%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM854+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 02:21:12 PM UTC 2026
% Result : Theorem 6.82s 1.49s
% Output : Proof 6.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 21 unt; 0 def)
% Number of atoms : 77 ( 44 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 85 ( 57 ~; 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 : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 87 ( 6 sgn 53 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
file('/export/starexec/sandbox2/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(t72,plain,
ifeq(greater(vmul(vd508,vd511),vmul(vd509,vd511)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f8,axiom,
! [Vd456,Vd457,Vd458] :
( greater(Vd457,Vd458)
=> greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456)) ),
file('/export/starexec/sandbox2/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/sandbox2/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(t26,plain,
greater(vmul(vd508,X1),vmul(vd509,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1]) ).
cnf(t398,plain,
greater(vmul(vd508,X1),vmul(vd509,X1)) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(t567,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t72,t398]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t93,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t568,plain,
false = true,
inference(step,[status(thm)],[t567,t93]) ).
cnf(t541,plain,
false = true,
inference(orient,[status(thm)],[t568]) ).
fof(f18,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd18) ).
fof(f18_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c19,plain,
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f19,axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd19) ).
fof(f19_nnf,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c20,plain,
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f20,axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd20) ).
fof(f20_nnf,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c21,plain,
( ~ greater(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f24,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd24) ).
fof(f24_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [Vd120,Vd121,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c27,plain,
( X1 != vplus(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f25,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd25) ).
fof(f25_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| ! [Vd123] : Vd120 != vplus(Vd121,Vd123) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [Vd120,Vd121,Vd123,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != vplus(Vd121,Vd123) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c28,plain,
( X1 != vplus(X0,X3)
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f26,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd26) ).
fof(f26_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd123] : Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [Vd120,Vd121,Vd123] :
( Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c29,plain,
( X0 != vplus(X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c19,c20,c21,c27,c28,c29]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t541]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM854+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 05:40:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.82/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.82/1.49 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------