%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX207+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 07:07:25 PM UTC 2026
% Result : Theorem 0.29s 0.47s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 32 unt; 0 nHn; 35 RR)
% Number of literals : 38 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
~ equal(pE,pB),
file('SWX207+1.p',unknown),
[] ).
cnf(5,axiom,
equal(linP(pE),nil),
file('SWX207+1.p',unknown),
[] ).
cnf(14,axiom,
equal(append(nil,u),u),
file('SWX207+1.p',unknown),
[] ).
cnf(16,axiom,
equal(tail(cons(u,v)),v),
file('SWX207+1.p',unknown),
[] ).
cnf(20,axiom,
equal(proj2C(c2(u,v)),v),
file('SWX207+1.p',unknown),
[] ).
cnf(22,axiom,
equal(cons(b,nil),linP(pB)),
file('SWX207+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ equal(linC(u),linC(v))
| equal(u,v) ),
file('SWX207+1.p',unknown),
[] ).
cnf(24,axiom,
equal(append(linP(u),linP(v)),linC(c2(u,v))),
file('SWX207+1.p',unknown),
[] ).
cnf(25,axiom,
equal(append(cons(u,v),w),cons(u,append(v,w))),
file('SWX207+1.p',unknown),
[] ).
cnf(27,axiom,
equal(append(cons(b,nil),append(linP(u),cons(b,nil))),linP(bP(u))),
file('SWX207+1.p',unknown),
[] ).
cnf(28,plain,
equal(append(linP(pB),linC(c2(u,pB))),linP(bP(u))),
inference(rew,[status(thm),theory(equality)],[24,27,22]),
[iquote('0:Rew:24.0,27.0,22.0,27.0')] ).
cnf(84,plain,
equal(append(linP(u),nil),linC(c2(u,pE))),
inference(spr,[status(thm),theory(equality)],[5,24]),
[iquote('0:SpR:5.0,24.0')] ).
cnf(85,plain,
equal(append(nil,linP(u)),linC(c2(pE,u))),
inference(spr,[status(thm),theory(equality)],[5,24]),
[iquote('0:SpR:5.0,24.0')] ).
cnf(86,plain,
equal(linC(c2(pE,u)),linP(u)),
inference(rew,[status(thm),theory(equality)],[14,85]),
[iquote('0:Rew:14.0,85.0')] ).
cnf(88,plain,
equal(append(linP(pB),linP(pB)),linP(bP(pE))),
inference(spr,[status(thm),theory(equality)],[86,28]),
[iquote('0:SpR:86.0,28.0')] ).
cnf(92,plain,
equal(linC(c2(pB,pB)),linP(bP(pE))),
inference(rew,[status(thm),theory(equality)],[24,88]),
[iquote('0:Rew:24.0,88.0')] ).
cnf(95,plain,
( ~ equal(linC(u),linP(bP(pE)))
| equal(u,c2(pB,pB)) ),
inference(spl,[status(thm),theory(equality)],[92,23]),
[iquote('0:SpL:92.0,23.0')] ).
cnf(127,plain,
equal(cons(b,append(nil,u)),append(linP(pB),u)),
inference(spr,[status(thm),theory(equality)],[22,25]),
[iquote('0:SpR:22.0,25.0')] ).
cnf(129,plain,
equal(append(linP(pB),u),cons(b,u)),
inference(rew,[status(thm),theory(equality)],[14,127]),
[iquote('0:Rew:14.0,127.0')] ).
cnf(130,plain,
equal(cons(b,linC(c2(u,pB))),linP(bP(u))),
inference(rew,[status(thm),theory(equality)],[129,28]),
[iquote('0:Rew:129.0,28.0')] ).
cnf(133,plain,
equal(cons(b,linP(u)),linC(c2(pB,u))),
inference(spr,[status(thm),theory(equality)],[129,24]),
[iquote('0:SpR:129.0,24.0')] ).
cnf(151,plain,
equal(linC(c2(u,pB)),tail(linP(bP(u)))),
inference(spr,[status(thm),theory(equality)],[130,16]),
[iquote('0:SpR:130.0,16.0')] ).
cnf(153,plain,
equal(cons(b,append(linC(c2(u,pB)),v)),append(linP(bP(u)),v)),
inference(spr,[status(thm),theory(equality)],[130,25]),
[iquote('0:SpR:130.0,25.0')] ).
cnf(159,plain,
equal(tail(linP(bP(pB))),linP(bP(pE))),
inference(rew,[status(thm),theory(equality)],[151,92]),
[iquote('0:Rew:151.0,92.0')] ).
cnf(162,plain,
equal(cons(b,append(tail(linP(bP(u))),v)),append(linP(bP(u)),v)),
inference(rew,[status(thm),theory(equality)],[151,153]),
[iquote('0:Rew:151.0,153.0')] ).
cnf(226,plain,
equal(tail(linP(bP(pE))),linP(pB)),
inference(spr,[status(thm),theory(equality)],[151,86]),
[iquote('0:SpR:151.0,86.0')] ).
cnf(268,plain,
equal(cons(b,append(linP(pB),u)),append(linP(bP(pE)),u)),
inference(spr,[status(thm),theory(equality)],[226,162]),
[iquote('0:SpR:226.0,162.0')] ).
cnf(270,plain,
equal(append(linP(bP(pE)),u),cons(b,cons(b,u))),
inference(rew,[status(thm),theory(equality)],[129,268]),
[iquote('0:Rew:129.0,268.0')] ).
cnf(358,plain,
equal(cons(b,cons(b,nil)),linC(c2(bP(pE),pE))),
inference(spr,[status(thm),theory(equality)],[270,84]),
[iquote('0:SpR:270.0,84.0')] ).
cnf(363,plain,
equal(linC(c2(bP(pE),pE)),linP(bP(pE))),
inference(rew,[status(thm),theory(equality)],[159,358,151,133,22]),
[iquote('0:Rew:159.0,358.0,151.0,358.0,133.0,358.0,22.0,358.0')] ).
cnf(415,plain,
( ~ equal(linP(bP(pE)),linP(bP(pE)))
| equal(c2(bP(pE),pE),c2(pB,pB)) ),
inference(spl,[status(thm),theory(equality)],[363,95]),
[iquote('0:SpL:363.0,95.0')] ).
cnf(417,plain,
equal(c2(bP(pE),pE),c2(pB,pB)),
inference(obv,[status(thm),theory(equality)],[415]),
[iquote('0:Obv:415.0')] ).
cnf(424,plain,
equal(proj2C(c2(pB,pB)),pE),
inference(spr,[status(thm),theory(equality)],[417,20]),
[iquote('0:SpR:417.0,20.0')] ).
cnf(429,plain,
equal(pE,pB),
inference(rew,[status(thm),theory(equality)],[20,424]),
[iquote('0:Rew:20.0,424.0')] ).
cnf(430,plain,
$false,
inference(mrr,[status(thm)],[429,4]),
[iquote('0:MRR:429.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX207+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.16/0.34 % Computer : n007.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 11:34:53 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.29/0.47
% 0.29/0.47 SPASS V 3.9
% 0.29/0.47 SPASS beiseite: Proof found.
% 0.29/0.47 % SZS status Theorem
% 0.29/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.29/0.47 SPASS derived 322 clauses, backtracked 0 clauses, performed 0 splits and kept 174 clauses.
% 0.29/0.47 SPASS allocated 85472 KBytes.
% 0.29/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.29/0.47 0:00:00.03 for the input.
% 0.29/0.47 0:00:00.02 for the FLOTTER CNF translation.
% 0.29/0.47 0:00:00.01 for inferences.
% 0.29/0.47 0:00:00.00 for the backtracking.
% 0.29/0.47 0:00:00.03 for the reduction.
% 0.29/0.47
% 0.29/0.47
% 0.29/0.47 Here is a proof with depth 6, length 35 :
% 0.29/0.47 % SZS output start Refutation
% See solution above
% 0.29/0.47 Formulae used in the proof : axiom_016 axiom_025 axiom_019 axiom_002 axiom_018 axiom_024 goal_027 axiom_026 axiom_020 axiom_022
% 0.29/0.47
%------------------------------------------------------------------------------