%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM851+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 02:21:11 PM UTC 2026
% Result : Theorem 87.44s 11.44s
% Output : Proof 87.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 65 unt; 0 def)
% Number of atoms : 89 ( 88 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 66 ( 54 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 100 ( 7 sgn 56 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
vmul(vplus(vd471,vd473),vd469) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t82,plain,
ifeq(vmul(vplus(vd471,vd473),vd469),vplus(vmul(vd471,vd469),vmul(vd473,vd469)),false,true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f19,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd19) ).
fof(f19_nnf,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [Vd79,Vd78] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c21,plain,
vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t20,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t264,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(orient,[status(thm)],[t20]) ).
cnf(t1925,plain,
ifeq(vmul(vplus(vd473,vd471),vd469),vplus(vmul(vd471,vd469),vmul(vd473,vd469)),false,true) = true,
inference(step,[status(thm)],[t82,t264]) ).
fof(f2,axiom,
vd470 = vplus(vd471,vd473),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd2) ).
fof(f2_nnf,plain,
vd470 = vplus(vd471,vd473),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
vd470 = vplus(vd471,vd473),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(t10,plain,
vplus(vd471,vd473) = vd470,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t1557,plain,
vplus(vd473,vd471) = vd470,
inference(step,[status(thm)],[t10,t264]) ).
cnf(t482,plain,
vplus(vd473,vd471) = vd470,
inference(orient,[status(thm)],[t1557]) ).
cnf(t1926,plain,
ifeq(vmul(vd470,vd469),vplus(vmul(vd471,vd469),vmul(vd473,vd469)),false,true) = true,
inference(step,[status(thm)],[t1925,t482]) ).
cnf(t1927,plain,
ifeq(vmul(vd470,vd469),vplus(vmul(vd473,vd469),vmul(vd471,vd469)),false,true) = true,
inference(step,[status(thm)],[t1926,t264]) ).
cnf(t1433,plain,
ifeq(vmul(vd470,vd469),vplus(vmul(vd473,vd469),vmul(vd471,vd469)),false,true) = true,
inference(orient,[status(thm)],[t1927]) ).
cnf(t0,plain,
not(false) = true,
introduced(definition) ).
cnf(t1519,plain,
not(false) = true,
inference(orient,[status(thm)],[t0]) ).
fof(f6,axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd6) ).
fof(f6_nnf,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t19,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t1520,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(orient,[status(thm)],[t19]) ).
fof(f5,axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd5) ).
fof(f5_nnf,plain,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t63,plain,
vplus(vmul(X1,X2),vmul(X1,X3)) = vmul(X1,vplus(X2,X3)),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t442,plain,
vplus(vmul(X1,X2),vmul(X1,X3)) = vmul(X1,vplus(X2,X3)),
inference(orient,[status(thm)],[t63]) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t18]) ).
fof(f14,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd14) ).
fof(f14_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Vd120,Vd121,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c16,plain,
( X1 != vplus(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f15,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd15) ).
fof(f15_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| ! [Vd123] : Vd120 != vplus(Vd121,Vd123) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [Vd120,Vd121,Vd123,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != vplus(Vd121,Vd123) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c17,plain,
( X1 != vplus(X0,X3)
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f16,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd16) ).
fof(f16_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd123] : Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [Vd120,Vd121,Vd123] :
( Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c18,plain,
( X0 != vplus(X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f18,axiom,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd18) ).
fof(f18_nnf,plain,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [Vd93,Vd92] : Vd93 != vplus(Vd92,Vd93),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c20,plain,
X1 != vplus(X0,X1),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f25,axiom,
! [Vd16] : vsucc(Vd16) != Vd16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd25) ).
fof(f25_nnf,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c28,plain,
vsucc(X0) != X0,
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c16,c17,c18,c20,c28]) ).
cnf(g0_0,plain,
true != ifeq(vmul(vd470,vd469),vplus(vmul(vd473,vd469),vmul(vd471,vd469)),false,true),
inference(rw,[status(thm)],[goal_0,t1433]) ).
cnf(g0_1,plain,
true != ifeq(vmul(vd470,vd469),vplus(vmul(vd471,vd469),vmul(vd473,vd469)),false,true),
inference(rw,[status(thm)],[g0_0,t264]) ).
cnf(g0_2,plain,
true != ifeq(vmul(vd470,vd469),vplus(vmul(vd471,vd469),vmul(vd473,vd469)),false,not(false)),
inference(rw,[status(thm)],[g0_1,t1519]) ).
cnf(g0_3,plain,
true != ifeq(vmul(vd470,vd469),vplus(vmul(vd471,vd469),vmul(vd469,vd473)),false,not(false)),
inference(rw,[status(thm)],[g0_2,t1520]) ).
cnf(g0_4,plain,
true != ifeq(vmul(vd470,vd469),vplus(vmul(vd469,vd471),vmul(vd469,vd473)),false,not(false)),
inference(rw,[status(thm)],[g0_3,t1520]) ).
cnf(g0_5,plain,
true != ifeq(vmul(vd470,vd469),vplus(vmul(vd469,vd473),vmul(vd469,vd471)),false,not(false)),
inference(rw,[status(thm)],[g0_4,t264]) ).
cnf(g0_6,plain,
true != ifeq(vmul(vd469,vd470),vplus(vmul(vd469,vd473),vmul(vd469,vd471)),false,not(false)),
inference(rw,[status(thm)],[g0_5,t1520]) ).
cnf(g0_7,plain,
true != ifeq(vmul(vd469,vd470),vplus(vmul(vd469,vd473),vmul(vd471,vd469)),false,not(false)),
inference(rw,[status(thm)],[g0_6,t1520]) ).
cnf(g0_8,plain,
true != ifeq(vmul(vd469,vd470),vplus(vmul(vd469,vd473),vmul(vd471,vd469)),false,true),
inference(rw,[status(thm)],[g0_7,t1519]) ).
cnf(g0_9,plain,
true != ifeq(vmul(vd469,vd470),vplus(vmul(vd471,vd469),vmul(vd469,vd473)),false,true),
inference(rw,[status(thm)],[g0_8,t264]) ).
cnf(g0_10,plain,
true != ifeq(vmul(vd469,vd470),vplus(vmul(vd469,vd471),vmul(vd469,vd473)),false,true),
inference(rw,[status(thm)],[g0_9,t1520]) ).
cnf(g0_11,plain,
true != ifeq(vmul(vd469,vd470),vmul(vd469,vplus(vd471,vd473)),false,true),
inference(rw,[status(thm)],[g0_10,t442]) ).
cnf(g0_12,plain,
true != ifeq(vmul(vd469,vd470),vmul(vd469,vplus(vd473,vd471)),false,true),
inference(rw,[status(thm)],[g0_11,t264]) ).
cnf(g0_13,plain,
true != ifeq(vmul(vd470,vd469),vmul(vd469,vplus(vd473,vd471)),false,true),
inference(rw,[status(thm)],[g0_12,t1520]) ).
cnf(g0_14,plain,
true != ifeq(vmul(vd470,vd469),vmul(vd469,vd470),false,true),
inference(rw,[status(thm)],[g0_13,t482]) ).
cnf(g0_15,plain,
true != ifeq(vmul(vd470,vd469),vmul(vd470,vd469),false,true),
inference(rw,[status(thm)],[g0_14,t1520]) ).
cnf(g0_16,plain,
true != false,
inference(rw,[status(thm)],[g0_15,t258]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM851+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 05:40:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 87.44/11.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 87.44/11.44 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------