%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL088-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 12:08:43 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 44 ( 14 unt; 3 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 97 ( 49 ~; 45 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [P,Q] :
( member(comb_app(P,Q),comb)
| ~ member(Q,comb)
| ~ member(P,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] :
( member(pair(A,A),rtrancl(contract))
| ~ member(A,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [R,A,B,C] :
( member(pair(A,C),R)
| ~ member(pair(B,C),R)
| ~ member(pair(A,B),R)
| ~ trans(R) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [R] : trans(rtrancl(R)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A,B] :
( member(B,comb)
| ~ member(pair(A,B),contract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [P3,Q3,R3,C] :
( member(pair(comb_app(P3,R3),C),rtrancl(contract))
| ~ member(pair(comb_app(Q3,R3),C),rtrancl(contract))
| ~ member(R3,comb)
| ~ member(pair(P3,Q3),contract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
member(r,comb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
member(pair(y,z),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
member(pair(comb_app(p,r),comb_app(y,r)),rtrancl(contract)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ member(pair(comb_app(p,r),comb_app(z,r)),rtrancl(contract)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,plain,
! [X0,X1] :
( member(comb_app(X0,X1),comb)
| ~ member(X1,comb)
| ~ member(X0,comb) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f60,plain,
! [X0] :
( member(pair(X0,X0),rtrancl(contract))
| ~ member(X0,comb) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f86,plain,
! [R,A,C] :
( member(pair(A,C),R)
| ! [B] :
( ~ member(pair(B,C),R)
| ~ member(pair(A,B),R)
| ~ trans(R) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( member(pair(X1,X3),X0)
| ~ member(pair(X2,X3),X0)
| ~ member(pair(X1,X2),X0)
| ~ trans(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
! [X0] : trans(rtrancl(X0)),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f89,plain,
! [B] :
( member(B,comb)
| ! [A] : ~ member(pair(A,B),contract) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f90,plain,
! [X0,X1] :
( member(X1,comb)
| ~ member(pair(X0,X1),contract) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f93,plain,
! [P3,R3,C] :
( member(pair(comb_app(P3,R3),C),rtrancl(contract))
| ! [Q3] :
( ~ member(pair(comb_app(Q3,R3),C),rtrancl(contract))
| ~ member(R3,comb)
| ~ member(pair(P3,Q3),contract) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( member(pair(comb_app(X0,X2),X3),rtrancl(contract))
| ~ member(pair(comb_app(X1,X2),X3),rtrancl(contract))
| ~ member(X2,comb)
| ~ member(pair(X0,X1),contract) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f97,plain,
member(r,comb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f100,plain,
member(pair(y,z),contract),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f101,plain,
member(pair(comb_app(p,r),comb_app(y,r)),rtrancl(contract)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f102,plain,
~ member(pair(comb_app(p,r),comb_app(z,r)),rtrancl(contract)),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f105,plain,
! [X0,X1] :
( member(pair(comb_app(y,X0),X1),rtrancl(contract))
| ~ member(pair(comb_app(z,X0),X1),rtrancl(contract))
| ~ member(X0,comb) ),
inference(resolution,[status(thm)],[f94,f100]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( member(pair(X0,X3),rtrancl(X2))
| ~ member(pair(X1,X3),rtrancl(X2))
| ~ member(pair(X0,X1),rtrancl(X2)) ),
inference(resolution,[status(thm)],[f87,f88]) ).
fof(f112,plain,
! [X0] :
( ~ member(pair(X0,comb_app(z,r)),rtrancl(contract))
| ~ member(pair(comb_app(p,r),X0),rtrancl(contract)) ),
inference(resolution,[status(thm)],[f109,f102]) ).
fof(f113,plain,
~ member(pair(comb_app(y,r),comb_app(z,r)),rtrancl(contract)),
inference(resolution,[status(thm)],[f112,f101]) ).
fof(f123,plain,
( ~ member(pair(comb_app(z,r),comb_app(z,r)),rtrancl(contract))
| ~ member(r,comb) ),
inference(resolution,[status(thm)],[f113,f105]) ).
fof(f125,definition,
( sQ2_spl
<=> member(r,comb) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( sQ2_spl
| ~ member(r,comb) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,definition,
( sQ3_spl
<=> member(pair(comb_app(z,r),comb_app(z,r)),rtrancl(contract)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( sQ3_spl
| ~ member(pair(comb_app(z,r),comb_app(z,r)),rtrancl(contract)) ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f123,f125,f128]) ).
fof(f132,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f97]) ).
fof(f133,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f132]) ).
fof(f134,plain,
( sQ3_spl
| ~ member(comb_app(z,r),comb) ),
inference(resolution,[status(thm)],[f130,f60]) ).
fof(f136,plain,
( sQ3_spl
| ~ member(r,comb)
| ~ member(z,comb) ),
inference(resolution,[status(thm)],[f134,f59]) ).
fof(f145,definition,
( sQ4_spl
<=> member(z,comb) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( sQ4_spl
| ~ member(z,comb) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f136,f145,f125,f128]) ).
fof(f156,plain,
! [X0] :
( sQ4_spl
| ~ member(pair(X0,z),contract) ),
inference(resolution,[status(thm)],[f147,f90]) ).
fof(f182,plain,
( sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f100,f156]) ).
fof(f184,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f182]) ).
fof(f185,plain,
$false,
inference(sat_refutation,[status(thm)],[f131,f133,f148,f184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL088-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.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 14:09:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.061979 seconds
% 0.12/0.43 % CPU time: 0.174505 seconds
% 0.12/0.43 % Total memory used: 82.284 MB
% 0.12/0.43 % Net memory used: 82.133 MB
%------------------------------------------------------------------------------