%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 11:48:57 AM UTC 2026
% Result : Theorem 1.52s 0.75s
% Output : CNFRefutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of formulae : 90 ( 52 unt; 2 def)
% Number of atoms : 152 ( 89 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 104 ( 42 ~; 37 |; 20 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 73 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : times(times(A,B),C) = times(B,times(C,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( element(B)
<=> ? [C] :
( times(B,B) = C
& times(B,C) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
! [A,B,C] :
( ( C = times(A,B)
& element(B)
& element(A) )
=> element(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ! [A,B,C] :
( ( C = times(A,B)
& element(B)
& element(A) )
=> element(C) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0,X1,X2] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [B] :
( ( ! [C] :
( times(B,B) != C
| times(B,C) != B )
| element(B) )
& ( ? [C] :
( times(B,B) = C
& times(B,C) = B )
| ~ element(B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
( ! [B] :
( ! [C] :
( times(B,B) != C
| times(B,C) != B )
| element(B) )
& ! [B] :
( ? [C] :
( times(B,B) = C
& times(B,C) = B )
| ~ element(B) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
( ! [B] :
( ! [C] :
( times(B,B) != C
| times(B,C) != B )
| element(B) )
& ! [B] :
( ( times(B,B) = sK0_skl(B)
& times(B,sK0_skl(B)) = B )
| ~ element(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B))],[f7]) ).
fof(f9,plain,
! [X0] :
( times(X0,sK0_skl(X0)) = X0
| ~ element(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0] :
( times(X0,X0) = sK0_skl(X0)
| ~ element(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
! [X0,X1] :
( times(X0,X0) != X1
| times(X0,X1) != X0
| element(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f12,plain,
? [A,B,C] :
( ~ element(C)
& C = times(A,B)
& element(B)
& element(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
? [C] :
( ~ element(C)
& ? [A,B] :
( C = times(A,B)
& element(B)
& element(A) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f14,plain,
( ~ element(sK1_skl)
& sK1_skl = times(sK2_skl,sK3_skl)
& element(sK3_skl)
& element(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(C,sK1_skl),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f13]) ).
fof(f15,plain,
element(sK2_skl),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
element(sK3_skl),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
sK1_skl = times(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,plain,
~ element(sK1_skl),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f19,plain,
! [X0] :
( times(X0,times(X0,X0)) != X0
| element(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f11]) ).
fof(f20,plain,
times(sK3_skl,sK0_skl(sK3_skl)) = sK3_skl,
inference(resolution,[status(thm)],[f9,f16]) ).
fof(f21,plain,
times(sK2_skl,sK0_skl(sK2_skl)) = sK2_skl,
inference(resolution,[status(thm)],[f9,f15]) ).
fof(f22,plain,
times(sK3_skl,sK3_skl) = sK0_skl(sK3_skl),
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f23,plain,
times(sK2_skl,sK2_skl) = sK0_skl(sK2_skl),
inference(resolution,[status(thm)],[f10,f15]) ).
fof(f24,plain,
! [X0,X1,X2,X3] : times(times(X0,times(X1,X2)),X3) = times(X1,times(X3,times(X2,X0))),
inference(paramodulation,[status(thm)],[f5,f5]) ).
fof(f25,plain,
! [X0] : times(sK1_skl,X0) = times(sK3_skl,times(X0,sK2_skl)),
inference(paramodulation,[status(thm)],[f17,f5]) ).
fof(f26,plain,
! [X0,X1,X2,X3] : times(times(X0,X1),times(X2,X3)) = times(X0,times(X2,times(X1,X3))),
inference(forward_demodulation,[status(thm)],[f5,f24]) ).
fof(f27,plain,
! [X0,X1,X2,X3] : times(X0,times(times(X1,X2),X3)) = times(X3,times(X1,times(X0,X2))),
inference(forward_demodulation,[status(thm)],[f5,f26]) ).
fof(f28,plain,
! [X0,X1,X2,X3] : times(X0,times(X1,times(X2,X3))) = times(X2,times(X3,times(X0,X1))),
inference(forward_demodulation,[status(thm)],[f5,f27]) ).
fof(f29,plain,
! [X0] : times(sK3_skl,X0) = times(sK0_skl(sK3_skl),times(X0,sK3_skl)),
inference(paramodulation,[status(thm)],[f20,f5]) ).
fof(f30,plain,
! [X0] : times(sK2_skl,X0) = times(sK0_skl(sK2_skl),times(X0,sK2_skl)),
inference(paramodulation,[status(thm)],[f21,f5]) ).
fof(f31,plain,
! [X0] : times(sK0_skl(sK3_skl),X0) = times(sK3_skl,times(X0,sK3_skl)),
inference(paramodulation,[status(thm)],[f22,f5]) ).
fof(f32,plain,
! [X0] : times(sK0_skl(sK2_skl),X0) = times(sK2_skl,times(X0,sK2_skl)),
inference(paramodulation,[status(thm)],[f23,f5]) ).
fof(f35,plain,
! [X0,X1] :
( times(times(X0,X1),times(X1,times(times(X0,X1),X0))) != times(X0,X1)
| element(times(X0,X1)) ),
inference(paramodulation,[status(thm)],[f5,f19]) ).
fof(f49,plain,
! [X0,X1] :
( times(X1,times(times(X1,times(times(X0,X1),X0)),X0)) != times(X0,X1)
| element(times(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f5,f35]) ).
fof(f50,plain,
! [X0,X1] :
( times(X1,times(times(times(X0,X1),X0),times(X0,X1))) != times(X0,X1)
| element(times(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f5,f49]) ).
fof(f51,plain,
! [X0,X1] :
( times(X1,times(X0,times(times(X0,X1),times(X0,X1)))) != times(X0,X1)
| element(times(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f5,f50]) ).
fof(f52,plain,
! [X0,X1] :
( times(X1,times(X0,times(X1,times(times(X0,X1),X0)))) != times(X0,X1)
| element(times(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f5,f51]) ).
fof(f53,plain,
! [X0,X1] :
( times(X1,times(X0,times(X1,times(X1,times(X0,X0))))) != times(X0,X1)
| element(times(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f5,f52]) ).
fof(f62,plain,
times(sK1_skl,sK2_skl) = times(sK3_skl,sK0_skl(sK2_skl)),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f63,plain,
! [X0,X1] : times(times(sK1_skl,X0),X1) = times(times(X0,sK2_skl),times(X1,sK3_skl)),
inference(paramodulation,[status(thm)],[f25,f5]) ).
fof(f64,plain,
! [X0,X1] : times(X0,times(X1,sK1_skl)) = times(times(X0,sK2_skl),times(X1,sK3_skl)),
inference(forward_demodulation,[status(thm)],[f5,f63]) ).
fof(f65,plain,
! [X0,X1] : times(X0,times(X1,sK1_skl)) = times(sK2_skl,times(times(X1,sK3_skl),X0)),
inference(forward_demodulation,[status(thm)],[f5,f64]) ).
fof(f66,plain,
! [X0,X1] : times(X0,times(X1,sK1_skl)) = times(sK2_skl,times(sK3_skl,times(X0,X1))),
inference(forward_demodulation,[status(thm)],[f5,f65]) ).
fof(f191,plain,
times(sK3_skl,sK3_skl) = times(sK0_skl(sK3_skl),sK0_skl(sK3_skl)),
inference(paramodulation,[status(thm)],[f22,f29]) ).
fof(f193,plain,
times(sK3_skl,sK2_skl) = times(sK0_skl(sK3_skl),sK1_skl),
inference(paramodulation,[status(thm)],[f17,f29]) ).
fof(f199,plain,
sK0_skl(sK3_skl) = times(sK0_skl(sK3_skl),sK0_skl(sK3_skl)),
inference(forward_demodulation,[status(thm)],[f22,f191]) ).
fof(f472,definition,
( sQ15_spl
<=> element(times(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( ~ sQ15_spl
| element(times(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f545,plain,
( ~ sQ15_spl
| element(sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f17,f473]) ).
fof(f546,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f545,f18]) ).
fof(f547,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f562,plain,
times(sK0_skl(sK2_skl),sK2_skl) = times(sK2_skl,sK0_skl(sK2_skl)),
inference(paramodulation,[status(thm)],[f23,f32]) ).
fof(f571,plain,
times(sK0_skl(sK2_skl),sK2_skl) = sK2_skl,
inference(forward_demodulation,[status(thm)],[f21,f562]) ).
fof(f595,plain,
times(sK1_skl,sK0_skl(sK2_skl)) = times(sK3_skl,sK2_skl),
inference(paramodulation,[status(thm)],[f571,f25]) ).
fof(f598,plain,
! [X0] : times(sK2_skl,X0) = times(sK2_skl,times(X0,sK0_skl(sK2_skl))),
inference(paramodulation,[status(thm)],[f571,f5]) ).
fof(f747,plain,
times(sK2_skl,sK3_skl) = times(sK2_skl,times(sK1_skl,sK2_skl)),
inference(paramodulation,[status(thm)],[f62,f598]) ).
fof(f753,plain,
! [X0,X1] : times(X0,times(sK0_skl(sK2_skl),times(X1,sK2_skl))) = times(X1,times(sK2_skl,X0)),
inference(paramodulation,[status(thm)],[f598,f28]) ).
fof(f759,plain,
sK1_skl = times(sK2_skl,times(sK1_skl,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f17,f747]) ).
fof(f760,plain,
sK1_skl = times(sK0_skl(sK2_skl),sK1_skl),
inference(forward_demodulation,[status(thm)],[f32,f759]) ).
fof(f771,plain,
! [X0,X1] : times(X0,times(sK2_skl,X1)) = times(X1,times(sK2_skl,X0)),
inference(forward_demodulation,[status(thm)],[f30,f753]) ).
fof(f800,plain,
times(sK0_skl(sK3_skl),times(sK0_skl(sK3_skl),sK1_skl)) = times(sK2_skl,times(sK3_skl,sK0_skl(sK3_skl))),
inference(paramodulation,[status(thm)],[f199,f66]) ).
fof(f813,plain,
times(sK2_skl,times(sK2_skl,sK1_skl)) = times(sK2_skl,times(sK3_skl,sK0_skl(sK2_skl))),
inference(paramodulation,[status(thm)],[f23,f66]) ).
fof(f844,plain,
times(sK0_skl(sK3_skl),times(sK3_skl,sK2_skl)) = times(sK2_skl,times(sK3_skl,sK0_skl(sK3_skl))),
inference(forward_demodulation,[status(thm)],[f193,f800]) ).
fof(f845,plain,
times(sK0_skl(sK3_skl),times(sK3_skl,sK2_skl)) = times(sK2_skl,sK3_skl),
inference(forward_demodulation,[status(thm)],[f20,f844]) ).
fof(f846,plain,
times(sK0_skl(sK3_skl),times(sK3_skl,sK2_skl)) = sK1_skl,
inference(forward_demodulation,[status(thm)],[f17,f845]) ).
fof(f880,plain,
times(sK2_skl,times(sK2_skl,sK1_skl)) = times(sK2_skl,sK3_skl),
inference(forward_demodulation,[status(thm)],[f598,f813]) ).
fof(f881,plain,
times(sK2_skl,times(sK2_skl,sK1_skl)) = sK1_skl,
inference(forward_demodulation,[status(thm)],[f17,f880]) ).
fof(f2143,plain,
sK1_skl = times(sK1_skl,times(sK2_skl,sK2_skl)),
inference(paramodulation,[status(thm)],[f881,f771]) ).
fof(f2158,plain,
! [X0] : times(X0,sK1_skl) = times(sK3_skl,times(sK2_skl,X0)),
inference(paramodulation,[status(thm)],[f17,f771]) ).
fof(f2267,plain,
sK1_skl = times(sK1_skl,sK0_skl(sK2_skl)),
inference(forward_demodulation,[status(thm)],[f23,f2143]) ).
fof(f2268,plain,
sK1_skl = times(sK3_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f595,f2267]) ).
fof(f3635,plain,
times(sK0_skl(sK3_skl),sK1_skl) = sK1_skl,
inference(backward_demodulation,[status(thm)],[f2268,f846]) ).
fof(f3643,plain,
times(sK1_skl,sK3_skl) = times(sK3_skl,sK1_skl),
inference(paramodulation,[status(thm)],[f2268,f25]) ).
fof(f5068,plain,
( times(times(sK3_skl,times(sK3_skl,times(sK2_skl,sK2_skl))),sK1_skl) != times(sK2_skl,sK3_skl)
| element(times(sK2_skl,sK3_skl)) ),
inference(paramodulation,[status(thm)],[f2158,f53]) ).
fof(f5198,definition,
( sQ38_spl
<=> times(times(sK3_skl,times(sK3_skl,times(sK2_skl,sK2_skl))),sK1_skl) = times(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f5200,plain,
( sQ38_spl
| times(times(sK3_skl,times(sK3_skl,times(sK2_skl,sK2_skl))),sK1_skl) != times(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f5198]) ).
fof(f5201,plain,
( ~ sQ38_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f5068,f472,f5198]) ).
fof(f5283,plain,
( sQ38_spl
| times(times(sK3_skl,times(sK2_skl,sK2_skl)),times(sK1_skl,sK3_skl)) != times(sK2_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f5,f5200]) ).
fof(f5284,plain,
( sQ38_spl
| times(times(sK2_skl,sK2_skl),times(times(sK1_skl,sK3_skl),sK3_skl)) != times(sK2_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f5,f5283]) ).
fof(f5285,plain,
( sQ38_spl
| times(sK2_skl,times(times(times(sK1_skl,sK3_skl),sK3_skl),sK2_skl)) != times(sK2_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f5,f5284]) ).
fof(f5286,plain,
( sQ38_spl
| times(sK0_skl(sK2_skl),times(times(sK1_skl,sK3_skl),sK3_skl)) != times(sK2_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f32,f5285]) ).
fof(f5287,plain,
( sQ38_spl
| times(sK0_skl(sK2_skl),times(sK3_skl,times(sK3_skl,sK1_skl))) != times(sK2_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f5,f5286]) ).
fof(f5288,plain,
( sQ38_spl
| times(sK0_skl(sK2_skl),times(sK3_skl,times(sK1_skl,sK3_skl))) != times(sK2_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f3643,f5287]) ).
fof(f5289,plain,
( sQ38_spl
| times(sK0_skl(sK2_skl),times(sK0_skl(sK3_skl),sK1_skl)) != times(sK2_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f31,f5288]) ).
fof(f5290,plain,
( sQ38_spl
| times(sK0_skl(sK2_skl),sK1_skl) != times(sK2_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f3635,f5289]) ).
fof(f5291,plain,
( sQ38_spl
| sK1_skl != times(sK2_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f760,f5290]) ).
fof(f5292,plain,
( sQ38_spl
| sK1_skl != sK1_skl ),
inference(forward_demodulation,[status(thm)],[f17,f5291]) ).
fof(f5293,plain,
( sQ38_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5292]) ).
fof(f5294,plain,
sQ38_spl,
inference(contradiction_clause,[status(thm)],[f5293]) ).
fof(f5295,plain,
$false,
inference(sat_refutation,[status(thm)],[f547,f5201,f5294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 13:01:37 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 1.52/0.75 % Refutation found
% 1.52/0.75 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.52/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.78 % Elapsed time: 0.460014 seconds
% 0.24/0.78 % CPU time: 3.446381 seconds
% 0.24/0.78 % Total memory used: 99.959 MB
% 0.24/0.78 % Net memory used: 98.880 MB
%------------------------------------------------------------------------------