%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM007+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:10:15 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 72 ( 11 unt; 6 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 208 ( 97 ~; 90 |; 8 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 83 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( reflexive_rewrite(a,c)
& reflexive_rewrite(a,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] :
( ( reflexive_rewrite(c,A)
& reflexive_rewrite(b,A) )
=> goal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : equalish(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( equalish(A,B)
=> equalish(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( ( reflexive_rewrite(B,C)
& equalish(A,B) )
=> reflexive_rewrite(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( equalish(A,B)
=> reflexive_rewrite(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( rewrite(A,B)
=> reflexive_rewrite(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( reflexive_rewrite(A,B)
=> ( rewrite(A,B)
| equalish(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( ( rewrite(A,C)
& rewrite(A,B) )
=> ? [D] :
( rewrite(C,D)
& rewrite(B,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
goal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ goal,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
reflexive_rewrite(a,b),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
reflexive_rewrite(a,c),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [A] :
( goal
| ~ reflexive_rewrite(c,A)
| ~ reflexive_rewrite(b,A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
( goal
| ! [A] :
( ~ reflexive_rewrite(c,A)
| ~ reflexive_rewrite(b,A) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0] :
( goal
| ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0] : equalish(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [A,B] :
( equalish(B,A)
| ~ equalish(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [A,B,C] :
( reflexive_rewrite(A,C)
| ~ reflexive_rewrite(B,C)
| ~ equalish(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [A,C] :
( reflexive_rewrite(A,C)
| ! [B] :
( ~ reflexive_rewrite(B,C)
| ~ equalish(A,B) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( reflexive_rewrite(X0,X2)
| ~ reflexive_rewrite(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [A,B] :
( reflexive_rewrite(A,B)
| ~ equalish(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
! [X0,X1] :
( reflexive_rewrite(X0,X1)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [A,B] :
( reflexive_rewrite(A,B)
| ~ rewrite(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0,X1] :
( reflexive_rewrite(X0,X1)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [A,B] :
( rewrite(A,B)
| equalish(A,B)
| ~ reflexive_rewrite(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
! [X0,X1] :
( rewrite(X0,X1)
| equalish(X0,X1)
| ~ reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [A,B,C] :
( ? [D] :
( rewrite(C,D)
& rewrite(B,D) )
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f30,plain,
! [B,C] :
( ? [D] :
( rewrite(C,D)
& rewrite(B,D) )
| ! [A] :
( ~ rewrite(A,C)
| ~ rewrite(A,B) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,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))],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( rewrite(X1,sK0_skl(X2,X1))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( rewrite(X2,sK0_skl(X2,X1))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
~ goal,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f35,definition,
! [X0] :
( sQ0_spl
<=> ( ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f36,plain,
! [X0] :
( ~ sQ0_spl
| ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,definition,
( sQ1_spl
<=> goal ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( ~ sQ1_spl
| goal ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f35,f38]) ).
fof(f43,plain,
! [X0] : reflexive_rewrite(X0,X0),
inference(resolution,[status(thm)],[f24,f17]) ).
fof(f44,plain,
( ~ sQ0_spl
| ~ reflexive_rewrite(b,c) ),
inference(resolution,[status(thm)],[f43,f36]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ equalish(X0,X2)
| reflexive_rewrite(X2,X1)
| ~ reflexive_rewrite(X0,X1) ),
inference(resolution,[status(thm)],[f22,f19]) ).
fof(f52,plain,
! [X0,X1,X2] :
( reflexive_rewrite(X1,sK0_skl(X2,X1))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(resolution,[status(thm)],[f32,f26]) ).
fof(f53,plain,
! [X0,X1,X2] :
( reflexive_rewrite(X2,sK0_skl(X2,X1))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(resolution,[status(thm)],[f33,f26]) ).
fof(f54,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ reflexive_rewrite(b,sK0_skl(X1,c))
| ~ rewrite(X0,X1)
| ~ rewrite(X0,c) ),
inference(resolution,[status(thm)],[f52,f36]) ).
fof(f56,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ rewrite(X1,b)
| ~ rewrite(X1,c)
| ~ rewrite(X0,b)
| ~ rewrite(X0,c) ),
inference(resolution,[status(thm)],[f54,f53]) ).
fof(f57,definition,
! [X0] :
( sQ2_spl
<=> ( ~ rewrite(X0,b)
| ~ rewrite(X0,c) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f58,plain,
! [X0] :
( ~ sQ2_spl
| ~ rewrite(X0,b)
| ~ rewrite(X0,c) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f56,f57,f35]) ).
fof(f61,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f39,f34]) ).
fof(f62,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ sQ2_spl
| equalish(X0,c)
| ~ reflexive_rewrite(X0,c)
| ~ rewrite(X0,b) ),
inference(resolution,[status(thm)],[f58,f28]) ).
fof(f71,plain,
! [X0] :
( ~ sQ2_spl
| equalish(X0,b)
| ~ reflexive_rewrite(X0,b)
| equalish(X0,c)
| ~ reflexive_rewrite(X0,c) ),
inference(resolution,[status(thm)],[f63,f28]) ).
fof(f72,plain,
( ~ sQ2_spl
| equalish(a,b)
| ~ reflexive_rewrite(a,b)
| equalish(a,c) ),
inference(resolution,[status(thm)],[f71,f13]) ).
fof(f74,definition,
( sQ3_spl
<=> equalish(a,c) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ3_spl
| equalish(a,c) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,definition,
( sQ4_spl
<=> reflexive_rewrite(a,b) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( sQ4_spl
| ~ reflexive_rewrite(a,b) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,definition,
( sQ5_spl
<=> equalish(a,b) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ5_spl
| equalish(a,b) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,plain,
( ~ sQ2_spl
| sQ5_spl
| ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f72,f74,f77,f80,f57]) ).
fof(f101,plain,
! [X0] :
( ~ sQ5_spl
| reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(a,X0) ),
inference(resolution,[status(thm)],[f81,f45]) ).
fof(f109,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ reflexive_rewrite(a,c) ),
inference(resolution,[status(thm)],[f101,f44]) ).
fof(f111,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f13]) ).
fof(f112,plain,
( ~ sQ0_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f111]) ).
fof(f113,plain,
! [X0] :
( ~ sQ3_spl
| reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(a,X0) ),
inference(resolution,[status(thm)],[f75,f45]) ).
fof(f120,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ3_spl
| ~ reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(a,X0) ),
inference(resolution,[status(thm)],[f113,f36]) ).
fof(f126,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f12]) ).
fof(f127,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f126]) ).
fof(f143,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ reflexive_rewrite(a,b) ),
inference(resolution,[status(thm)],[f120,f43]) ).
fof(f144,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f143,f77,f74,f35]) ).
fof(f145,plain,
$false,
inference(sat_refutation,[status(thm)],[f41,f60,f62,f83,f112,f127,f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM007+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 14:08:57 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.041146 seconds
% 0.13/0.40 % CPU time: 0.116629 seconds
% 0.13/0.40 % Total memory used: 16.748 MB
% 0.13/0.40 % Net memory used: 16.264 MB
%------------------------------------------------------------------------------