%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN986+1.003 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 03:36:29 PM UTC 2026
% Result : Theorem 5.20s 1.18s
% Output : Proof 5.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 16 unt; 0 def)
% Number of atoms : 48 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 21 ~; 15 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 17 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 53 ( 2 sgn 23 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Y,X,Z,Z1] :
( r(Y,X,Z)
=> ( r(Z,X,Z1)
=> r(Y,succ(X),Z1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp2) ).
fof(f1_nnf,plain,
! [Y,X,Z,Z1] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [Y,X,Z,Z1] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( r(X0,succ(X1),X3)
| ~ r(X2,X1,X3)
| ~ r(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(r(X0,X1,X2),true,ifeq(r(X2,X1,X3),true,r(X0,succ(X1),X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
fof(f0,axiom,
! [Y] : r(Y,zero,succ(Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp1) ).
fof(f0_nnf,plain,
! [Y] : r(Y,zero,succ(Y)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [Y] : r(Y,zero,succ(Y)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
r(X0,zero,succ(X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
r(X0,zero,succ(X0)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
r(V0,succ(zero),succ(succ(V0))) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi0,hi0]) ).
cnf(h1,plain,
r(V0,succ(succ(zero)),succ(succ(succ(succ(V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi1,h0,h0]) ).
cnf(h2,plain,
r(V0,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(V0))))))))) = true,
inference(hyper_resolution,[status(thm)],[hi1,h1,h1]) ).
cnf(h3,plain,
r(V0,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(V0))))))))))))))))) = true,
inference(hyper_resolution,[status(thm)],[hi1,h2,h2]) ).
fof(f2,conjecture,
? [Z3,Z2,Z1,Z0] :
( r(zero,Z1,Z0)
& r(zero,Z2,Z1)
& r(zero,Z3,Z2)
& r(zero,zero,Z3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ck) ).
fof(f2_neg,negated_conjecture,
~ ? [Z3,Z2,Z1,Z0] :
( r(zero,Z1,Z0)
& r(zero,Z2,Z1)
& r(zero,Z3,Z2)
& r(zero,zero,Z3) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
! [Z3,Z2,Z1,Z0] :
( ~ r(zero,Z1,Z0)
| ~ r(zero,Z2,Z1)
| ~ r(zero,Z3,Z2)
| ~ r(zero,zero,Z3) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
! [Z3,Z2,Z1,Z0] :
( ~ r(zero,Z1,Z0)
| ~ r(zero,Z2,Z1)
| ~ r(zero,Z3,Z2)
| ~ r(zero,zero,Z3) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ r(zero,X2,X3)
| ~ r(zero,X1,X2)
| ~ r(zero,X0,X1)
| ~ r(zero,zero,X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,negated_conjecture,
ifeq(r(zero,zero,X0),true,ifeq(r(zero,X0,X1),true,ifeq(r(zero,X1,X2),true,ifeq(r(zero,X2,X3),true,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi2,hi0,h0,h1,h3]) ).
cnf(t47,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t47]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN986+1.003 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.38 % Computer : n001.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Fri Sep 25 02:49:41 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.20/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.20/1.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------