%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG057+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 61.79s 8.38s
% Output : CNFRefutation 61.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 24
% Syntax : Number of formulae : 82 ( 20 unt; 12 def)
% Number of atoms : 194 ( 8 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 194 ( 82 ~; 85 |; 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(f179,plain,
aScalar0(xC),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f181,plain,
aScalar0(xD),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f183,plain,
aScalar0(xE),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f189,plain,
aScalar0(xH),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f199,plain,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f200,plain,
sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f201,plain,
xN = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f202,plain,
~ sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f303,definition,
( sQ14_spl
<=> aScalar0(sdtasdt0(xH,xH)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( ~ sQ14_spl
| aScalar0(sdtasdt0(xH,xH)) ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f305,plain,
( sQ14_spl
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f306,definition,
( sQ15_spl
<=> aScalar0(sdtasdt0(xC,xD)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( sQ15_spl
| ~ aScalar0(sdtasdt0(xC,xD)) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f313,definition,
( sQ17_spl
<=> aScalar0(sdtasdt0(xE,xE)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( sQ17_spl
| ~ aScalar0(sdtasdt0(xE,xE)) ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f320,definition,
( sQ19_spl
<=> aScalar0(xE) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( sQ19_spl
| ~ aScalar0(xE) ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,definition,
( sQ20_spl
<=> aScalar0(xH) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( sQ20_spl
| ~ aScalar0(xH) ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f354,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f325,f189]) ).
fof(f355,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f354]) ).
fof(f356,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f183]) ).
fof(f357,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f754,plain,
( sQ14_spl
| ~ aScalar0(xH)
| ~ aScalar0(xH) ),
inference(resolution,[status(thm)],[f305,f85]) ).
fof(f755,plain,
( sQ14_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f754,f323,f303]) ).
fof(f1499,plain,
( sQ17_spl
| ~ aScalar0(xE)
| ~ aScalar0(xE) ),
inference(resolution,[status(thm)],[f315,f85]) ).
fof(f1500,plain,
( sQ17_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1499,f320,f313]) ).
fof(f1649,definition,
( sQ138_spl
<=> aScalar0(xC) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1651,plain,
( sQ138_spl
| ~ aScalar0(xC) ),
inference(component_clause,[status(thm)],[f1649]) ).
fof(f1661,plain,
( sQ138_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1651,f179]) ).
fof(f1662,plain,
sQ138_spl,
inference(contradiction_clause,[status(thm)],[f1661]) ).
fof(f1668,definition,
( sQ141_spl
<=> aScalar0(xD) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1670,plain,
( sQ141_spl
| ~ aScalar0(xD) ),
inference(component_clause,[status(thm)],[f1668]) ).
fof(f1680,plain,
( sQ141_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1670,f181]) ).
fof(f1681,plain,
sQ141_spl,
inference(contradiction_clause,[status(thm)],[f1680]) ).
fof(f1695,plain,
( sQ15_spl
| ~ aScalar0(xD)
| ~ aScalar0(xC) ),
inference(resolution,[status(thm)],[f308,f85]) ).
fof(f1696,plain,
( sQ15_spl
| ~ sQ141_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f1695,f1649,f1668,f306]) ).
fof(f1757,plain,
( ~ sQ14_spl
| sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)) ),
inference(resolution,[status(thm)],[f304,f115]) ).
fof(f1767,definition,
( sQ145_spl
<=> sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1769,plain,
( sQ145_spl
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)) ),
inference(component_clause,[status(thm)],[f1767]) ).
fof(f2250,definition,
( sQ182_spl
<=> sdtlseqdt0(sz0z00,sdtasdt0(xE,xE)) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f2252,plain,
( sQ182_spl
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE)) ),
inference(component_clause,[status(thm)],[f2250]) ).
fof(f2342,plain,
( sQ182_spl
| ~ aScalar0(xE) ),
inference(resolution,[status(thm)],[f2252,f130]) ).
fof(f2344,plain,
( sQ182_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2342,f320,f2250]) ).
fof(f2385,plain,
! [X0,X1] :
( sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),X1)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),X0)
| ~ aScalar0(X1)
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(X0)
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(paramodulation,[status(thm)],[f200,f123]) ).
fof(f2499,definition,
! [X0,X1] :
( sQ207_spl
<=> ( sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),X1)
| ~ sdtlseqdt0(sdtasdt0(xH,xH),X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2500,plain,
! [X0,X1] :
( ~ sQ207_spl
| sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),X1)
| ~ sdtlseqdt0(sdtasdt0(xH,xH),X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(component_clause,[status(thm)],[f2499]) ).
fof(f2502,plain,
( ~ sQ182_spl
| ~ sQ17_spl
| sQ207_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2385,f303,f2499,f313,f2250]) ).
fof(f3094,plain,
( sQ145_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1769,f1757]) ).
fof(f3095,plain,
( sQ145_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f3094]) ).
fof(f3121,plain,
( ~ sQ207_spl
| sdtlseqdt0(sdtasdt0(xP,xP),xN)
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(paramodulation,[status(thm)],[f201,f2500]) ).
fof(f3195,definition,
( sQ340_spl
<=> sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f3196,plain,
( ~ sQ340_spl
| sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
inference(component_clause,[status(thm)],[f3195]) ).
fof(f3252,definition,
( sQ355_spl
<=> sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f3254,plain,
( sQ355_spl
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(component_clause,[status(thm)],[f3252]) ).
fof(f3255,plain,
( ~ sQ207_spl
| sQ340_spl
| ~ sQ355_spl
| ~ sQ145_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3121,f303,f306,f1767,f3252,f3195,f2499]) ).
fof(f3258,plain,
( ~ sQ340_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3196,f202]) ).
fof(f3259,plain,
~ sQ340_spl,
inference(contradiction_clause,[status(thm)],[f3258]) ).
fof(f3260,plain,
( sQ355_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3254,f199]) ).
fof(f3261,plain,
sQ355_spl,
inference(contradiction_clause,[status(thm)],[f3260]) ).
fof(f3262,plain,
$false,
inference(sat_refutation,[status(thm)],[f355,f357,f755,f1500,f1662,f1681,f1696,f2344,f2502,f3095,f3255,f3259,f3261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG057+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n006.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 04:16:12 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 61.79/8.38 % Refutation found
% 61.79/8.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 61.79/8.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.56/8.49 % Elapsed time: 8.019894 seconds
% 9.56/8.49 % CPU time: 62.445297 seconds
% 9.56/8.49 % Total memory used: 314.607 MB
% 9.56/8.49 % Net memory used: 299.212 MB
%------------------------------------------------------------------------------