%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG045+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n004.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 08:55:00 AM UTC 2026
% Result : Theorem 0.88s 1.17s
% Output : Proof 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 30 unt; 0 def)
% Number of atoms : 77 ( 30 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 62 ( 27 ~; 23 |; 11 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDistr,axiom,
! [W0,W1,W2] :
( ( aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mDistr) ).
fof(m__674,hypothesis,
( aScalar0(xv)
& aScalar0(xu)
& aScalar0(xy)
& aScalar0(xx) ),
file('theBenchmark.p',m__674) ).
fof(m__733,hypothesis,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
file('theBenchmark.p',m__733) ).
fof(m__,conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
file('theBenchmark.p',m__) ).
fof(f_15_1,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mDistr]) ).
fof(f_15_2,plain,
! [U_21,U_20,U_19] :
( ( sdtasdt0(sdtpldt0(U_21,U_20),U_19) = sdtpldt0(sdtasdt0(U_21,U_19),sdtasdt0(U_20,U_19))
& sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19)) )
| ~ aScalar0(U_19)
| ~ aScalar0(U_20)
| ~ aScalar0(U_21) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19))
| ~ aScalar0(U_19)
| ~ aScalar0(U_20)
| ~ aScalar0(U_21) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
( aScalar0(xv)
& aScalar0(xu)
& aScalar0(xy)
& aScalar0(xx) ),
inference(fof_nnf,[status(thm)],[m__674]) ).
cnf(f_16_2,plain,
aScalar0(xx),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
aScalar0(xy),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_4,plain,
aScalar0(xu),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_5,plain,
aScalar0(xv),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
inference(fof_nnf,[status(thm)],[m__733]) ).
cnf(f_17_2,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,negated_conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(negate,[status(cth)],[m__]) ).
fof(f_18_2,negated_conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,negated_conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_5,axiom,
( sdtpldt0(Eq_x_0,Eq_x_1) = sdtpldt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(start,[status(thm),parent(0:0)],[f_18_3]) ).
cnf(t2,plain,
( sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)))
| sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv)))
| sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
inference(extension,[status(thm),parent(t2:2)],[f_17_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))
| sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv))
| sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) = sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))) ),
inference(extension,[status(thm),parent(t2:3)],[equality_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ aScalar0(xu)
| ~ aScalar0(xv)
| ~ aScalar0(xx)
| sdtasdt0(xx,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) ),
inference(extension,[status(thm),parent(t6:2)],[f_15_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
aScalar0(xx),
inference(extension,[status(thm),parent(t8:2)],[f_16_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
aScalar0(xv),
inference(extension,[status(thm),parent(t8:3)],[f_16_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
aScalar0(xu),
inference(extension,[status(thm),parent(t8:4)],[f_16_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:4]) ).
cnf(t16,plain,
( ~ aScalar0(xu)
| ~ aScalar0(xv)
| ~ aScalar0(xy)
| sdtasdt0(xy,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) ),
inference(extension,[status(thm),parent(t6:3)],[f_15_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t6:3]) ).
cnf(t18,plain,
aScalar0(xy),
inference(extension,[status(thm),parent(t16:2)],[f_16_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
aScalar0(xv),
inference(extension,[status(thm),parent(t16:3)],[f_16_5]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
aScalar0(xu),
inference(extension,[status(thm),parent(t16:4)],[f_16_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG045+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.08/0.35 % Computer : n004.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 : Sat Sep 19 20:45:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.88/1.17 % SZS status Theorem for theBenchmark
% 0.88/1.17 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------