%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KRS105+1 : TPTP v9.3.1. Released v3.1.0.
% 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 08:47:17 AM UTC 2026
% Result : Unsatisfiable 0.13s 20.61s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 17 unt; 0 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 177 ( 75 ~; 72 |; 21 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 87 ( 1 sgn 65 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
=> cdxcomp(X) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cUnsatisfiable(X)
=> cc(X) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cc(X)
=> ! [Y] :
( rr(X,Y)
=> cc(Y) ) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( cd(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( cdxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X] :
( ca_Ax2(X)
<=> ! [Y] :
( rr(X,Y)
=> cc(Y) ) ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_8,axiom,
! [X] :
( ca_Ax2(X)
=> cd(X) ),
file('theBenchmark.p',axiom_8) ).
fof(axiom_9,axiom,
cUnsatisfiable(i2003_11_14_17_20_53634),
file('theBenchmark.p',axiom_9) ).
fof(f_3_1,plain,
! [X] :
( cdxcomp(X)
| ~ cUnsatisfiable(X) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(f_3_2,plain,
! [U_6] :
( cdxcomp(U_6)
| ~ cUnsatisfiable(U_6) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_6] :
( cdxcomp(U_6)
| ~ cUnsatisfiable(U_6) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( cdxcomp(U_6)
| ~ cUnsatisfiable(U_6) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [X] :
( cc(X)
| ~ cUnsatisfiable(X) ),
inference(fof_nnf,[status(thm)],[axiom_3]) ).
fof(f_4_2,plain,
! [U_7] :
( cc(U_7)
| ~ cUnsatisfiable(U_7) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_7] :
( cc(U_7)
| ~ cUnsatisfiable(U_7) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( cc(U_7)
| ~ cUnsatisfiable(U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [X] :
( ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
| ~ cc(X) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(f_5_2,plain,
! [U_9] :
( ! [U_8] :
( cc(U_8)
| ~ rr(U_9,U_8) )
| ~ cc(U_9) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_9,U_8] :
( cc(U_8)
| ~ rr(U_9,U_8)
| ~ cc(U_9) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( cc(U_8)
| ~ rr(U_9,U_8)
| ~ cc(U_9) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [X] :
( ( cd(X)
| ? [Y] : ra_Px1(X,Y) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_5]) ).
fof(f_6_2,plain,
! [U_12] :
( ( cd(U_12)
| ? [U_11] : ra_Px1(U_12,U_11) )
& ( ! [U_10] : ~ ra_Px1(U_12,U_10)
| ~ cd(U_12) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_14] :
( cd(U_14)
| ? [U_11] : ra_Px1(U_14,U_11) )
& ! [U_13] :
( ! [U_10] : ~ ra_Px1(U_13,U_10)
| ~ cd(U_13) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_14] :
( cd(U_14)
| ra_Px1(U_14,sK1(U_14)) )
& ! [U_13] :
( ! [U_10] : ~ ra_Px1(U_13,U_10)
| ~ cd(U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_11,sK1(U_14))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_14] :
( cd(U_14)
| ra_Px1(U_14,sK1(U_14)) )
& ! [U_13,U_10] :
( ~ ra_Px1(U_13,U_10)
| ~ cd(U_13) ) ),
inference(definitional_conversion,[status(esa)],[f_6_4]) ).
cnf(f_6_6,plain,
( ~ ra_Px1(U_13,U_10)
| ~ cd(U_13) ),
inference(clausify,[status(thm)],[f_6_5]) ).
fof(f_7_1,plain,
! [X] :
( ( cdxcomp(X)
| ! [Y0] : ~ ra_Px1(X,Y0) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cdxcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(f_7_2,plain,
! [U_17] :
( ( cdxcomp(U_17)
| ! [U_16] : ~ ra_Px1(U_17,U_16) )
& ( ? [U_15] : ra_Px1(U_17,U_15)
| ~ cdxcomp(U_17) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_19] :
( cdxcomp(U_19)
| ! [U_16] : ~ ra_Px1(U_19,U_16) )
& ! [U_18] :
( ? [U_15] : ra_Px1(U_18,U_15)
| ~ cdxcomp(U_18) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_19] :
( cdxcomp(U_19)
| ! [U_16] : ~ ra_Px1(U_19,U_16) )
& ! [U_18] :
( ra_Px1(U_18,sK2(U_18))
| ~ cdxcomp(U_18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_15,sK2(U_18))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_16,U_19] :
( cdxcomp(U_19)
| ~ ra_Px1(U_19,U_16) )
& ! [U_18] :
( ra_Px1(U_18,sK2(U_18))
| ~ cdxcomp(U_18) ) ),
inference(definitional_conversion,[status(esa)],[f_7_4]) ).
cnf(f_7_6,plain,
( ra_Px1(U_18,sK2(U_18))
| ~ cdxcomp(U_18) ),
inference(clausify,[status(thm)],[f_7_5]) ).
fof(f_8_1,plain,
! [X] :
( ( ca_Ax2(X)
| ? [Y] :
( ~ cc(Y)
& rr(X,Y) ) )
& ( ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
| ~ ca_Ax2(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_7]) ).
fof(f_8_2,plain,
! [U_22] :
( ( ca_Ax2(U_22)
| ? [U_21] :
( ~ cc(U_21)
& rr(U_22,U_21) ) )
& ( ! [U_20] :
( cc(U_20)
| ~ rr(U_22,U_20) )
| ~ ca_Ax2(U_22) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_24] :
( ca_Ax2(U_24)
| ? [U_21] :
( ~ cc(U_21)
& rr(U_24,U_21) ) )
& ! [U_23] :
( ! [U_20] :
( cc(U_20)
| ~ rr(U_23,U_20) )
| ~ ca_Ax2(U_23) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_24] :
( ca_Ax2(U_24)
| ( ~ cc(sK3(U_24))
& rr(U_24,sK3(U_24)) ) )
& ! [U_23] :
( ! [U_20] :
( cc(U_20)
| ~ rr(U_23,U_20) )
| ~ ca_Ax2(U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_21,sK3(U_24))],[f_8_3]) ).
fof(f_8_5,plain,
( ! [U_24] :
( ~ cc(sK3(U_24))
| ~ sP0(U_24) )
& ! [U_24] :
( rr(U_24,sK3(U_24))
| ~ sP0(U_24) )
& ! [U_24] :
( ca_Ax2(U_24)
| sP0(U_24) )
& ! [U_20,U_23] :
( cc(U_20)
| ~ rr(U_23,U_20)
| ~ ca_Ax2(U_23) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_8_4]) ).
cnf(f_8_7,plain,
( ca_Ax2(U_24)
| sP0(U_24) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_8,plain,
( rr(U_24,sK3(U_24))
| ~ sP0(U_24) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_9,plain,
( ~ cc(sK3(U_24))
| ~ sP0(U_24) ),
inference(clausify,[status(thm)],[f_8_5]) ).
fof(f_9_1,plain,
! [X] :
( cd(X)
| ~ ca_Ax2(X) ),
inference(fof_nnf,[status(thm)],[axiom_8]) ).
fof(f_9_2,plain,
! [U_25] :
( cd(U_25)
| ~ ca_Ax2(U_25) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_25] :
( cd(U_25)
| ~ ca_Ax2(U_25) ),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
( cd(U_25)
| ~ ca_Ax2(U_25) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
cUnsatisfiable(i2003_11_14_17_20_53634),
inference(fof_nnf,[status(thm)],[axiom_9]) ).
fof(f_10_2,plain,
cUnsatisfiable(i2003_11_14_17_20_53634),
inference(definitional_conversion,[status(esa)],[f_10_1]) ).
cnf(f_10_3,plain,
cUnsatisfiable(i2003_11_14_17_20_53634),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(t1,plain,
( ~ ra_Px1(i2003_11_14_17_20_53634,sK2(i2003_11_14_17_20_53634))
| ~ cd(i2003_11_14_17_20_53634) ),
inference(start,[status(thm),parent(0:0)],[f_6_6]) ).
cnf(t2,plain,
( ~ ca_Ax2(i2003_11_14_17_20_53634)
| cd(i2003_11_14_17_20_53634) ),
inference(extension,[status(thm),parent(t1:1)],[f_9_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sP0(i2003_11_14_17_20_53634)
| ca_Ax2(i2003_11_14_17_20_53634) ),
inference(extension,[status(thm),parent(t2:2)],[f_8_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ cc(sK3(i2003_11_14_17_20_53634))
| ~ sP0(i2003_11_14_17_20_53634) ),
inference(extension,[status(thm),parent(t4:2)],[f_8_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ rr(i2003_11_14_17_20_53634,sK3(i2003_11_14_17_20_53634))
| ~ cc(i2003_11_14_17_20_53634)
| cc(sK3(i2003_11_14_17_20_53634)) ),
inference(extension,[status(thm),parent(t6:2)],[f_5_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_53634)
| cc(i2003_11_14_17_20_53634) ),
inference(extension,[status(thm),parent(t8:2)],[f_4_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
cUnsatisfiable(i2003_11_14_17_20_53634),
inference(extension,[status(thm),parent(t10:2)],[f_10_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ sP0(i2003_11_14_17_20_53634)
| rr(i2003_11_14_17_20_53634,sK3(i2003_11_14_17_20_53634)) ),
inference(extension,[status(thm),parent(t8:3)],[f_8_8]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:3]) ).
cnf(t16,plain,
$false,
inference(reduction,[status(thm),parent(t14:2)],[t14:2,t4:2]) ).
cnf(t17,plain,
( ~ cdxcomp(i2003_11_14_17_20_53634)
| ra_Px1(i2003_11_14_17_20_53634,sK2(i2003_11_14_17_20_53634)) ),
inference(extension,[status(thm),parent(t1:2)],[f_7_6]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t1:2]) ).
cnf(t19,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_53634)
| cdxcomp(i2003_11_14_17_20_53634) ),
inference(extension,[status(thm),parent(t17:2)],[f_3_4]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t17:2]) ).
cnf(t21,plain,
cUnsatisfiable(i2003_11_14_17_20_53634),
inference(extension,[status(thm),parent(t19:2)],[f_10_3]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS105+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 This is a FOF_UNS_RFO_NEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/20.59 % Computer : n013.cluster.edu
% 0.09/20.59 % Model : x86_64 x86_64
% 0.09/20.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/20.59 % Memory : 8046.5625MB
% 0.09/20.59 % OS : Linux 6.8.0-71-generic
% 0.09/20.59 % CPULimit : 300
% 0.09/20.59 % WCLimit : 300
% 0.09/20.59 % DateTime : Sat Sep 19 12:12:29 UTC 2026
% 0.09/20.59 % CPUTime :
% 0.13/20.61 % SZS status Unsatisfiable for theBenchmark
% 0.13/20.61 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------