%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN981+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 03:36:28 PM UTC 2026
% Result : Theorem 5.22s 6.26s
% Output : Proof 5.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 28 unt; 0 def)
% Number of atoms : 56 ( 25 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 34 ( 12 ~; 6 |; 8 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 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 ( 12 sgn 6 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ( ? [Y] :
( q(Y)
=> r(Y) )
& ! [X] :
( p(X)
=> q(X) ) )
=> ? [Z] :
( p(Z)
=> r(Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f0_neg,negated_conjecture,
~ ( ( ? [Y] :
( q(Y)
=> r(Y) )
& ! [X] :
( p(X)
=> q(X) ) )
=> ? [Z] :
( p(Z)
=> r(Z) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ! [Z] :
( ~ r(Z)
& p(Z) )
& ? [Y] :
( r(Y)
| ~ q(Y) )
& ! [X] :
( q(X)
| ~ p(X) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Z] :
( ~ r(Z)
& p(Z)
& ( r(sk0)
| ~ q(sk0) )
& ( q(X)
| ~ p(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c3,plain,
~ r(X2),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t2,plain,
eq(r(X1),true) = efalse,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t12,plain,
eq(r(X1),true) = efalse,
inference(orient,[status(thm)],[t2]) ).
cnf(c1,plain,
( r(sk0)
| ~ q(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t5,plain,
ifeq(q(sk0),true,r(sk0),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t8,plain,
ifeq(q(sk0),true,r(sk0),true) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(c0,plain,
( q(X0)
| ~ p(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
ifeq(p(X1),true,q(X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t7,plain,
ifeq(p(X1),true,q(X1),true) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(c2,plain,
p(X2),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t0,plain,
p(X1) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t9,plain,
p(X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t20,plain,
ifeq(true,true,q(X1),true) = true,
inference(step,[status(thm)],[t7,t9]) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t21,plain,
q(X1) = true,
inference(step,[status(thm)],[t20,t6]) ).
cnf(t10,plain,
q(X1) = true,
inference(rw,[status(thm)],[t21]) ).
cnf(t13,plain,
q(X1) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t22,plain,
ifeq(true,true,r(sk0),true) = true,
inference(step,[status(thm)],[t8,t13]) ).
cnf(t23,plain,
r(sk0) = true,
inference(step,[status(thm)],[t22,t6]) ).
cnf(t14,plain,
r(sk0) = true,
inference(rw,[status(thm)],[t23]) ).
cnf(t15,plain,
r(sk0) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t16,plain,
efalse = eq(true,true),
inference(cp,[status(thm)],[t12,t15]) ).
cnf(t1,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t11,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t1]) ).
cnf(t24,plain,
efalse = etrue,
inference(step,[status(thm)],[t16,t11]) ).
cnf(t17,plain,
efalse = etrue,
inference(orient,[status(thm)],[t24]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t17]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN981+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n002.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 02:45:26 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.22/6.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.22/6.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------