%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG060+2 : 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 : n011.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 08:55:02 AM UTC 2026
% Result : Theorem 30.24s 30.56s
% Output : Proof 30.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 35 unt; 0 def)
% Number of atoms : 116 ( 52 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 95 ( 41 ~; 37 |; 15 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mNegSc,axiom,
! [W0] :
( aScalar0(W0)
=> aScalar0(smndt0(W0)) ),
file('theBenchmark.p',mNegSc) ).
fof(mDistr2,axiom,
! [W0,W1,W2,W3] :
( ( aScalar0(W3)
& aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ),
file('theBenchmark.p',mDistr2) ).
fof(m__1892,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('theBenchmark.p',m__1892) ).
fof(m__1930,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('theBenchmark.p',m__1930) ).
fof(m__2144,hypothesis,
( sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(xR,smndt0(xS)) = smndt0(xN) ),
file('theBenchmark.p',m__2144) ).
fof(m__,conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
file('theBenchmark.p',m__) ).
fof(f_12_1,plain,
! [W0] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mNegSc]) ).
fof(f_12_2,plain,
! [U_14] :
( aScalar0(smndt0(U_14))
| ~ aScalar0(U_14) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_14] :
( aScalar0(smndt0(U_14))
| ~ aScalar0(U_14) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( aScalar0(smndt0(U_14))
| ~ aScalar0(U_14) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_16_1,plain,
! [W0,W1,W2,W3] :
( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3)))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(fof_nnf,[status(thm)],[mDistr2]) ).
fof(f_16_2,plain,
! [U_25,U_24,U_23,U_22] :
( sdtasdt0(sdtpldt0(U_25,U_24),sdtpldt0(U_23,U_22)) = sdtpldt0(sdtpldt0(sdtasdt0(U_25,U_23),sdtasdt0(U_25,U_22)),sdtpldt0(sdtasdt0(U_24,U_23),sdtasdt0(U_24,U_22)))
| ~ aScalar0(U_22)
| ~ aScalar0(U_23)
| ~ aScalar0(U_24)
| ~ aScalar0(U_25) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_23,U_22,U_24,U_25] :
( sdtasdt0(sdtpldt0(U_25,U_24),sdtpldt0(U_23,U_22)) = sdtpldt0(sdtpldt0(sdtasdt0(U_25,U_23),sdtasdt0(U_25,U_22)),sdtpldt0(sdtasdt0(U_24,U_23),sdtasdt0(U_24,U_22)))
| ~ aScalar0(U_22)
| ~ aScalar0(U_23)
| ~ aScalar0(U_24)
| ~ aScalar0(U_25) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( sdtasdt0(sdtpldt0(U_25,U_24),sdtpldt0(U_23,U_22)) = sdtpldt0(sdtpldt0(sdtasdt0(U_25,U_23),sdtasdt0(U_25,U_22)),sdtpldt0(sdtasdt0(U_24,U_23),sdtasdt0(U_24,U_22)))
| ~ aScalar0(U_22)
| ~ aScalar0(U_23)
| ~ aScalar0(U_24)
| ~ aScalar0(U_25) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_52_1,plain,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
inference(fof_nnf,[status(thm)],[m__1892]) ).
fof(f_52_2,plain,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
inference(definitional_conversion,[status(esa)],[f_52_1]) ).
cnf(f_52_3,plain,
aScalar0(xR),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_54_1,plain,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
inference(fof_nnf,[status(thm)],[m__1930]) ).
fof(f_54_2,plain,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
inference(definitional_conversion,[status(esa)],[f_54_1]) ).
cnf(f_54_3,plain,
aScalar0(xS),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_58_1,plain,
( sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(xR,smndt0(xS)) = smndt0(xN) ),
inference(fof_nnf,[status(thm)],[m__2144]) ).
fof(f_58_2,plain,
( sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(xR,smndt0(xS)) = smndt0(xN) ),
inference(definitional_conversion,[status(esa)],[f_58_1]) ).
cnf(f_58_3,plain,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(clausify,[status(thm)],[f_58_2]) ).
cnf(f_58_4,plain,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
inference(clausify,[status(thm)],[f_58_2]) ).
cnf(f_58_5,plain,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(negate,[status(cth)],[m__]) ).
fof(f_59_2,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(definitional_conversion,[status(esa)],[f_59_1]) ).
cnf(f_59_3,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(clausify,[status(thm)],[f_59_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(start,[status(thm),parent(0:0)],[f_59_3]) ).
cnf(t2,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),xR),sdtasdt0(smndt0(xS),smndt0(xS)))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)))
| sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),xR),sdtasdt0(smndt0(xS),smndt0(xS))))
| sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) ),
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,
( ~ aScalar0(smndt0(xS))
| ~ aScalar0(xR)
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(xR)
| sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),xR),sdtasdt0(smndt0(xS),smndt0(xS)))) ),
inference(extension,[status(thm),parent(t2:2)],[f_16_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
aScalar0(xR),
inference(extension,[status(thm),parent(t4:2)],[f_52_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(l3,lemma,
aScalar0(xR),
inference(lemma,[status(cth),parent(t4:2),below(t2:2)],[t4:2]) ).
cnf(t8,plain,
( ~ aScalar0(xS)
| aScalar0(smndt0(xS)) ),
inference(extension,[status(thm),parent(t4:3)],[f_12_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
aScalar0(xS),
inference(extension,[status(thm),parent(t8:2)],[f_54_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(l4,lemma,
aScalar0(smndt0(xS)),
inference(lemma,[status(cth),parent(t4:3),below(t2:2)],[t4:3]) ).
cnf(t12,plain,
aScalar0(xR),
inference(lemma_extension,[status(thm),parent(t4:4)],[l3:1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:4]) ).
cnf(t14,plain,
aScalar0(smndt0(xS)),
inference(lemma_extension,[status(thm),parent(t4:5)],[l4:1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:5]) ).
cnf(t16,plain,
( sdtpldt0(sdtasdt0(smndt0(xS),xR),sdtasdt0(smndt0(xS),smndt0(xS))) != sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))
| sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,smndt0(xS))) != sdtpldt0(sdtasdt0(xR,xR),smndt0(xN))
| sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),xR),sdtasdt0(smndt0(xS),smndt0(xS)))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) ),
inference(extension,[status(thm),parent(t2:3)],[equality_5]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:3]) ).
cnf(t18,plain,
( sdtasdt0(xR,smndt0(xS)) != smndt0(xN)
| sdtasdt0(xR,xR) != sdtasdt0(xR,xR)
| sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,smndt0(xS))) = sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)) ),
inference(extension,[status(thm),parent(t16:2)],[equality_5]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
sdtasdt0(xR,xR) = sdtasdt0(xR,xR),
inference(extension,[status(thm),parent(t18:2)],[equality_1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(extension,[status(thm),parent(t18:3)],[f_58_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
( sdtasdt0(smndt0(xS),smndt0(xS)) != sdtasdt0(xS,xS)
| sdtasdt0(smndt0(xS),xR) != smndt0(xN)
| sdtpldt0(sdtasdt0(smndt0(xS),xR),sdtasdt0(smndt0(xS),smndt0(xS))) = sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)) ),
inference(extension,[status(thm),parent(t16:3)],[equality_5]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t16:3]) ).
cnf(t26,plain,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
inference(extension,[status(thm),parent(t24:2)],[f_58_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(extension,[status(thm),parent(t24:3)],[f_58_5]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG060+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.09/0.38 % Computer : n011.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 19 20:46:54 UTC 2026
% 0.09/0.38 % CPUTime :
% 30.24/30.56 % SZS status Theorem for theBenchmark
% 30.24/30.56 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------