%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX186-1 : 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 : n006.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 09:16:16 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 40 ( 12 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom,axiom,
! [VAR_0] : impl(btrue,VAR_0) = VAR_0,
file('theBenchmark.p',axiom) ).
cnf(c_1,plain,
impl(btrue,A) = A,
inference(clausify,[status(thm)],[axiom]) ).
fof(axiom_002,axiom,
! [VAR_0] : drop(s(VAR_0),nil) = nil,
file('theBenchmark.p',axiom_002) ).
cnf(c_3,plain,
drop(s(A),nil) = nil,
inference(clausify,[status(thm)],[axiom_002]) ).
fof(axiom_003,axiom,
! [VAR_0,VAR_1,VAR_2] : drop(s(VAR_0),cons(VAR_1,VAR_2)) = drop(VAR_0,VAR_2),
file('theBenchmark.p',axiom_003) ).
cnf(c_4,plain,
drop(s(A),cons(B,C)) = drop(A,C),
inference(clausify,[status(thm)],[axiom_003]) ).
fof(axiom_005,axiom,
! [VAR_0,VAR_1,VAR_2] : prop_drop_inj2(VAR_0,VAR_1,VAR_2) = impl(eq(drop(VAR_0,VAR_1),drop(VAR_0,VAR_2)),eq(VAR_1,VAR_2)),
file('theBenchmark.p',axiom_005) ).
cnf(c_6,plain,
prop_drop_inj2(A,B,C) = impl(eq(drop(A,B),drop(A,C)),eq(B,C)),
inference(clausify,[status(thm)],[axiom_005]) ).
fof(axiom_011,axiom,
! [VAR_0] : eq(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_011) ).
cnf(c_12,plain,
eq(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_011]) ).
fof(axiom_013,axiom,
! [VAR_0] : eq3(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_013) ).
cnf(c_14,plain,
eq3(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_013]) ).
fof(axiom_016,axiom,
! [VAR_0,VAR_1] : eq(nil,cons(VAR_0,VAR_1)) = bfalse,
file('theBenchmark.p',axiom_016) ).
cnf(c_17,plain,
eq(nil,cons(A,B)) = bfalse,
inference(clausify,[status(thm)],[axiom_016]) ).
fof(goal,axiom,
! [VAR_0,VAR_1,VAR_2] : eq3(prop_drop_inj2(VAR_0,VAR_1,VAR_2),bfalse) != btrue,
file('theBenchmark.p',goal) ).
cnf(c_19,plain,
eq3(prop_drop_inj2(A,B,C),bfalse) != btrue,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_20,plain,
eq3(impl(eq(drop(A,B),drop(A,C)),eq(B,C)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_6,c_19]) ).
cnf(c_28,plain,
eq3(impl(eq(nil,drop(s(A),B)),eq(nil,B)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_3,c_20]) ).
cnf(c_39,plain,
eq3(impl(eq(nil,drop(A,B)),eq(nil,cons(C,B))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_4,c_28]) ).
cnf(c_37,plain,
eq3(impl(eq(nil,drop(A,B)),bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_17,c_39]) ).
cnf(c_40,plain,
eq3(impl(eq(nil,nil),bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_3,c_37]) ).
cnf(c_41,plain,
eq3(impl(btrue,bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_12,c_40]) ).
cnf(c_42,plain,
eq3(bfalse,bfalse) != btrue,
inference(paramod,[status(thm)],[c_1,c_41]) ).
cnf(c_43,plain,
btrue != btrue,
inference(paramod,[status(thm)],[c_14,c_42]) ).
cnf(c_38,plain,
$false,
inference(copy,[status(thm)],[c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX186-1 : 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 : n006.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
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 16:51:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 1711604 was started by sandbox on n006,
% 0.11/0.38 % Sat Sep 26 16:51:11 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.40
% 0.11/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.40
% 0.11/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.40 % Length of proof is 12.
% 0.11/0.40 % Level of proof is 4.
% 0.11/0.40 % Maximum clause weight is 16.000.
% 0.11/0.40 % Given clauses 24.
% 0.11/0.40
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------