%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG104+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 02:04:58 PM UTC 2026
% Result : Theorem 4.38s 1.09s
% Output : CNFRefutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 17 unt; 6 def)
% Number of atoms : 123 ( 28 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 113 ( 49 ~; 48 |; 7 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& aElementOf0(xx,slsdtgt0(xc)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f54,plain,
! [W0,W1] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f55,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f66,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f67,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f69,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f195,plain,
aElement0(xc),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f198,plain,
aElement0(xz),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f199,plain,
aElement0(xu),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f200,plain,
sdtasdt0(xc,xu) = xx,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f204,plain,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f236,plain,
! [X0] :
( sdtasdt0(X0,xc) = sdtasdt0(xc,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f195,f67]) ).
fof(f245,plain,
! [X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),xc) = sdtasdt0(X0,sdtasdt0(X1,xc))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f69,f195]) ).
fof(f251,plain,
! [X0] :
( sdtasdt0(X0,xu) = sdtasdt0(xu,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f199,f67]) ).
fof(f252,plain,
( aElement0(xx)
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(paramodulation,[status(thm)],[f200,f55]) ).
fof(f253,definition,
( sQ0_spl
<=> aElement0(xc) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( sQ0_spl
| ~ aElement0(xc) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,definition,
( sQ1_spl
<=> aElement0(xu) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( sQ1_spl
| ~ aElement0(xu) ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,definition,
( sQ2_spl
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( ~ sQ2_spl
| aElement0(xx) ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f252,f253,f256,f259]) ).
fof(f267,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,xx) = sdtasdt0(xx,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f260,f67]) ).
fof(f276,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f195]) ).
fof(f277,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f276]) ).
fof(f278,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f199]) ).
fof(f279,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f278]) ).
fof(f365,plain,
sdtasdt0(xz,xu) = sdtasdt0(xu,xz),
inference(resolution,[status(thm)],[f251,f198]) ).
fof(f366,plain,
sdtasdt0(xc,xu) = sdtasdt0(xu,xc),
inference(resolution,[status(thm)],[f251,f195]) ).
fof(f368,plain,
xx = sdtasdt0(xu,xc),
inference(forward_demodulation,[status(thm)],[f200,f366]) ).
fof(f438,plain,
( aElement0(sdtasdt0(xu,xz))
| ~ aElement0(xu)
| ~ aElement0(xz) ),
inference(paramodulation,[status(thm)],[f365,f55]) ).
fof(f443,definition,
( sQ8_spl
<=> aElement0(xz) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( sQ8_spl
| ~ aElement0(xz) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,definition,
( sQ9_spl
<=> aElement0(sdtasdt0(xu,xz)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f438,f443,f256,f446]) ).
fof(f450,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f445,f198]) ).
fof(f451,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f450]) ).
fof(f608,plain,
( ~ sQ2_spl
| sdtasdt0(xz,xx) = sdtasdt0(xx,xz) ),
inference(resolution,[status(thm)],[f267,f198]) ).
fof(f613,plain,
( ~ sQ2_spl
| sdtasdt0(xx,xz) != sdtasdt0(xc,sdtasdt0(xu,xz)) ),
inference(backward_demodulation,[status(thm)],[f608,f204]) ).
fof(f640,plain,
! [X0] :
( sdtasdt0(sdtasdt0(X0,xu),xc) = sdtasdt0(X0,sdtasdt0(xu,xc))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f245,f199]) ).
fof(f646,plain,
! [X0] :
( sdtasdt0(sdtasdt0(X0,xu),xc) = sdtasdt0(X0,xx)
| ~ aElement0(X0) ),
inference(forward_demodulation,[status(thm)],[f368,f640]) ).
fof(f1315,plain,
sdtasdt0(sdtasdt0(xz,xu),xc) = sdtasdt0(xz,xx),
inference(resolution,[status(thm)],[f646,f198]) ).
fof(f1324,plain,
sdtasdt0(sdtasdt0(xu,xz),xc) = sdtasdt0(xz,xx),
inference(forward_demodulation,[status(thm)],[f365,f1315]) ).
fof(f1325,plain,
( ~ sQ2_spl
| sdtasdt0(sdtasdt0(xu,xz),xc) = sdtasdt0(xx,xz) ),
inference(forward_demodulation,[status(thm)],[f608,f1324]) ).
fof(f1580,plain,
( ~ sQ2_spl
| sdtasdt0(xx,xz) = sdtasdt0(xc,sdtasdt0(xu,xz))
| ~ aElement0(sdtasdt0(xu,xz)) ),
inference(paramodulation,[status(thm)],[f1325,f236]) ).
fof(f1582,definition,
( sQ43_spl
<=> sdtasdt0(xx,xz) = sdtasdt0(xc,sdtasdt0(xu,xz)) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1583,plain,
( ~ sQ43_spl
| sdtasdt0(xx,xz) = sdtasdt0(xc,sdtasdt0(xu,xz)) ),
inference(component_clause,[status(thm)],[f1582]) ).
fof(f1585,plain,
( ~ sQ2_spl
| sQ43_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1580,f446,f1582,f259]) ).
fof(f1587,plain,
( ~ sQ43_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1583,f613]) ).
fof(f1588,plain,
( ~ sQ43_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f1587]) ).
fof(f1589,plain,
$false,
inference(sat_refutation,[status(thm)],[f262,f277,f279,f449,f451,f1585,f1588]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG104+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:22:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 4.38/1.09 % Refutation found
% 4.38/1.09 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.38/1.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.14/1.12 % Elapsed time: 0.738829 seconds
% 1.14/1.12 % CPU time: 5.247482 seconds
% 1.14/1.12 % Total memory used: 167.698 MB
% 1.14/1.12 % Net memory used: 161.500 MB
%------------------------------------------------------------------------------