%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX185-1 : TPTP v9.3.1. Released v9.3.0.
% 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 09:16:16 AM UTC 2026
% Result : Unsatisfiable 42.29s 5.74s
% Output : CNFRefutation 42.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 22
% Syntax : Number of formulae : 108 ( 99 unt; 0 def)
% Number of atoms : 117 ( 116 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 33 ( 24 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 8 con; 0-2 aty)
% Number of variables : 173 ( 24 sgn 36 !; 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_004,axiom,
! [VAR_0] : assoc(z(eX,VAR_0)) = z(assoc(eX),assoc(VAR_0)),
file('theBenchmark.p',axiom_004) ).
cnf(c_6,plain,
assoc(z(eX,A)) = z(assoc(eX),assoc(A)),
inference(clausify,[status(thm)],[axiom_004]) ).
cnf(c_7,plain,
z(assoc(eX),assoc(A)) = assoc(z(eX,A)),
inference(copy,[status(thm)],[c_6]) ).
fof(axiom_006,axiom,
! [VAR_0,VAR_1] : assoc(x2(VAR_0,VAR_1)) = x2(assoc(VAR_0),assoc(VAR_1)),
file('theBenchmark.p',axiom_006) ).
cnf(c_10,plain,
assoc(x2(A,B)) = x2(assoc(A),assoc(B)),
inference(clausify,[status(thm)],[axiom_006]) ).
cnf(c_11,plain,
x2(assoc(A),assoc(B)) = assoc(x2(A,B)),
inference(copy,[status(thm)],[c_10]) ).
fof(axiom_007,axiom,
assoc(eX) = eX,
file('theBenchmark.p',axiom_007) ).
cnf(c_12,plain,
assoc(eX) = eX,
inference(clausify,[status(thm)],[axiom_007]) ).
fof(axiom_009,axiom,
! [VAR_0] : append(nil,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_009) ).
cnf(c_14,plain,
append(nil,A) = A,
inference(clausify,[status(thm)],[axiom_009]) ).
fof(axiom_010,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_010) ).
cnf(c_15,plain,
append(cons(A,B),C) = cons(A,append(B,C)),
inference(clausify,[status(thm)],[axiom_010]) ).
fof(axiom_011,axiom,
! [VAR_0,VAR_1] : linTerm(x2(VAR_0,VAR_1)) = append(cons(c,nil),append(lin(z(VAR_0,VAR_1)),cons(d,nil))),
file('theBenchmark.p',axiom_011) ).
cnf(c_16,plain,
linTerm(x2(A,B)) = append(cons(c,nil),append(lin(z(A,B)),cons(d,nil))),
inference(clausify,[status(thm)],[axiom_011]) ).
cnf(c_17363,plain,
linTerm(x2(A,B)) = cons(c,append(nil,append(lin(z(A,B)),cons(d,nil)))),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_17364,plain,
linTerm(x2(A,B)) = cons(c,append(lin(z(A,B)),cons(d,nil))),
inference(paramod,[status(thm)],[c_14,c_17363]) ).
cnf(c_17,plain,
cons(c,append(lin(z(A,B)),cons(d,nil))) = linTerm(x2(A,B)),
inference(copy,[status(thm)],[c_17364]) ).
fof(axiom_012,axiom,
! [VAR_0,VAR_1] : linTerm(z(VAR_0,VAR_1)) = lin(z(VAR_0,VAR_1)),
file('theBenchmark.p',axiom_012) ).
cnf(c_18,plain,
linTerm(z(A,B)) = lin(z(A,B)),
inference(clausify,[status(thm)],[axiom_012]) ).
fof(axiom_013,axiom,
linTerm(eX) = lin(eX),
file('theBenchmark.p',axiom_013) ).
cnf(c_19,plain,
linTerm(eX) = lin(eX),
inference(clausify,[status(thm)],[axiom_013]) ).
fof(axiom_015,axiom,
! [VAR_0,VAR_1] : lin(z(VAR_0,VAR_1)) = append(linTerm(VAR_0),append(cons(plus,nil),linTerm(VAR_1))),
file('theBenchmark.p',axiom_015) ).
cnf(c_21,plain,
lin(z(A,B)) = append(linTerm(A),append(cons(plus,nil),linTerm(B))),
inference(clausify,[status(thm)],[axiom_015]) ).
cnf(c_17365,plain,
lin(z(A,B)) = append(linTerm(A),cons(plus,append(nil,linTerm(B)))),
inference(paramod,[status(thm)],[c_15,c_21]) ).
cnf(c_17366,plain,
lin(z(A,B)) = append(linTerm(A),cons(plus,linTerm(B))),
inference(paramod,[status(thm)],[c_14,c_17365]) ).
cnf(c_22,plain,
append(linTerm(A),cons(plus,linTerm(B))) = lin(z(A,B)),
inference(copy,[status(thm)],[c_17366]) ).
fof(axiom_017,axiom,
lin(eX) = cons(x,nil),
file('theBenchmark.p',axiom_017) ).
cnf(c_25,plain,
lin(eX) = cons(x,nil),
inference(clausify,[status(thm)],[axiom_017]) ).
cnf(c_26,plain,
cons(x,nil) = lin(eX),
inference(copy,[status(thm)],[c_25]) ).
fof(axiom_019,axiom,
! [VAR_0,VAR_1] : prop_unambig(VAR_0,VAR_1) = impl(eq(lin(VAR_0),lin(VAR_1)),eq3(assoc(VAR_0),assoc(VAR_1))),
file('theBenchmark.p',axiom_019) ).
cnf(c_29,plain,
prop_unambig(A,B) = impl(eq(lin(A),lin(B)),eq3(assoc(A),assoc(B))),
inference(clausify,[status(thm)],[axiom_019]) ).
fof(axiom_020,axiom,
eq2(c,d) = bfalse,
file('theBenchmark.p',axiom_020) ).
cnf(c_30,plain,
eq2(c,d) = bfalse,
inference(clausify,[status(thm)],[axiom_020]) ).
cnf(c_31,plain,
bfalse = eq2(c,d),
inference(copy,[status(thm)],[c_30]) ).
fof(axiom_055,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( eq3(z(VAR_0,VAR_2),z(VAR_1,VAR_3)) = eq3(VAR_2,VAR_3)
| eq3(VAR_0,VAR_1) != btrue ),
file('theBenchmark.p',axiom_055) ).
cnf(c_100,plain,
( eq3(z(A,C),z(B,D)) = eq3(C,D)
| eq3(A,B) != btrue ),
inference(clausify,[status(thm)],[axiom_055]) ).
fof(axiom_056,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( eq3(x2(VAR_0,VAR_2),x2(VAR_1,VAR_3)) = bfalse
| eq3(VAR_0,VAR_1) != bfalse ),
file('theBenchmark.p',axiom_056) ).
cnf(c_101,plain,
( eq3(x2(A,C),x2(B,D)) = bfalse
| eq3(A,B) != bfalse ),
inference(clausify,[status(thm)],[axiom_056]) ).
cnf(c_17367,plain,
( eq3(x2(A,C),x2(B,D)) = bfalse
| eq3(A,B) != eq2(c,d) ),
inference(paramod,[status(thm)],[c_31,c_101]) ).
cnf(c_17368,plain,
( eq3(x2(A,C),x2(B,D)) = eq2(c,d)
| eq3(A,B) != eq2(c,d) ),
inference(paramod,[status(thm)],[c_31,c_17367]) ).
cnf(c_102,plain,
( eq3(x2(A,C),x2(B,D)) = eq2(c,d)
| eq2(c,d) != eq3(A,B) ),
inference(copy,[status(thm)],[c_17368]) ).
fof(axiom_064,axiom,
! [VAR_0,VAR_1] : eq3(eX,z(VAR_0,VAR_1)) = bfalse,
file('theBenchmark.p',axiom_064) ).
cnf(c_116,plain,
eq3(eX,z(A,B)) = bfalse,
inference(clausify,[status(thm)],[axiom_064]) ).
cnf(c_117,plain,
eq3(eX,z(A,B)) = eq2(c,d),
inference(paramod,[status(thm)],[c_31,c_116]) ).
fof(axiom_068,axiom,
! [VAR_0] : eq(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_068) ).
cnf(c_124,plain,
eq(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_068]) ).
fof(axiom_069,axiom,
! [VAR_0] : eq2(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_069) ).
cnf(c_125,plain,
eq2(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_069]) ).
fof(axiom_070,axiom,
! [VAR_0] : eq3(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_070) ).
cnf(c_126,plain,
eq3(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_070]) ).
fof(axiom_071,axiom,
! [VAR_0] : eq4(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_071) ).
cnf(c_127,plain,
eq4(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_071]) ).
fof(axiom_073,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( eq(cons(VAR_0,VAR_2),cons(VAR_1,VAR_3)) = eq(VAR_2,VAR_3)
| eq2(VAR_0,VAR_1) != btrue ),
file('theBenchmark.p',axiom_073) ).
cnf(c_130,plain,
( eq(cons(A,C),cons(B,D)) = eq(C,D)
| eq2(A,B) != btrue ),
inference(clausify,[status(thm)],[axiom_073]) ).
fof(goal,axiom,
! [VAR_0,VAR_1] : eq4(prop_unambig(VAR_0,VAR_1),bfalse) != btrue,
file('theBenchmark.p',goal) ).
cnf(c_135,plain,
eq4(prop_unambig(A,B),bfalse) != btrue,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_17369,plain,
eq4(impl(eq(lin(A),lin(B)),eq3(assoc(A),assoc(B))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_29,c_135]) ).
cnf(c_136,plain,
eq4(impl(eq(lin(A),lin(B)),eq3(assoc(A),assoc(B))),eq2(c,d)) != btrue,
inference(paramod,[status(thm)],[c_31,c_17369]) ).
cnf(c_17370,plain,
z(eX,assoc(A)) = assoc(z(eX,A)),
inference(paramod,[status(thm)],[c_12,c_7]) ).
cnf(c_137,plain,
assoc(z(eX,A)) = z(eX,assoc(A)),
inference(copy,[status(thm)],[c_17370]) ).
cnf(c_17371,plain,
x2(eX,assoc(A)) = assoc(x2(eX,A)),
inference(paramod,[status(thm)],[c_12,c_11]) ).
cnf(c_146,plain,
assoc(x2(eX,A)) = x2(eX,assoc(A)),
inference(copy,[status(thm)],[c_17371]) ).
cnf(c_154,plain,
append(lin(z(A,B)),cons(plus,linTerm(C))) = lin(z(z(A,B),C)),
inference(paramod,[status(thm)],[c_18,c_22]) ).
cnf(c_155,plain,
append(linTerm(A),cons(plus,lin(z(B,C)))) = lin(z(A,z(B,C))),
inference(paramod,[status(thm)],[c_18,c_22]) ).
cnf(c_156,plain,
append(lin(eX),cons(plus,linTerm(A))) = lin(z(eX,A)),
inference(paramod,[status(thm)],[c_19,c_22]) ).
cnf(c_157,plain,
append(linTerm(A),cons(plus,lin(eX))) = lin(z(A,eX)),
inference(paramod,[status(thm)],[c_19,c_22]) ).
cnf(c_17372,plain,
append(lin(eX),A) = cons(x,append(nil,A)),
inference(paramod,[status(thm)],[c_26,c_15]) ).
cnf(c_160,plain,
append(lin(eX),A) = cons(x,A),
inference(paramod,[status(thm)],[c_14,c_17372]) ).
cnf(c_161,plain,
cons(x,cons(plus,linTerm(A))) = lin(z(eX,A)),
inference(paramod,[status(thm)],[c_160,c_156]) ).
cnf(c_17373,plain,
eq2(c,d) = eq3(eX,z(A,B)),
inference(copy,[status(thm)],[c_117]) ).
cnf(c_188,plain,
eq3(x2(eX,A),x2(z(B,C),D)) = eq2(c,d),
inference(resolve,[status(thm)],[c_102,c_17373]) ).
cnf(c_201,plain,
eq3(z(A,B),z(A,C)) = eq3(B,C),
inference(resolve,[status(thm)],[c_100,c_126]) ).
cnf(c_232,plain,
eq(cons(A,B),cons(A,C)) = eq(B,C),
inference(resolve,[status(thm)],[c_130,c_125]) ).
cnf(c_247,plain,
x2(z(eX,assoc(A)),assoc(B)) = assoc(x2(z(eX,A),B)),
inference(paramod,[status(thm)],[c_137,c_11]) ).
cnf(c_249,plain,
eq4(impl(eq(lin(z(eX,A)),lin(B)),eq3(z(eX,assoc(A)),assoc(B))),eq2(c,d)) != btrue,
inference(paramod,[status(thm)],[c_137,c_136]) ).
cnf(c_17374,plain,
eq4(impl(eq(lin(z(eX,A)),lin(z(eX,B))),eq3(z(eX,assoc(A)),z(eX,assoc(B)))),eq2(c,d)) != btrue,
inference(paramod,[status(thm)],[c_137,c_249]) ).
cnf(c_453,plain,
eq4(impl(eq(lin(z(eX,A)),lin(z(eX,B))),eq3(assoc(A),assoc(B))),eq2(c,d)) != btrue,
inference(paramod,[status(thm)],[c_201,c_17374]) ).
cnf(c_17375,plain,
append(lin(eX),cons(plus,lin(z(A,B)))) = lin(z(eX,z(A,B))),
inference(paramod,[status(thm)],[c_19,c_155]) ).
cnf(c_593,plain,
cons(x,cons(plus,lin(z(A,B)))) = lin(z(eX,z(A,B))),
inference(paramod,[status(thm)],[c_160,c_17375]) ).
cnf(c_17376,plain,
append(lin(eX),cons(plus,lin(eX))) = lin(z(eX,eX)),
inference(paramod,[status(thm)],[c_19,c_157]) ).
cnf(c_613,plain,
cons(x,cons(plus,lin(eX))) = lin(z(eX,eX)),
inference(paramod,[status(thm)],[c_160,c_17376]) ).
cnf(c_707,plain,
eq(lin(z(eX,A)),cons(x,B)) = eq(cons(plus,linTerm(A)),B),
inference(paramod,[status(thm)],[c_161,c_232]) ).
cnf(c_1392,plain,
eq4(impl(eq(lin(z(eX,x2(eX,A))),lin(z(eX,B))),eq3(x2(eX,assoc(A)),assoc(B))),eq2(c,d)) != btrue,
inference(paramod,[status(thm)],[c_146,c_453]) ).
cnf(c_17377,plain,
append(lin(z(eX,eX)),A) = cons(x,append(cons(plus,lin(eX)),A)),
inference(paramod,[status(thm)],[c_613,c_15]) ).
cnf(c_17378,plain,
append(lin(z(eX,eX)),A) = cons(x,cons(plus,append(lin(eX),A))),
inference(paramod,[status(thm)],[c_15,c_17377]) ).
cnf(c_17379,plain,
append(lin(z(eX,eX)),A) = cons(x,cons(plus,cons(x,A))),
inference(paramod,[status(thm)],[c_160,c_17378]) ).
cnf(c_1502,plain,
cons(x,cons(plus,cons(x,A))) = append(lin(z(eX,eX)),A),
inference(copy,[status(thm)],[c_17379]) ).
cnf(c_17380,plain,
x2(z(eX,eX),assoc(A)) = assoc(x2(z(eX,eX),A)),
inference(paramod,[status(thm)],[c_12,c_247]) ).
cnf(c_1658,plain,
assoc(x2(z(eX,eX),A)) = x2(z(eX,eX),assoc(A)),
inference(copy,[status(thm)],[c_17380]) ).
cnf(c_17381,plain,
eq(lin(z(eX,A)),lin(z(eX,B))) = eq(cons(plus,linTerm(A)),cons(plus,linTerm(B))),
inference(paramod,[status(thm)],[c_161,c_707]) ).
cnf(c_3019,plain,
eq(lin(z(eX,A)),lin(z(eX,B))) = eq(linTerm(A),linTerm(B)),
inference(paramod,[status(thm)],[c_232,c_17381]) ).
cnf(c_3060,plain,
eq4(impl(eq(linTerm(x2(eX,A)),linTerm(B)),eq3(x2(eX,assoc(A)),assoc(B))),eq2(c,d)) != btrue,
inference(paramod,[status(thm)],[c_3019,c_1392]) ).
cnf(c_17382,plain,
eq4(impl(eq(linTerm(x2(eX,A)),linTerm(x2(z(eX,eX),B))),eq3(x2(eX,assoc(A)),x2(z(eX,eX),assoc(B)))),eq2(c,d)) != btrue,
inference(paramod,[status(thm)],[c_1658,c_3060]) ).
cnf(c_6679,plain,
eq4(impl(eq(linTerm(x2(eX,A)),linTerm(x2(z(eX,eX),B))),eq2(c,d)),eq2(c,d)) != btrue,
inference(paramod,[status(thm)],[c_188,c_17382]) ).
cnf(c_17383,plain,
cons(x,cons(plus,cons(x,cons(plus,linTerm(A))))) = lin(z(z(eX,eX),A)),
inference(paramod,[status(thm)],[c_154,c_1502]) ).
cnf(c_17384,plain,
cons(x,cons(plus,lin(z(eX,A)))) = lin(z(z(eX,eX),A)),
inference(paramod,[status(thm)],[c_161,c_17383]) ).
cnf(c_17385,plain,
lin(z(eX,z(eX,A))) = lin(z(z(eX,eX),A)),
inference(paramod,[status(thm)],[c_593,c_17384]) ).
cnf(c_6997,plain,
lin(z(z(eX,eX),A)) = lin(z(eX,z(eX,A))),
inference(copy,[status(thm)],[c_17385]) ).
cnf(c_17386,plain,
cons(c,append(lin(z(eX,z(eX,A))),cons(d,nil))) = linTerm(x2(z(eX,eX),A)),
inference(paramod,[status(thm)],[c_6997,c_17]) ).
cnf(c_17387,plain,
linTerm(x2(eX,z(eX,A))) = linTerm(x2(z(eX,eX),A)),
inference(paramod,[status(thm)],[c_17,c_17386]) ).
cnf(c_7190,plain,
linTerm(x2(z(eX,eX),A)) = linTerm(x2(eX,z(eX,A))),
inference(copy,[status(thm)],[c_17387]) ).
cnf(c_7201,plain,
eq4(impl(eq(linTerm(x2(eX,A)),linTerm(x2(eX,z(eX,B)))),eq2(c,d)),eq2(c,d)) != btrue,
inference(paramod,[status(thm)],[c_7190,c_6679]) ).
cnf(c_17388,plain,
eq4(impl(btrue,eq2(c,d)),eq2(c,d)) != btrue,
inference(paramod,[status(thm)],[c_124,c_7201]) ).
cnf(c_17389,plain,
eq4(eq2(c,d),eq2(c,d)) != btrue,
inference(paramod,[status(thm)],[c_1,c_17388]) ).
cnf(c_17390,plain,
btrue != btrue,
inference(paramod,[status(thm)],[c_127,c_17389]) ).
cnf(c_17362,plain,
$false,
inference(copy,[status(thm)],[c_17390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX185-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 16:51:37 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 2192404 was started by sandbox on n004,
% 0.09/0.37 % Sat Sep 26 16:51:37 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 42.29/5.74
% 42.29/5.74 % given #500 (F,wt=49): 3323 eq4(impl(eq(linTerm(x2(eX,A)),linTerm(x2(eY,eY))),eq2(c,d)),eq2(c,d)) != btrue. [para(146(a,1),3203(a,1,1,2,1)),rewrite([167(15)])].
% 42.29/5.74
% 42.29/5.74 % SZS status Unsatisfiable for theBenchmark
% 42.29/5.74
% 42.29/5.74 % Proof 1 at 4.48 (+ 0.82) seconds.
% 42.29/5.74 % Length of proof is 58.
% 42.29/5.74 % Level of proof is 9.
% 42.29/5.74 % Maximum clause weight is 60.000.
% 42.29/5.74 % Given clauses 959.
% 42.29/5.74
% 42.29/5.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------