%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL893+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 02:03:18 PM UTC 2026
% Result : Theorem 35.63s 10.00s
% Output : Proof 35.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 78 ( 58 unt; 0 def)
% Number of atoms : 110 ( 61 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 26 ~; 20 |; 6 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 123 ( 15 sgn 47 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [A] : h(A) = qtd4(h(A),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_14) ).
fof(f13_nnf,plain,
! [A] : h(A) = qtd4(h(A),A),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A] : h(A) = qtd4(h(A),A),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
h(X0) = qtd4(h(X0),X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t10,plain,
qtd4(h(X1),X1) = h(X1),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t402,plain,
qtd4(h(X1),X1) = h(X1),
inference(orient,[status(thm)],[t10]) ).
fof(f14,conjecture,
! [X17] :
( h(X17) = X17
=> X17 = qtd1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
fof(f14_neg,negated_conjecture,
~ ! [X17] :
( h(X17) = X17
=> X17 = qtd1 ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X17] :
( X17 != qtd1
& h(X17) = X17 ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( sk0 != qtd1
& h(sk0) = sk0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f14_nnf]) ).
cnf(c15,plain,
h(sk0) = sk0,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t0,plain,
h(sk0) = sk0,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t936,plain,
h(sk0) = sk0,
inference(orient,[status(thm)],[t0]) ).
cnf(t937,plain,
h(sk0) = qtd4(sk0,sk0),
inference(cp,[status(thm)],[t402,t936]) ).
cnf(t1019,plain,
sk0 = qtd4(sk0,sk0),
inference(step,[status(thm)],[t937,t936]) ).
fof(f7,axiom,
! [X5,X6,X7] :
( qtd3(qtd0(X5,X6),X7)
<=> qtd3(X6,qtd4(X5,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(f7_nnf,plain,
! [X5,X6,X7] :
( ( ~ qtd3(X6,qtd4(X5,X7))
| qtd3(qtd0(X5,X6),X7) )
& ( qtd3(X6,qtd4(X5,X7))
| ~ qtd3(qtd0(X5,X6),X7) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X5,X6,X7] :
( ( ~ qtd3(X6,qtd4(X5,X7))
| qtd3(qtd0(X5,X6),X7) )
& ( qtd3(X6,qtd4(X5,X7))
| ~ qtd3(qtd0(X5,X6),X7) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( qtd3(X1,qtd4(X0,X2))
| ~ qtd3(qtd0(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(qtd3(qtd0(X0,X1),X2),true,qtd3(X1,qtd4(X0,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f4,axiom,
! [A] : qtd3(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(f4_nnf,plain,
! [A] : qtd3(A,A),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A] : qtd3(A,A),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
qtd3(X0,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
qtd3(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h3,plain,
qtd3(V0,qtd4(V1,qtd0(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi4]) ).
fof(f8,axiom,
! [A] : qtd3(A,qtd1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(f8_nnf,plain,
! [A] : qtd3(A,qtd1),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A] : qtd3(A,qtd1),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c9,plain,
qtd3(X0,qtd1),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi9,axiom,
qtd3(X0,qtd1) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h7,plain,
qtd3(V0,qtd4(V1,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi9]) ).
fof(f6,axiom,
! [X3,X4] :
( ( qtd3(X4,X3)
& qtd3(X3,X4) )
=> X3 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(f6_nnf,plain,
! [X3,X4] :
( X3 = X4
| ~ qtd3(X4,X3)
| ~ qtd3(X3,X4) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X3,X4] :
( X3 = X4
| ~ qtd3(X4,X3)
| ~ qtd3(X3,X4) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( X0 = X1
| ~ qtd3(X1,X0)
| ~ qtd3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(qtd3(X0,X1),true,ifeq(qtd3(X1,X0),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t68,plain,
qtd4(X1,qtd0(X1,qtd4(X2,qtd1))) = qtd4(X2,qtd1),
inference(hyper_resolution,[status(thm)],[hi6,h7,h3]) ).
cnf(h36,plain,
qtd3(V0,qtd4(V1,qtd4(V2,qtd0(V2,qtd0(V1,V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h3]) ).
fof(f11,axiom,
! [X14,X15,X16] :
( qtd3(X14,X15)
=> qtd3(qtd4(X16,X14),qtd4(X16,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(f11_nnf,plain,
! [X14,X15,X16] :
( qtd3(qtd4(X16,X14),qtd4(X16,X15))
| ~ qtd3(X14,X15) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X14,X15,X16] :
( qtd3(qtd4(X16,X14),qtd4(X16,X15))
| ~ qtd3(X14,X15) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c12,plain,
( qtd3(qtd4(X2,X0),qtd4(X2,X1))
| ~ qtd3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi12,axiom,
ifeq(qtd3(X0,X1),true,qtd3(qtd4(X2,X0),qtd4(X2,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h0,plain,
qtd3(qtd4(V0,V1),qtd4(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi4]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( qtd3(X1,X2)
& qtd3(X0,X1) )
=> qtd3(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(f5_nnf,plain,
! [X0,X1,X2] :
( qtd3(X0,X2)
| ~ qtd3(X1,X2)
| ~ qtd3(X0,X1) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X0,X1,X2] :
( qtd3(X0,X2)
| ~ qtd3(X1,X2)
| ~ qtd3(X0,X1) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( qtd3(X0,X2)
| ~ qtd3(X1,X2)
| ~ qtd3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(qtd3(X0,X1),true,ifeq(qtd3(X1,X2),true,qtd3(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h11,plain,
qtd3(qtd4(V0,V1),qtd1) = true,
inference(hyper_resolution,[status(thm)],[hi5,h0,hi9]) ).
cnf(t74,plain,
qtd4(X1,qtd4(X2,qtd0(X2,qtd0(X1,qtd1)))) = qtd1,
inference(hyper_resolution,[status(thm)],[hi6,h11,h36]) ).
fof(f2,axiom,
! [A] : qtd0(A,qtd1) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(f2_nnf,plain,
! [A] : qtd0(A,qtd1) = A,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] : qtd0(A,qtd1) = A,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
qtd0(X0,qtd1) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t1,plain,
qtd0(X1,qtd1) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t256,plain,
qtd0(X1,qtd1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t986,plain,
qtd4(X1,qtd4(X2,qtd0(X2,X1))) = qtd1,
inference(step,[status(thm)],[t74,t256]) ).
cnf(h489,plain,
qtd3(qtd4(V0,V1),qtd4(V2,qtd4(V3,qtd0(V3,qtd0(V2,qtd1))))) = true,
inference(hyper_resolution,[status(thm)],[hi5,h11,h36]) ).
cnf(h4,plain,
qtd3(qtd4(V0,V1),qtd4(V0,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi9]) ).
cnf(h8,plain,
qtd3(qtd4(V0,qtd4(V1,V2)),qtd4(V0,qtd4(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi12,h0]) ).
cnf(h72,plain,
qtd3(qtd4(V0,qtd4(V1,V2)),qtd4(V0,qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi5,h8,h4]) ).
cnf(t154,plain,
qtd4(X1,qtd4(X2,qtd0(X2,qtd0(X1,qtd1)))) = qtd4(X1,qtd1),
inference(hyper_resolution,[status(thm)],[hi6,h72,h489]) ).
cnf(t985,plain,
qtd4(X1,qtd4(X2,qtd0(X2,X1))) = qtd4(X1,qtd1),
inference(step,[status(thm)],[t154,t256]) ).
cnf(t267,plain,
qtd4(X1,qtd4(X2,qtd0(X2,X1))) = qtd4(X1,qtd1),
inference(orient,[status(thm)],[t985]) ).
cnf(t987,plain,
qtd4(X1,qtd1) = qtd1,
inference(step,[status(thm)],[t986,t267]) ).
cnf(t268,plain,
qtd4(X1,qtd1) = qtd1,
inference(orient,[status(thm)],[t987]) ).
cnf(t997,plain,
qtd4(X1,qtd0(X1,qtd1)) = qtd4(X2,qtd1),
inference(step,[status(thm)],[t68,t268]) ).
cnf(t998,plain,
qtd4(X1,X1) = qtd4(X2,qtd1),
inference(step,[status(thm)],[t997,t256]) ).
cnf(t999,plain,
qtd4(X1,X1) = qtd1,
inference(step,[status(thm)],[t998,t268]) ).
cnf(t337,plain,
qtd4(X1,X1) = qtd1,
inference(orient,[status(thm)],[t999]) ).
cnf(t1020,plain,
sk0 = qtd1,
inference(step,[status(thm)],[t1019,t337]) ).
cnf(t938,plain,
qtd1 = sk0,
inference(orient,[status(thm)],[t1020]) ).
cnf(c16,plain,
sk0 != qtd1,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(goal_0,negated_conjecture,
sk0 != qtd1,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(g0_0,plain,
sk0 != sk0,
inference(rw,[status(thm)],[goal_0,t938]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL893+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.36 % Computer : n026.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Thu Sep 24 00:41:59 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 35.63/10.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.63/10.00 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------