%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX186-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 07:07:21 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 16 RR)
% Number of literals : 16 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(impl(btrue,u),u),
file('SWX186-1.p',unknown),
[] ).
cnf(3,axiom,
equal(drop(s(u),nil),nil),
file('SWX186-1.p',unknown),
[] ).
cnf(4,axiom,
equal(drop(s(u),cons(v,w)),drop(u,w)),
file('SWX186-1.p',unknown),
[] ).
cnf(6,axiom,
equal(impl(eq(drop(u,v),drop(u,w)),eq(v,w)),prop_drop_inj2(u,v,w)),
file('SWX186-1.p',unknown),
[] ).
cnf(12,axiom,
equal(eq(u,u),btrue),
file('SWX186-1.p',unknown),
[] ).
cnf(14,axiom,
equal(eq3(u,u),btrue),
file('SWX186-1.p',unknown),
[] ).
cnf(18,axiom,
equal(eq(cons(u,v),nil),bfalse),
file('SWX186-1.p',unknown),
[] ).
cnf(19,axiom,
~ equal(eq3(prop_drop_inj2(u,v,w),bfalse),btrue),
file('SWX186-1.p',unknown),
[] ).
cnf(45,plain,
equal(impl(eq(drop(s(u),v),nil),eq(v,nil)),prop_drop_inj2(s(u),v,nil)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(91,plain,
equal(impl(eq(drop(s(u),cons(v,w)),nil),bfalse),prop_drop_inj2(s(u),cons(v,w),nil)),
inference(spr,[status(thm),theory(equality)],[18,45]),
[iquote('0:SpR:18.0,45.0')] ).
cnf(96,plain,
equal(impl(eq(drop(u,v),nil),bfalse),prop_drop_inj2(s(u),cons(w,v),nil)),
inference(rew,[status(thm),theory(equality)],[4,91]),
[iquote('0:Rew:4.0,91.0')] ).
cnf(101,plain,
equal(prop_drop_inj2(s(s(u)),cons(v,nil),nil),impl(eq(nil,nil),bfalse)),
inference(spr,[status(thm),theory(equality)],[3,96]),
[iquote('0:SpR:3.0,96.0')] ).
cnf(104,plain,
equal(prop_drop_inj2(s(s(u)),cons(v,nil),nil),bfalse),
inference(rew,[status(thm),theory(equality)],[1,101,12]),
[iquote('0:Rew:1.0,101.0,12.0,101.0')] ).
cnf(107,plain,
~ equal(eq3(bfalse,bfalse),btrue),
inference(spl,[status(thm),theory(equality)],[104,19]),
[iquote('0:SpL:104.0,19.0')] ).
cnf(108,plain,
~ equal(btrue,btrue),
inference(rew,[status(thm),theory(equality)],[14,107]),
[iquote('0:Rew:14.0,107.0')] ).
cnf(109,plain,
$false,
inference(obv,[status(thm),theory(equality)],[108]),
[iquote('0:Obv:108.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX186-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.18/0.34 % Computer : n018.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue May 5 09:38:31 EDT 2026
% 0.18/0.34 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 65 clauses, backtracked 0 clauses, performed 0 splits and kept 42 clauses.
% 0.20/0.43 SPASS allocated 63230 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.43 0:00:00.04 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.00 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 4, length 16 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : axiom axiom_002 axiom_003 axiom_005 axiom_011 axiom_013 axiom_017 goal
% 0.20/0.43
%------------------------------------------------------------------------------