%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL004-1 : 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 : n010.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 3.71s 0.99s
% Output : CNFRefutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 8 sgn 6 !; 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,
! [VAR_0] : apply(apply(VAR_0,f(VAR_0)),g(VAR_0)) != apply(g(VAR_0),apply(apply(f(VAR_0),f(VAR_0)),g(VAR_0))),
file('theBenchmark.p',prove_u_combinator) ).
cnf(c_3,plain,
apply(apply(A,f(A)),g(A)) != apply(g(A),apply(apply(f(A),f(A)),g(A))),
inference(clausify,[status(thm)],[prove_u_combinator]) ).
cnf(c_4,plain,
apply(g(A),apply(apply(f(A),f(A)),g(A))) != apply(apply(A,f(A)),g(A)),
inference(copy,[status(thm)],[c_3]) ).
cnf(c_5,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_11,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,A),apply(k,B)),C) = apply(apply(A,C),B),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_13,plain,
apply(apply(apply(s,k),A),B) = B,
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_35,plain,
apply(apply(apply(s,apply(apply(s,k),A)),B),C) = apply(C,apply(B,C)),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_1310,plain,
apply(apply(apply(s,apply(apply(s,A),B)),apply(k,C)),D) = apply(apply(apply(A,D),apply(B,D)),C),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_36,plain,
apply(apply(apply(apply(s,A),B),C),D) = apply(apply(apply(A,C),apply(B,C)),D),
inference(paramod,[status(thm)],[c_12,c_1310]) ).
cnf(c_40,plain,
apply(apply(apply(s,A),apply(apply(s,k),B)),C) = apply(apply(A,C),C),
inference(paramod,[status(thm)],[c_13,c_1]) ).
cnf(c_192,plain,
apply(apply(apply(apply(s,s),apply(s,k)),A),B) = apply(apply(A,B),B),
inference(paramod,[status(thm)],[c_1,c_40]) ).
cnf(c_318,plain,
apply(apply(apply(apply(s,s),apply(s,k)),apply(apply(s,k),A)),B) = apply(B,B),
inference(paramod,[status(thm)],[c_13,c_192]) ).
cnf(c_537,plain,
apply(apply(apply(apply(s,apply(apply(s,apply(k,A)),B)),C),D),E) = apply(apply(apply(A,apply(B,D)),apply(C,D)),E),
inference(paramod,[status(thm)],[c_11,c_36]) ).
cnf(c_841,plain,
apply(apply(apply(s,apply(apply(s,k),A)),apply(f(B),f(B))),g(B)) != apply(apply(B,f(B)),g(B)),
inference(paramod,[status(thm)],[c_35,c_4]) ).
cnf(c_1308,plain,
apply(apply(apply(s,apply(apply(s,k),A)),apply(apply(apply(apply(s,s),apply(s,k)),apply(apply(s,k),B)),f(C))),g(C)) != apply(apply(C,f(C)),g(C)),
inference(paramod,[status(thm)],[c_318,c_841]) ).
cnf(c_1311,plain,
apply(apply(apply(A,apply(B,D)),apply(C,D)),E) = apply(apply(apply(apply(s,apply(apply(s,apply(k,A)),B)),C),D),E),
inference(copy,[status(thm)],[c_537]) ).
cnf(c_1309,plain,
$false,
inference(resolve,[status(thm)],[c_1308,c_1311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n010.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 23:04:46 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 257763 was started by sandbox2 on n010,
% 0.15/0.43 % Sat Sep 26 23:04:46 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 3.71/0.99
% 3.71/0.99 % SZS status Unsatisfiable for theBenchmark
% 3.71/0.99
% 3.71/0.99 % Proof 1 at 0.43 (+ 0.11) seconds.
% 3.71/0.99 % Length of proof is 17.
% 3.71/0.99 % Level of proof is 6.
% 3.71/0.99 % Maximum clause weight is 94.000.
% 3.71/0.99 % Given clauses 51.
% 3.71/0.99
% 3.71/0.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------