%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 : Sun Sep 27 06:57:22 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 3 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(s,VAR_0),VAR_1),VAR_2) = apply(apply(VAR_0,VAR_2),apply(VAR_1,VAR_2)),
file('theBenchmark.p',s_definition) ).
cnf(c_1,plain,
apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)),
inference(clausify,[status(thm)],[s_definition]) ).
fof(k_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(k,VAR_0),VAR_1) = VAR_0,
file('theBenchmark.p',k_definition) ).
cnf(c_2,plain,
apply(apply(k,A),B) = A,
inference(clausify,[status(thm)],[k_definition]) ).
fof(prove_u_combinator,axiom,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
file('theBenchmark.p',prove_u_combinator) ).
cnf(c_3,plain,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
inference(clausify,[status(thm)],[prove_u_combinator]) ).
cnf(c_4,plain,
apply(apply(apply(s,apply(apply(s,A),B)),C),D) = apply(apply(apply(A,D),apply(B,D)),apply(C,D)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
apply(apply(apply(s,apply(k,A)),B),C) = apply(A,apply(B,C)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_12,plain,
apply(apply(apply(s,k),A),B) = B,
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_13,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) != apply(y,apply(apply(x,x),y)),
inference(paramod,[status(thm)],[c_10,c_3]) ).
cnf(c_32,plain,
apply(apply(apply(s,apply(apply(s,k),A)),B),C) = apply(C,apply(B,C)),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_44,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x))),y) != apply(y,apply(apply(x,x),y)),
inference(paramod,[status(thm)],[c_1,c_13]) ).
cnf(c_45,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(x,apply(apply(apply(s,k),k),x))),y) != apply(y,apply(apply(x,x),y)),
inference(paramod,[status(thm)],[c_12,c_44]) ).
cnf(c_42,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(x,x)),y) != apply(y,apply(apply(x,x),y)),
inference(paramod,[status(thm)],[c_12,c_45]) ).
cnf(c_43,plain,
$false,
inference(resolve,[status(thm)],[c_42,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n012.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 23:04:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 1714352 was started by sandbox2 on n012,
% 0.14/0.36 % Sat Sep 26 23:04:20 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.36
% 0.14/0.36 % From the command line: assign(max_seconds, 300).
% 0.14/0.37
% 0.14/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.37
% 0.14/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.37 % Length of proof is 10.
% 0.14/0.37 % Level of proof is 4.
% 0.14/0.37 % Maximum clause weight is 37.000.
% 0.14/0.37 % Given clauses 4.
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------