%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL011-1 : 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 : n001.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 06:57:24 AM UTC 2026
% Result : Unsatisfiable 0.61s 0.54s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(o_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(o,VAR_0),VAR_1) = apply(VAR_1,apply(VAR_0,VAR_1)),
file('theBenchmark.p',o_definition) ).
cnf(c_1,plain,
apply(apply(o,A),B) = apply(B,apply(A,B)),
inference(clausify,[status(thm)],[o_definition]) ).
fof(q1_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(q1,VAR_0),VAR_1),VAR_2) = apply(VAR_0,apply(VAR_2,VAR_1)),
file('theBenchmark.p',q1_definition) ).
cnf(c_2,plain,
apply(apply(apply(q1,A),B),C) = apply(A,apply(C,B)),
inference(clausify,[status(thm)],[q1_definition]) ).
fof(prove_fixed_point,axiom,
! [VAR_0] : VAR_0 != apply(combinator,VAR_0),
file('theBenchmark.p',prove_fixed_point) ).
cnf(c_3,plain,
A != apply(combinator,A),
inference(clausify,[status(thm)],[prove_fixed_point]) ).
cnf(c_4,plain,
apply(combinator,A) != A,
inference(copy,[status(thm)],[c_3]) ).
cnf(c_8,plain,
apply(apply(o,A),apply(apply(q1,B),C)) = apply(B,apply(apply(A,apply(apply(q1,B),C)),C)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_21,plain,
apply(apply(apply(q1,combinator),A),B) != apply(B,A),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_45,plain,
apply(apply(apply(apply(q1,apply(q1,combinator)),A),B),C) != apply(C,apply(B,A)),
inference(paramod,[status(thm)],[c_2,c_21]) ).
cnf(c_297,plain,
apply(apply(apply(apply(o,A),apply(apply(q1,q1),B)),C),D) = apply(apply(apply(A,apply(apply(q1,q1),B)),B),apply(D,C)),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_299,plain,
apply(C,apply(B,A)) != apply(apply(apply(apply(q1,apply(q1,combinator)),A),B),C),
inference(copy,[status(thm)],[c_45]) ).
cnf(c_298,plain,
$false,
inference(resolve,[status(thm)],[c_297,c_299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n001.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 23:11:13 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 2896839 was started by sandbox2 on n001,
% 0.16/0.43 % Sat Sep 26 23:11:13 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.61/0.54
% 0.61/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.61/0.54
% 0.61/0.54 % Proof 1 at 0.08 (+ 0.01) seconds.
% 0.61/0.54 % Length of proof is 9.
% 0.61/0.54 % Level of proof is 4.
% 0.61/0.54 % Maximum clause weight is 27.000.
% 0.61/0.54 % Given clauses 13.
% 0.61/0.54
% 0.61/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------