%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG069+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 12:53:20 PM UTC 2026
% Result : Theorem 3.69s 6.49s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 52 ( 10 unt; 0 def)
% Number of atoms : 163 ( 48 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 182 ( 71 ~; 62 |; 29 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 76 !; 4 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ? [X1] :
( op1(X1,X1) = X0
& sorti1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ? [X1] :
( op2(X1,X1) = X0
& sorti2(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f5,conjecture,
( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f6,negated_conjecture,
~ ( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f9,plain,
! [X0] :
( ~ sorti1(X0)
| ? [X1] :
( op1(X1,X1) = X0
& sorti1(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
? [X0] :
( sorti2(X0)
& ! [X1] :
( op2(X1,X1) != X0
| ~ sorti2(X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f11,plain,
( ! [X1] :
( ~ sorti2(X1)
| sorti1(j(X1)) )
& ! [X0] :
( ~ sorti1(X0)
| sorti2(h(X0)) )
& ! [X7] :
( ~ sorti1(X7)
| j(h(X7)) = X7 )
& ! [X6] :
( ~ sorti2(X6)
| h(j(X6)) = X6 )
& ! [X4] :
( ~ sorti2(X4)
| ! [X5] :
( ~ sorti2(X5)
| j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( ~ sorti1(X2)
| ! [X3] :
( ~ sorti1(X3)
| h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
( ! [X1] :
( ~ sorti2(X1)
| sorti1(j(X1)) )
& ! [X0] :
( ~ sorti1(X0)
| sorti2(h(X0)) )
& ! [X7] :
( ~ sorti1(X7)
| j(h(X7)) = X7 )
& ! [X6] :
( ~ sorti2(X6)
| h(j(X6)) = X6 )
& ! [X4] :
( ~ sorti2(X4)
| ! [X5] :
( ~ sorti2(X5)
| j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( ~ sorti1(X2)
| ! [X3] :
( ~ sorti1(X3)
| h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ~ sorti1(X0)
| ( op1(sK0(X0),sK0(X0)) = X0
& sorti1(sK0(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f9]) ).
fof(f14,plain,
( sorti2(sK1)
& ! [X1] :
( op2(X1,X1) != sK1
| ~ sorti2(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f10]) ).
fof(f15,plain,
( ! [X7] :
( ~ sorti2(X7)
| sorti1(j(X7)) )
& ! [X6] :
( ~ sorti1(X6)
| sorti2(h(X6)) )
& ! [X5] :
( ~ sorti1(X5)
| j(h(X5)) = X5 )
& ! [X4] :
( ~ sorti2(X4)
| h(j(X4)) = X4 )
& ! [X2] :
( ~ sorti2(X2)
| ! [X3] :
( ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3)) ) )
& ! [X0] :
( ~ sorti1(X0)
| ! [X1] :
( ~ sorti1(X1)
| h(op1(X0,X1)) = op2(h(X0),h(X1)) ) ) ),
inference(rectify,[],[f12]) ).
fof(f18,plain,
! [X0] :
( ~ sorti1(X0)
| op1(sK0(X0),sK0(X0)) = X0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
! [X0] :
( ~ sorti1(X0)
| sorti1(sK0(X0)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
! [X1] :
( op2(X1,X1) != sK1
| ~ sorti2(X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X7] :
( ~ sorti2(X7)
| sorti1(j(X7)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X6] :
( ~ sorti1(X6)
| sorti2(h(X6)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X5] :
( ~ sorti1(X5)
| j(h(X5)) = X5 ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X4] :
( ~ sorti2(X4)
| h(j(X4)) = X4 ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| h(op1(X0,X1)) = op2(h(X0),h(X1)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_51,plain,
! [X0: $i] :
( sorti1(sK0(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_52,plain,
! [X0: $i] :
( ( op1(sK0(X0),sK0(X0)) = X0 )
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_53,plain,
! [X0: $i] :
( ~ sorti2(X0)
| ( op2(X0,X0) != sK1 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_54,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f20]) ).
tcf(c_55,negated_conjecture,
! [X0: $i,X1: $i] :
( ( op2(h(X0),h(X1)) = h(op1(X0,X1)) )
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_57,negated_conjecture,
! [X0: $i] :
( ( h(j(X0)) = X0 )
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] :
( ( j(h(X0)) = X0 )
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_59,negated_conjecture,
! [X0: $i] :
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_60,negated_conjecture,
! [X0: $i] :
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_61,plain,
( sorti1(j(sK1))
| ~ sorti2(sK1) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_185,negated_conjecture,
! [X0: $i] :
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_186,negated_conjecture,
! [X0: $i] :
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_187,negated_conjecture,
! [X0: $i] :
( ( j(h(X0)) = X0 )
| ~ sorti1(X0) ),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_188,negated_conjecture,
! [X0: $i] :
( ( h(j(X0)) = X0 )
| ~ sorti2(X0) ),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_190,negated_conjecture,
! [X0: $i,X1: $i] :
( ( op2(h(X0),h(X1)) = h(op1(X0,X1)) )
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_469,plain,
h(j(sK1)) = sK1,
inference(superposition,[status(thm)],[c_54,c_188]) ).
tcf(c_479,plain,
! [X0: $i] :
( ( j(h(sK0(X0))) = sK0(X0) )
| ~ sorti1(X0) ),
inference(superposition,[status(thm)],[c_51,c_187]) ).
tcf(c_556,plain,
! [X0: $i] :
( ( op1(sK0(j(X0)),sK0(j(X0))) = j(X0) )
| ~ sorti2(X0) ),
inference(superposition,[status(thm)],[c_185,c_52]) ).
tcf(c_575,plain,
! [X0: $i] :
( ( j(h(sK0(j(X0)))) = sK0(j(X0)) )
| ~ sorti2(X0) ),
inference(superposition,[status(thm)],[c_185,c_479]) ).
tcf(c_589,plain,
! [X0: $i] :
( sorti1(sK0(j(X0)))
| ~ sorti1(j(X0)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_590,plain,
( sorti1(sK0(j(sK1)))
| ~ sorti1(j(sK1)) ),
inference(instantiation,[status(thm)],[c_589]) ).
tcf(c_634,plain,
j(h(sK0(j(sK1)))) = sK0(j(sK1)),
inference(superposition,[status(thm)],[c_54,c_575]) ).
tcf(c_651,plain,
! [X0: $i] :
( sorti2(h(sK0(j(X0))))
| ~ sorti1(sK0(j(X0))) ),
inference(instantiation,[status(thm)],[c_186]) ).
tcf(c_652,plain,
( sorti2(h(sK0(j(sK1))))
| ~ sorti1(sK0(j(sK1))) ),
inference(instantiation,[status(thm)],[c_651]) ).
tcf(c_676,plain,
op1(sK0(j(sK1)),sK0(j(sK1))) = j(sK1),
inference(superposition,[status(thm)],[c_54,c_556]) ).
tcf(c_747,plain,
( sorti1(sK0(j(sK1)))
| ~ sorti2(h(sK0(j(sK1)))) ),
inference(superposition,[status(thm)],[c_634,c_185]) ).
tcf(c_764,plain,
sorti1(sK0(j(sK1))),
inference(global_subsumption_just,[status(thm)],[c_747,c_54,c_61,c_590]) ).
tcf(c_766,plain,
! [X0: $i] :
( ( op2(h(X0),h(sK0(j(sK1)))) = h(op1(X0,sK0(j(sK1)))) )
| ~ sorti1(X0) ),
inference(superposition,[status(thm)],[c_764,c_190]) ).
tcf(c_1836,plain,
op2(h(sK0(j(sK1))),h(sK0(j(sK1)))) = h(op1(sK0(j(sK1)),sK0(j(sK1)))),
inference(superposition,[status(thm)],[c_764,c_766]) ).
tcf(c_1841,plain,
op2(h(sK0(j(sK1))),h(sK0(j(sK1)))) = sK1,
inference(light_normalisation,[status(thm)],[c_1836,c_469,c_676]) ).
tcf(c_2076,plain,
~ sorti2(h(sK0(j(sK1)))),
inference(superposition,[status(thm)],[c_1841,c_53]) ).
tcf(c_2077,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2076,c_652,c_590,c_61,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG069+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.57 % Computer : n006.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.57 % CPULimit : 300
% 0.09/5.57 % WCLimit : 300
% 0.09/5.57 % DateTime : Fri Sep 25 04:41:22 UTC 2026
% 0.09/5.58 % CPUTime :
% 0.09/5.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.61 Running first-order theorem proving
% 0.14/5.61 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.62
% 0.14/5.62 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.62
% 0.14/5.63 % Detected problem language: tptp
% 0.14/5.64 % Proving...
% 3.69/6.49 % SZS status Started for theBenchmark.p
% 3.69/6.49 % SZS status Theorem for theBenchmark.p
% 3.69/6.49
% 3.69/6.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.69/6.49
% 3.69/6.49 % ------ iProver source info
% 3.69/6.49
% 3.69/6.49 % git: date: 2026-07-19 20:42:38 +0200
% 3.69/6.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.69/6.49 % git: non_committed_changes: false
% 3.69/6.49
% 3.69/6.49 % ------ Parsing...
% 3.69/6.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.69/6.49
% 3.69/6.49 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.69/6.49
% 3.69/6.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.69/6.49
% 3.69/6.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.69/6.49 % ------ Proving...
% 3.69/6.49 % ------ Problem Properties
% 3.69/6.49
% 3.69/6.49 %
% 3.69/6.49 % clauses 12
% 3.69/6.49 % conjectures 6
% 3.69/6.49 % EPR 1
% 3.69/6.49 % Horn 12
% 3.69/6.49 % unary 1
% 3.69/6.49 % binary 7
% 3.69/6.49 % lits 27
% 3.69/6.49 % lits eq 6
% 3.69/6.49 % fd_pure 0
% 3.69/6.49 % fd_pseudo 0
% 3.69/6.49 % fd_cond 0
% 3.69/6.49 % fd_pseudo_cond 0
% 3.69/6.49 % AC symbols 0
% 3.69/6.49
% 3.69/6.49 % ------ Schedule dynamic 5 is on
% 3.69/6.49
% 3.69/6.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.69/6.49
% 3.69/6.49
% 3.69/6.49 % ------
% 3.69/6.49 % Current options:
% 3.69/6.49 % ------
% 3.69/6.49
% 3.69/6.49
% 3.69/6.49 %
% 3.69/6.49
% 3.69/6.49 % ------ Proving...
% 3.69/6.49 %
% 3.69/6.49
% 3.69/6.49 % SZS status Theorem for theBenchmark.p
% 3.69/6.49
% 3.69/6.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.69/6.49
% 3.69/6.49
%------------------------------------------------------------------------------