%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX207-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 09:16:20 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 53 unt; 0 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 20 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-2 aty)
% Number of variables : 78 ( 33 sgn 19 !; 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] : append(nil,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_002) ).
cnf(c_3,plain,
append(nil,A) = A,
inference(clausify,[status(thm)],[axiom_002]) ).
fof(axiom_003,axiom,
! [VAR_0,VAR_1,VAR_2] : append(cons(VAR_0,VAR_1),VAR_2) = cons(VAR_0,append(VAR_1,VAR_2)),
file('theBenchmark.p',axiom_003) ).
cnf(c_4,plain,
append(cons(A,B),C) = cons(A,append(B,C)),
inference(clausify,[status(thm)],[axiom_003]) ).
cnf(c_5,plain,
cons(A,append(B,C)) = append(cons(A,B),C),
inference(copy,[status(thm)],[c_4]) ).
fof(axiom_006,axiom,
linP(pA) = cons(a,nil),
file('theBenchmark.p',axiom_006) ).
cnf(c_10,plain,
linP(pA) = cons(a,nil),
inference(clausify,[status(thm)],[axiom_006]) ).
cnf(c_11,plain,
cons(a,nil) = linP(pA),
inference(copy,[status(thm)],[c_10]) ).
fof(axiom_008,axiom,
linP(pE) = nil,
file('theBenchmark.p',axiom_008) ).
cnf(c_14,plain,
linP(pE) = nil,
inference(clausify,[status(thm)],[axiom_008]) ).
fof(axiom_009,axiom,
! [VAR_0,VAR_1] : linC(c2(VAR_0,VAR_1)) = append(linP(VAR_0),linP(VAR_1)),
file('theBenchmark.p',axiom_009) ).
cnf(c_15,plain,
linC(c2(A,B)) = append(linP(A),linP(B)),
inference(clausify,[status(thm)],[axiom_009]) ).
fof(axiom_010,axiom,
! [VAR_0,VAR_1] : unambig(VAR_0,VAR_1) = impl(eq(linC(VAR_0),linC(VAR_1)),eq4(VAR_0,VAR_1)),
file('theBenchmark.p',axiom_010) ).
cnf(c_16,plain,
unambig(A,B) = impl(eq(linC(A),linC(B)),eq4(A,B)),
inference(clausify,[status(thm)],[axiom_010]) ).
fof(axiom_011,axiom,
eq2(a,b) = bfalse,
file('theBenchmark.p',axiom_011) ).
cnf(c_17,plain,
eq2(a,b) = bfalse,
inference(clausify,[status(thm)],[axiom_011]) ).
cnf(c_18,plain,
bfalse = eq2(a,b),
inference(copy,[status(thm)],[c_17]) ).
fof(axiom_014,axiom,
eq3(pA,pE) = bfalse,
file('theBenchmark.p',axiom_014) ).
cnf(c_23,plain,
eq3(pA,pE) = bfalse,
inference(clausify,[status(thm)],[axiom_014]) ).
cnf(c_24,plain,
eq3(pA,pE) = eq2(a,b),
inference(paramod,[status(thm)],[c_18,c_23]) ).
fof(axiom_037,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( eq4(c2(VAR_0,VAR_2),c2(VAR_1,VAR_3)) = bfalse
| eq3(VAR_0,VAR_1) != bfalse ),
file('theBenchmark.p',axiom_037) ).
cnf(c_67,plain,
( eq4(c2(A,C),c2(B,D)) = bfalse
| eq3(A,B) != bfalse ),
inference(clausify,[status(thm)],[axiom_037]) ).
cnf(c_328,plain,
( eq4(c2(A,C),c2(B,D)) = bfalse
| eq3(A,B) != eq2(a,b) ),
inference(paramod,[status(thm)],[c_18,c_67]) ).
cnf(c_68,plain,
( eq4(c2(A,C),c2(B,D)) = eq2(a,b)
| eq3(A,B) != eq2(a,b) ),
inference(paramod,[status(thm)],[c_18,c_328]) ).
fof(axiom_039,axiom,
! [VAR_0] : eq(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_039) ).
cnf(c_70,plain,
eq(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_039]) ).
fof(axiom_043,axiom,
! [VAR_0] : eq5(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_043) ).
cnf(c_74,plain,
eq5(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_043]) ).
fof(axiom_046,axiom,
! [VAR_0,VAR_1] : eq(nil,cons(VAR_0,VAR_1)) = bfalse,
file('theBenchmark.p',axiom_046) ).
cnf(c_78,plain,
eq(nil,cons(A,B)) = bfalse,
inference(clausify,[status(thm)],[axiom_046]) ).
cnf(c_329,plain,
eq(nil,cons(A,B)) = eq2(a,b),
inference(paramod,[status(thm)],[c_18,c_78]) ).
cnf(c_79,plain,
eq2(a,b) = eq(nil,cons(A,B)),
inference(copy,[status(thm)],[c_329]) ).
fof(goal,axiom,
! [VAR_0,VAR_1] : eq5(unambig(VAR_0,VAR_1),bfalse) != btrue,
file('theBenchmark.p',goal) ).
cnf(c_82,plain,
eq5(unambig(A,B),bfalse) != btrue,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_330,plain,
eq5(impl(eq(linC(A),linC(B)),eq4(A,B)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_16,c_82]) ).
cnf(c_83,plain,
eq5(impl(eq(linC(A),linC(B)),eq4(A,B)),eq2(a,b)) != btrue,
inference(paramod,[status(thm)],[c_18,c_330]) ).
cnf(c_331,plain,
cons(a,append(nil,A)) = append(linP(pA),A),
inference(paramod,[status(thm)],[c_11,c_5]) ).
cnf(c_88,plain,
cons(a,A) = append(linP(pA),A),
inference(paramod,[status(thm)],[c_3,c_331]) ).
cnf(c_89,plain,
append(linP(pA),nil) = linP(pA),
inference(paramod,[status(thm)],[c_88,c_11]) ).
cnf(c_110,plain,
eq4(c2(pA,A),c2(pE,B)) = eq2(a,b),
inference(resolve,[status(thm)],[c_68,c_24]) ).
cnf(c_155,plain,
eq2(a,b) = eq(nil,append(linP(pA),A)),
inference(paramod,[status(thm)],[c_88,c_79]) ).
cnf(c_332,plain,
eq5(impl(eq(linC(c2(pA,A)),linC(c2(pE,B))),eq2(a,b)),eq2(a,b)) != btrue,
inference(paramod,[status(thm)],[c_110,c_83]) ).
cnf(c_333,plain,
eq5(impl(eq(append(linP(pA),linP(A)),linC(c2(pE,B))),eq2(a,b)),eq2(a,b)) != btrue,
inference(paramod,[status(thm)],[c_15,c_332]) ).
cnf(c_334,plain,
eq5(impl(eq(append(linP(pA),linP(A)),append(linP(pE),linP(B))),eq2(a,b)),eq2(a,b)) != btrue,
inference(paramod,[status(thm)],[c_15,c_333]) ).
cnf(c_335,plain,
eq5(impl(eq(append(linP(pA),linP(A)),append(nil,linP(B))),eq2(a,b)),eq2(a,b)) != btrue,
inference(paramod,[status(thm)],[c_14,c_334]) ).
cnf(c_183,plain,
eq5(impl(eq(append(linP(pA),linP(A)),linP(B)),eq2(a,b)),eq2(a,b)) != btrue,
inference(paramod,[status(thm)],[c_3,c_335]) ).
cnf(c_228,plain,
eq2(a,b) = eq(nil,linP(pA)),
inference(paramod,[status(thm)],[c_89,c_155]) ).
cnf(c_336,plain,
eq5(impl(eq(append(linP(pA),linP(A)),linP(B)),eq(nil,linP(pA))),eq2(a,b)) != btrue,
inference(paramod,[status(thm)],[c_228,c_183]) ).
cnf(c_244,plain,
eq5(impl(eq(append(linP(pA),linP(A)),linP(B)),eq(nil,linP(pA))),eq(nil,linP(pA))) != btrue,
inference(paramod,[status(thm)],[c_228,c_336]) ).
cnf(c_337,plain,
eq5(impl(eq(append(linP(pA),nil),linP(A)),eq(nil,linP(pA))),eq(nil,linP(pA))) != btrue,
inference(paramod,[status(thm)],[c_14,c_244]) ).
cnf(c_324,plain,
eq5(impl(eq(linP(pA),linP(A)),eq(nil,linP(pA))),eq(nil,linP(pA))) != btrue,
inference(paramod,[status(thm)],[c_89,c_337]) ).
cnf(c_338,plain,
eq5(impl(btrue,eq(nil,linP(pA))),eq(nil,linP(pA))) != btrue,
inference(paramod,[status(thm)],[c_70,c_324]) ).
cnf(c_339,plain,
eq5(eq(nil,linP(pA)),eq(nil,linP(pA))) != btrue,
inference(paramod,[status(thm)],[c_1,c_338]) ).
cnf(c_340,plain,
btrue != btrue,
inference(paramod,[status(thm)],[c_74,c_339]) ).
cnf(c_327,plain,
$false,
inference(copy,[status(thm)],[c_340]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX207-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 16:55:31 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3661894 was started by sandbox2 on n014,
% 0.10/0.36 % Sat Sep 26 16:55:31 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.43
% 0.10/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.43
% 0.10/0.43 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.10/0.43 % Length of proof is 30.
% 0.10/0.43 % Level of proof is 7.
% 0.10/0.43 % Maximum clause weight is 50.000.
% 0.10/0.43 % Given clauses 107.
% 0.10/0.43
% 0.10/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------