInteger0(xm),true,sdtasdt0(xq,sdtasdt0(xp,xm)),sdtpldt0(xa,smndt0(xb))),sdtasdt0(sdtasdt0(xq,xp),xm)),sdtasdt0(sdtasdt0(xq,xp),xm)),
inference(step,[status(thm)],[t18546,t539]) ).
cnf(t122,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t122]) ).
cnf(t18548,plain,
sdtpldt0(xa,smndt0(xb)) = ifeq(aInteger0(xp),true,ifeq(aInteger0(xm),true,sdtasdt0(xq,sdtasdt0(xp,xm)),sdtpldt0(xa,smndt0(xb))),sdtasdt0(sdtasdt0(xq,xp),xm)),
inference(step,[status(thm)],[t18547,t256]) ).
cnf(t6,plain,
aInteger0(xp) = true,
inference(equality_encoding,[status(esa)],[c35]) ).
cnf(t531,plain,
aInteger0(xp) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t18549,plain,
sdtpldt0(xa,smndt0(xb)) = ifeq(true,true,ifeq(aInteger0(xm),true,sdtasdt0(xq,sdtasdt0(xp,xm)),sdtpldt0(xa,smndt0(xb))),sdtasdt0(sdtasdt0(xq,xp),xm)),
inference(step,[status(thm)],[t18548,t531]) ).
cnf(t18550,plain,
sdtpldt0(xa,smndt0(xb)) = ifeq(aInteger0(xm),true,sdtasdt0(xq,sdtasdt0(xp,xm)),sdtpldt0(xa,smndt0(xb))),
inference(step,[status(thm)],[t18549,t256]) ).
cnf(c44,plain,
aInteger0(xm),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t5,plain,
aInteger0(xm) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(t543,plain,
aInteger0(xm) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t18551,plain,
sdtpldt0(xa,smndt0(xb)) = ifeq(true,true,sdtasdt0(xq,sdtasdt0(xp,xm)),sdtpldt0(xa,smndt0(xb))),
inference(step,[status(thm)],[t18550,t543]) ).
cnf(t18552,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(step,[status(thm)],[t18551,t256]) ).
cnf(t17821,plain,
sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(orient,[status(thm)],[t18552]) ).
cnf(t18553,plain,
eq(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xa,smndt0(xb))) = false,
inference(step,[status(thm)],[t4397,t17821]) ).
cnf(t18,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t1775,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t18554,plain,
true = false,
inference(step,[status(thm)],[t18553,t1775]) ).
cnf(t17843,plain,
true = false,
inference(rw,[status(thm)],[t18554]) ).
cnf(t17845,plain,
false = true,
inference(orient,[status(thm)],[t17843]) ).
fof(f17,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('/export/starexec/sandbox/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]) ).
cnf(c36,plain,
xp != sz00,
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(c38,plain,
xq != sz00,
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
fof(f23,hypothesis,
( sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& ? [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) )
& sdtasdt0(xp,xq) != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1003) ).
fof(f23_nnf,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& ? [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) )
& sdtasdt0(xp,xq) != sz00 ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& sdtasdt0(sdtasdt0(xp,xq),sk1) = sdtpldt0(xa,smndt0(xb))
& aInteger0(sk1)
& sdtasdt0(xp,xq) != sz00 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f23_nnf]) ).
cnf(c39,plain,
sdtasdt0(xp,xq) != sz00,
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c24,c36,c38,c39,c46]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t17845]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM435+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.58 % Computer : n005.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Thu Sep 24 03:57:49 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 78.65/10.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 78.65/10.69 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------