%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN373+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 : n026.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 09:10:12 AM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 47 ( 17 unt; 0 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 160 ( 65 ~; 55 |; 34 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 90 ( 22 sgn 44 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2124,conjecture,
( ? [X] :
( big_p(X)
=> big_q(X) )
<=> ( ! [X] : big_p(X)
=> ? [X] : big_q(X) ) ),
file('theBenchmark.p',x2124) ).
fof(f_1_1,negated_conjecture,
~ ( ? [X] :
( big_p(X)
=> big_q(X) )
<=> ( ! [X] : big_p(X)
=> ? [X] : big_q(X) ) ),
inference(negate,[status(cth)],[x2124]) ).
fof(f_1_2,negated_conjecture,
( ( ! [X] :
( ~ big_q(X)
& big_p(X) )
& ( ? [X] : big_q(X)
| ? [X] : ~ big_p(X) ) )
| ( ! [X] : ~ big_q(X)
& ! [X] : big_p(X)
& ? [X] :
( big_q(X)
| ~ big_p(X) ) ) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
( ( ! [U_5] :
( ~ big_q(U_5)
& big_p(U_5) )
& ( ? [U_4] : big_q(U_4)
| ? [U_3] : ~ big_p(U_3) ) )
| ( ! [U_2] : ~ big_q(U_2)
& ! [U_1] : big_p(U_1)
& ? [U_0] :
( big_q(U_0)
| ~ big_p(U_0) ) ) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ( ! [U_9] : ~ big_q(U_9)
& ! [U_8] : big_p(U_8)
& ( ? [U_4] : big_q(U_4)
| ? [U_3] : ~ big_p(U_3) ) )
| ( ! [U_2] : ~ big_q(U_2)
& ! [U_1] : big_p(U_1)
& ( ? [U_7] : big_q(U_7)
| ? [U_6] : ~ big_p(U_6) ) ) ),
inference(miniscope,[status(thm)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ( ! [U_9] : ~ big_q(U_9)
& ! [U_8] : big_p(U_8)
& ( ? [U_4] : big_q(U_4)
| ? [U_3] : ~ big_p(U_3) ) )
| ( ! [U_2] : ~ big_q(U_2)
& ! [U_1] : big_p(U_1)
& ( ? [U_7] : big_q(U_7)
| ~ big_p(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_6,sK1)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ( ! [U_9] : ~ big_q(U_9)
& ! [U_8] : big_p(U_8)
& ( ? [U_4] : big_q(U_4)
| ? [U_3] : ~ big_p(U_3) ) )
| ( ! [U_2] : ~ big_q(U_2)
& ! [U_1] : big_p(U_1)
& ( big_q(sK2)
| ~ big_p(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_7,sK2)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ( ! [U_9] : ~ big_q(U_9)
& ! [U_8] : big_p(U_8)
& ( ? [U_4] : big_q(U_4)
| ~ big_p(sK3) ) )
| ( ! [U_2] : ~ big_q(U_2)
& ! [U_1] : big_p(U_1)
& ( big_q(sK2)
| ~ big_p(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_3,sK3)],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ( ! [U_9] : ~ big_q(U_9)
& ! [U_8] : big_p(U_8)
& ( big_q(sK4)
| ~ big_p(sK3) ) )
| ( ! [U_2] : ~ big_q(U_2)
& ! [U_1] : big_p(U_1)
& ( big_q(sK2)
| ~ big_p(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_4,sK4)],[f_1_7]) ).
fof(f_1_9,negated_conjecture,
( ! [U_9,U_8] :
( ~ big_q(U_9)
| ~ sP1(U_9,U_8) )
& ! [U_9,U_8] :
( big_p(U_8)
| ~ sP1(U_9,U_8) )
& ! [U_9,U_8] :
( big_q(sK4)
| ~ big_p(sK3)
| ~ sP1(U_9,U_8) )
& ! [U_1,U_2] :
( ~ big_q(U_2)
| ~ sP0(U_1,U_2) )
& ! [U_1,U_2] :
( big_p(U_1)
| ~ sP0(U_1,U_2) )
& ! [U_1,U_2] :
( big_q(sK2)
| ~ big_p(sK1)
| ~ sP0(U_1,U_2) )
& ! [U_9,U_1,U_2,U_8] :
( sP1(U_9,U_8)
| sP0(U_1,U_2) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_1_8]) ).
cnf(f_1_10,negated_conjecture,
( sP1(U_9,U_8)
| sP0(U_1,U_2) ),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_11,negated_conjecture,
( big_q(sK2)
| ~ big_p(sK1)
| ~ sP0(U_1,U_2) ),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_12,negated_conjecture,
( big_p(U_1)
| ~ sP0(U_1,U_2) ),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_13,negated_conjecture,
( ~ big_q(U_2)
| ~ sP0(U_1,U_2) ),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_14,negated_conjecture,
( big_q(sK4)
| ~ big_p(sK3)
| ~ sP1(U_9,U_8) ),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_15,negated_conjecture,
( big_p(U_8)
| ~ sP1(U_9,U_8) ),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_16,negated_conjecture,
( ~ big_q(U_9)
| ~ sP1(U_9,U_8) ),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(t1,plain,
( ~ big_q(sK4)
| ~ sP0(U_92,sK4) ),
inference(start,[status(thm),parent(0:0)],[f_1_13]) ).
cnf(t2,plain,
( sP1(sK4,sK3)
| sP0(U_92,sK4) ),
inference(extension,[status(thm),parent(t1:1)],[f_1_10]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ big_q(sK4)
| ~ sP1(sK4,sK3) ),
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_p(sK3)
| ~ sP1(sK4,sK3)
| big_q(sK4) ),
inference(extension,[status(thm),parent(t4:2)],[f_1_14]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
$false,
inference(reduction,[status(thm),parent(t6:2)],[t6:2,t2:2]) ).
cnf(t9,plain,
( ~ sP1(sK4,sK3)
| big_p(sK3) ),
inference(extension,[status(thm),parent(t6:3)],[f_1_15]) ).
cnf(t10,plain,
$false,
inference(connection,[status(thm),parent(t9:1)],[t9:1,t6:3]) ).
cnf(t11,plain,
$false,
inference(reduction,[status(thm),parent(t9:2)],[t9:2,t2:2]) ).
cnf(t12,plain,
( ~ big_p(sK3)
| ~ sP1(U_106,U_107)
| big_q(sK4) ),
inference(extension,[status(thm),parent(t1:2)],[f_1_14]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t1:2]) ).
cnf(t14,plain,
( sP0(sK1,sK2)
| sP1(U_106,U_107) ),
inference(extension,[status(thm),parent(t12:2)],[f_1_10]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ big_p(sK1)
| big_q(sK2)
| ~ sP0(sK1,sK2) ),
inference(extension,[status(thm),parent(t14:2)],[f_1_11]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ sP0(sK1,sK2)
| ~ big_q(sK2) ),
inference(extension,[status(thm),parent(t16:2)],[f_1_13]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
$false,
inference(reduction,[status(thm),parent(t18:2)],[t18:2,t14:2]) ).
cnf(t21,plain,
( ~ sP0(sK1,sK2)
| big_p(sK1) ),
inference(extension,[status(thm),parent(t16:3)],[f_1_12]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t16:3]) ).
cnf(t23,plain,
$false,
inference(reduction,[status(thm),parent(t21:2)],[t21:2,t14:2]) ).
cnf(t24,plain,
( ~ sP1(U_118,sK3)
| big_p(sK3) ),
inference(extension,[status(thm),parent(t12:3)],[f_1_15]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t12:3]) ).
cnf(t26,plain,
( sP0(sK3,U_121)
| sP1(U_118,sK3) ),
inference(extension,[status(thm),parent(t24:2)],[f_1_10]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( big_p(sK3)
| ~ sP0(sK3,U_121) ),
inference(extension,[status(thm),parent(t26:2)],[f_1_12]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
$false,
inference(reduction,[status(thm),parent(t28:2)],[t28:2,t12:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN373+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
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 06:32:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.40 % SZS status Theorem for theBenchmark
% 0.11/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------