%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWX207-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n006.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 06:56:36 PM UTC 2026
% Result : Unsatisfiable 21.63s 11.05s
% Output : CNFRefutation 21.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 52 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-2 aty)
% Number of variables : 66 ( 66 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ unambig > impl > eq5 > eq4 > eq3 > eq2 > eq > cons > c2 > append > #nlpp > linP > linC > bP > aP > pE > pB > pA > nil > btrue > bfalse > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(eq,type,
eq: ( $i * $i ) > $i ).
tff(eq3,type,
eq3: ( $i * $i ) > $i ).
tff(linC,type,
linC: $i > $i ).
tff(a,type,
a: $i ).
tff(pE,type,
pE: $i ).
tff(c2,type,
c2: ( $i * $i ) > $i ).
tff(unambig,type,
unambig: ( $i * $i ) > $i ).
tff(linP,type,
linP: $i > $i ).
tff(b,type,
b: $i ).
tff(pB,type,
pB: $i ).
tff(pA,type,
pA: $i ).
tff(eq4,type,
eq4: ( $i * $i ) > $i ).
tff(impl,type,
impl: ( $i * $i ) > $i ).
tff(append,type,
append: ( $i * $i ) > $i ).
tff(aP,type,
aP: $i > $i ).
tff(cons,type,
cons: ( $i * $i ) > $i ).
tff(bP,type,
bP: $i > $i ).
tff(eq5,type,
eq5: ( $i * $i ) > $i ).
tff(bfalse,type,
bfalse: $i ).
tff(eq2,type,
eq2: ( $i * $i ) > $i ).
tff(nil,type,
nil: $i ).
tff(btrue,type,
btrue: $i ).
tff(f_102,axiom,
! [X] : ( eq5(X,X) = btrue ),
file(unknown,unknown) ).
tff(f_23,axiom,
! [Q] : ( impl(btrue,Q) = Q ),
file(unknown,unknown) ).
tff(f_94,axiom,
! [X] : ( eq(X,X) = btrue ),
file(unknown,unknown) ).
tff(f_36,axiom,
linP(pE) = nil,
file(unknown,unknown) ).
tff(f_46,axiom,
eq3(pB,pE) = bfalse,
file(unknown,unknown) ).
tff(f_96,axiom,
! [X] : ( eq2(X,X) = btrue ),
file(unknown,unknown) ).
tff(f_38,axiom,
! [P,Q] : ( linC(c2(P,Q)) = append(linP(P),linP(Q)) ),
file(unknown,unknown) ).
tff(f_35,axiom,
linP(pB) = cons(b,nil),
file(unknown,unknown) ).
tff(f_27,axiom,
! [Y] : ( append(nil,Y) = Y ),
file(unknown,unknown) ).
tff(f_29,axiom,
! [Z,Xs,Y] : ( append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)) ),
file(unknown,unknown) ).
tff(f_112,axiom,
! [X,Z,Y,X2] :
( ( eq2(X,Z) != btrue )
| ( eq(cons(X,Y),cons(Z,X2)) = eq(Y,X2) ) ),
file(unknown,unknown) ).
tff(f_87,axiom,
! [X,Z,Y,X2] :
( ( eq3(X,Z) != bfalse )
| ( eq4(c2(X,Y),c2(Z,X2)) = bfalse ) ),
file(unknown,unknown) ).
tff(f_40,axiom,
! [X,Y] : ( unambig(X,Y) = impl(eq(linC(X),linC(Y)),eq4(X,Y)) ),
file(unknown,unknown) ).
tff(f_119,axiom,
! [X,Y] : ( eq5(unambig(X,Y),bfalse) != btrue ),
file(unknown,unknown) ).
tff(c_88,plain,
! [X_45] : ( eq5(X_45,X_45) = btrue ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_2,plain,
! [Q_1] : ( impl(btrue,Q_1) = Q_1 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_80,plain,
! [X_41] : ( eq(X_41,X_41) = btrue ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_18,plain,
linP(pE) = nil,
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_34,plain,
eq3(pB,pE) = bfalse,
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_82,plain,
! [X_42] : ( eq2(X_42,X_42) = btrue ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_20,plain,
! [P_9,Q_10] : ( append(linP(P_9),linP(Q_10)) = linC(c2(P_9,Q_10)) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_16,plain,
cons(b,nil) = linP(pB),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_6,plain,
! [Y_3] : ( append(nil,Y_3) = Y_3 ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_453,plain,
! [Z_99,Xs_100,Y_101] : ( cons(Z_99,append(Xs_100,Y_101)) = append(cons(Z_99,Xs_100),Y_101) ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_859,plain,
! [Z_140,Y_141] : ( append(cons(Z_140,nil),Y_141) = cons(Z_140,Y_141) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_453]) ).
tff(c_970,plain,
! [Y_145] : ( append(linP(pB),Y_145) = cons(b,Y_145) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_859]) ).
tff(c_1001,plain,
! [Q_10] : ( cons(b,linP(Q_10)) = linC(c2(pB,Q_10)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_970]) ).
tff(c_766,plain,
! [X_130,Y_131,Z_132,X2_133] :
( ( eq(cons(X_130,Y_131),cons(Z_132,X2_133)) = eq(Y_131,X2_133) )
| ( eq2(X_130,Z_132) != btrue ) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_2187,plain,
! [X_240,Y_241] :
( ( eq(cons(X_240,Y_241),linP(pB)) = eq(Y_241,nil) )
| ( eq2(X_240,b) != btrue ) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_766]) ).
tff(c_2214,plain,
! [Q_10] :
( ( eq(linC(c2(pB,Q_10)),linP(pB)) = eq(linP(Q_10),nil) )
| ( eq2(b,b) != btrue ) ),
inference(superposition,[status(thm),theory(equality)],[c_1001,c_2187]) ).
tff(c_2231,plain,
! [Q_10] : ( eq(linC(c2(pB,Q_10)),linP(pB)) = eq(linP(Q_10),nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_2214]) ).
tff(c_388,plain,
! [P_94,Q_95] : ( append(linP(P_94),linP(Q_95)) = linC(c2(P_94,Q_95)) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_397,plain,
! [Q_95] : ( append(nil,linP(Q_95)) = linC(c2(pE,Q_95)) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_388]) ).
tff(c_403,plain,
! [Q_95] : ( linC(c2(pE,Q_95)) = linP(Q_95) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_397]) ).
tff(c_632,plain,
! [X_115,Y_116,Z_117,X2_118] :
( ( eq4(c2(X_115,Y_116),c2(Z_117,X2_118)) = bfalse )
| ( eq3(X_115,Z_117) != bfalse ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_22,plain,
! [X_11,Y_12] : ( impl(eq(linC(X_11),linC(Y_12)),eq4(X_11,Y_12)) = unambig(X_11,Y_12) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_5455,plain,
! [X_372,Y_373,Z_374,X2_375] :
( ( impl(eq(linC(c2(X_372,Y_373)),linC(c2(Z_374,X2_375))),bfalse) = unambig(c2(X_372,Y_373),c2(Z_374,X2_375)) )
| ( eq3(X_372,Z_374) != bfalse ) ),
inference(superposition,[status(thm),theory(equality)],[c_632,c_22]) ).
tff(c_11977,plain,
! [X_687,Y_688,Q_689] :
( ( impl(eq(linC(c2(X_687,Y_688)),linP(Q_689)),bfalse) = unambig(c2(X_687,Y_688),c2(pE,Q_689)) )
| ( eq3(X_687,pE) != bfalse ) ),
inference(superposition,[status(thm),theory(equality)],[c_403,c_5455]) ).
tff(c_12058,plain,
! [Q_10] :
( ( unambig(c2(pB,Q_10),c2(pE,pB)) = impl(eq(linP(Q_10),nil),bfalse) )
| ( eq3(pB,pE) != bfalse ) ),
inference(superposition,[status(thm),theory(equality)],[c_2231,c_11977]) ).
tff(c_40492,plain,
! [Q_1358] : ( unambig(c2(pB,Q_1358),c2(pE,pB)) = impl(eq(linP(Q_1358),nil),bfalse) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_12058]) ).
tff(c_98,plain,
! [X_58,Y_59] : ( eq5(unambig(X_58,Y_59),bfalse) != btrue ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_40535,plain,
! [Q_1359] : ( eq5(impl(eq(linP(Q_1359),nil),bfalse),bfalse) != btrue ),
inference(superposition,[status(thm),theory(equality)],[c_40492,c_98]) ).
tff(c_40553,plain,
eq5(impl(eq(nil,nil),bfalse),bfalse) != btrue,
inference(superposition,[status(thm),theory(equality)],[c_18,c_40535]) ).
tff(c_40564,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2,c_80,c_40553]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX207-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.16/0.34 % Computer : n006.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 11:36:30 EDT 2026
% 0.16/0.34 % CPUTime :
% 21.63/11.05 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.63/11.06
% 21.63/11.06 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------