%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL063-1 : 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 : n017.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 06:57:34 AM UTC 2026
% Result : Unsatisfiable 49.32s 7.53s
% Output : CNFRefutation 49.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(b_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(b,VAR_0),VAR_1),VAR_2) = apply(VAR_0,apply(VAR_1,VAR_2)),
file('theBenchmark.p',b_definition) ).
cnf(c_1,plain,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
inference(clausify,[status(thm)],[b_definition]) ).
fof(t_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(t,VAR_0),VAR_1) = apply(VAR_1,VAR_0),
file('theBenchmark.p',t_definition) ).
cnf(c_2,plain,
apply(apply(t,A),B) = apply(B,A),
inference(clausify,[status(thm)],[t_definition]) ).
fof(prove_f_combinator,axiom,
! [VAR_0] : apply(apply(apply(VAR_0,f(VAR_0)),g(VAR_0)),h(VAR_0)) != apply(apply(h(VAR_0),g(VAR_0)),f(VAR_0)),
file('theBenchmark.p',prove_f_combinator) ).
cnf(c_3,plain,
apply(apply(apply(A,f(A)),g(A)),h(A)) != apply(apply(h(A),g(A)),f(A)),
inference(clausify,[status(thm)],[prove_f_combinator]) ).
cnf(c_4,plain,
apply(apply(h(A),g(A)),f(A)) != apply(apply(apply(A,f(A)),g(A)),h(A)),
inference(copy,[status(thm)],[c_3]) ).
cnf(c_7573,plain,
apply(apply(apply(b,A),apply(t,B)),C) = apply(A,apply(C,B)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_5,plain,
apply(A,apply(apply(t,B),C)) = apply(A,apply(C,B)),
inference(paramod,[status(thm)],[c_1,c_7573]) ).
cnf(c_6,plain,
apply(apply(apply(apply(t,A),b),B),C) = apply(A,apply(B,C)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_7,plain,
apply(apply(apply(t,A),apply(b,B)),C) = apply(B,apply(A,C)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_8,plain,
apply(apply(t,A),apply(apply(b,B),C)) = apply(B,apply(C,A)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_18,plain,
apply(apply(h(A),g(A)),f(A)) != apply(apply(apply(apply(t,f(A)),A),g(A)),h(A)),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_28,plain,
apply(apply(t,A),apply(apply(t,B),C)) = apply(apply(C,B),A),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_128,plain,
apply(apply(t,A),apply(apply(t,B),apply(b,C))) = apply(C,apply(B,A)),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_142,plain,
apply(apply(t,A),apply(apply(b,B),C)) = apply(B,apply(apply(t,A),C)),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_501,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(t,C),b))) = apply(C,apply(B,A)),
inference(paramod,[status(thm)],[c_28,c_6]) ).
cnf(c_507,plain,
apply(apply(t,A),apply(apply(b,apply(t,B)),apply(t,C))) = apply(apply(A,C),B),
inference(paramod,[status(thm)],[c_28,c_8]) ).
cnf(c_536,plain,
apply(apply(h(A),g(A)),f(A)) != apply(apply(t,h(A)),apply(apply(t,g(A)),apply(apply(t,f(A)),A))),
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_3319,plain,
apply(apply(t,apply(A,B)),C) = apply(apply(t,B),apply(apply(t,A),apply(b,C))),
inference(paramod,[status(thm)],[c_128,c_2]) ).
cnf(c_6937,plain,
apply(apply(h(apply(apply(b,A),B)),g(apply(apply(b,A),B))),f(apply(apply(b,A),B))) != apply(apply(t,h(apply(apply(b,A),B))),apply(apply(t,g(apply(apply(b,A),B))),apply(A,apply(apply(t,f(apply(apply(b,A),B))),B)))),
inference(paramod,[status(thm)],[c_142,c_536]) ).
cnf(c_7574,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(t,t),apply(apply(t,apply(b,apply(t,C))),b)))) = apply(apply(A,B),C),
inference(paramod,[status(thm)],[c_501,c_507]) ).
cnf(c_7575,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(t,t),apply(apply(t,apply(t,C)),apply(apply(t,b),apply(b,b)))))) = apply(apply(A,B),C),
inference(paramod,[status(thm)],[c_3319,c_7574]) ).
cnf(c_7571,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(t,t),apply(apply(t,C),apply(apply(t,t),apply(b,apply(apply(t,b),apply(b,b)))))))) = apply(apply(A,B),C),
inference(paramod,[status(thm)],[c_3319,c_7575]) ).
cnf(c_7576,plain,
apply(apply(t,h(apply(apply(b,A),B))),apply(apply(t,g(apply(apply(b,A),B))),apply(A,apply(apply(t,f(apply(apply(b,A),B))),B)))) != apply(apply(h(apply(apply(b,A),B)),g(apply(apply(b,A),B))),f(apply(apply(b,A),B))),
inference(copy,[status(thm)],[c_6937]) ).
cnf(c_7572,plain,
$false,
inference(resolve,[status(thm)],[c_7571,c_7576]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL063-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 23:05:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1889661 was started by sandbox2 on n017,
% 0.09/0.36 % Sat Sep 26 23:05:19 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 49.32/7.53
% 49.32/7.53 % SZS status Unsatisfiable for theBenchmark
% 49.32/7.53
% 49.32/7.53 % Proof 1 at 6.57 (+ 0.56) seconds.
% 49.32/7.53 % Length of proof is 19.
% 49.32/7.53 % Level of proof is 5.
% 49.32/7.53 % Maximum clause weight is 51.000.
% 49.32/7.53 % Given clauses 101.
% 49.32/7.53
% 49.32/7.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------