%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG057+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:04:48 PM UTC 2026
% Result : Theorem 34.25s 4.75s
% Output : CNFRefutation 34.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 24
% Syntax : Number of formulae : 82 ( 20 unt; 12 def)
% Number of atoms : 197 ( 8 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 200 ( 85 ~; 88 |; 10 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 13 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aScalar0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [W0,W1,W2,W3] :
( ( aScalar0(W3)
& aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( ( sdtlseqdt0(W2,W3)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [W0] :
( aScalar0(W0)
=> sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,hypothesis,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,hypothesis,
( xH = sdtasdt0(xA,xB)
& aScalar0(xH) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,hypothesis,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,hypothesis,
sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,hypothesis,
xN = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,conjecture,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f84,plain,
! [W0,W1] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f85,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f114,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f115,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f122,plain,
! [W0,W1,W2,W3] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(sz0z00,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f129,plain,
! [W0] :
( sdtlseqdt0(sz0z00,sdtasdt0(W0,W0))
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f130,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f173,plain,
aScalar0(xC),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f175,plain,
aScalar0(xD),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f177,plain,
aScalar0(xE),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f183,plain,
aScalar0(xH),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f193,plain,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f194,plain,
sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f195,plain,
xN = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f196,plain,
~ sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f296,definition,
( sQ14_spl
<=> aScalar0(sdtasdt0(xH,xH)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( ~ sQ14_spl
| aScalar0(sdtasdt0(xH,xH)) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f298,plain,
( sQ14_spl
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,definition,
( sQ15_spl
<=> aScalar0(sdtasdt0(xC,xD)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( sQ15_spl
| ~ aScalar0(sdtasdt0(xC,xD)) ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f306,definition,
( sQ17_spl
<=> aScalar0(sdtasdt0(xE,xE)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( sQ17_spl
| ~ aScalar0(sdtasdt0(xE,xE)) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f313,definition,
( sQ19_spl
<=> aScalar0(xE) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( sQ19_spl
| ~ aScalar0(xE) ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f316,definition,
( sQ20_spl
<=> aScalar0(xH) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f318,plain,
( sQ20_spl
| ~ aScalar0(xH) ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f347,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f318,f183]) ).
fof(f348,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f347]) ).
fof(f349,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f315,f177]) ).
fof(f350,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f349]) ).
fof(f747,plain,
( sQ14_spl
| ~ aScalar0(xH)
| ~ aScalar0(xH) ),
inference(resolution,[status(thm)],[f298,f85]) ).
fof(f748,plain,
( sQ14_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f747,f316,f296]) ).
fof(f1494,plain,
( sQ17_spl
| ~ aScalar0(xE)
| ~ aScalar0(xE) ),
inference(resolution,[status(thm)],[f308,f85]) ).
fof(f1495,plain,
( sQ17_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1494,f313,f306]) ).
fof(f1634,definition,
( sQ138_spl
<=> aScalar0(xC) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1636,plain,
( sQ138_spl
| ~ aScalar0(xC) ),
inference(component_clause,[status(thm)],[f1634]) ).
fof(f1646,plain,
( sQ138_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1636,f173]) ).
fof(f1647,plain,
sQ138_spl,
inference(contradiction_clause,[status(thm)],[f1646]) ).
fof(f1653,definition,
( sQ141_spl
<=> aScalar0(xD) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1655,plain,
( sQ141_spl
| ~ aScalar0(xD) ),
inference(component_clause,[status(thm)],[f1653]) ).
fof(f1665,plain,
( sQ141_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1655,f175]) ).
fof(f1666,plain,
sQ141_spl,
inference(contradiction_clause,[status(thm)],[f1665]) ).
fof(f1680,plain,
( sQ15_spl
| ~ aScalar0(xD)
| ~ aScalar0(xC) ),
inference(resolution,[status(thm)],[f301,f85]) ).
fof(f1681,plain,
( sQ15_spl
| ~ sQ141_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f1680,f1634,f1653,f299]) ).
fof(f1742,plain,
( ~ sQ14_spl
| sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)) ),
inference(resolution,[status(thm)],[f297,f115]) ).
fof(f1752,definition,
( sQ145_spl
<=> sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1754,plain,
( sQ145_spl
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)) ),
inference(component_clause,[status(thm)],[f1752]) ).
fof(f2235,definition,
( sQ182_spl
<=> sdtlseqdt0(sz0z00,sdtasdt0(xE,xE)) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f2237,plain,
( sQ182_spl
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE)) ),
inference(component_clause,[status(thm)],[f2235]) ).
fof(f2288,plain,
! [X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),xN)
| ~ sdtlseqdt0(X1,sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(X0,sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(X1)
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(X0) ),
inference(paramodulation,[status(thm)],[f195,f123]) ).
fof(f2471,definition,
! [X0,X1] :
( sQ229_spl
<=> ( sdtlseqdt0(sdtasdt0(X0,X1),xN)
| ~ sdtlseqdt0(X1,sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(X0,sdtasdt0(xH,xH))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2472,plain,
! [X0,X1] :
( ~ sQ229_spl
| sdtlseqdt0(sdtasdt0(X0,X1),xN)
| ~ sdtlseqdt0(X1,sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(X0,sdtasdt0(xH,xH))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(component_clause,[status(thm)],[f2471]) ).
fof(f2474,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f2288,f2471,f296,f299]) ).
fof(f2577,plain,
( sQ182_spl
| ~ aScalar0(xE) ),
inference(resolution,[status(thm)],[f2237,f130]) ).
fof(f2579,plain,
( sQ182_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2577,f313,f2235]) ).
fof(f3101,plain,
( sQ145_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1754,f1742]) ).
fof(f3102,plain,
( sQ145_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f3101]) ).
fof(f3138,plain,
( ~ sQ229_spl
| sdtlseqdt0(sdtasdt0(xP,xP),xN)
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(paramodulation,[status(thm)],[f194,f2472]) ).
fof(f3223,definition,
( sQ332_spl
<=> sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f3225,plain,
( sQ332_spl
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(component_clause,[status(thm)],[f3223]) ).
fof(f3226,definition,
( sQ333_spl
<=> sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f3227,plain,
( ~ sQ333_spl
| sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
inference(component_clause,[status(thm)],[f3226]) ).
fof(f3229,plain,
( ~ sQ229_spl
| sQ333_spl
| ~ sQ332_spl
| ~ sQ182_spl
| ~ sQ145_spl
| ~ sQ17_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3138,f296,f306,f1752,f2235,f3223,f3226,f2471]) ).
fof(f3234,plain,
( sQ332_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3225,f193]) ).
fof(f3235,plain,
sQ332_spl,
inference(contradiction_clause,[status(thm)],[f3234]) ).
fof(f3236,plain,
( ~ sQ333_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3227,f196]) ).
fof(f3237,plain,
~ sQ333_spl,
inference(contradiction_clause,[status(thm)],[f3236]) ).
fof(f3238,plain,
$false,
inference(sat_refutation,[status(thm)],[f348,f350,f748,f1495,f1647,f1666,f1681,f2474,f2579,f3102,f3229,f3235,f3237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG057+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:16:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 34.25/4.75 % Refutation found
% 34.25/4.75 % SZS status Theorem for theBenchmark: Theorem is valid
% 34.25/4.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.50/4.91 % Elapsed time: 4.532986 seconds
% 2.50/4.91 % CPU time: 34.821100 seconds
% 2.50/4.91 % Total memory used: 295.638 MB
% 2.50/4.91 % Net memory used: 279.334 MB
%------------------------------------------------------------------------------