%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM854+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 : n010.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 02:21:12 PM UTC 2026
% Result : Theorem 9.89s 1.93s
% Output : Proof 9.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 29 unt; 0 def)
% Number of atoms : 85 ( 52 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 97 ( 69 ~; 27 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 96 ( 6 sgn 65 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [Vd456,Vd457,Vd458] :
( greater(Vd457,Vd458)
=> greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd8) ).
fof(f8_nnf,plain,
! [Vd456,Vd457,Vd458] :
( greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456))
| ~ greater(Vd457,Vd458) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Vd457,Vd458,Vd456] :
( greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456))
| ~ greater(Vd457,Vd458) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( greater(vmul(X1,X0),vmul(X2,X0))
| ~ greater(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi7,axiom,
ifeq(greater(X0,X1),true,greater(vmul(X0,X2),vmul(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
fof(f2,axiom,
greater(vd508,vd509),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd2) ).
fof(f2_nnf,plain,
greater(vd508,vd509),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
greater(vd508,vd509),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi1,axiom,
greater(vd508,vd509) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h33,plain,
greater(vmul(vd508,V0),vmul(vd509,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1]) ).
fof(f0,conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi59,negated_conjecture,
ifeq(greater(vmul(vd508,vd511),vmul(vd509,vd511)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi59,h33]) ).
cnf(t270,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f38,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd38) ).
fof(f38_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c45,plain,
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
fof(f39,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd39) ).
fof(f39_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c46,plain,
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f40,axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd40) ).
fof(f40_nnf,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c47,plain,
( ~ greater(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
fof(f44,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd44) ).
fof(f44_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [Vd120,Vd121,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c53,plain,
( X1 != vplus(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
fof(f45,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd45) ).
fof(f45_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| ! [Vd123] : Vd120 != vplus(Vd121,Vd123) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [Vd120,Vd121,Vd123,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != vplus(Vd121,Vd123) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c54,plain,
( X1 != vplus(X0,X3)
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
fof(f46,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd46) ).
fof(f46_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd123] : Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [Vd120,Vd121,Vd123] :
( Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c55,plain,
( X0 != vplus(X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
fof(f48,axiom,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd48) ).
fof(f48_nnf,plain,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [Vd93,Vd92] : Vd93 != vplus(Vd92,Vd93),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c57,plain,
X1 != vplus(X0,X1),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
fof(f55,axiom,
! [Vd16] : vsucc(Vd16) != Vd16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd55) ).
fof(f55_nnf,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [Vd16] : vsucc(Vd16) != Vd16,
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c65,plain,
vsucc(X0) != X0,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
fof(f58,axiom,
! [Vd1] : vsucc(Vd1) != v1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd58) ).
fof(f58_nnf,plain,
! [Vd1] : vsucc(Vd1) != v1,
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
! [Vd1] : vsucc(Vd1) != v1,
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c68,plain,
vsucc(X0) != v1,
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c45,c46,c47,c53,c54,c55,c57,c65,c68]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t270]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM854+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 05:35:13 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.89/1.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.89/1.93 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------