%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN350+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 : Thu Sep 24 09:10:08 AM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 40 ( 14 unt; 0 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 155 ( 59 ~; 53 |; 35 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 32 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_18_2,conjecture,
! [X] :
? [Y1,Y2] :
! [Z] :
( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( big_f(X,Z)
<=> ( ( big_f(Y1,Z)
=> big_f(Y1,Y2) )
& big_f(Y2,Z) ) ) ),
file('theBenchmark.p',church_46_18_2) ).
fof(f_1_1,negated_conjecture,
~ ! [X] :
? [Y1,Y2] :
! [Z] :
( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( big_f(X,Z)
<=> ( ( big_f(Y1,Z)
=> big_f(Y1,Y2) )
& big_f(Y2,Z) ) ) ),
inference(negate,[status(cth)],[church_46_18_2]) ).
fof(f_1_2,negated_conjecture,
? [X] :
! [Y1,Y2] :
? [Z] :
( ( ( ~ big_f(X,Z)
& ( big_f(Y1,Y2)
| ~ big_f(Y1,Z) )
& big_f(Y2,Z) )
| ( ( ( ~ big_f(Y1,Y2)
& big_f(Y1,Z) )
| ~ big_f(Y2,Z) )
& big_f(X,Z) ) )
& ( big_f(X,Z)
| ~ big_f(Z,X) )
& ( big_f(Z,X)
| ~ big_f(X,Z) ) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_3] :
! [U_2,U_1] :
? [U_0] :
( ( ( ~ big_f(U_3,U_0)
& ( big_f(U_2,U_1)
| ~ big_f(U_2,U_0) )
& big_f(U_1,U_0) )
| ( ( ( ~ big_f(U_2,U_1)
& big_f(U_2,U_0) )
| ~ big_f(U_1,U_0) )
& big_f(U_3,U_0) ) )
& ( big_f(U_3,U_0)
| ~ big_f(U_0,U_3) )
& ( big_f(U_0,U_3)
| ~ big_f(U_3,U_0) ) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
! [U_2,U_1] :
? [U_0] :
( ( ( ~ big_f(sK1,U_0)
& ( big_f(U_2,U_1)
| ~ big_f(U_2,U_0) )
& big_f(U_1,U_0) )
| ( ( ( ~ big_f(U_2,U_1)
& big_f(U_2,U_0) )
| ~ big_f(U_1,U_0) )
& big_f(sK1,U_0) ) )
& ( big_f(sK1,U_0)
| ~ big_f(U_0,sK1) )
& ( big_f(U_0,sK1)
| ~ big_f(sK1,U_0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
! [U_2,U_1] :
( ( ( ~ big_f(sK1,sK2(U_2,U_1))
& ( big_f(U_2,U_1)
| ~ big_f(U_2,sK2(U_2,U_1)) )
& big_f(U_1,sK2(U_2,U_1)) )
| ( ( ( ~ big_f(U_2,U_1)
& big_f(U_2,sK2(U_2,U_1)) )
| ~ big_f(U_1,sK2(U_2,U_1)) )
& big_f(sK1,sK2(U_2,U_1)) ) )
& ( big_f(sK1,sK2(U_2,U_1))
| ~ big_f(sK2(U_2,U_1),sK1) )
& ( big_f(sK2(U_2,U_1),sK1)
| ~ big_f(sK1,sK2(U_2,U_1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_0,sK2(U_2,U_1))],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ! [U_2,U_1] :
( ~ big_f(sK1,sK2(U_2,U_1))
| ~ sP2(U_2,U_1) )
& ! [U_2,U_1] :
( big_f(U_2,U_1)
| ~ big_f(U_2,sK2(U_2,U_1))
| ~ sP2(U_2,U_1) )
& ! [U_2,U_1] :
( big_f(U_1,sK2(U_2,U_1))
| ~ sP2(U_2,U_1) )
& ! [U_2,U_1] :
( ~ big_f(U_2,U_1)
| ~ sP0(U_2,U_1) )
& ! [U_2,U_1] :
( big_f(U_2,sK2(U_2,U_1))
| ~ sP0(U_2,U_1) )
& ! [U_2,U_1] :
( sP0(U_2,U_1)
| ~ big_f(U_1,sK2(U_2,U_1))
| ~ sP1(U_2,U_1) )
& ! [U_2,U_1] :
( big_f(sK1,sK2(U_2,U_1))
| ~ sP1(U_2,U_1) )
& ! [U_2,U_1] :
( sP2(U_2,U_1)
| sP1(U_2,U_1) )
& ! [U_2,U_1] :
( big_f(sK1,sK2(U_2,U_1))
| ~ big_f(sK2(U_2,U_1),sK1) )
& ! [U_2,U_1] :
( big_f(sK2(U_2,U_1),sK1)
| ~ big_f(sK1,sK2(U_2,U_1)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2])],[f_1_5]) ).
cnf(f_1_7,negated_conjecture,
( big_f(sK2(U_2,U_1),sK1)
| ~ big_f(sK1,sK2(U_2,U_1)) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_9,negated_conjecture,
( sP2(U_2,U_1)
| sP1(U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_10,negated_conjecture,
( big_f(sK1,sK2(U_2,U_1))
| ~ sP1(U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_11,negated_conjecture,
( sP0(U_2,U_1)
| ~ big_f(U_1,sK2(U_2,U_1))
| ~ sP1(U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_13,negated_conjecture,
( ~ big_f(U_2,U_1)
| ~ sP0(U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_14,negated_conjecture,
( big_f(U_1,sK2(U_2,U_1))
| ~ sP2(U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_16,negated_conjecture,
( ~ big_f(sK1,sK2(U_2,U_1))
| ~ sP2(U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(t1,plain,
( ~ big_f(sK2(U_126,sK1),sK1)
| ~ sP0(sK2(U_126,sK1),sK1) ),
inference(start,[status(thm),parent(0:0)],[f_1_13]) ).
cnf(t2,plain,
( ~ big_f(sK1,sK2(sK2(U_126,sK1),sK1))
| ~ sP1(sK2(U_126,sK1),sK1)
| sP0(sK2(U_126,sK1),sK1) ),
inference(extension,[status(thm),parent(t1:1)],[f_1_11]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sP2(sK2(U_126,sK1),sK1)
| sP1(sK2(U_126,sK1),sK1) ),
inference(extension,[status(thm),parent(t2:2)],[f_1_9]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ big_f(sK1,sK2(sK2(U_126,sK1),sK1))
| ~ sP2(sK2(U_126,sK1),sK1) ),
inference(extension,[status(thm),parent(t4:2)],[f_1_16]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ sP2(sK2(U_126,sK1),sK1)
| big_f(sK1,sK2(sK2(U_126,sK1),sK1)) ),
inference(extension,[status(thm),parent(t6:2)],[f_1_14]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
$false,
inference(reduction,[status(thm),parent(t8:2)],[t8:2,t4:2]) ).
cnf(t11,plain,
( ~ sP2(sK2(U_126,sK1),sK1)
| big_f(sK1,sK2(sK2(U_126,sK1),sK1)) ),
inference(extension,[status(thm),parent(t2:3)],[f_1_14]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t2:3]) ).
cnf(t13,plain,
( sP1(sK2(U_126,sK1),sK1)
| sP2(sK2(U_126,sK1),sK1) ),
inference(extension,[status(thm),parent(t11:2)],[f_1_9]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t11:2]) ).
cnf(t15,plain,
( big_f(sK1,sK2(sK2(U_126,sK1),sK1))
| ~ sP1(sK2(U_126,sK1),sK1) ),
inference(extension,[status(thm),parent(t13:2)],[f_1_10]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
$false,
inference(reduction,[status(thm),parent(t15:2)],[t15:2,t2:3]) ).
cnf(t18,plain,
( ~ big_f(sK1,sK2(U_126,sK1))
| big_f(sK2(U_126,sK1),sK1) ),
inference(extension,[status(thm),parent(t1:2)],[f_1_7]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t1:2]) ).
cnf(t20,plain,
( ~ sP2(U_126,sK1)
| big_f(sK1,sK2(U_126,sK1)) ),
inference(extension,[status(thm),parent(t18:2)],[f_1_14]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( sP1(U_126,sK1)
| sP2(U_126,sK1) ),
inference(extension,[status(thm),parent(t20:2)],[f_1_9]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( big_f(sK1,sK2(U_126,sK1))
| ~ sP1(U_126,sK1) ),
inference(extension,[status(thm),parent(t22:2)],[f_1_10]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
$false,
inference(reduction,[status(thm),parent(t24:2)],[t24:2,t18:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN350+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.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 : Sun Sep 20 06:28:42 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------