%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX222-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 09:16:23 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 6 con; 0-4 aty)
% Number of variables : 57 ( 7 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_001,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : aux(VAR_0,VAR_1,VAR_2,just(VAR_3)) = eq(VAR_3,VAR_1),
file('theBenchmark.p',axiom_001) ).
cnf(c_2,plain,
aux(A,B,C,just(D)) = eq(D,B),
inference(clausify,[status(thm)],[axiom_001]) ).
fof(axiom_002,axiom,
notb(btrue) = bfalse,
file('theBenchmark.p',axiom_002) ).
cnf(c_3,plain,
notb(btrue) = bfalse,
inference(clausify,[status(thm)],[axiom_002]) ).
fof(axiom_005,axiom,
! [VAR_0,VAR_1] : index(cons(VAR_0,VAR_1),zero) = just(VAR_0),
file('theBenchmark.p',axiom_005) ).
cnf(c_6,plain,
index(cons(A,B),zero) = just(A),
inference(clausify,[status(thm)],[axiom_005]) ).
fof(axiom_007,axiom,
! [VAR_0] : andb(btrue,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_007) ).
cnf(c_8,plain,
andb(btrue,A) = A,
inference(clausify,[status(thm)],[axiom_007]) ).
fof(axiom_012,axiom,
! [VAR_0] : nf(lam(VAR_0)) = nf(VAR_0),
file('theBenchmark.p',axiom_012) ).
cnf(c_13,plain,
nf(lam(A)) = nf(A),
inference(clausify,[status(thm)],[axiom_012]) ).
fof(axiom_013,axiom,
! [VAR_0] : nf(var(VAR_0)) = btrue,
file('theBenchmark.p',axiom_013) ).
cnf(c_14,plain,
nf(var(A)) = btrue,
inference(clausify,[status(thm)],[axiom_013]) ).
fof(axiom_015,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : tc(VAR_0,lam(VAR_1),arr(VAR_2,VAR_3)) = tc(cons(VAR_2,VAR_0),VAR_1,VAR_3),
file('theBenchmark.p',axiom_015) ).
cnf(c_17,plain,
tc(A,lam(B),arr(C,D)) = tc(cons(C,A),B,D),
inference(clausify,[status(thm)],[axiom_015]) ).
fof(axiom_019,axiom,
! [VAR_0,VAR_1,VAR_2] : tc(VAR_0,var(VAR_1),VAR_2) = aux(VAR_0,VAR_2,VAR_1,index(VAR_0,VAR_1)),
file('theBenchmark.p',axiom_019) ).
cnf(c_21,plain,
tc(A,var(B),C) = aux(A,C,B,index(A,B)),
inference(clausify,[status(thm)],[axiom_019]) ).
cnf(c_22,plain,
aux(A,B,C,index(A,C)) = tc(A,var(C),B),
inference(copy,[status(thm)],[c_21]) ).
fof(axiom_020,axiom,
! [VAR_0] : sat_synth_nf_k(VAR_0) = notb(andb(nf(VAR_0),tc(nil,VAR_0,arr(a,arr(b,b))))),
file('theBenchmark.p',axiom_020) ).
cnf(c_23,plain,
sat_synth_nf_k(A) = notb(andb(nf(A),tc(nil,A,arr(a,arr(b,b))))),
inference(clausify,[status(thm)],[axiom_020]) ).
fof(axiom_051,axiom,
! [VAR_0] : eq(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_051) ).
cnf(c_55,plain,
eq(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_051]) ).
fof(axiom_054,axiom,
! [VAR_0] : eq4(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_054) ).
cnf(c_59,plain,
eq4(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_054]) ).
fof(goal,axiom,
! [VAR_0] : eq4(sat_synth_nf_k(VAR_0),bfalse) != btrue,
file('theBenchmark.p',goal) ).
cnf(c_60,plain,
eq4(sat_synth_nf_k(A),bfalse) != btrue,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_61,plain,
eq4(notb(andb(nf(A),tc(nil,A,arr(a,arr(b,b))))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_23,c_60]) ).
cnf(c_151,plain,
aux(cons(A,B),C,zero,just(A)) = tc(cons(A,B),var(zero),C),
inference(paramod,[status(thm)],[c_6,c_22]) ).
cnf(c_152,plain,
eq(A,C) = tc(cons(A,B),var(zero),C),
inference(paramod,[status(thm)],[c_2,c_151]) ).
cnf(c_80,plain,
tc(cons(A,B),var(zero),C) = eq(A,C),
inference(copy,[status(thm)],[c_152]) ).
cnf(c_153,plain,
eq4(notb(andb(nf(A),tc(nil,lam(A),arr(a,arr(b,b))))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_13,c_61]) ).
cnf(c_111,plain,
eq4(notb(andb(nf(A),tc(cons(a,nil),A,arr(b,b)))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_17,c_153]) ).
cnf(c_154,plain,
eq4(notb(andb(nf(A),tc(cons(a,nil),lam(A),arr(b,b)))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_13,c_111]) ).
cnf(c_122,plain,
eq4(notb(andb(nf(A),tc(cons(b,cons(a,nil)),A,b))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_17,c_154]) ).
cnf(c_155,plain,
eq4(notb(andb(nf(var(zero)),eq(b,b))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_80,c_122]) ).
cnf(c_156,plain,
eq4(notb(andb(btrue,eq(b,b))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_14,c_155]) ).
cnf(c_157,plain,
eq4(notb(andb(btrue,btrue)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_55,c_156]) ).
cnf(c_158,plain,
eq4(notb(btrue),bfalse) != btrue,
inference(paramod,[status(thm)],[c_8,c_157]) ).
cnf(c_159,plain,
eq4(bfalse,bfalse) != btrue,
inference(paramod,[status(thm)],[c_3,c_158]) ).
cnf(c_160,plain,
btrue != btrue,
inference(paramod,[status(thm)],[c_59,c_159]) ).
cnf(c_150,plain,
$false,
inference(copy,[status(thm)],[c_160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX222-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 16:59:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3763046 was started by sandbox on n010,
% 0.11/0.37 % Sat Sep 26 16:59:30 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.42
% 0.15/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.42
% 0.15/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.15/0.42 % Length of proof is 18.
% 0.15/0.42 % Level of proof is 4.
% 0.15/0.42 % Maximum clause weight is 53.000.
% 0.15/0.42 % Given clauses 74.
% 0.15/0.42
% 0.15/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------