%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN939+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 03:18:32 PM UTC 2026
% Result : Theorem 0.11s 0.60s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 3 unt; 7 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 173 ( 74 ~; 66 |; 20 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 71 ( 61 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [C,B] :
( ! [Z] : q(f(Z))
=> ? [X,Y] :
( q(X)
& ( r(Y)
=> ( r(C)
& r(B) ) )
& ( p(f(Y))
=> p(X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [C,B] :
( ! [Z] : q(f(Z))
=> ? [X,Y] :
( q(X)
& ( r(Y)
=> ( r(C)
& r(B) ) )
& ( p(f(Y))
=> p(X) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [C,B] :
( ! [X,Y] :
( ~ q(X)
| ( ( ~ r(C)
| ~ r(B) )
& r(Y) )
| ( ~ p(X)
& p(f(Y)) ) )
& ! [Z] : q(f(Z)) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X,Y] :
( sP0_prd(Y,X)
<=> ( ~ p(X)
& p(f(Y)) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
? [C,B] :
( ! [X,Y] :
( ~ q(X)
| ( ( ~ r(C)
| ~ r(B) )
& r(Y) )
| sP0_prd(Y,X) )
& ! [Z] : q(f(Z)) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ? [C,B] :
! [X] :
( ~ q(X)
| ! [Y] :
( ( ( ~ r(C)
| ~ r(B) )
& r(Y) )
| sP0_prd(Y,X) ) )
& ! [Z] : q(f(Z)) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f7,plain,
( ! [X] :
( ~ q(X)
| ! [Y] :
( ( ( ~ r(sK0_skl)
| ~ r(sK1_skl) )
& r(Y) )
| sP0_prd(Y,X) ) )
& ! [Z] : q(f(Z)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl),skolemize(B,sK1_skl)],[f6]) ).
fof(f8,plain,
! [X0] : q(f(X0)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( ~ q(X1)
| r(X0)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( ~ q(X1)
| ~ r(sK0_skl)
| ~ r(sK1_skl)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X,Y] :
( ( p(X)
| ~ p(f(Y))
| sP0_prd(Y,X) )
& ( ( ~ p(X)
& p(f(Y)) )
| ~ sP0_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
( ! [X,Y] :
( p(X)
| ~ p(f(Y))
| sP0_prd(Y,X) )
& ! [X,Y] :
( ( ~ p(X)
& p(f(Y)) )
| ~ sP0_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( p(f(X0))
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ~ p(X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,definition,
! [X0,X1] :
( sQ0_spl
<=> ( ~ q(X1)
| sP0_prd(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f17,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ q(X1)
| sP0_prd(X0,X1) ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f19,definition,
( sQ1_spl
<=> r(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f21,plain,
( sQ1_spl
| ~ r(sK1_skl) ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f22,definition,
( sQ2_spl
<=> r(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f24,plain,
( sQ2_spl
| ~ r(sK0_skl) ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f25,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f16,f19,f22]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,f(X0))
| ~ sP0_prd(X0,X1) ),
inference(resolution,[status(thm)],[f13,f14]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ q(f(X0))
| r(X2)
| ~ sP0_prd(X0,X1) ),
inference(resolution,[status(thm)],[f26,f9]) ).
fof(f28,definition,
! [X0,X1] :
( sQ3_spl
<=> ( ~ q(f(X0))
| ~ sP0_prd(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f29,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ q(f(X0))
| ~ sP0_prd(X0,X1) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,definition,
! [X2] :
( sQ4_spl
<=> r(X2) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f32,plain,
! [X0] :
( ~ sQ4_spl
| r(X0) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f27,f28,f31]) ).
fof(f35,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f8]) ).
fof(f36,plain,
( sQ2_spl
| ~ sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f24,f32]) ).
fof(f37,plain,
( sQ2_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ q(X1)
| r(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f9,f35]) ).
fof(f39,plain,
! [X0] :
( sQ1_spl
| ~ sQ3_spl
| ~ q(X0) ),
inference(resolution,[status(thm)],[f38,f21]) ).
fof(f41,plain,
( sQ1_spl
| ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f8,f39]) ).
fof(f42,plain,
( sQ1_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f41]) ).
fof(f44,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ q(f(X0))
| ~ sP0_prd(X0,X1) ),
inference(resolution,[status(thm)],[f26,f17]) ).
fof(f45,plain,
( ~ sQ0_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f44,f28,f16]) ).
fof(f53,definition,
! [X1] :
( sQ7_spl
<=> ~ q(X1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f54,plain,
! [X0] :
( ~ sQ7_spl
| ~ q(X0) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( ~ sQ3_spl
| sQ7_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f38,f31,f53,f28]) ).
fof(f59,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ3_spl
| ~ q(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f17,f35]) ).
fof(f60,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f8,f59]) ).
fof(f61,plain,
( ~ sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f62,plain,
( sQ1_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f21,f32]) ).
fof(f63,plain,
( sQ1_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f62]) ).
fof(f66,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8,f54]) ).
fof(f67,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f66]) ).
fof(f68,plain,
$false,
inference(sat_refutation,[status(thm)],[f25,f34,f37,f42,f45,f56,f61,f63,f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN939+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n004.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Mon Sep 21 11:30:35 UTC 2026
% 0.11/0.57 % CPUTime :
% 0.11/0.58 % Drodi V4.1.1
% 0.11/0.60 % Refutation found
% 0.11/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.62 % Elapsed time: 0.036178 seconds
% 0.11/0.62 % CPU time: 0.097352 seconds
% 0.11/0.62 % Total memory used: 12.440 MB
% 0.11/0.62 % Net memory used: 12.032 MB
%------------------------------------------------------------------------------