%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM007+2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:10:16 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 65 ( 8 unt; 7 def)
% Number of atoms : 162 ( 12 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 184 ( 87 ~; 78 |; 7 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 56 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( reflexive_rewrite(a,c)
& reflexive_rewrite(a,b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] :
( ( reflexive_rewrite(c,A)
& reflexive_rewrite(b,A) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( A = B
=> reflexive_rewrite(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( rewrite(A,B)
=> reflexive_rewrite(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( reflexive_rewrite(A,B)
=> ( rewrite(A,B)
| A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( ( rewrite(A,C)
& rewrite(A,B) )
=> ? [D] :
( rewrite(C,D)
& rewrite(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ goal,
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
reflexive_rewrite(a,b),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
reflexive_rewrite(a,c),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [A] :
( goal
| ~ reflexive_rewrite(c,A)
| ~ reflexive_rewrite(b,A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
( goal
| ! [A] :
( ~ reflexive_rewrite(c,A)
| ~ reflexive_rewrite(b,A) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0] :
( goal
| ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [A,B] :
( reflexive_rewrite(A,B)
| A != B ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( reflexive_rewrite(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [A,B] :
( reflexive_rewrite(A,B)
| ~ rewrite(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( reflexive_rewrite(X0,X1)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [A,B] :
( rewrite(A,B)
| A = B
| ~ reflexive_rewrite(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
! [X0,X1] :
( rewrite(X0,X1)
| X0 = X1
| ~ reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [A,B,C] :
( ? [D] :
( rewrite(C,D)
& rewrite(B,D) )
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [B,C] :
( ? [D] :
( rewrite(C,D)
& rewrite(B,D) )
| ! [A] :
( ~ rewrite(A,C)
| ~ rewrite(A,B) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [B,C] :
( ( rewrite(C,sK0_skl(C,B))
& rewrite(B,sK0_skl(C,B)) )
| ! [A] :
( ~ rewrite(A,C)
| ~ rewrite(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( rewrite(X1,sK0_skl(X2,X1))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( rewrite(X2,sK0_skl(X2,X1))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
~ goal,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,definition,
! [X0] :
( sQ0_spl
<=> ( ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f27,plain,
! [X0] :
( ~ sQ0_spl
| ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0) ),
inference(component_clause,[status(thm)],[f26]) ).
fof(f29,definition,
( sQ1_spl
<=> goal ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f30,plain,
( ~ sQ1_spl
| goal ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f13,f26,f29]) ).
fof(f33,plain,
! [X0] : reflexive_rewrite(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f15]) ).
fof(f34,plain,
( ~ sQ0_spl
| ~ reflexive_rewrite(b,c) ),
inference(resolution,[status(thm)],[f33,f27]) ).
fof(f35,plain,
( rewrite(a,c)
| a = c ),
inference(resolution,[status(thm)],[f19,f10]) ).
fof(f36,plain,
( rewrite(a,b)
| a = b ),
inference(resolution,[status(thm)],[f19,f9]) ).
fof(f38,definition,
( sQ2_spl
<=> a = c ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( ~ sQ2_spl
| a = c ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,definition,
( sQ3_spl
<=> rewrite(a,c) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f42,plain,
( ~ sQ3_spl
| rewrite(a,c) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f35,f38,f41]) ).
fof(f45,definition,
( sQ4_spl
<=> a = b ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( ~ sQ4_spl
| a = b ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,definition,
( sQ5_spl
<=> rewrite(a,b) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( ~ sQ5_spl
| rewrite(a,b) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f36,f45,f48]) ).
fof(f53,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ reflexive_rewrite(a,c) ),
inference(backward_demodulation,[status(thm)],[f46,f34]) ).
fof(f55,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f10]) ).
fof(f56,plain,
( ~ sQ0_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f55]) ).
fof(f57,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f25]) ).
fof(f58,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f57]) ).
fof(f60,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ2_spl
| ~ reflexive_rewrite(a,X0)
| ~ reflexive_rewrite(b,X0) ),
inference(backward_demodulation,[status(thm)],[f39,f27]) ).
fof(f63,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ reflexive_rewrite(a,b) ),
inference(resolution,[status(thm)],[f60,f33]) ).
fof(f64,plain,
( ~ sQ5_spl
| reflexive_rewrite(a,b) ),
inference(resolution,[status(thm)],[f49,f17]) ).
fof(f65,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f64,f63]) ).
fof(f66,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f65]) ).
fof(f68,plain,
! [X0,X1,X2] :
( reflexive_rewrite(X1,sK0_skl(X2,X1))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(resolution,[status(thm)],[f23,f17]) ).
fof(f69,plain,
! [X0,X1,X2] :
( reflexive_rewrite(X2,sK0_skl(X2,X1))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(resolution,[status(thm)],[f24,f17]) ).
fof(f75,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ reflexive_rewrite(b,sK0_skl(X1,c))
| ~ rewrite(X0,X1)
| ~ rewrite(X0,c) ),
inference(resolution,[status(thm)],[f68,f27]) ).
fof(f79,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ rewrite(X1,b)
| ~ rewrite(X1,c)
| ~ rewrite(X0,b)
| ~ rewrite(X0,c) ),
inference(resolution,[status(thm)],[f75,f69]) ).
fof(f80,definition,
! [X0] :
( sQ6_spl
<=> ( ~ rewrite(X0,b)
| ~ rewrite(X0,c) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f81,plain,
! [X0] :
( ~ sQ6_spl
| ~ rewrite(X0,b)
| ~ rewrite(X0,c) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,plain,
( ~ sQ0_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f79,f80,f26]) ).
fof(f84,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ rewrite(a,b) ),
inference(resolution,[status(thm)],[f81,f42]) ).
fof(f85,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f49]) ).
fof(f86,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f85]) ).
fof(f87,plain,
$false,
inference(sat_refutation,[status(thm)],[f32,f44,f51,f56,f58,f66,f83,f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM007+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 14:13:49 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.049945 seconds
% 0.13/0.41 % CPU time: 0.097205 seconds
% 0.13/0.41 % Total memory used: 32.615 MB
% 0.13/0.41 % Net memory used: 32.438 MB
%------------------------------------------------------------------------------