%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 06:48:05 AM UTC 2026
% Result : Theorem 37.32s 6.94s
% Output : CNFRefutation 37.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 83 ( 75 unt; 0 def)
% Number of atoms : 97 ( 81 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 9 ~; 6 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
! [X0,X1,X2] : times(times(X0,X1),X2) = times(X1,times(X2,X0)) ).
fof(axiom_2,axiom,
! [X0] :
( element(X0)
<=> ? [X1] :
( times(X0,X0) = X1
& times(X0,X1) = X0 ) ) ).
fof(conjecture_1,conjecture,
! [X0,X1,X2] :
( ( X2 = times(X0,X1)
& element(X1)
& element(X0) )
=> element(X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( X2 = times(X0,X1)
& element(X1)
& element(X0) )
=> element(X2) ),
inference(negate_conjecture,[status(cth)],[conjecture_1]) ).
cnf(c0,plain,
times(X0,times(X1,X2)) = times(times(X2,X0),X1),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c1,plain,
( times(X0,sK4(X0)) = X0
| ~ element(X0) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c2,plain,
( times(X0,X0) = sK4(X0)
| ~ element(X0) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c3,plain,
( times(X0,X0) != X1
| times(X0,X1) != X0
| element(X0) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c4,plain,
element(sK7),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c5,plain,
times(sK6,sK7) = sK8,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c6,plain,
element(sK6),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c7,plain,
~ element(sK8),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( element(X0)
| times(X0,times(X0,X0)) != X0 ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(d1,plain,
times(sK7,sK7) = sK4(sK7),
inference(resolution,[status(thm)],[c2,c4]) ).
cnf(d2,plain,
times(sK7,sK4(sK7)) = sK7,
inference(resolution,[status(thm)],[c1,c4]) ).
cnf(d3,plain,
times(sK4(sK7),times(X0,sK7)) = times(sK7,X0),
inference(superposition,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
times(times(X0,sK7),times(X1,sK4(sK7))) = times(times(sK7,X0),X1),
inference(superposition,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
times(sK7,times(times(X1,sK4(sK7)),X0)) = times(times(sK7,X0),X1),
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
times(sK7,times(sK4(sK7),times(X1,X0))) = times(times(sK7,X1),X0),
inference(demodulation,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
times(sK7,times(sK4(sK7),times(X0,X1))) = times(X0,times(X1,sK7)),
inference(demodulation,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
times(sK7,times(sK7,X0)) = times(X0,times(sK7,sK7)),
inference(superposition,[status(thm)],[d3,d7]) ).
cnf(d9,plain,
times(sK7,times(sK7,X0)) = times(X0,sK4(sK7)),
inference(demodulation,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
times(sK7,times(X0,sK6)) = times(sK8,X0),
inference(superposition,[status(thm)],[c5,c0]) ).
cnf(d11,plain,
times(sK7,times(X1,times(sK6,X0))) = times(sK8,times(X0,X1)),
inference(superposition,[status(thm)],[c0,d10]) ).
cnf(d12,plain,
times(sK7,times(X0,sK8)) = times(sK8,times(sK7,X0)),
inference(superposition,[status(thm)],[c5,d11]) ).
cnf(d13,plain,
times(sK7,times(X0,sK7)) = times(sK4(sK7),X0),
inference(superposition,[status(thm)],[d1,c0]) ).
cnf(d14,plain,
times(sK7,sK8) = times(sK4(sK7),sK6),
inference(superposition,[status(thm)],[c5,d13]) ).
cnf(d15,plain,
times(sK6,times(X0,sK4(sK7))) = times(times(sK7,sK8),X0),
inference(superposition,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
times(sK6,times(X0,sK4(sK7))) = times(sK8,times(X0,sK7)),
inference(demodulation,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
times(sK7,sK4(sK7)) = times(sK4(sK7),sK7),
inference(superposition,[status(thm)],[d1,d13]) ).
cnf(d18,plain,
sK7 = times(sK4(sK7),sK7),
inference(demodulation,[status(thm)],[d17,d2]) ).
cnf(d19,plain,
times(sK4(sK7),sK7) = times(sK7,sK4(sK7)),
inference(superposition,[status(thm)],[d18,d3]) ).
cnf(d20,plain,
sK7 = times(sK7,sK4(sK7)),
inference(demodulation,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
times(sK6,sK7) = times(sK8,times(sK7,sK7)),
inference(superposition,[status(thm)],[d20,d16]) ).
cnf(d22,plain,
sK8 = times(sK8,times(sK7,sK7)),
inference(demodulation,[status(thm)],[d21,c5]) ).
cnf(d23,plain,
sK8 = times(sK7,times(sK7,sK8)),
inference(demodulation,[status(thm)],[d22,d12]) ).
cnf(d24,plain,
sK8 = times(sK8,sK4(sK7)),
inference(demodulation,[status(thm)],[d23,d9]) ).
cnf(d25,plain,
times(sK7,times(X0,sK4(sK7))) = times(sK7,X0),
inference(superposition,[status(thm)],[d18,c0]) ).
cnf(d26,plain,
times(sK6,sK6) = sK4(sK6),
inference(resolution,[status(thm)],[c2,c6]) ).
cnf(d27,plain,
times(sK6,times(X0,sK6)) = times(sK4(sK6),X0),
inference(superposition,[status(thm)],[d26,c0]) ).
cnf(d28,plain,
times(sK6,sK4(sK6)) = sK6,
inference(resolution,[status(thm)],[c1,c6]) ).
cnf(d29,plain,
times(sK6,sK4(sK6)) = times(sK4(sK6),sK6),
inference(superposition,[status(thm)],[d26,d27]) ).
cnf(d30,plain,
sK6 = times(sK4(sK6),sK6),
inference(demodulation,[status(thm)],[d29,d28]) ).
cnf(d31,plain,
times(sK6,times(X0,sK4(sK6))) = times(sK6,X0),
inference(superposition,[status(thm)],[d30,c0]) ).
cnf(d32,plain,
times(sK7,sK4(sK6)) = times(sK8,sK6),
inference(superposition,[status(thm)],[d26,d10]) ).
cnf(d33,plain,
times(sK6,times(sK8,sK6)) = times(sK6,sK7),
inference(superposition,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
times(sK4(sK6),sK8) = times(sK6,sK7),
inference(demodulation,[status(thm)],[d33,d27]) ).
cnf(d35,plain,
times(sK4(sK6),sK8) = sK8,
inference(demodulation,[status(thm)],[d34,c5]) ).
cnf(d36,plain,
times(sK4(sK6),times(X0,sK7)) = times(times(sK8,sK6),X0),
inference(superposition,[status(thm)],[d32,c0]) ).
cnf(d37,plain,
times(sK4(sK6),times(X0,sK7)) = times(sK6,times(X0,sK8)),
inference(demodulation,[status(thm)],[d36,c0]) ).
cnf(d38,plain,
times(sK4(sK6),sK8) = times(sK6,times(sK6,sK8)),
inference(superposition,[status(thm)],[c5,d37]) ).
cnf(d39,plain,
sK8 = times(sK6,times(sK6,sK8)),
inference(demodulation,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
times(sK7,sK8) = times(sK8,times(sK8,sK6)),
inference(superposition,[status(thm)],[d39,d11]) ).
cnf(d41,plain,
times(sK8,times(X0,sK4(sK6))) = times(sK8,X0),
inference(superposition,[status(thm)],[d35,c0]) ).
cnf(d42,plain,
times(sK8,times(sK8,sK6)) = times(sK8,sK7),
inference(superposition,[status(thm)],[d32,d41]) ).
cnf(d43,plain,
times(sK7,sK8) = times(sK8,sK7),
inference(demodulation,[status(thm)],[d42,d40]) ).
cnf(d44,plain,
times(sK4(sK7),sK8) = times(sK7,sK6),
inference(superposition,[status(thm)],[c5,d3]) ).
cnf(d45,plain,
times(sK8,times(X0,sK4(sK7))) = times(times(sK7,sK6),X0),
inference(superposition,[status(thm)],[d44,c0]) ).
cnf(d46,plain,
times(sK8,times(X0,sK4(sK7))) = times(sK6,times(X0,sK7)),
inference(demodulation,[status(thm)],[d45,c0]) ).
cnf(d47,plain,
times(sK8,sK7) = times(sK6,times(sK7,sK7)),
inference(superposition,[status(thm)],[d20,d46]) ).
cnf(d48,plain,
times(sK8,sK7) = times(sK6,sK4(sK7)),
inference(demodulation,[status(thm)],[d47,d1]) ).
cnf(d49,plain,
times(sK7,sK8) = times(sK6,sK4(sK7)),
inference(demodulation,[status(thm)],[d48,d43]) ).
cnf(d50,plain,
times(sK7,times(sK7,sK8)) = times(sK7,sK6),
inference(superposition,[status(thm)],[d49,d25]) ).
cnf(d51,plain,
times(sK7,times(sK7,sK8)) = times(sK8,sK4(sK7)),
inference(superposition,[status(thm)],[d14,d10]) ).
cnf(d52,plain,
times(sK7,sK6) = times(sK8,sK4(sK7)),
inference(demodulation,[status(thm)],[d51,d50]) ).
cnf(d53,plain,
times(sK7,sK6) = sK8,
inference(demodulation,[status(thm)],[d52,d24]) ).
cnf(d54,plain,
times(sK7,sK6) = times(sK8,sK4(sK6)),
inference(superposition,[status(thm)],[d30,d10]) ).
cnf(d55,plain,
sK8 = times(sK8,sK4(sK6)),
inference(demodulation,[status(thm)],[d54,d53]) ).
cnf(d56,plain,
times(sK7,times(sK7,sK8)) = times(sK4(sK7),sK8),
inference(superposition,[status(thm)],[d43,d13]) ).
cnf(d57,plain,
times(sK7,sK6) = times(sK4(sK7),sK8),
inference(demodulation,[status(thm)],[d56,d50]) ).
cnf(d58,plain,
sK8 = times(sK4(sK7),sK8),
inference(demodulation,[status(thm)],[d57,d53]) ).
cnf(d59,plain,
times(sK8,times(X0,sK4(sK7))) = times(sK8,X0),
inference(superposition,[status(thm)],[d58,c0]) ).
cnf(d60,plain,
times(sK6,times(X0,sK7)) = times(sK8,X0),
inference(superposition,[status(thm)],[d53,c0]) ).
cnf(d61,plain,
times(sK7,times(sK7,sK6)) = times(sK7,sK8),
inference(superposition,[status(thm)],[d52,d25]) ).
cnf(d62,plain,
times(sK8,sK7) = times(sK7,sK8),
inference(demodulation,[status(thm)],[d61,d10]) ).
cnf(d63,plain,
times(sK6,times(sK7,sK8)) = times(sK8,sK8),
inference(superposition,[status(thm)],[d62,d60]) ).
cnf(d64,plain,
times(sK6,times(sK7,sK8)) = times(sK4(sK6),sK4(sK7)),
inference(superposition,[status(thm)],[d14,d27]) ).
cnf(d65,plain,
times(sK8,sK8) = times(sK4(sK6),sK4(sK7)),
inference(demodulation,[status(thm)],[d64,d63]) ).
cnf(d66,plain,
times(sK8,times(sK8,sK8)) = times(sK8,sK4(sK6)),
inference(superposition,[status(thm)],[d65,d59]) ).
cnf(d67,plain,
times(sK8,times(sK8,sK8)) = sK8,
inference(demodulation,[status(thm)],[d66,d55]) ).
cnf(d68,plain,
( element(sK8)
| sK8 != sK8 ),
inference(superposition,[status(thm)],[d67,d0]) ).
cnf(d69,plain,
sK8 != sK8,
inference(resolution,[status(thm)],[c7,d68]) ).
cnf(d70,plain,
$false,
inference(equality_resolution,[status(thm)],[d69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n003.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Sat Sep 26 21:27:40 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.32/6.94 % SZS status Theorem for theBenchmark.p
% 37.32/6.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------