%------------------------------------------------------------------------------
% 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 : n027.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 : Theorem 3.48s 1.95s
% Output : CNFRefutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 3 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 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 : 19 ( 19 usr; 6 con; 0-2 aty)
% Number of variables : 25 ( 23 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ cons > c2 > append > #nlpp > tail > proj2C > proj1C > proj1BP > proj1AP > linP > linC > head > bP > aP > pE > pB > pA > nil > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(linC,type,
linC: $i > $i ).
tff(a,type,
a: $i ).
tff(pE,type,
pE: $i ).
tff(proj1C,type,
proj1C: $i > $i ).
tff(proj1AP,type,
proj1AP: $i > $i ).
tff(c2,type,
c2: ( $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(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(tail,type,
tail: $i > $i ).
tff(proj2C,type,
proj2C: $i > $i ).
tff(proj1BP,type,
proj1BP: $i > $i ).
tff(head,type,
head: $i > $i ).
tff(nil,type,
nil: $i ).
tff(f_64,axiom,
pB != pE,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
tff(f_66,axiom,
! [X,X2] : ( proj1C(c2(X,X2)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
tff(f_81,axiom,
! [P,Q] : ( linC(c2(P,Q)) = append(linP(P),linP(Q)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
tff(f_70,axiom,
! [Y] : ( append(nil,Y) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
tff(f_79,axiom,
linP(pE) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
tff(f_78,axiom,
linP(pB) = cons(b,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
tff(f_76,axiom,
! [Q] : ( linP(bP(Q)) = append(cons(b,nil),append(linP(Q),cons(b,nil))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
tff(f_87,negated_conjecture,
~ ? [U,V] :
~ ( ( linC(U) = linC(V) )
=> ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_027) ).
tff(c_32,plain,
pE != pB,
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_34,plain,
! [X_17,X2_18] : ( proj1C(c2(X_17,X2_18)) = X_17 ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_52,plain,
! [P_27,Q_28] : ( append(linP(P_27),linP(Q_28)) = linC(c2(P_27,Q_28)) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_38,plain,
! [Y_21] : ( append(nil,Y_21) = Y_21 ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_50,plain,
linP(pE) = nil,
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_177,plain,
! [P_54,Q_55] : ( append(linP(P_54),linP(Q_55)) = linC(c2(P_54,Q_55)) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_186,plain,
! [Q_55] : ( append(nil,linP(Q_55)) = linC(c2(pE,Q_55)) ),
inference(superposition,[status(thm),theory(equality)],[c_50,c_177]) ).
tff(c_192,plain,
! [Q_55] : ( linC(c2(pE,Q_55)) = linP(Q_55) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_186]) ).
tff(c_48,plain,
cons(b,nil) = linP(pB),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_44,plain,
! [Q_26] : ( append(cons(b,nil),append(linP(Q_26),cons(b,nil))) = linP(bP(Q_26)) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_229,plain,
! [Q_61] : ( append(linP(pB),linC(c2(Q_61,pB))) = linP(bP(Q_61)) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_48,c_48,c_44]) ).
tff(c_239,plain,
append(linP(pB),linP(pB)) = linP(bP(pE)),
inference(superposition,[status(thm),theory(equality)],[c_192,c_229]) ).
tff(c_242,plain,
linP(bP(pE)) = linC(c2(pB,pB)),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_239]) ).
tff(c_193,plain,
! [Q_56] : ( linC(c2(pE,Q_56)) = linP(Q_56) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_186]) ).
tff(c_54,plain,
! [V_30,U_29] :
( ( V_30 = U_29 )
| ( linC(V_30) != linC(U_29) ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_199,plain,
! [Q_56,U_29] :
( ( c2(pE,Q_56) = U_29 )
| ( linP(Q_56) != linC(U_29) ) ),
inference(superposition,[status(thm),theory(equality)],[c_193,c_54]) ).
tff(c_245,plain,
! [U_29] :
( ( c2(pE,bP(pE)) = U_29 )
| ( linC(c2(pB,pB)) != linC(U_29) ) ),
inference(superposition,[status(thm),theory(equality)],[c_242,c_199]) ).
tff(c_468,plain,
c2(pE,bP(pE)) = c2(pB,pB),
inference(reflexivity,[status(thm),theory(equality)],[c_245]) ).
tff(c_488,plain,
proj1C(c2(pB,pB)) = pE,
inference(superposition,[status(thm),theory(equality)],[c_468,c_34]) ).
tff(c_507,plain,
pE = pB,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_488]) ).
tff(c_509,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWX207+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.14 % 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
% 0.17/0.35 % Computer : n027.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue May 5 11:35:34 EDT 2026
% 0.17/0.35 % CPUTime :
% 3.48/1.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.48/1.95
% 3.48/1.95 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------