%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM836+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 02:21:07 PM UTC 2026
% Result : Theorem 8.07s 6.54s
% Output : Proof 8.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 14 unt; 0 def)
% Number of atoms : 78 ( 51 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 85 ( 49 ~; 28 |; 6 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 72 ( 6 sgn 42 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [Vd198,Vd199] :
( less(Vd199,Vd198)
<=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd2) ).
fof(f2_nnf,plain,
! [Vd198,Vd199] :
( ( ! [Vd201] : Vd198 != vplus(Vd199,Vd201)
| less(Vd199,Vd198) )
& ( ? [Vd201] : Vd198 = vplus(Vd199,Vd201)
| ~ less(Vd199,Vd198) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [Vd199,Vd198,Vd201] :
( ( Vd198 != vplus(Vd199,Vd201)
| less(Vd199,Vd198) )
& ( Vd198 = vplus(Vd199,sk0(Vd198,Vd199))
| ~ less(Vd199,Vd198) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c3,plain,
( X0 = vplus(X1,sk0(X0,X1))
| ~ less(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(less(X0,X1),true,X1,vplus(X0,sk0(X1,X0))) = vplus(X0,sk0(X1,X0)),
inference(equality_encoding,[status(esa)],[c3]) ).
fof(f0,conjecture,
( ~ less(vd203,vd204)
| ~ greater(vd203,vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
~ ( ~ less(vd203,vd204)
| ~ greater(vd203,vd204) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( less(vd203,vd204)
& greater(vd203,vd204) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
( less(vd203,vd204)
& greater(vd203,vd204) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c1,plain,
less(vd203,vd204),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,negated_conjecture,
less(vd203,vd204) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h1,plain,
vd204 = vplus(vd203,sk0(vd204,vd203)),
inference(hyper_resolution,[status(thm)],[hi2,hi1]) ).
fof(f3,axiom,
! [Vd193,Vd194] :
( greater(Vd194,Vd193)
<=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd3) ).
fof(f3_nnf,plain,
! [Vd193,Vd194] :
( ( ! [Vd196] : Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ( ? [Vd196] : Vd194 = vplus(Vd193,Vd196)
| ~ greater(Vd194,Vd193) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [Vd194,Vd193,Vd196] :
( ( Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ( Vd194 = vplus(Vd193,sk1(Vd193,Vd194))
| ~ greater(Vd194,Vd193) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c5,plain,
( X1 = vplus(X0,sk1(X0,X1))
| ~ greater(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi4,axiom,
ifeq(greater(X0,X1),true,X0,vplus(X1,sk1(X1,X0))) = vplus(X1,sk1(X1,X0)),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(c0,plain,
greater(vd203,vd204),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
greater(vd203,vd204) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
vd203 = vplus(vd204,sk1(vd204,vd203)),
inference(hyper_resolution,[status(thm)],[hi4,hi0]) ).
fof(f6,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd6) ).
fof(f6_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| ! [Vd123] : Vd120 != vplus(Vd121,Vd123) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Vd120,Vd121,Vd123,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != vplus(Vd121,Vd123) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c9,plain,
( X1 != vplus(X0,X3)
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi13,axiom,
ifeq(X0,vplus(X1,X2),ifeq(X1,vplus(X0,X3),false,true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi13,h0,h1]) ).
cnf(t60,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f1,axiom,
( ~ greater(vd203,vd204)
| vd203 != vd204 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd1) ).
fof(f1_nnf,plain,
( ~ greater(vd203,vd204)
| vd203 != vd204 ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
( ~ greater(vd203,vd204)
| vd203 != vd204 ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( ~ greater(vd203,vd204)
| vd203 != vd204 ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f5,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd5) ).
fof(f5_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Vd120,Vd121,Vd125] :
( Vd121 != vplus(Vd120,Vd125)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c8,plain,
( X1 != vplus(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f7,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd7) ).
fof(f7_nnf,plain,
! [Vd120,Vd121] :
( ! [Vd123] : Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Vd120,Vd121,Vd123] :
( Vd120 != vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c10,plain,
( X0 != vplus(X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2,c8,c9,c10]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t60]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM836+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n026.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 05:35:15 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.07/6.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.07/6.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------