%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN353+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 03:39:49 PM UTC 2026
% Result : Theorem 0.41s 1.18s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 1
% Syntax : Number of formulae : 94 ( 10 unt; 0 def)
% Number of atoms : 412 ( 0 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 468 ( 150 ~; 208 |; 74 &)
% ( 14 <=>; 20 =>; 0 <=; 2 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-3 aty)
% Number of variables : 225 ( 0 sgn 211 !; 14 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
? [X1,X2,X3] :
! [X4] :
( ( big_f(X1,X2,X3)
=> ( big_f(X0,X0,X4)
=> ( big_f(X3,X1,X2)
| big_f(X2,X3,X1) ) ) )
=> ( ( ( big_f(X3,X1,X2)
=> ( big_f(X2,X3,X1)
& big_f(X1,X2,X3) ) )
<=> big_f(X2,X1,X4) )
=> ( ( ( big_f(X2,X3,X1)
=> ( big_f(X3,X1,X2)
& big_f(X1,X2,X3) ) )
<=> big_f(X1,X4,X2) )
=> ( ( ( ( big_f(X3,X1,X2)
=> ~ big_f(X2,X3,X1) )
=> big_f(X1,X2,X3) )
<=> big_f(X4,X2,X1) )
=> ( ( big_f(X3,X1,X2)
& big_f(X2,X3,X1)
& big_f(X1,X2,X3) )
<=> big_f(X4,X4,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_18_5) ).
fof(f2,negated_conjecture,
~ ! [X0] :
? [X1,X2,X3] :
! [X4] :
( ( big_f(X1,X2,X3)
=> ( big_f(X0,X0,X4)
=> ( big_f(X3,X1,X2)
| big_f(X2,X3,X1) ) ) )
=> ( ( ( big_f(X3,X1,X2)
=> ( big_f(X2,X3,X1)
& big_f(X1,X2,X3) ) )
<=> big_f(X2,X1,X4) )
=> ( ( ( big_f(X2,X3,X1)
=> ( big_f(X3,X1,X2)
& big_f(X1,X2,X3) ) )
<=> big_f(X1,X4,X2) )
=> ( ( ( ( big_f(X3,X1,X2)
=> ~ big_f(X2,X3,X1) )
=> big_f(X1,X2,X3) )
<=> big_f(X4,X2,X1) )
=> ( ( big_f(X3,X1,X2)
& big_f(X2,X3,X1)
& big_f(X1,X2,X3) )
<=> big_f(X4,X4,X4) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0] :
! [X1,X2,X3] :
? [X4] :
( ( ~ big_f(X1,X2,X3)
| ~ big_f(X0,X0,X4)
| big_f(X3,X1,X2)
| big_f(X2,X3,X1) )
& ( ( ~ big_f(X3,X1,X2)
| ( big_f(X2,X3,X1)
& big_f(X1,X2,X3) ) )
<=> big_f(X2,X1,X4) )
& ( ( ~ big_f(X2,X3,X1)
| ( big_f(X3,X1,X2)
& big_f(X1,X2,X3) ) )
<=> big_f(X1,X4,X2) )
& ( ( ( big_f(X3,X1,X2)
& big_f(X2,X3,X1) )
| big_f(X1,X2,X3) )
<=> big_f(X4,X2,X1) )
& ( ( big_f(X3,X1,X2)
& big_f(X2,X3,X1)
& big_f(X1,X2,X3) )
<~> big_f(X4,X4,X4) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0] :
! [X1,X2,X3] :
? [X4] :
( ( ~ big_f(X1,X2,X3)
| ~ big_f(X0,X0,X4)
| big_f(X3,X1,X2)
| big_f(X2,X3,X1) )
& ( ( ~ big_f(X3,X1,X2)
| ( big_f(X2,X3,X1)
& big_f(X1,X2,X3) ) )
<=> big_f(X2,X1,X4) )
& ( ( ~ big_f(X2,X3,X1)
| ( big_f(X3,X1,X2)
& big_f(X1,X2,X3) ) )
<=> big_f(X1,X4,X2) )
& ( ( ( big_f(X3,X1,X2)
& big_f(X2,X3,X1) )
| big_f(X1,X2,X3) )
<=> big_f(X4,X2,X1) )
& ( ( big_f(X3,X1,X2)
& big_f(X2,X3,X1)
& big_f(X1,X2,X3) )
<~> big_f(X4,X4,X4) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0] :
! [X1,X2,X3] :
? [X4] :
( ( ~ big_f(X1,X2,X3)
| ~ big_f(X0,X0,X4)
| big_f(X3,X1,X2)
| big_f(X2,X3,X1) )
& ( ( big_f(X3,X1,X2)
& ( ~ big_f(X2,X3,X1)
| ~ big_f(X1,X2,X3) ) )
| big_f(X2,X1,X4) )
& ( ~ big_f(X2,X1,X4)
| ~ big_f(X3,X1,X2)
| ( big_f(X2,X3,X1)
& big_f(X1,X2,X3) ) )
& ( ( big_f(X2,X3,X1)
& ( ~ big_f(X3,X1,X2)
| ~ big_f(X1,X2,X3) ) )
| big_f(X1,X4,X2) )
& ( ~ big_f(X1,X4,X2)
| ~ big_f(X2,X3,X1)
| ( big_f(X3,X1,X2)
& big_f(X1,X2,X3) ) )
& ( ( ( ~ big_f(X3,X1,X2)
| ~ big_f(X2,X3,X1) )
& ~ big_f(X1,X2,X3) )
| big_f(X4,X2,X1) )
& ( ~ big_f(X4,X2,X1)
| ( big_f(X3,X1,X2)
& big_f(X2,X3,X1) )
| big_f(X1,X2,X3) )
& ( ( big_f(X3,X1,X2)
& big_f(X2,X3,X1)
& big_f(X1,X2,X3) )
| big_f(X4,X4,X4) )
& ( ~ big_f(X3,X1,X2)
| ~ big_f(X2,X3,X1)
| ~ big_f(X1,X2,X3)
| ~ big_f(X4,X4,X4) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0] :
! [X1,X2,X3] :
? [X4] :
( ( ~ big_f(X1,X2,X3)
| ~ big_f(X0,X0,X4)
| big_f(X3,X1,X2)
| big_f(X2,X3,X1) )
& ( ( big_f(X3,X1,X2)
& ( ~ big_f(X2,X3,X1)
| ~ big_f(X1,X2,X3) ) )
| big_f(X2,X1,X4) )
& ( ~ big_f(X2,X1,X4)
| ~ big_f(X3,X1,X2)
| ( big_f(X2,X3,X1)
& big_f(X1,X2,X3) ) )
& ( ( big_f(X2,X3,X1)
& ( ~ big_f(X3,X1,X2)
| ~ big_f(X1,X2,X3) ) )
| big_f(X1,X4,X2) )
& ( ~ big_f(X1,X4,X2)
| ~ big_f(X2,X3,X1)
| ( big_f(X3,X1,X2)
& big_f(X1,X2,X3) ) )
& ( ( ( ~ big_f(X3,X1,X2)
| ~ big_f(X2,X3,X1) )
& ~ big_f(X1,X2,X3) )
| big_f(X4,X2,X1) )
& ( ~ big_f(X4,X2,X1)
| ( big_f(X3,X1,X2)
& big_f(X2,X3,X1) )
| big_f(X1,X2,X3) )
& ( ( big_f(X3,X1,X2)
& big_f(X2,X3,X1)
& big_f(X1,X2,X3) )
| big_f(X4,X4,X4) )
& ( ~ big_f(X3,X1,X2)
| ~ big_f(X2,X3,X1)
| ~ big_f(X1,X2,X3)
| ~ big_f(X4,X4,X4) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X1,X2,X3] :
( ( ~ big_f(X1,X2,X3)
| ~ big_f(sK0,sK0,sK1(X1,X2,X3))
| big_f(X3,X1,X2)
| big_f(X2,X3,X1) )
& ( ( big_f(X3,X1,X2)
& ( ~ big_f(X2,X3,X1)
| ~ big_f(X1,X2,X3) ) )
| big_f(X2,X1,sK1(X1,X2,X3)) )
& ( ~ big_f(X2,X1,sK1(X1,X2,X3))
| ~ big_f(X3,X1,X2)
| ( big_f(X2,X3,X1)
& big_f(X1,X2,X3) ) )
& ( ( big_f(X2,X3,X1)
& ( ~ big_f(X3,X1,X2)
| ~ big_f(X1,X2,X3) ) )
| big_f(X1,sK1(X1,X2,X3),X2) )
& ( ~ big_f(X1,sK1(X1,X2,X3),X2)
| ~ big_f(X2,X3,X1)
| ( big_f(X3,X1,X2)
& big_f(X1,X2,X3) ) )
& ( ( ( ~ big_f(X3,X1,X2)
| ~ big_f(X2,X3,X1) )
& ~ big_f(X1,X2,X3) )
| big_f(sK1(X1,X2,X3),X2,X1) )
& ( ~ big_f(sK1(X1,X2,X3),X2,X1)
| ( big_f(X3,X1,X2)
& big_f(X2,X3,X1) )
| big_f(X1,X2,X3) )
& ( ( big_f(X3,X1,X2)
& big_f(X2,X3,X1)
& big_f(X1,X2,X3) )
| big_f(sK1(X1,X2,X3),sK1(X1,X2,X3),sK1(X1,X2,X3)) )
& ( ~ big_f(X3,X1,X2)
| ~ big_f(X2,X3,X1)
| ~ big_f(X1,X2,X3)
| ~ big_f(sK1(X1,X2,X3),sK1(X1,X2,X3),sK1(X1,X2,X3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X4,sK1(X1,X2,X3))],[f6]) ).
fof(f8,plain,
! [X2,X3,X1] :
( ~ big_f(X1,X2,X3)
| ~ big_f(sK0,sK0,sK1(X1,X2,X3))
| big_f(X3,X1,X2)
| big_f(X2,X3,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X2,X3,X1] :
( big_f(X3,X1,X2)
| big_f(X2,X1,sK1(X1,X2,X3)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X2,X3,X1] :
( ~ big_f(X2,X1,sK1(X1,X2,X3))
| ~ big_f(X3,X1,X2)
| big_f(X2,X3,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X3,X1] :
( ~ big_f(X2,X1,sK1(X1,X2,X3))
| ~ big_f(X3,X1,X2)
| big_f(X1,X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X2,X3,X1] :
( big_f(X2,X3,X1)
| big_f(X1,sK1(X1,X2,X3),X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X2,X3,X1] :
( ~ big_f(X1,sK1(X1,X2,X3),X2)
| ~ big_f(X2,X3,X1)
| big_f(X3,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
! [X2,X3,X1] :
( ~ big_f(X1,sK1(X1,X2,X3),X2)
| ~ big_f(X2,X3,X1)
| big_f(X1,X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X2,X3,X1] :
( ~ big_f(X3,X1,X2)
| ~ big_f(X2,X3,X1)
| big_f(sK1(X1,X2,X3),X2,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f18,plain,
! [X2,X3,X1] :
( ~ big_f(X1,X2,X3)
| big_f(sK1(X1,X2,X3),X2,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f19,plain,
! [X2,X3,X1] :
( ~ big_f(sK1(X1,X2,X3),X2,X1)
| big_f(X3,X1,X2)
| big_f(X1,X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X2,X3,X1] :
( ~ big_f(sK1(X1,X2,X3),X2,X1)
| big_f(X2,X3,X1)
| big_f(X1,X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f24,plain,
! [X2,X3,X1] :
( ~ big_f(X3,X1,X2)
| ~ big_f(X2,X3,X1)
| ~ big_f(X1,X2,X3)
| ~ big_f(sK1(X1,X2,X3),sK1(X1,X2,X3),sK1(X1,X2,X3)) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ big_f(X2,X0,X1)
| ~ big_f(X1,X2,X0)
| ~ big_f(X0,X1,X2)
| ~ big_f(sK1(X0,X1,X2),sK1(X0,X1,X2),sK1(X0,X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X1,X2,X0)
| big_f(X0,X1,X2)
| ~ big_f(sK1(X0,X1,X2),X1,X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X2,X0,X1)
| big_f(X0,X1,X2)
| ~ big_f(sK1(X0,X1,X2),X1,X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_55,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(sK1(X0,X1,X2),X1,X0)
| ~ big_f(X0,X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_56,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(sK1(X2,X0,X1),X0,X2)
| ~ big_f(X1,X2,X0)
| ~ big_f(X0,X1,X2) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_57,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X0,X1,X2)
| ~ big_f(X1,X2,X0)
| ~ big_f(X0,sK1(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_58,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X2,X0,X1)
| ~ big_f(X1,X2,X0)
| ~ big_f(X0,sK1(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_60,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X1,X2,X0)
| big_f(X0,sK1(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_61,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X1,X0,X2)
| ~ big_f(X2,X1,X0)
| ~ big_f(X0,X1,sK1(X1,X0,X2)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_62,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X0,X2,X1)
| ~ big_f(X2,X1,X0)
| ~ big_f(X0,X1,sK1(X1,X0,X2)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_64,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X2,X1,X0)
| big_f(X0,X1,sK1(X1,X0,X2)) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_65,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X2,X0,X1)
| big_f(X1,X2,X0)
| ~ big_f(X0,X1,X2)
| ~ big_f(sK0,sK0,sK1(X0,X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_168,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X2,X0,X1)
| big_f(X1,X2,X0)
| ~ big_f(X0,X1,X2)
| ~ big_f(sK0,sK0,sK1(X0,X1,X2)) ),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_169,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X2,X1,X0)
| big_f(X0,X1,sK1(X1,X0,X2)) ),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_171,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X0,X2,X1)
| ~ big_f(X2,X1,X0)
| ~ big_f(X0,X1,sK1(X1,X0,X2)) ),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_172,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X1,X0,X2)
| ~ big_f(X2,X1,X0)
| ~ big_f(X0,X1,sK1(X1,X0,X2)) ),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_173,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X1,X2,X0)
| big_f(X0,sK1(X0,X1,X2),X1) ),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_175,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X2,X0,X1)
| ~ big_f(X1,X2,X0)
| ~ big_f(X0,sK1(X0,X1,X2),X1) ),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_176,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X0,X1,X2)
| ~ big_f(X1,X2,X0)
| ~ big_f(X0,sK1(X0,X1,X2),X1) ),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_177,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(sK1(X2,X0,X1),X0,X2)
| ~ big_f(X1,X2,X0)
| ~ big_f(X0,X1,X2) ),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_178,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(sK1(X0,X1,X2),X1,X0)
| ~ big_f(X0,X1,X2) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_179,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X2,X0,X1)
| big_f(X0,X1,X2)
| ~ big_f(sK1(X0,X1,X2),X1,X0) ),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_180,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X1,X2,X0)
| big_f(X0,X1,X2)
| ~ big_f(sK1(X0,X1,X2),X1,X0) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_184,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ big_f(X2,X0,X1)
| ~ big_f(X1,X2,X0)
| ~ big_f(X0,X1,X2)
| ~ big_f(sK1(X0,X1,X2),sK1(X0,X1,X2),sK1(X0,X1,X2)) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_542,plain,
! [X0: $i] :
( big_f(sK0,X0,sK0)
| big_f(X0,sK0,sK0)
| ~ big_f(sK0,sK0,X0) ),
inference(superposition,[status(thm)],[c_169,c_168]) ).
tcf(c_555,plain,
! [X0: $i] :
( big_f(sK0,X0,sK0)
| big_f(X0,sK0,sK0)
| ~ big_f(sK0,sK0,X0) ),
inference(superposition,[status(thm)],[c_169,c_168]) ).
tcf(c_626,plain,
! [X0: $i] :
( big_f(X0,sK0,sK0)
| big_f(sK0,sK1(sK0,sK0,X0),sK0)
| big_f(sK1(sK0,sK0,X0),sK0,sK0) ),
inference(superposition,[status(thm)],[c_169,c_542]) ).
tcf(c_641,plain,
! [X0: $i] :
( big_f(X0,sK0,sK0)
| big_f(sK0,sK1(sK0,sK0,X0),sK0)
| big_f(sK1(sK0,sK0,X0),sK0,sK0) ),
inference(superposition,[status(thm)],[c_169,c_555]) ).
tcf(c_728,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| big_f(X0,sK0,sK0)
| big_f(sK0,sK1(sK0,sK0,X0),sK0) ),
inference(superposition,[status(thm)],[c_626,c_179]) ).
tcf(c_743,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| big_f(X0,sK0,sK0)
| big_f(sK0,sK1(sK0,sK0,X0),sK0) ),
inference(superposition,[status(thm)],[c_641,c_179]) ).
tcf(c_797,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| big_f(X0,sK0,sK0)
| ~ big_f(sK0,X0,sK0) ),
inference(superposition,[status(thm)],[c_728,c_176]) ).
tcf(c_808,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| big_f(X0,sK0,sK0)
| ~ big_f(sK0,X0,sK0) ),
inference(superposition,[status(thm)],[c_743,c_176]) ).
tcf(c_840,plain,
! [X0: $i] :
( big_f(sK0,X0,sK0)
| big_f(sK0,sK0,sK1(sK0,sK0,X0))
| big_f(sK1(sK0,sK0,X0),sK0,sK0) ),
inference(superposition,[status(thm)],[c_173,c_797]) ).
tcf(c_860,plain,
! [X0: $i] :
( big_f(sK0,X0,sK0)
| big_f(sK0,sK0,sK1(sK0,sK0,X0))
| big_f(sK1(sK0,sK0,X0),sK0,sK0) ),
inference(superposition,[status(thm)],[c_173,c_808]) ).
tcf(c_955,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| big_f(sK0,X0,sK0)
| big_f(sK0,sK0,sK1(sK0,sK0,X0)) ),
inference(superposition,[status(thm)],[c_840,c_180]) ).
tcf(c_971,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| big_f(sK0,X0,sK0)
| big_f(X0,sK0,sK0)
| big_f(sK0,sK0,sK1(sK0,sK0,X0)) ),
inference(superposition,[status(thm)],[c_860,c_179]) ).
tcf(c_1057,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| big_f(sK0,X0,sK0)
| ~ big_f(X0,sK0,sK0) ),
inference(superposition,[status(thm)],[c_955,c_172]) ).
tcf(c_1121,plain,
! [X0: $i] :
( big_f(sK0,sK0,sK1(sK0,sK0,X0))
| big_f(sK0,sK1(sK0,sK0,X0),sK0)
| ~ big_f(sK0,sK0,X0) ),
inference(superposition,[status(thm)],[c_178,c_1057]) ).
tcf(c_1122,plain,
! [X0: $i] :
( big_f(sK0,sK0,sK1(sK0,sK0,X0))
| big_f(sK0,sK1(sK0,sK0,X0),sK0)
| ~ big_f(sK0,X0,sK0)
| ~ big_f(X0,sK0,sK0) ),
inference(superposition,[status(thm)],[c_177,c_1057]) ).
tcf(c_1123,plain,
! [X0: $i] :
( big_f(sK0,X0,sK0)
| big_f(sK0,sK0,sK1(sK0,sK0,X0))
| big_f(sK0,sK1(sK0,sK0,X0),sK0) ),
inference(superposition,[status(thm)],[c_840,c_1057]) ).
tcf(c_1124,plain,
! [X0: $i] :
( big_f(X0,sK0,sK0)
| big_f(sK0,sK0,sK1(sK0,sK0,X0))
| big_f(sK0,sK1(sK0,sK0,X0),sK0) ),
inference(superposition,[status(thm)],[c_626,c_1057]) ).
tcf(c_1220,plain,
! [X0: $i] :
( big_f(sK0,sK0,sK1(sK0,sK0,X0))
| big_f(sK0,sK1(sK0,sK0,X0),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_1121,c_1124,c_1123,c_1122]) ).
tcf(c_1227,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| big_f(sK0,sK0,sK1(sK0,sK0,X0))
| ~ big_f(sK0,X0,sK0) ),
inference(superposition,[status(thm)],[c_1220,c_176]) ).
tcf(c_1241,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| big_f(sK0,sK0,sK1(sK0,sK0,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_971,c_955,c_1227]) ).
tcf(c_1247,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| ~ big_f(X0,sK0,sK0) ),
inference(superposition,[status(thm)],[c_1241,c_172]) ).
tcf(c_1256,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| big_f(sK0,sK0,sK1(sK0,sK0,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_1227,c_1241]) ).
tcf(c_1262,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| ~ big_f(X0,sK0,sK0) ),
inference(superposition,[status(thm)],[c_1256,c_172]) ).
tcf(c_1275,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| ~ big_f(sK0,X0,sK0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_797,c_1262]) ).
tcf(c_1340,plain,
! [X0: $i] : big_f(sK0,sK0,sK1(sK0,sK0,X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_1220,c_1275]) ).
tcf(c_1351,plain,
! [X0: $i] :
( big_f(sK0,X0,sK0)
| ~ big_f(X0,sK0,sK0) ),
inference(superposition,[status(thm)],[c_1340,c_171]) ).
tcf(c_1363,plain,
! [X0: $i] :
( big_f(sK0,X0,sK0)
| ~ big_f(sK0,sK0,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_542,c_1351]) ).
tcf(c_1379,plain,
! [X0: $i] : big_f(sK0,sK1(sK0,sK0,X0),sK0),
inference(superposition,[status(thm)],[c_1340,c_1363]) ).
tcf(c_1394,plain,
! [X0: $i] :
( big_f(X0,sK0,sK0)
| ~ big_f(sK0,X0,sK0) ),
inference(superposition,[status(thm)],[c_1379,c_175]) ).
tcf(c_1404,plain,
! [X0: $i] : big_f(sK1(sK0,sK0,X0),sK0,sK0),
inference(superposition,[status(thm)],[c_1379,c_1394]) ).
tcf(c_1406,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| big_f(sK0,X0,sK0) ),
inference(superposition,[status(thm)],[c_1404,c_180]) ).
tcf(c_1407,plain,
! [X0: $i] :
( big_f(sK0,sK0,X0)
| big_f(X0,sK0,sK0) ),
inference(superposition,[status(thm)],[c_1404,c_179]) ).
tcf(c_1415,plain,
! [X0: $i] : big_f(sK0,sK0,X0),
inference(global_subsumption_just,[status(thm)],[c_1406,c_1247,c_1407]) ).
tcf(c_1418,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X2,X0,X1)
| big_f(X1,X2,X0)
| ~ big_f(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_168,c_1415]) ).
tcf(c_1439,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X2,sK1(X2,X0,X1),X0)
| big_f(X0,X2,sK1(X2,X0,X1))
| ~ big_f(X1,X2,X0)
| ~ big_f(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_177,c_1418]) ).
tcf(c_1441,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X1,X2,X0)
| big_f(X1,X0,sK1(X0,X1,X2))
| big_f(sK1(X0,X1,X2),X1,X0) ),
inference(superposition,[status(thm)],[c_173,c_1418]) ).
tcf(c_1475,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X1,X0,X2)
| big_f(X0,X2,X1)
| big_f(X0,X1,sK1(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_1441,c_180]) ).
tcf(c_1661,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X1,sK1(X1,X0,X2),X0)
| big_f(X0,X1,sK1(X1,X0,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1439,c_169,c_173]) ).
tcf(c_1669,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X2,X0,X1)
| big_f(X0,X2,sK1(X2,X0,X1))
| ~ big_f(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1661,c_176]) ).
tcf(c_1693,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X1,X0,X2)
| big_f(X0,X1,sK1(X1,X0,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1669,c_1475]) ).
tcf(c_1700,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X1,X2,X0)
| ~ big_f(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_172,c_1693]) ).
tcf(c_1711,plain,
! [X0: $i,X1: $i,X2: $i] : big_f(X0,sK1(X0,X1,X2),X1),
inference(backward_subsumption_resolution,[status(thm)],[c_1661,c_1700]) ).
tcf(c_1714,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X0,X1,X2)
| ~ big_f(sK1(X0,X1,X2),X1,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_179,c_1700]) ).
tcf(c_1717,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ big_f(X2,X0,X1)
| ~ big_f(X0,X1,X2)
| ~ big_f(sK1(X0,X1,X2),sK1(X0,X1,X2),sK1(X0,X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_184,c_1700]) ).
tcf(c_1727,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X2,X0,X1)
| ~ big_f(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_176,c_1711]) ).
tcf(c_1730,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ big_f(X0,X1,X2)
| ~ big_f(sK1(X0,X1,X2),sK1(X0,X1,X2),sK1(X0,X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1717,c_1727]) ).
tcf(c_1744,plain,
! [X0: $i,X1: $i,X2: $i] : big_f(sK1(X0,X1,X2),X1,X0),
inference(superposition,[status(thm)],[c_1711,c_1700]) ).
tcf(c_1745,plain,
! [X0: $i,X1: $i,X2: $i] : big_f(X2,X0,X1),
inference(global_subsumption_just,[status(thm)],[c_1727,c_1727,c_1714,c_1744]) ).
tcf(c_1746,plain,
! [X0: $i,X1: $i,X2: $i] : big_f(X0,X1,X2),
inference(renaming,[status(thm)],[c_1745]) ).
tcf(c_1765,plain,
! [X0: $i,X1: $i,X2: $i] : ~ big_f(sK1(X0,X1,X2),sK1(X0,X1,X2),sK1(X0,X1,X2)),
inference(global_subsumption_just,[status(thm)],[c_1730,c_1714,c_1730,c_1744]) ).
tcf(c_1768,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1765,c_1746]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN353+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 01:01:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 0.41/1.18 % SZS status Started for theBenchmark.p
% 0.41/1.18 % SZS status Theorem for theBenchmark.p
% 0.41/1.18
% 0.41/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.41/1.18
% 0.41/1.18 % ------ iProver source info
% 0.41/1.18
% 0.41/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 0.41/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.41/1.18 % git: non_committed_changes: false
% 0.41/1.18
% 0.41/1.18 % ------ Parsing...
% 0.41/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.41/1.18
% 0.41/1.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.41/1.18
% 0.41/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.41/1.18 % ------ Proving...
% 0.41/1.18 % ------ Problem Properties
% 0.41/1.18
% 0.41/1.18 %
% 0.41/1.18 % clauses 17
% 0.41/1.18 % conjectures 17
% 0.41/1.18 % EPR 0
% 0.41/1.18 % Horn 9
% 0.41/1.18 % unary 0
% 0.41/1.18 % binary 6
% 0.41/1.18 % lits 47
% 0.41/1.18 % lits eq 0
% 0.41/1.18 % fd_pure 0
% 0.41/1.18 % fd_pseudo 0
% 0.41/1.18 % fd_cond 0
% 0.41/1.18 % fd_pseudo_cond 0
% 0.41/1.18 % AC symbols 0
% 0.41/1.18
% 0.41/1.18 % ------ Schedule dynamic 5 is on
% 0.41/1.18
% 0.41/1.18 % ------ no equalities: superposition off
% 0.41/1.18
% 0.41/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.41/1.18
% 0.41/1.18
% 0.41/1.18 % ------
% 0.41/1.18 % Current options:
% 0.41/1.18 % ------
% 0.41/1.18
% 0.41/1.18
% 0.41/1.18 %
% 0.41/1.18
% 0.41/1.18 % ------ Proving...
% 0.41/1.18 %
% 0.41/1.18
% 0.41/1.18 % SZS status Theorem for theBenchmark.p
% 0.41/1.18
% 0.41/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.41/1.18
% 0.41/1.18
%------------------------------------------------------------------------------