%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG077+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 : n002.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 02:04:53 PM UTC 2026
% Result : Theorem 0.13s 0.58s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 29
% Syntax : Number of formulae : 99 ( 20 unt; 16 def)
% Number of atoms : 233 ( 39 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 227 ( 93 ~; 92 |; 22 &)
% ( 16 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 17 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
& sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
& sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
& sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
( aVector0(xt)
& aVector0(xs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
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(f53,hypothesis,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,conjecture,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f82,plain,
! [W0,W1] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f83,plain,
! [X0,X1] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
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(f97,plain,
! [W0,W1,W2] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
& sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
& sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
& sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f98,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f101,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f102,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(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f103,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f159,plain,
aVector0(xs),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f175,plain,
aScalar0(xA),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f177,plain,
aScalar0(xB),
inference(cnf_transformation,[status(thm)],[f45]) ).
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(f194,plain,
xP = sdtasdt0(xE,xH),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f202,plain,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f203,definition,
! [X0] :
( sQ0_spl
<=> ~ aScalar0(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f204,plain,
! [X0] :
( ~ sQ0_spl
| ~ aScalar0(X0) ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f214,definition,
! [X0,X1] :
( sQ3_spl
<=> ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f215,plain,
! [X0,X1] :
( ~ sQ3_spl
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,plain,
( sQ0_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f101,f214,f203]) ).
fof(f221,plain,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(xP,sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(backward_demodulation,[status(thm)],[f194,f202]) ).
fof(f222,plain,
( aScalar0(xP)
| ~ aScalar0(xH)
| ~ aScalar0(xE) ),
inference(paramodulation,[status(thm)],[f194,f85]) ).
fof(f223,definition,
( sQ4_spl
<=> aScalar0(xE) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ4_spl
| ~ aScalar0(xE) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
( sQ5_spl
<=> aScalar0(xH) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( sQ5_spl
| ~ aScalar0(xH) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,definition,
( sQ6_spl
<=> aScalar0(xP) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f232,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f222,f223,f226,f229]) ).
fof(f238,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f189]) ).
fof(f239,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f240,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f183]) ).
fof(f241,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f240]) ).
fof(f242,plain,
! [X0] :
( sdtasdt0(xE,sdtpldt0(xH,X0)) = sdtpldt0(xP,sdtasdt0(xE,X0))
| ~ aScalar0(X0)
| ~ aScalar0(xH)
| ~ aScalar0(xE) ),
inference(paramodulation,[status(thm)],[f194,f103]) ).
fof(f244,definition,
! [X0] :
( sQ8_spl
<=> ( sdtasdt0(xE,sdtpldt0(xH,X0)) = sdtpldt0(xP,sdtasdt0(xE,X0))
| ~ aScalar0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f245,plain,
! [X0] :
( ~ sQ8_spl
| sdtasdt0(xE,sdtpldt0(xH,X0)) = sdtpldt0(xP,sdtasdt0(xE,X0))
| ~ aScalar0(X0) ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f242,f223,f226,f244]) ).
fof(f252,plain,
( ~ sQ8_spl
| sdtasdt0(xE,sdtpldt0(xH,xH)) = sdtpldt0(xP,xP)
| ~ aScalar0(xH) ),
inference(paramodulation,[status(thm)],[f194,f245]) ).
fof(f253,definition,
( sQ10_spl
<=> sdtasdt0(xE,sdtpldt0(xH,xH)) = sdtpldt0(xP,xP) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( ~ sQ10_spl
| sdtasdt0(xE,sdtpldt0(xH,xH)) = sdtpldt0(xP,xP) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ sQ8_spl
| sQ10_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f252,f226,f253,f244]) ).
fof(f261,plain,
( ~ sQ10_spl
| aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xH,xH))
| ~ aScalar0(xE) ),
inference(paramodulation,[status(thm)],[f254,f85]) ).
fof(f262,definition,
( sQ11_spl
<=> aScalar0(sdtpldt0(xH,xH)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( sQ11_spl
| ~ aScalar0(sdtpldt0(xH,xH)) ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f281,definition,
( sQ16_spl
<=> aScalar0(sdtpldt0(xP,xP)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( ~ sQ16_spl
| aScalar0(sdtpldt0(xP,xP)) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,plain,
( ~ sQ10_spl
| sQ16_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f261,f223,f262,f281,f253]) ).
fof(f285,plain,
( sQ11_spl
| ~ aScalar0(xH)
| ~ aScalar0(xH) ),
inference(resolution,[status(thm)],[f264,f83]) ).
fof(f286,plain,
( sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f285,f226,f262]) ).
fof(f347,plain,
( ~ sQ16_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f282,f204]) ).
fof(f351,plain,
( ~ sQ16_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f347]) ).
fof(f356,plain,
( ~ sQ3_spl
| xP = sdtasdt0(xH,xE)
| ~ aScalar0(xH)
| ~ aScalar0(xE) ),
inference(paramodulation,[status(thm)],[f194,f215]) ).
fof(f358,definition,
( sQ29_spl
<=> xP = sdtasdt0(xH,xE) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f359,plain,
( ~ sQ29_spl
| xP = sdtasdt0(xH,xE) ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,plain,
( ~ sQ3_spl
| sQ29_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f356,f223,f226,f358,f214]) ).
fof(f363,plain,
( ~ sQ29_spl
| sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH))) ),
inference(backward_demodulation,[status(thm)],[f359,f221]) ).
fof(f498,definition,
( sQ50_spl
<=> aVector0(xs) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( sQ50_spl
| ~ aVector0(xs) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f505,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f159]) ).
fof(f506,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f517,definition,
( sQ53_spl
<=> aScalar0(xA) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ53_spl
| ~ aScalar0(xA) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f545,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f175]) ).
fof(f546,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f545]) ).
fof(f892,plain,
( ~ sQ29_spl
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(xP)
| ~ aScalar0(xP) ),
inference(resolution,[status(thm)],[f98,f363]) ).
fof(f895,definition,
( sQ123_spl
<=> aScalar0(sdtasdt0(xH,xH)) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f897,plain,
( sQ123_spl
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(component_clause,[status(thm)],[f895]) ).
fof(f898,plain,
( ~ sQ29_spl
| ~ sQ123_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f892,f229,f895,f358]) ).
fof(f919,definition,
( sQ126_spl
<=> aScalar0(xB) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f921,plain,
( sQ126_spl
| ~ aScalar0(xB) ),
inference(component_clause,[status(thm)],[f919]) ).
fof(f962,plain,
( sQ126_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f921,f177]) ).
fof(f963,plain,
sQ126_spl,
inference(contradiction_clause,[status(thm)],[f962]) ).
fof(f1030,definition,
( sQ147_spl
<=> aScalar0(xC) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1032,plain,
( sQ147_spl
| ~ aScalar0(xC) ),
inference(component_clause,[status(thm)],[f1030]) ).
fof(f1078,plain,
( sQ147_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1032,f179]) ).
fof(f1079,plain,
sQ147_spl,
inference(contradiction_clause,[status(thm)],[f1078]) ).
fof(f1090,definition,
( sQ159_spl
<=> aScalar0(xD) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1092,plain,
( sQ159_spl
| ~ aScalar0(xD) ),
inference(component_clause,[status(thm)],[f1090]) ).
fof(f1133,plain,
( sQ159_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1092,f181]) ).
fof(f1134,plain,
sQ159_spl,
inference(contradiction_clause,[status(thm)],[f1133]) ).
fof(f1192,plain,
( sQ123_spl
| ~ aScalar0(xH)
| ~ aScalar0(xH) ),
inference(resolution,[status(thm)],[f897,f85]) ).
fof(f1193,plain,
( sQ123_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1192,f226,f895]) ).
fof(f1194,plain,
$false,
inference(sat_refutation,[status(thm)],[f217,f232,f239,f241,f247,f256,f284,f286,f351,f361,f506,f546,f898,f963,f1079,f1134,f1193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG077+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.53 % Computer : n002.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Mon Sep 21 04:20:48 UTC 2026
% 0.09/0.53 % CPUTime :
% 0.09/0.54 % Drodi V4.1.1
% 0.13/0.58 % Refutation found
% 0.13/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.60 % Elapsed time: 0.070878 seconds
% 0.13/0.60 % CPU time: 0.240791 seconds
% 0.13/0.60 % Total memory used: 108.053 MB
% 0.13/0.60 % Net memory used: 107.790 MB
%------------------------------------------------------------------------------