%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN940+1 : TPTP v9.3.1. Released v3.1.0.
% 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 03:36:22 PM UTC 2026
% Result : Theorem 3.97s 1.09s
% Output : Proof 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 49 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 48 ( 18 ~; 12 |; 12 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 32 ( 10 sgn 12 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
! [B,C] :
( ! [Z] : q(f(Z))
=> ? [X,Y] :
( q(X)
& ( p(f(Y))
=> ( ( r(Y)
=> ( r(C)
& r(B) ) )
& p(X) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f0_neg,negated_conjecture,
~ ! [B,C] :
( ! [Z] : q(f(Z))
=> ? [X,Y] :
( q(X)
& ( p(f(Y))
=> ( ( r(Y)
=> ( r(C)
& r(B) ) )
& p(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [B,C] :
( ! [X,Y] :
( ~ q(X)
| ( ( ( ( ~ r(C)
| ~ r(B) )
& r(Y) )
| ~ p(X) )
& p(f(Y)) ) )
& ! [Z] : q(f(Z)) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Z,Y,X] :
( ( ~ q(X)
| ( ( ( ( ~ r(sk1)
| ~ r(sk0) )
& r(Y) )
| ~ p(X) )
& p(f(Y)) ) )
& q(f(Z)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c1,plain,
( ~ q(X3)
| p(f(X4)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,negated_conjecture,
ifeq(q(X0),true,p(f(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c0,plain,
q(f(X2)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
q(f(X0)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
p(f(V0)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi0]) ).
cnf(c2,plain,
( ~ q(X3)
| r(X4)
| ~ p(X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,negated_conjecture,
ifeq(p(X0),true,ifeq(q(X0),true,r(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h1,plain,
r(V0) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0,hi0]) ).
cnf(c3,plain,
( ~ q(X3)
| ~ r(sk1)
| ~ r(sk0)
| ~ p(X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi3,negated_conjecture,
ifeq(p(X0),true,ifeq(r(sk0),true,ifeq(r(sk1),true,ifeq(q(X0),true,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi3,h0,h1,h1,hi0]) ).
cnf(t20,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t20]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN940+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 02:36:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.97/1.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.97/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------