%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM847+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 02:21:10 PM UTC 2026
% Result : Theorem 99.98s 13.04s
% Output : Proof 99.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 32 unt; 0 def)
% Number of atoms : 80 ( 63 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 90 ( 66 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 100 ( 6 sgn 65 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t247,plain,
eq(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) = false,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f49,axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd49) ).
fof(f49_nnf,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c58,plain,
vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(t163,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(t962,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(orient,[status(thm)],[t163]) ).
cnf(t1980,plain,
eq(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) = false,
inference(step,[status(thm)],[t247,t962]) ).
cnf(t2,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t286,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t1981,plain,
true = false,
inference(step,[status(thm)],[t1980,t286]) ).
cnf(t1877,plain,
false = true,
inference(orient,[status(thm)],[t1981]) ).
fof(f35,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd35) ).
fof(f35_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c42,plain,
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f36,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd36) ).
fof(f36_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c43,plain,
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
fof(f37,axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd37) ).
fof(f37_nnf,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c44,plain,
( ~ greater(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
fof(f41,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd41) ).
fof(f41_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [Vd120,Vd121,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c50,plain,
( X1 != vplus(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
fof(f42,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd42) ).
fof(f42_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| ! [Vd123] : Vd120 != vplus(Vd121,Vd123) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [Vd120,Vd121,Vd123,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != vplus(Vd121,Vd123) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c51,plain,
( X1 != vplus(X0,X3)
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
fof(f43,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd43) ).
fof(f43_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd123] : Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [Vd120,Vd121,Vd123] :
( Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c52,plain,
( X0 != vplus(X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
fof(f45,axiom,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd45) ).
fof(f45_nnf,plain,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [Vd93,Vd92] : Vd93 != vplus(Vd92,Vd93),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c54,plain,
X1 != vplus(X0,X1),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
fof(f52,axiom,
! [Vd16] : vsucc(Vd16) != Vd16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd52) ).
fof(f52_nnf,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c62,plain,
vsucc(X0) != X0,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
fof(f55,axiom,
! [Vd1] : vsucc(Vd1) != v1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd55) ).
fof(f55_nnf,plain,
! [Vd1] : vsucc(Vd1) != v1,
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [Vd1] : vsucc(Vd1) != v1,
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c65,plain,
vsucc(X0) != v1,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c42,c43,c44,c50,c51,c52,c54,c62,c65]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1877]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM847+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 05:34:19 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 99.98/13.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 99.98/13.04 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------