%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL034-1 : 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 : n026.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 07:57:48 AM UTC 2026
% Result : Unsatisfiable 2.60s 0.75s
% Output : CNFRefutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 3
% Syntax : Number of formulae : 63 ( 33 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 34 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 209 ( 94 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [VAR_0,VAR_1] :
( is_a_theorem(VAR_1)
| ~ is_a_theorem(VAR_0)
| ~ is_a_theorem(implies(VAR_0,VAR_1)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(c_1,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(c0_CAMeredith,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : is_a_theorem(implies(implies(implies(implies(implies(VAR_0,VAR_1),implies(VAR_2,falsehood)),VAR_3),VAR_4),implies(implies(VAR_4,VAR_0),implies(VAR_2,VAR_0)))),
file('theBenchmark.p',c0_CAMeredith) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E),implies(implies(E,A),implies(C,A)))),
inference(clausify,[status(thm)],[c0_CAMeredith]) ).
fof(prove_c0_3,axiom,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('theBenchmark.p',prove_c0_3) ).
cnf(c_3,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(clausify,[status(thm)],[prove_c0_3]) ).
cnf(c_1661,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),implies(B,D)),implies(E,implies(B,D)))),
inference(resolve,[status(thm)],[c_1661,c_2]) ).
cnf(c_1662,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(implies(A,implies(falsehood,B)),C),implies(D,C))),
inference(resolve,[status(thm)],[c_1662,c_4]) ).
cnf(c_1663,plain,
( is_a_theorem(implies(D,C))
| ~ is_a_theorem(implies(implies(A,implies(falsehood,B)),C)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_14,plain,
is_a_theorem(implies(A,implies(B,implies(falsehood,C)))),
inference(resolve,[status(thm)],[c_1663,c_6]) ).
cnf(c_1664,plain,
( is_a_theorem(implies(B,implies(falsehood,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_18,plain,
is_a_theorem(implies(A,implies(falsehood,B))),
inference(resolve,[status(thm)],[c_1664,c_14]) ).
cnf(c_1665,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_26,plain,
is_a_theorem(implies(implies(implies(falsehood,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_1665,c_18]) ).
cnf(c_1666,plain,
( is_a_theorem(implies(E,implies(B,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(B,D))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_28,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_1666,c_26]) ).
cnf(c_1667,plain,
( is_a_theorem(implies(B,implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_28]) ).
cnf(c_29,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_1667,c_28]) ).
cnf(c_1668,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_34,plain,
is_a_theorem(implies(implies(implies(A,implies(implies(implies(B,C),implies(D,falsehood)),E)),B),implies(D,B))),
inference(resolve,[status(thm)],[c_1668,c_29]) ).
cnf(c_1669,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_67,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(B,D),implies(A,falsehood)),C))),
inference(resolve,[status(thm)],[c_1669,c_34]) ).
cnf(c_1670,plain,
( is_a_theorem(implies(implies(implies(B,D),implies(A,falsehood)),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_67]) ).
cnf(c_127,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,falsehood)),implies(D,implies(C,A)))),
inference(resolve,[status(thm)],[c_1670,c_29]) ).
cnf(c_1671,plain,
( is_a_theorem(implies(implies(implies(B,D),implies(A,falsehood)),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_67]) ).
cnf(c_128,plain,
is_a_theorem(implies(implies(implies(A,B),implies(implies(falsehood,C),falsehood)),implies(D,A))),
inference(resolve,[status(thm)],[c_1671,c_26]) ).
cnf(c_1672,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_139,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),B),implies(D,B))),
inference(resolve,[status(thm)],[c_1672,c_128]) ).
cnf(c_1673,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_144,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_1673,c_139]) ).
cnf(c_1674,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_153,plain,
is_a_theorem(implies(implies(implies(implies(A,falsehood),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_1674,c_144]) ).
cnf(c_1675,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,falsehood),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_153]) ).
cnf(c_261,plain,
is_a_theorem(implies(implies(A,falsehood),implies(A,B))),
inference(resolve,[status(thm)],[c_1675,c_153]) ).
cnf(c_1676,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_267,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(C,A))),
inference(resolve,[status(thm)],[c_1676,c_153]) ).
cnf(c_1677,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,falsehood),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_153]) ).
cnf(c_276,plain,
is_a_theorem(implies(A,implies(implies(A,falsehood),B))),
inference(resolve,[status(thm)],[c_1677,c_261]) ).
cnf(c_1678,plain,
( is_a_theorem(implies(D,implies(C,A)))
| ~ is_a_theorem(implies(implies(A,B),implies(C,falsehood))) ),
inference(resolve,[status(thm)],[c_1,c_127]) ).
cnf(c_277,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_1678,c_261]) ).
cnf(c_1679,plain,
( is_a_theorem(implies(B,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_277]) ).
cnf(c_281,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_1679,c_277]) ).
cnf(c_1680,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_286,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_1680,c_277]) ).
cnf(c_1681,plain,
( is_a_theorem(implies(implies(implies(B,D),implies(A,falsehood)),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_67]) ).
cnf(c_287,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,falsehood)),implies(C,A))),
inference(resolve,[status(thm)],[c_1681,c_281]) ).
cnf(c_1682,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,falsehood),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_153]) ).
cnf(c_298,plain,
is_a_theorem(implies(A,implies(implies(implies(implies(A,falsehood),B),falsehood),C))),
inference(resolve,[status(thm)],[c_1682,c_276]) ).
cnf(c_1683,plain,
( is_a_theorem(implies(C,A))
| ~ is_a_theorem(implies(implies(A,B),implies(C,falsehood))) ),
inference(resolve,[status(thm)],[c_1,c_287]) ).
cnf(c_1011,plain,
is_a_theorem(implies(implies(implies(implies(implies(A,B),falsehood),C),falsehood),A)),
inference(resolve,[status(thm)],[c_1683,c_298]) ).
cnf(c_1684,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_1551,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_1684,c_1011]) ).
cnf(c_1685,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_1551]) ).
cnf(c_1600,plain,
is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))),
inference(resolve,[status(thm)],[c_1685,c_286]) ).
cnf(c_1686,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_1551]) ).
cnf(c_1602,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_1686,c_267]) ).
cnf(c_1687,plain,
( is_a_theorem(implies(implies(implies(B,B),C),C))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1600]) ).
cnf(c_1622,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_1687,c_1600]) ).
cnf(c_1688,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_1622]) ).
cnf(c_1659,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_1688,c_1602]) ).
cnf(c_1660,plain,
$false,
inference(resolve,[status(thm)],[c_1659,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL034-1 : 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 : n026.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 : Fri Sep 25 21:47:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3526915 was started by sandbox2 on n026,
% 0.09/0.37 % Fri Sep 25 21:47:54 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 2.60/0.75
% 2.60/0.75 % SZS status Unsatisfiable for theBenchmark
% 2.60/0.75
% 2.60/0.75 % Proof 1 at 0.21 (+ 0.13) seconds.
% 2.60/0.75 % Length of proof is 32.
% 2.60/0.75 % Level of proof is 23.
% 2.60/0.75 % Maximum clause weight is 20.000.
% 2.60/0.75 % Given clauses 140.
% 2.60/0.75
% 2.60/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------