%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN356+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 : n011.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 03:34:29 PM UTC 2026
% Result : Theorem 4.56s 1.11s
% Output : Proof 4.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 31 ( 23 unt; 0 def)
% Number of atoms : 63 ( 21 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 48 ( 16 ~; 10 |; 16 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 34 ( 4 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ( ! [U,V] :
( big_q(U,V)
=> big_q(U,U) )
& ! [X,Y] :
( big_r(X,Y)
=> ( big_q(X,Y)
& big_r(Y,X) ) )
& big_r(a,b) )
=> ( big_q(b,b)
& big_q(a,a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2107) ).
fof(f0_neg,negated_conjecture,
~ ( ( ! [U,V] :
( big_q(U,V)
=> big_q(U,U) )
& ! [X,Y] :
( big_r(X,Y)
=> ( big_q(X,Y)
& big_r(Y,X) ) )
& big_r(a,b) )
=> ( big_q(b,b)
& big_q(a,a) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ( ~ big_q(b,b)
| ~ big_q(a,a) )
& ! [U,V] :
( big_q(U,U)
| ~ big_q(U,V) )
& ! [X,Y] :
( ( big_q(X,Y)
& big_r(Y,X) )
| ~ big_r(X,Y) )
& big_r(a,b) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Y,U,V] :
( ( ~ big_q(b,b)
| ~ big_q(a,a) )
& ( big_q(U,U)
| ~ big_q(U,V) )
& ( ( big_q(X,Y)
& big_r(Y,X) )
| ~ big_r(X,Y) )
& big_r(a,b) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c4,plain,
( ~ big_q(b,b)
| ~ big_q(a,a) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t11,plain,
ifeq(big_q(a,a),true,ifeq(big_q(b,b),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(c2,plain,
( big_q(X0,X1)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,negated_conjecture,
ifeq(big_r(X0,X1),true,big_q(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(c0,plain,
big_r(a,b),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
big_r(a,b) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
big_q(a,b) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi0]) ).
cnf(c3,plain,
( big_q(X2,X2)
| ~ big_q(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi3,negated_conjecture,
ifeq(big_q(X0,X1),true,big_q(X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t1,plain,
big_q(a,a) = true,
inference(hyper_resolution,[status(thm)],[hi3,h0]) ).
cnf(t13,plain,
big_q(a,a) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t21,plain,
ifeq(true,true,ifeq(big_q(b,b),true,false,true),true) = true,
inference(step,[status(thm)],[t11,t13]) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t7]) ).
cnf(t22,plain,
ifeq(big_q(b,b),true,false,true) = true,
inference(step,[status(thm)],[t21,t12]) ).
cnf(c1,plain,
( big_r(X1,X0)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,negated_conjecture,
ifeq(big_r(X0,X1),true,big_r(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h1,plain,
big_r(b,a) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi0]) ).
cnf(h3,plain,
big_q(b,a) = true,
inference(hyper_resolution,[status(thm)],[hi2,h1]) ).
cnf(t4,plain,
big_q(b,b) = true,
inference(hyper_resolution,[status(thm)],[hi3,h3]) ).
cnf(t16,plain,
big_q(b,b) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t23,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t22,t16]) ).
cnf(t24,plain,
false = true,
inference(step,[status(thm)],[t23,t12]) ).
cnf(t20,plain,
false = true,
inference(orient,[status(thm)],[t24]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4]) ).
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 : SYN356+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 00:58:12 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.56/1.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.56/1.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------