%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC105-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 08:56:51 AM UTC 2026
% Result : Unsatisfiable 41.14s 21.36s
% Output : CNFRefutation 41.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 24
% Syntax : Number of formulae : 116 ( 29 unt; 0 def)
% Number of atoms : 277 ( 73 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 300 ( 139 ~; 161 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 40 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_14,axiom,
( rearsegP(sk4,sk3)
| nil = sk3 ),
file('theBenchmark.p',co1_14) ).
cnf(c_51,plain,
( rearsegP(sk4,sk3)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_52,plain,
( rearsegP(sk4,sk3)
| sk3 = nil ),
inference(copy,[status(thm)],[c_51]) ).
fof(co1_13,axiom,
( neq(sk3,nil)
| nil = sk3 ),
file('theBenchmark.p',co1_13) ).
cnf(c_53,plain,
( neq(sk3,nil)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_54,plain,
( neq(sk3,nil)
| sk3 = nil ),
inference(copy,[status(thm)],[c_53]) ).
fof(co1_11,axiom,
( neq(sk3,nil)
| nil = sk4 ),
file('theBenchmark.p',co1_11) ).
cnf(c_57,plain,
( neq(sk3,nil)
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_58,plain,
( neq(sk3,nil)
| sk4 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_9,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_9) ).
cnf(c_61,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_62,plain,
( neq(sk2,nil)
| sk1 != nil ),
inference(copy,[status(thm)],[c_61]) ).
fof(co1_8,axiom,
( ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
file('theBenchmark.p',co1_8) ).
cnf(c_63,plain,
( ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_64,plain,
( ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil)
| sk2 = nil ),
inference(copy,[status(thm)],[c_63]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| nil = sk2 ),
file('theBenchmark.p',co1_7) ).
cnf(c_65,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_66,plain,
( neq(sk2,nil)
| sk2 = nil ),
inference(copy,[status(thm)],[c_65]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_67,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_68,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_69,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_68]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_70,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_71,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_72,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_73,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
fof(clause153,axiom,
! [VAR_0,VAR_1,VAR_2] :
( rearsegP(VAR_0,VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_2)
| ~ rearsegP(VAR_1,VAR_2)
| ~ rearsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause153) ).
cnf(c_98,plain,
( rearsegP(A,C)
| ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ~ rearsegP(B,C)
| ~ rearsegP(A,B) ),
inference(clausify,[status(thm)],[clause153]) ).
fof(clause129,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ frontsegP(VAR_1,VAR_0)
| ~ frontsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause129) ).
cnf(c_121,plain,
( B = A
| ~ ssList(B)
| ~ ssList(A)
| ~ frontsegP(B,A)
| ~ frontsegP(A,B) ),
inference(clausify,[status(thm)],[clause129]) ).
fof(clause128,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ rearsegP(VAR_1,VAR_0)
| ~ rearsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause128) ).
cnf(c_122,plain,
( B = A
| ~ ssList(B)
| ~ ssList(A)
| ~ rearsegP(B,A)
| ~ rearsegP(A,B) ),
inference(clausify,[status(thm)],[clause128]) ).
fof(clause127,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ segmentP(VAR_1,VAR_0)
| ~ segmentP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause127) ).
cnf(c_123,plain,
( B = A
| ~ ssList(B)
| ~ ssList(A)
| ~ segmentP(B,A)
| ~ segmentP(A,B) ),
inference(clausify,[status(thm)],[clause127]) ).
fof(clause115,axiom,
! [VAR_0,VAR_1] :
( ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ neq(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',clause115) ).
cnf(c_134,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause83,axiom,
! [VAR_0] :
( frontsegP(nil,VAR_0)
| ~ ssList(VAR_0)
| nil != VAR_0 ),
file('theBenchmark.p',clause83) ).
cnf(c_159,plain,
( frontsegP(nil,A)
| ~ ssList(A)
| nil != A ),
inference(clausify,[status(thm)],[clause83]) ).
fof(clause81,axiom,
! [VAR_0] :
( rearsegP(nil,VAR_0)
| ~ ssList(VAR_0)
| nil != VAR_0 ),
file('theBenchmark.p',clause81) ).
cnf(c_161,plain,
( rearsegP(nil,A)
| ~ ssList(A)
| nil != A ),
inference(clausify,[status(thm)],[clause81]) ).
fof(clause79,axiom,
! [VAR_0] :
( segmentP(nil,VAR_0)
| ~ ssList(VAR_0)
| nil != VAR_0 ),
file('theBenchmark.p',clause79) ).
cnf(c_163,plain,
( segmentP(nil,A)
| ~ ssList(A)
| nil != A ),
inference(clausify,[status(thm)],[clause79]) ).
fof(clause60,axiom,
! [VAR_0] :
( frontsegP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause60) ).
cnf(c_174,plain,
( frontsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause60]) ).
fof(clause58,axiom,
! [VAR_0] :
( rearsegP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause58) ).
cnf(c_176,plain,
( rearsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause58]) ).
fof(clause56,axiom,
! [VAR_0] :
( segmentP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause56) ).
cnf(c_178,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause56]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_226,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_839,plain,
( ~ rearsegP(sk2,sk1)
| ~ neq(sk3,nil)
| sk2 = nil ),
inference(paramod,[status(thm)],[c_67,c_64]) ).
cnf(c_840,plain,
( rearsegP(sk2,sk3)
| sk3 = nil ),
inference(paramod,[status(thm)],[c_69,c_52]) ).
cnf(c_15816,plain,
( frontsegP(nil,sk3)
| nil != sk3 ),
inference(resolve,[status(thm)],[c_159,c_71]) ).
cnf(c_1084,plain,
( frontsegP(nil,sk3)
| sk3 != nil ),
inference(copy,[status(thm)],[c_15816]) ).
cnf(c_15817,plain,
( rearsegP(nil,sk2)
| nil != sk2 ),
inference(resolve,[status(thm)],[c_161,c_72]) ).
cnf(c_1087,plain,
( rearsegP(nil,sk2)
| sk2 != nil ),
inference(copy,[status(thm)],[c_15817]) ).
cnf(c_15818,plain,
( rearsegP(nil,sk3)
| nil != sk3 ),
inference(resolve,[status(thm)],[c_161,c_71]) ).
cnf(c_1088,plain,
( rearsegP(nil,sk3)
| sk3 != nil ),
inference(copy,[status(thm)],[c_15818]) ).
cnf(c_15819,plain,
( segmentP(nil,sk4)
| nil != sk4 ),
inference(resolve,[status(thm)],[c_163,c_70]) ).
cnf(c_1093,plain,
( segmentP(nil,sk4)
| sk4 != nil ),
inference(copy,[status(thm)],[c_15819]) ).
cnf(c_1114,plain,
frontsegP(sk1,nil),
inference(resolve,[status(thm)],[c_174,c_73]) ).
cnf(c_1122,plain,
rearsegP(sk1,nil),
inference(resolve,[status(thm)],[c_176,c_73]) ).
cnf(c_1123,plain,
rearsegP(sk2,nil),
inference(resolve,[status(thm)],[c_176,c_72]) ).
cnf(c_1131,plain,
segmentP(sk2,nil),
inference(resolve,[status(thm)],[c_178,c_72]) ).
cnf(c_15820,plain,
( sk1 = nil
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ frontsegP(nil,sk1) ),
inference(resolve,[status(thm)],[c_1114,c_121]) ).
cnf(c_15821,plain,
( sk1 = nil
| ~ ssList(sk1)
| ~ frontsegP(nil,sk1) ),
inference(resolve,[status(thm)],[c_226,c_15820]) ).
cnf(c_11574,plain,
( sk1 = nil
| ~ frontsegP(nil,sk1) ),
inference(resolve,[status(thm)],[c_73,c_15821]) ).
cnf(c_15822,plain,
( sk1 = nil
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ rearsegP(nil,sk1) ),
inference(resolve,[status(thm)],[c_1122,c_122]) ).
cnf(c_15823,plain,
( sk1 = nil
| ~ ssList(sk1)
| ~ rearsegP(nil,sk1) ),
inference(resolve,[status(thm)],[c_226,c_15822]) ).
cnf(c_11702,plain,
( sk1 = nil
| ~ rearsegP(nil,sk1) ),
inference(resolve,[status(thm)],[c_73,c_15823]) ).
cnf(c_15824,plain,
( sk2 = nil
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ segmentP(nil,sk2) ),
inference(resolve,[status(thm)],[c_1131,c_123]) ).
cnf(c_15825,plain,
( sk2 = nil
| ~ ssList(sk2)
| ~ segmentP(nil,sk2) ),
inference(resolve,[status(thm)],[c_226,c_15824]) ).
cnf(c_11862,plain,
( sk2 = nil
| ~ segmentP(nil,sk2) ),
inference(resolve,[status(thm)],[c_72,c_15825]) ).
cnf(c_13215,plain,
( neq(sk3,nil)
| frontsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_1084,c_54]) ).
cnf(c_13544,plain,
( neq(sk2,nil)
| rearsegP(nil,sk2) ),
inference(resolve,[status(thm)],[c_1087,c_66]) ).
cnf(c_13545,plain,
( rearsegP(sk2,sk3)
| rearsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_1088,c_840]) ).
cnf(c_13902,plain,
( neq(sk3,nil)
| segmentP(nil,sk4) ),
inference(resolve,[status(thm)],[c_1093,c_58]) ).
cnf(c_13914,plain,
( sk1 = nil
| ~ frontsegP(nil,sk3) ),
inference(paramod,[status(thm)],[c_67,c_11574]) ).
cnf(c_14262,plain,
( sk1 = nil
| ~ rearsegP(nil,sk3) ),
inference(paramod,[status(thm)],[c_67,c_11702]) ).
cnf(c_15826,plain,
( rearsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ rearsegP(A,nil)
| rearsegP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_13545,c_98]) ).
cnf(c_15827,plain,
( rearsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(nil)
| ~ rearsegP(A,nil)
| rearsegP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_71,c_15826]) ).
cnf(c_14961,plain,
( rearsegP(A,sk3)
| ~ ssList(A)
| ~ rearsegP(A,nil)
| rearsegP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_226,c_15827]) ).
cnf(c_15828,plain,
( rearsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk2)
| ~ ssList(sk3)
| ~ rearsegP(A,sk2)
| rearsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_13545,c_98]) ).
cnf(c_15829,plain,
( rearsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk2)
| ~ rearsegP(A,sk2)
| rearsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_71,c_15828]) ).
cnf(c_14968,plain,
( rearsegP(A,sk3)
| ~ ssList(A)
| ~ rearsegP(A,sk2)
| rearsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_72,c_15829]) ).
cnf(c_15830,plain,
( ~ ssList(sk2)
| ~ rearsegP(sk2,nil)
| rearsegP(sk2,sk3) ),
inference(factor,[status(thm)],[c_14961]) ).
cnf(c_15831,plain,
( ~ ssList(sk2)
| rearsegP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_1123,c_15830]) ).
cnf(c_14970,plain,
rearsegP(sk2,sk3),
inference(resolve,[status(thm)],[c_72,c_15831]) ).
cnf(c_15832,plain,
( ~ ssList(nil)
| ~ rearsegP(nil,sk2)
| rearsegP(nil,sk3) ),
inference(factor,[status(thm)],[c_14968]) ).
cnf(c_14971,plain,
( ~ rearsegP(nil,sk2)
| rearsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_226,c_15832]) ).
cnf(c_15833,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| sk3 != nil
| segmentP(nil,sk4) ),
inference(resolve,[status(thm)],[c_13902,c_134]) ).
cnf(c_15834,plain,
( ~ ssList(sk3)
| sk3 != nil
| segmentP(nil,sk4) ),
inference(resolve,[status(thm)],[c_226,c_15833]) ).
cnf(c_15185,plain,
( sk3 != nil
| segmentP(nil,sk4) ),
inference(resolve,[status(thm)],[c_71,c_15834]) ).
cnf(c_15187,plain,
( neq(sk3,nil)
| sk1 = nil ),
inference(resolve,[status(thm)],[c_13914,c_13215]) ).
cnf(c_15329,plain,
( neq(sk2,nil)
| rearsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_14971,c_13544]) ).
cnf(c_15474,plain,
( ~ rearsegP(sk2,sk1)
| sk2 = nil
| sk1 = nil ),
inference(resolve,[status(thm)],[c_15187,c_839]) ).
cnf(c_15477,plain,
( sk1 = nil
| neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_15329,c_14262]) ).
cnf(c_15835,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_15477,c_62]) ).
cnf(c_15552,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_15835]) ).
cnf(c_15836,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_15552,c_134]) ).
cnf(c_15837,plain,
( ~ ssList(sk2)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_226,c_15836]) ).
cnf(c_15553,plain,
sk2 != nil,
inference(resolve,[status(thm)],[c_72,c_15837]) ).
cnf(c_15554,plain,
( ~ rearsegP(sk2,sk1)
| sk1 = nil ),
inference(resolve,[status(thm)],[c_15553,c_15474]) ).
cnf(c_15564,plain,
~ segmentP(nil,sk2),
inference(resolve,[status(thm)],[c_15553,c_11862]) ).
cnf(c_15838,plain,
( ~ rearsegP(sk2,sk3)
| sk1 = nil ),
inference(paramod,[status(thm)],[c_67,c_15554]) ).
cnf(c_15608,plain,
sk1 = nil,
inference(resolve,[status(thm)],[c_14970,c_15838]) ).
cnf(c_15839,plain,
nil = sk3,
inference(paramod,[status(thm)],[c_15608,c_67]) ).
cnf(c_15615,plain,
sk3 = nil,
inference(copy,[status(thm)],[c_15839]) ).
cnf(c_15623,plain,
segmentP(nil,sk4),
inference(resolve,[status(thm)],[c_15615,c_15185]) ).
cnf(c_15840,plain,
segmentP(nil,sk2),
inference(paramod,[status(thm)],[c_69,c_15623]) ).
cnf(c_15815,plain,
$false,
inference(resolve,[status(thm)],[c_15564,c_15840]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC105-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/15.38 % Computer : n004.cluster.edu
% 0.09/15.38 % Model : x86_64 x86_64
% 0.09/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.38 % Memory : 8046.5625MB
% 0.09/15.38 % OS : Linux 6.8.0-71-generic
% 0.09/15.38 % CPULimit : 300
% 0.09/15.38 % WCLimit : 300
% 0.09/15.38 % DateTime : Sat Sep 26 12:15:52 UTC 2026
% 0.09/15.38 % CPUTime :
% 0.09/15.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/15.38 % Process 1672368 was started by sandbox on n004,
% 0.09/15.38 % Sat Sep 26 12:15:52 2026
% 0.09/15.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/15.39
% 0.09/15.39 % From the command line: assign(max_seconds, 300).
% 41.14/21.36
% 41.14/21.36 % given #500 (I,wt=66): 569 app(app(A,cons(B,C)),cons(D,C)) != C | -ssList(C) | -ssList(A) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | app(app(skaf61(C),cons(skaf59(C),skaf62(C))),cons(skaf60(C),skaf63(C))) = C. [factor(308,b,f)].
% 41.14/21.36
% 41.14/21.36 % given #1000 (F,wt=22): 11598 cons(skac2,skaf81(A)) != skaf81(A). [resolve(6602,b,220,a)].
% 41.14/21.36
% 41.14/21.36 % SZS status Unsatisfiable for theBenchmark
% 41.14/21.36
% 41.14/21.36 % Proof 1 at 5.28 (+ 0.59) seconds.
% 41.14/21.36 % Length of proof is 67.
% 41.14/21.36 % Level of proof is 14.
% 41.14/21.36 % Maximum clause weight is 20.000.
% 41.14/21.36 % Given clauses 1038.
% 41.14/21.36
% 41.14/21.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------