%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN351+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 165 ( 53 ~; 44 |; 54 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 75 ( 3 sgn 42 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_18_3,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,Y2,X1,Z)
=> ( ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
=> ( big_f(X1,Y1,X1,Y2)
=> ( ( big_f(X1,Z,Y1,Z)
=> ( big_f(X1,Y1,X1,Y2)
<=> big_f(X1,Y2,Y1,Y2) ) )
& ( big_f(X1,Y2,Y1,Y2)
=> big_f(X1,Z,Y1,Z) ) ) ) ) ),
file('theBenchmark.p',church_46_18_3) ).
fof(f_1_1,negated_conjecture,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,Y2,X1,Z)
=> ( ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
=> ( big_f(X1,Y1,X1,Y2)
=> ( ( big_f(X1,Z,Y1,Z)
=> ( big_f(X1,Y1,X1,Y2)
<=> big_f(X1,Y2,Y1,Y2) ) )
& ( big_f(X1,Y2,Y1,Y2)
=> big_f(X1,Z,Y1,Z) ) ) ) ) ),
inference(negate,[status(cth)],[church_46_18_3]) ).
fof(f_1_2,negated_conjecture,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ( ( ( ~ big_f(X1,Y1,X1,Y2)
& big_f(X1,Y2,Y1,Y2) )
| ( ~ big_f(X1,Y2,Y1,Y2)
& big_f(X1,Y1,X1,Y2) ) )
& big_f(X1,Z,Y1,Z) )
| ( ~ big_f(X1,Z,Y1,Z)
& big_f(X1,Y2,Y1,Y2) ) )
& big_f(X1,Y1,X1,Y2)
& ( big_f(X1,Y1,X1,Y2)
| ~ big_f(Y1,X2,Y1,Y2) )
& ( big_f(Y1,X2,Y1,Y2)
| ~ big_f(X1,Y1,X1,Y2) )
& big_f(X1,Y2,X1,Z) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_4,U_3] :
! [U_2,U_1] :
? [U_0] :
( ( ( ( ( ~ big_f(U_4,U_2,U_4,U_1)
& big_f(U_4,U_1,U_2,U_1) )
| ( ~ big_f(U_4,U_1,U_2,U_1)
& big_f(U_4,U_2,U_4,U_1) ) )
& big_f(U_4,U_0,U_2,U_0) )
| ( ~ big_f(U_4,U_0,U_2,U_0)
& big_f(U_4,U_1,U_2,U_1) ) )
& big_f(U_4,U_2,U_4,U_1)
& ( big_f(U_4,U_2,U_4,U_1)
| ~ big_f(U_2,U_3,U_2,U_1) )
& ( big_f(U_2,U_3,U_2,U_1)
| ~ big_f(U_4,U_2,U_4,U_1) )
& big_f(U_4,U_1,U_4,U_0) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
? [U_3] :
! [U_2,U_1] :
? [U_0] :
( ( ( ( ( ~ big_f(sK1,U_2,sK1,U_1)
& big_f(sK1,U_1,U_2,U_1) )
| ( ~ big_f(sK1,U_1,U_2,U_1)
& big_f(sK1,U_2,sK1,U_1) ) )
& big_f(sK1,U_0,U_2,U_0) )
| ( ~ big_f(sK1,U_0,U_2,U_0)
& big_f(sK1,U_1,U_2,U_1) ) )
& big_f(sK1,U_2,sK1,U_1)
& ( big_f(sK1,U_2,sK1,U_1)
| ~ big_f(U_2,U_3,U_2,U_1) )
& ( big_f(U_2,U_3,U_2,U_1)
| ~ big_f(sK1,U_2,sK1,U_1) )
& big_f(sK1,U_1,sK1,U_0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_4,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
! [U_2,U_1] :
? [U_0] :
( ( ( ( ( ~ big_f(sK1,U_2,sK1,U_1)
& big_f(sK1,U_1,U_2,U_1) )
| ( ~ big_f(sK1,U_1,U_2,U_1)
& big_f(sK1,U_2,sK1,U_1) ) )
& big_f(sK1,U_0,U_2,U_0) )
| ( ~ big_f(sK1,U_0,U_2,U_0)
& big_f(sK1,U_1,U_2,U_1) ) )
& big_f(sK1,U_2,sK1,U_1)
& ( big_f(sK1,U_2,sK1,U_1)
| ~ big_f(U_2,sK2,U_2,U_1) )
& ( big_f(U_2,sK2,U_2,U_1)
| ~ big_f(sK1,U_2,sK1,U_1) )
& big_f(sK1,U_1,sK1,U_0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_3,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
! [U_2,U_1] :
( ( ( ( ( ~ big_f(sK1,U_2,sK1,U_1)
& big_f(sK1,U_1,U_2,U_1) )
| ( ~ big_f(sK1,U_1,U_2,U_1)
& big_f(sK1,U_2,sK1,U_1) ) )
& big_f(sK1,sK3(U_2,U_1),U_2,sK3(U_2,U_1)) )
| ( ~ big_f(sK1,sK3(U_2,U_1),U_2,sK3(U_2,U_1))
& big_f(sK1,U_1,U_2,U_1) ) )
& big_f(sK1,U_2,sK1,U_1)
& ( big_f(sK1,U_2,sK1,U_1)
| ~ big_f(U_2,sK2,U_2,U_1) )
& ( big_f(U_2,sK2,U_2,U_1)
| ~ big_f(sK1,U_2,sK1,U_1) )
& big_f(sK1,U_1,sK1,sK3(U_2,U_1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_0,sK3(U_2,U_1))],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ! [U_1,U_2] :
( ~ big_f(sK1,U_2,sK1,U_1)
| ~ sP2(U_1,U_2) )
& ! [U_1,U_2] :
( big_f(sK1,U_1,U_2,U_1)
| ~ sP2(U_1,U_2) )
& ! [U_1,U_2] :
( ~ big_f(sK1,U_1,U_2,U_1)
| ~ sP1(U_1,U_2) )
& ! [U_1,U_2] :
( big_f(sK1,U_2,sK1,U_1)
| ~ sP1(U_1,U_2) )
& ! [U_1,U_2] :
( sP2(U_1,U_2)
| sP1(U_1,U_2)
| ~ sP3(U_1,U_2) )
& ! [U_1,U_2] :
( big_f(sK1,sK3(U_2,U_1),U_2,sK3(U_2,U_1))
| ~ sP3(U_1,U_2) )
& ! [U_1,U_2] :
( ~ big_f(sK1,sK3(U_2,U_1),U_2,sK3(U_2,U_1))
| ~ sP0(U_1,U_2) )
& ! [U_1,U_2] :
( big_f(sK1,U_1,U_2,U_1)
| ~ sP0(U_1,U_2) )
& ! [U_1,U_2] :
( sP3(U_1,U_2)
| sP0(U_1,U_2) )
& ! [U_1,U_2] : big_f(sK1,U_2,sK1,U_1)
& ! [U_1,U_2] :
( big_f(sK1,U_2,sK1,U_1)
| ~ big_f(U_2,sK2,U_2,U_1) )
& ! [U_1,U_2] :
( big_f(U_2,sK2,U_2,U_1)
| ~ big_f(sK1,U_2,sK1,U_1) )
& ! [U_1,U_2] : big_f(sK1,U_1,sK1,sK3(U_2,U_1)) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3])],[f_1_6]) ).
cnf(f_1_11,negated_conjecture,
big_f(sK1,U_2,sK1,U_1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_12,negated_conjecture,
( sP3(U_1,U_2)
| sP0(U_1,U_2) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_14,negated_conjecture,
( ~ big_f(sK1,sK3(U_2,U_1),U_2,sK3(U_2,U_1))
| ~ sP0(U_1,U_2) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_16,negated_conjecture,
( sP2(U_1,U_2)
| sP1(U_1,U_2)
| ~ sP3(U_1,U_2) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_18,negated_conjecture,
( ~ big_f(sK1,U_1,U_2,U_1)
| ~ sP1(U_1,U_2) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_20,negated_conjecture,
( ~ big_f(sK1,U_2,sK1,U_1)
| ~ sP2(U_1,U_2) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(t1,plain,
( ~ big_f(sK1,sK3(sK1,U_148),sK1,sK3(sK1,U_148))
| ~ sP0(U_148,sK1) ),
inference(start,[status(thm),parent(0:0)],[f_1_14]) ).
cnf(t2,plain,
( sP3(U_148,sK1)
| sP0(U_148,sK1) ),
inference(extension,[status(thm),parent(t1:1)],[f_1_12]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sP1(U_148,sK1)
| sP2(U_148,sK1)
| ~ sP3(U_148,sK1) ),
inference(extension,[status(thm),parent(t2:2)],[f_1_16]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ big_f(sK1,sK1,sK1,U_148)
| ~ sP2(U_148,sK1) ),
inference(extension,[status(thm),parent(t4:2)],[f_1_20]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
big_f(sK1,sK1,sK1,U_148),
inference(extension,[status(thm),parent(t6:2)],[f_1_11]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ big_f(sK1,U_148,sK1,U_148)
| ~ sP1(U_148,sK1) ),
inference(extension,[status(thm),parent(t4:3)],[f_1_18]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
big_f(sK1,U_148,sK1,U_148),
inference(extension,[status(thm),parent(t10:2)],[f_1_11]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
big_f(sK1,sK3(sK1,U_148),sK1,sK3(sK1,U_148)),
inference(extension,[status(thm),parent(t1:2)],[f_1_11]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t1:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN351+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 06:29:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------