%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN361+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 03:34:30 PM UTC 2026
% Result : Theorem 4.50s 1.16s
% Output : Proof 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 31 ( 25 unt; 0 def)
% Number of atoms : 53 ( 22 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 38 ( 16 ~; 6 |; 10 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 52 ( 11 sgn 16 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ( ! [X,Y] :
( big_p(X,Y)
=> ~ big_q(X,Y) )
& ! [X] :
( big_s(X)
=> ? [Y] : big_q(Y,X) )
& ? [V] :
! [X] : big_p(X,V) )
=> ? [U] : ~ big_s(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2112) ).
fof(f0_neg,negated_conjecture,
~ ( ( ! [X,Y] :
( big_p(X,Y)
=> ~ big_q(X,Y) )
& ! [X] :
( big_s(X)
=> ? [Y] : big_q(Y,X) )
& ? [V] :
! [X] : big_p(X,V) )
=> ? [U] : ~ big_s(U) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ! [U] : big_s(U)
& ! [X,Y] :
( ~ big_q(X,Y)
| ~ big_p(X,Y) )
& ! [X] :
( ? [Y] : big_q(Y,X)
| ~ big_s(X) )
& ? [V] :
! [X] : big_p(X,V) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Y,U] :
( big_s(U)
& ( ~ big_q(X,Y)
| ~ big_p(X,Y) )
& ( big_q(sk1(X),X)
| ~ big_s(X) )
& big_p(X,sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c2,plain,
( ~ big_q(X1,X2)
| ~ big_p(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
ifeq(big_p(X1,X2),true,ifeq(big_q(X1,X2),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t7,plain,
ifeq(big_p(X1,X2),true,ifeq(big_q(X1,X2),true,false,true),true) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(c0,plain,
big_p(X1,sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
big_p(X1,sk0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t10,plain,
big_p(X1,sk0) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t11,plain,
true = ifeq(true,true,ifeq(big_q(X1,sk0),true,false,true),true),
inference(cp,[status(thm)],[t7,t10]) ).
cnf(t2,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t21,plain,
true = ifeq(big_q(X1,sk0),true,false,true),
inference(step,[status(thm)],[t11,t5]) ).
cnf(t14,plain,
ifeq(big_q(X1,sk0),true,false,true) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(c1,plain,
( big_q(sk1(X1),X1)
| ~ big_s(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t3,plain,
ifeq(big_s(X1),true,big_q(sk1(X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t6,plain,
ifeq(big_s(X1),true,big_q(sk1(X1),X1),true) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(c3,plain,
big_s(X3),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t0,plain,
big_s(X1) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t8,plain,
big_s(X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t19,plain,
ifeq(true,true,big_q(sk1(X1),X1),true) = true,
inference(step,[status(thm)],[t6,t8]) ).
cnf(t20,plain,
big_q(sk1(X1),X1) = true,
inference(step,[status(thm)],[t19,t5]) ).
cnf(t9,plain,
big_q(sk1(X1),X1) = true,
inference(rw,[status(thm)],[t20]) ).
cnf(t12,plain,
big_q(sk1(X1),X1) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t15,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t14,t12]) ).
cnf(t22,plain,
true = false,
inference(step,[status(thm)],[t15,t5]) ).
cnf(t16,plain,
false = true,
inference(orient,[status(thm)],[t22]) ).
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,t16]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN361+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 01:01:07 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.50/1.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.50/1.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------