%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG055+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 : n016.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 45.55s 6.48s
% Output : CNFRefutation 45.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 12 unt; 2 def)
% Number of atoms : 101 ( 34 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 103 ( 46 ~; 41 |; 12 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f57,conjecture,
sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
inference(negated_conjecture,[status(cth)],[f57]) ).
fof(f82,plain,
! [W0,W1] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f83,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f95,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] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f99,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f175,plain,
aScalar0(xE),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f181,plain,
aScalar0(xH),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f185,plain,
aScalar0(xP),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f186,plain,
sdtasdt0(xE,xH) = xP,
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f192,plain,
sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != sdtasdt0(xP,xP),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f193,definition,
! [X0] :
( sQ0_spl
<=> ~ aScalar0(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f194,plain,
! [X0] :
( ~ sQ0_spl
| ~ aScalar0(X0) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f204,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(f205,plain,
! [X0,X1] :
( ~ sQ3_spl
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( sQ0_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f99,f204,f193]) ).
fof(f896,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f185,f194]) ).
fof(f901,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f896]) ).
fof(f902,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(xE,xE)) = sdtasdt0(sdtasdt0(X0,xE),xE)
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[f175,f98]) ).
fof(f903,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtasdt0(X1,xE)) = sdtasdt0(sdtasdt0(X0,X1),xE)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[f175,f98]) ).
fof(f915,plain,
! [X0] :
( ~ sQ3_spl
| sdtasdt0(X0,xP) = sdtasdt0(xP,X0)
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[f205,f185]) ).
fof(f917,plain,
! [X0] :
( ~ sQ3_spl
| ~ aScalar0(X0)
| sdtasdt0(xE,X0) = sdtasdt0(X0,xE) ),
inference(resolution,[status(thm)],[f205,f175]) ).
fof(f919,plain,
! [X0] :
( ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,xH)) ),
inference(resolution,[status(thm)],[f83,f181]) ).
fof(f976,plain,
( ~ sQ3_spl
| sdtasdt0(xH,xP) = sdtasdt0(xP,xH) ),
inference(resolution,[status(thm)],[f915,f181]) ).
fof(f1032,plain,
( ~ sQ3_spl
| sdtasdt0(xE,xH) = sdtasdt0(xH,xE) ),
inference(resolution,[status(thm)],[f917,f181]) ).
fof(f1034,plain,
( ~ sQ3_spl
| xP = sdtasdt0(xH,xE) ),
inference(forward_demodulation,[status(thm)],[f186,f1032]) ).
fof(f2944,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(xH,xE)) = sdtasdt0(sdtasdt0(X0,xH),xE)
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[f903,f181]) ).
fof(f2948,plain,
! [X0] :
( ~ sQ3_spl
| ~ aScalar0(X0)
| sdtasdt0(sdtasdt0(X0,xH),xE) = sdtasdt0(X0,xP) ),
inference(forward_demodulation,[status(thm)],[f1034,f2944]) ).
fof(f2961,plain,
( ~ sQ3_spl
| sdtasdt0(sdtasdt0(xP,xH),xE) = sdtasdt0(xP,xP) ),
inference(resolution,[status(thm)],[f2948,f185]) ).
fof(f2962,plain,
( ~ sQ3_spl
| sdtasdt0(xH,xP) = sdtasdt0(sdtasdt0(xH,xH),xE) ),
inference(resolution,[status(thm)],[f2948,f181]) ).
fof(f2969,plain,
( ~ sQ3_spl
| sdtasdt0(sdtasdt0(xH,xP),xE) = sdtasdt0(xP,xP) ),
inference(forward_demodulation,[status(thm)],[f976,f2961]) ).
fof(f3134,plain,
aScalar0(sdtasdt0(xH,xH)),
inference(resolution,[status(thm)],[f919,f181]) ).
fof(f5300,plain,
sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = sdtasdt0(sdtasdt0(sdtasdt0(xH,xH),xE),xE),
inference(resolution,[status(thm)],[f3134,f902]) ).
fof(f5424,plain,
( ~ sQ3_spl
| sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = sdtasdt0(sdtasdt0(xH,xP),xE) ),
inference(forward_demodulation,[status(thm)],[f2962,f5300]) ).
fof(f5425,plain,
( ~ sQ3_spl
| sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = sdtasdt0(xP,xP) ),
inference(forward_demodulation,[status(thm)],[f2969,f5424]) ).
fof(f5426,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5425,f192]) ).
fof(f5427,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f5426]) ).
fof(f5428,plain,
$false,
inference(sat_refutation,[status(thm)],[f207,f901,f5427]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG055+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.33 % Computer : n016.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8046.5625MB
% 0.09/0.33 % OS : Linux 6.8.0-71-generic
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Mon Sep 21 04:20:39 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 45.55/6.48 % Refutation found
% 45.55/6.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 45.55/6.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 34.25/6.55 % Elapsed time: 6.194245 seconds
% 34.25/6.55 % CPU time: 48.785463 seconds
% 34.25/6.55 % Total memory used: 368.659 MB
% 34.25/6.55 % Net memory used: 350.122 MB
%------------------------------------------------------------------------------