%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN059+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 : n014.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 09:09:21 AM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 91 ( 47 unt; 0 def)
% Number of atoms : 279 ( 0 equ)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 310 ( 122 ~; 113 |; 67 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 104 ( 24 sgn 54 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel29_1,axiom,
? [X] : big_f(X),
file('theBenchmark.p',pel29_1) ).
fof(pel29_2,axiom,
? [Y] : big_g(Y),
file('theBenchmark.p',pel29_2) ).
fof(pel29,conjecture,
( ( ! [U] :
( big_g(U)
=> big_j(U) )
& ! [X] :
( big_f(X)
=> big_h(X) ) )
<=> ! [W,Y] :
( ( big_g(Y)
& big_f(W) )
=> ( big_j(Y)
& big_h(W) ) ) ),
file('theBenchmark.p',pel29) ).
fof(f_1_1,plain,
? [X] : big_f(X),
inference(fof_nnf,[status(thm)],[pel29_1]) ).
fof(f_1_2,plain,
? [U_0] : big_f(U_0),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
big_f(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1)],[f_1_2]) ).
cnf(f_1_4,plain,
big_f(sK1),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
? [Y] : big_g(Y),
inference(fof_nnf,[status(thm)],[pel29_2]) ).
fof(f_2_2,plain,
? [U_1] : big_g(U_1),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
big_g(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2)],[f_2_2]) ).
cnf(f_2_4,plain,
big_g(sK2),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,negated_conjecture,
~ ( ( ! [U] :
( big_g(U)
=> big_j(U) )
& ! [X] :
( big_f(X)
=> big_h(X) ) )
<=> ! [W,Y] :
( ( big_g(Y)
& big_f(W) )
=> ( big_j(Y)
& big_h(W) ) ) ),
inference(negate,[status(cth)],[pel29]) ).
fof(f_3_2,negated_conjecture,
( ( ( ? [U] :
( ~ big_j(U)
& big_g(U) )
| ? [X] :
( ~ big_h(X)
& big_f(X) ) )
& ! [W,Y] :
( ( big_j(Y)
& big_h(W) )
| ~ big_g(Y)
| ~ big_f(W) ) )
| ( ? [W,Y] :
( ( ~ big_j(Y)
| ~ big_h(W) )
& big_g(Y)
& big_f(W) )
& ! [U] :
( big_j(U)
| ~ big_g(U) )
& ! [X] :
( big_h(X)
| ~ big_f(X) ) ) ),
inference(fof_nnf,[status(thm)],[f_3_1]) ).
fof(f_3_3,negated_conjecture,
( ( ( ? [U_9] :
( ~ big_j(U_9)
& big_g(U_9) )
| ? [U_8] :
( ~ big_h(U_8)
& big_f(U_8) ) )
& ! [U_7,U_6] :
( ( big_j(U_6)
& big_h(U_7) )
| ~ big_g(U_6)
| ~ big_f(U_7) ) )
| ( ? [U_5,U_4] :
( ( ~ big_j(U_4)
| ~ big_h(U_5) )
& big_g(U_4)
& big_f(U_5) )
& ! [U_3] :
( big_j(U_3)
| ~ big_g(U_3) )
& ! [U_2] :
( big_h(U_2)
| ~ big_f(U_2) ) ) ),
inference(variable_rename,[status(thm)],[f_3_2]) ).
fof(f_3_4,negated_conjecture,
( ( ( ? [U_9] :
( ~ big_j(U_9)
& big_g(U_9) )
| ? [U_8] :
( ~ big_h(U_8)
& big_f(U_8) ) )
& ! [U_7,U_6] :
( ( big_j(U_6)
& big_h(U_7) )
| ~ big_g(U_6)
| ~ big_f(U_7) ) )
| ( ? [U_4] :
( ( ~ big_j(U_4)
| ~ big_h(sK3) )
& big_g(U_4)
& big_f(sK3) )
& ! [U_3] :
( big_j(U_3)
| ~ big_g(U_3) )
& ! [U_2] :
( big_h(U_2)
| ~ big_f(U_2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_5,sK3)],[f_3_3]) ).
fof(f_3_5,negated_conjecture,
( ( ( ? [U_9] :
( ~ big_j(U_9)
& big_g(U_9) )
| ? [U_8] :
( ~ big_h(U_8)
& big_f(U_8) ) )
& ! [U_7,U_6] :
( ( big_j(U_6)
& big_h(U_7) )
| ~ big_g(U_6)
| ~ big_f(U_7) ) )
| ( ( ~ big_j(sK4)
| ~ big_h(sK3) )
& big_g(sK4)
& big_f(sK3)
& ! [U_3] :
( big_j(U_3)
| ~ big_g(U_3) )
& ! [U_2] :
( big_h(U_2)
| ~ big_f(U_2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_4,sK4)],[f_3_4]) ).
fof(f_3_6,negated_conjecture,
( ( ( ? [U_9] :
( ~ big_j(U_9)
& big_g(U_9) )
| ( ~ big_h(sK5)
& big_f(sK5) ) )
& ! [U_7,U_6] :
( ( big_j(U_6)
& big_h(U_7) )
| ~ big_g(U_6)
| ~ big_f(U_7) ) )
| ( ( ~ big_j(sK4)
| ~ big_h(sK3) )
& big_g(sK4)
& big_f(sK3)
& ! [U_3] :
( big_j(U_3)
| ~ big_g(U_3) )
& ! [U_2] :
( big_h(U_2)
| ~ big_f(U_2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_8,sK5)],[f_3_5]) ).
fof(f_3_7,negated_conjecture,
( ( ( ( ~ big_j(sK6)
& big_g(sK6) )
| ( ~ big_h(sK5)
& big_f(sK5) ) )
& ! [U_7,U_6] :
( ( big_j(U_6)
& big_h(U_7) )
| ~ big_g(U_6)
| ~ big_f(U_7) ) )
| ( ( ~ big_j(sK4)
| ~ big_h(sK3) )
& big_g(sK4)
& big_f(sK3)
& ! [U_3] :
( big_j(U_3)
| ~ big_g(U_3) )
& ! [U_2] :
( big_h(U_2)
| ~ big_f(U_2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_9,sK6)],[f_3_6]) ).
fof(f_3_8,negated_conjecture,
( ( ~ big_j(sK6)
| ~ sP3 )
& ( big_g(sK6)
| ~ sP3 )
& ( ~ big_h(sK5)
| ~ sP2 )
& ( big_f(sK5)
| ~ sP2 )
& ! [U_6,U_7] :
( big_j(U_6)
| ~ sP1(U_6,U_7) )
& ! [U_6,U_7] :
( big_h(U_7)
| ~ sP1(U_6,U_7) )
& ! [U_6,U_7] :
( sP3
| sP2
| ~ sP4(U_6,U_7) )
& ! [U_6,U_7] :
( sP1(U_6,U_7)
| ~ big_g(U_6)
| ~ big_f(U_7)
| ~ sP4(U_6,U_7) )
& ! [U_2,U_3] :
( ~ big_j(sK4)
| ~ big_h(sK3)
| ~ sP0(U_2,U_3) )
& ! [U_2,U_3] :
( big_g(sK4)
| ~ sP0(U_2,U_3) )
& ! [U_2,U_3] :
( big_f(sK3)
| ~ sP0(U_2,U_3) )
& ! [U_2,U_3] :
( big_j(U_3)
| ~ big_g(U_3)
| ~ sP0(U_2,U_3) )
& ! [U_2,U_3] :
( big_h(U_2)
| ~ big_f(U_2)
| ~ sP0(U_2,U_3) )
& ! [U_2,U_6,U_3,U_7] :
( sP4(U_6,U_7)
| sP0(U_2,U_3) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3,sP4])],[f_3_7]) ).
cnf(f_3_9,negated_conjecture,
( sP4(U_6,U_7)
| sP0(U_2,U_3) ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_10,negated_conjecture,
( big_h(U_2)
| ~ big_f(U_2)
| ~ sP0(U_2,U_3) ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_11,negated_conjecture,
( big_j(U_3)
| ~ big_g(U_3)
| ~ sP0(U_2,U_3) ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_12,negated_conjecture,
( big_f(sK3)
| ~ sP0(U_2,U_3) ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_13,negated_conjecture,
( big_g(sK4)
| ~ sP0(U_2,U_3) ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_14,negated_conjecture,
( ~ big_j(sK4)
| ~ big_h(sK3)
| ~ sP0(U_2,U_3) ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_15,negated_conjecture,
( sP1(U_6,U_7)
| ~ big_g(U_6)
| ~ big_f(U_7)
| ~ sP4(U_6,U_7) ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_16,negated_conjecture,
( sP3
| sP2
| ~ sP4(U_6,U_7) ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_17,negated_conjecture,
( big_h(U_7)
| ~ sP1(U_6,U_7) ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_18,negated_conjecture,
( big_j(U_6)
| ~ sP1(U_6,U_7) ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_19,negated_conjecture,
( big_f(sK5)
| ~ sP2 ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_20,negated_conjecture,
( ~ big_h(sK5)
| ~ sP2 ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_21,negated_conjecture,
( big_g(sK6)
| ~ sP3 ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(f_3_22,negated_conjecture,
( ~ big_j(sK6)
| ~ sP3 ),
inference(clausify,[status(thm)],[f_3_8]) ).
cnf(t1,plain,
( ~ big_h(sK5)
| ~ sP2 ),
inference(start,[status(thm),parent(0:0)],[f_3_20]) ).
cnf(t2,plain,
( sP3
| ~ sP4(U_124,U_125)
| sP2 ),
inference(extension,[status(thm),parent(t1:1)],[f_3_16]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sP0(sK3,sK4)
| sP4(U_124,U_125) ),
inference(extension,[status(thm),parent(t2:2)],[f_3_9]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ big_h(sK3)
| ~ big_j(sK4)
| ~ sP0(sK3,sK4) ),
inference(extension,[status(thm),parent(t4:2)],[f_3_14]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ big_g(sK4)
| ~ sP0(sK3,sK4)
| big_j(sK4) ),
inference(extension,[status(thm),parent(t6:2)],[f_3_11]) ).
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,
( ~ sP0(sK3,sK4)
| big_g(sK4) ),
inference(extension,[status(thm),parent(t8:3)],[f_3_13]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t8:3]) ).
cnf(t13,plain,
$false,
inference(reduction,[status(thm),parent(t11:2)],[t11:2,t4:2]) ).
cnf(t14,plain,
( ~ big_f(sK3)
| ~ sP0(sK3,sK4)
| big_h(sK3) ),
inference(extension,[status(thm),parent(t6:3)],[f_3_10]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
$false,
inference(reduction,[status(thm),parent(t14:2)],[t14:2,t4:2]) ).
cnf(t17,plain,
( ~ sP0(sK3,sK4)
| big_f(sK3) ),
inference(extension,[status(thm),parent(t14:3)],[f_3_12]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t14:3]) ).
cnf(t19,plain,
$false,
inference(reduction,[status(thm),parent(t17:2)],[t17:2,t4:2]) ).
cnf(t20,plain,
( big_g(sK6)
| ~ sP3 ),
inference(extension,[status(thm),parent(t2:3)],[f_3_21]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:3]) ).
cnf(t22,plain,
( ~ big_f(sK1)
| sP1(sK6,sK1)
| ~ sP4(sK6,sK1)
| ~ big_g(sK6) ),
inference(extension,[status(thm),parent(t20:2)],[f_3_15]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( sP0(U_142,sK6)
| sP4(sK6,sK1) ),
inference(extension,[status(thm),parent(t22:2)],[f_3_9]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ big_g(sK6)
| big_j(sK6)
| ~ sP0(U_142,sK6) ),
inference(extension,[status(thm),parent(t24:2)],[f_3_11]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( ~ sP3
| ~ big_j(sK6) ),
inference(extension,[status(thm),parent(t26:2)],[f_3_22]) ).
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,t2:3]) ).
cnf(t31,plain,
$false,
inference(reduction,[status(thm),parent(t26:3)],[t26:3,t20:2]) ).
cnf(t32,plain,
( big_j(sK6)
| ~ sP1(sK6,sK1) ),
inference(extension,[status(thm),parent(t22:3)],[f_3_18]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t22:3]) ).
cnf(t34,plain,
( ~ sP3
| ~ big_j(sK6) ),
inference(extension,[status(thm),parent(t32:2)],[f_3_22]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
$false,
inference(reduction,[status(thm),parent(t34:2)],[t34:2,t2:3]) ).
cnf(t37,plain,
big_f(sK1),
inference(extension,[status(thm),parent(t22:4)],[f_1_4]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t22:4]) ).
cnf(l1,lemma,
sP2,
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t39,plain,
( ~ sP1(sK2,sK5)
| big_h(sK5) ),
inference(extension,[status(thm),parent(t1:2)],[f_3_17]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t1:2]) ).
cnf(t41,plain,
( ~ big_f(sK5)
| ~ big_g(sK2)
| ~ sP4(sK2,sK5)
| sP1(sK2,sK5) ),
inference(extension,[status(thm),parent(t39:2)],[f_3_15]) ).
cnf(t42,plain,
$false,
inference(connection,[status(thm),parent(t41:1)],[t41:1,t39:2]) ).
cnf(t43,plain,
( sP0(sK5,U_155)
| sP4(sK2,sK5) ),
inference(extension,[status(thm),parent(t41:2)],[f_3_9]) ).
cnf(t44,plain,
$false,
inference(connection,[status(thm),parent(t43:1)],[t43:1,t41:2]) ).
cnf(t45,plain,
( ~ big_f(sK5)
| big_h(sK5)
| ~ sP0(sK5,U_155) ),
inference(extension,[status(thm),parent(t43:2)],[f_3_10]) ).
cnf(t46,plain,
$false,
inference(connection,[status(thm),parent(t45:1)],[t45:1,t43:2]) ).
cnf(t47,plain,
$false,
inference(reduction,[status(thm),parent(t45:2)],[t45:2,t1:2]) ).
cnf(t48,plain,
( ~ sP2
| big_f(sK5) ),
inference(extension,[status(thm),parent(t45:3)],[f_3_19]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t45:3]) ).
cnf(t50,plain,
sP2,
inference(lemma_extension,[status(thm),parent(t48:2)],[l1:1]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
big_g(sK2),
inference(extension,[status(thm),parent(t41:3)],[f_2_4]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t41:3]) ).
cnf(t54,plain,
( ~ sP2
| big_f(sK5) ),
inference(extension,[status(thm),parent(t41:4)],[f_3_19]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t41:4]) ).
cnf(t56,plain,
sP2,
inference(lemma_extension,[status(thm),parent(t54:2)],[l1:1]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN059+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
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 06:23:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.41 % SZS status Theorem for theBenchmark
% 0.10/0.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------