%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYO629-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 : Fri Sep 25 03:48:33 PM UTC 2026
% Result : Unsatisfiable 4.28s 1.18s
% Output : Proof 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 19 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 84 ( 35 ~; 49 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 48 ( 3 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
( qtd2(f(B_0),qtd1)
| qtd0(qtd1,f(B_0))
| ~ iLEQ(A_1,B_0)
| ~ qtd2(f(A_1),s(qtd1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10_06) ).
fof(f5_nnf,plain,
! [A_1,B_0] :
( qtd2(f(B_0),qtd1)
| qtd0(qtd1,f(B_0))
| ~ iLEQ(A_1,B_0)
| ~ qtd2(f(A_1),s(qtd1)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A_1,B_0] :
( qtd2(f(B_0),qtd1)
| qtd0(qtd1,f(B_0))
| ~ iLEQ(A_1,B_0)
| ~ qtd2(f(A_1),s(qtd1)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( qtd2(f(X1),qtd1)
| qtd0(qtd1,f(X1))
| ~ iLEQ(X0,X1)
| ~ qtd2(f(X0),s(qtd1)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f3,axiom,
( qtd2(f(A),s(qtd1))
| qtd0(s(qtd1),f(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6_04) ).
fof(f3_nnf,plain,
! [A] :
( qtd2(f(A),s(qtd1))
| qtd0(s(qtd1),f(A)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] :
( qtd2(f(A),s(qtd1))
| qtd0(s(qtd1),f(A)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( qtd2(f(X0),s(qtd1))
| qtd0(s(qtd1),f(X0)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p12,plain,
( qtd0(s(qtd1),f(X0))
| qtd2(f(X1),qtd1)
| qtd0(qtd1,f(X1))
| ~ iLEQ(X0,X1) ),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(f8,axiom,
iLEQ(A_3,g(A_3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3_09) ).
fof(f8_nnf,plain,
! [A_3] : iLEQ(A_3,g(A_3)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A_3] : iLEQ(A_3,g(A_3)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
iLEQ(X0,g(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p14,plain,
( qtd0(s(qtd1),f(X0))
| qtd2(f(g(X0)),qtd1)
| qtd0(qtd1,f(g(X0))) ),
inference(resolution,[status(thm)],[p12,c8]) ).
cnf(f4,axiom,
~ qtd2(f(A_3),qtd1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_05) ).
fof(f4_nnf,plain,
! [A_3] : ~ qtd2(f(A_3),qtd1),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A_3] : ~ qtd2(f(A_3),qtd1),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ qtd2(f(X0),qtd1),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p16,plain,
( qtd0(s(qtd1),f(X0))
| qtd0(qtd1,f(g(X0))) ),
inference(resolution,[status(thm)],[p14,c4]) ).
cnf(f6,axiom,
( qtd0(f(A_2),f(g(A_2)))
| ~ qtd0(s(qtd1),f(g(A_2)))
| ~ qtd0(s(qtd1),f(A_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_07) ).
fof(f6_nnf,plain,
! [A_2] :
( qtd0(f(A_2),f(g(A_2)))
| ~ qtd0(s(qtd1),f(g(A_2)))
| ~ qtd0(s(qtd1),f(A_2)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A_2] :
( qtd0(f(A_2),f(g(A_2)))
| ~ qtd0(s(qtd1),f(g(A_2)))
| ~ qtd0(s(qtd1),f(A_2)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( qtd0(f(X0),f(g(X0)))
| ~ qtd0(s(qtd1),f(g(X0)))
| ~ qtd0(s(qtd1),f(X0)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p17,plain,
( qtd0(f(X0),f(g(X0)))
| ~ qtd0(s(qtd1),f(g(X0)))
| qtd0(qtd1,f(g(X0))) ),
inference(resolution,[status(thm)],[p16,c6]) ).
cnf(f1,axiom,
iLEQ(A_3,A_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_0_02) ).
fof(f1_nnf,plain,
! [A_3] : iLEQ(A_3,A_3),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A_3] : iLEQ(A_3,A_3),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
iLEQ(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p13,plain,
( qtd0(s(qtd1),f(X0))
| qtd2(f(X0),qtd1)
| qtd0(qtd1,f(X0)) ),
inference(resolution,[status(thm)],[p12,c1]) ).
cnf(p18,plain,
( qtd2(f(g(X0)),qtd1)
| qtd0(qtd1,f(g(X0)))
| qtd0(f(X0),f(g(X0)))
| qtd0(qtd1,f(g(X0))) ),
inference(resolution,[status(thm)],[p17,p13]) ).
cnf(p26,plain,
( qtd2(f(g(X0)),qtd1)
| qtd0(f(X0),f(g(X0)))
| qtd0(qtd1,f(g(X0))) ),
inference(factoring,[status(thm)],[p18]) ).
cnf(f0,axiom,
~ qtd0(f(A_3),f(g(A_3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8_01) ).
fof(f0_nnf,plain,
! [A_3] : ~ qtd0(f(A_3),f(g(A_3))),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A_3] : ~ qtd0(f(A_3),f(g(A_3))),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ qtd0(f(X0),f(g(X0))),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p27,plain,
( qtd2(f(g(X0)),qtd1)
| qtd0(qtd1,f(g(X0))) ),
inference(resolution,[status(thm)],[p26,c0]) ).
cnf(p28,plain,
qtd0(qtd1,f(g(X0))),
inference(resolution,[status(thm)],[p27,c4]) ).
cnf(f2,axiom,
( qtd0(f(A_3),f(g(A_3)))
| ~ qtd0(qtd1,f(g(A_3)))
| ~ qtd0(qtd1,f(A_3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11_03) ).
fof(f2_nnf,plain,
! [A_3] :
( qtd0(f(A_3),f(g(A_3)))
| ~ qtd0(qtd1,f(g(A_3)))
| ~ qtd0(qtd1,f(A_3)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A_3] :
( qtd0(f(A_3),f(g(A_3)))
| ~ qtd0(qtd1,f(g(A_3)))
| ~ qtd0(qtd1,f(A_3)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( qtd0(f(X0),f(g(X0)))
| ~ qtd0(qtd1,f(g(X0)))
| ~ qtd0(qtd1,f(X0)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p29,plain,
( qtd0(f(g(X0)),f(g(g(X0))))
| ~ qtd0(qtd1,f(g(g(X0)))) ),
inference(resolution,[status(thm)],[p28,c2]) ).
cnf(p30,plain,
qtd0(f(g(X0)),f(g(g(X0)))),
inference(resolution,[status(thm)],[p29,p28]) ).
cnf(p31,plain,
$false,
inference(resolution,[status(thm)],[p30,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO629-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 03:17:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.28/1.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.28/1.18 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------