%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG019+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 12:53:11 PM UTC 2026
% Result : Theorem 4.24s 1.32s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 57 ( 12 unt; 0 def)
% Number of atoms : 177 ( 49 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 199 ( 79 ~; 67 |; 30 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 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 : 89 ( 0 sgn 84 !; 5 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f3,axiom,
~ ? [X0] :
( ! [X1] :
( sorti1(X1)
=> op1(X1,X1) = X0 )
& sorti1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ~ ? [X0] :
( ! [X1] :
( sorti2(X1)
=> op2(X1,X1) = X0 )
& sorti2(X0) ),
file('/export/starexec/sandbox/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/sandbox/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(f7,plain,
? [X0] :
( ! [X1] :
( sorti2(X1)
=> op2(X1,X1) = X0 )
& sorti2(X0) ),
inference(flattening,[],[f4]) ).
fof(f8,plain,
! [X0] :
( ~ sorti1(X0)
| ! [X1] :
( ~ sorti1(X1)
| sorti1(op1(X0,X1)) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f10,plain,
! [X0] :
( ? [X1] :
( sorti1(X1)
& op1(X1,X1) != X0 )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
? [X0] :
( ! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) = X0 )
& sorti2(X0) ),
inference(ennf_transformation,[],[f7]) ).
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(ennf_transformation,[],[f6]) ).
fof(f13,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,[],[f12]) ).
fof(f14,plain,
! [X0] :
( ( sorti1(sK0(X0))
& op1(sK0(X0),sK0(X0)) != X0 )
| ~ sorti1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f10]) ).
fof(f15,plain,
( ! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) = sK1 )
& sorti2(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f11]) ).
fof(f16,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,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| sorti1(op1(X0,X1)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f19,plain,
! [X0] :
( sorti1(sK0(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f20,plain,
! [X0] :
( op1(sK0(X0),sK0(X0)) != X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) = sK1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X7] :
( ~ sorti2(X7)
| sorti1(j(X7)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f24,plain,
! [X6] :
( ~ sorti1(X6)
| sorti2(h(X6)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X5] :
( ~ sorti1(X5)
| j(h(X5)) = X5 ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| h(op1(X0,X1)) = op2(h(X0),h(X1)) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_51,plain,
! [X0: $i] :
( ~ sorti1(X0)
| ( op1(sK0(X0),sK0(X0)) != X0 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_52,plain,
! [X0: $i] :
( sorti1(sK0(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_53,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f22]) ).
tcf(c_54,plain,
! [X0: $i] :
( ( op2(X0,X0) = sK1 )
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f21]) ).
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,[],[f28]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] :
( ( j(h(X0)) = X0 )
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_59,negated_conjecture,
! [X0: $i] :
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_60,negated_conjecture,
! [X0: $i] :
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f23]) ).
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_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_479,plain,
! [X0: $i] :
( ( j(h(sK0(X0))) = sK0(X0) )
| ~ sorti1(X0) ),
inference(superposition,[status(thm)],[c_52,c_187]) ).
tcf(c_499,plain,
! [X0: $i] :
( ( op2(h(X0),h(X0)) = sK1 )
| ~ sorti1(X0) ),
inference(superposition,[status(thm)],[c_186,c_54]) ).
tcf(c_512,plain,
! [X0: $i,X1: $i] :
( ( j(h(op1(X0,X1))) = op1(X0,X1) )
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(superposition,[status(thm)],[c_49,c_187]) ).
tcf(c_569,plain,
! [X0: $i] :
( ( j(h(sK0(j(X0)))) = sK0(j(X0)) )
| ~ sorti2(X0) ),
inference(superposition,[status(thm)],[c_185,c_479]) ).
tcf(c_583,plain,
! [X0: $i] :
( sorti1(sK0(j(X0)))
| ~ sorti1(j(X0)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_584,plain,
( sorti1(sK0(j(sK1)))
| ~ sorti1(j(sK1)) ),
inference(instantiation,[status(thm)],[c_583]) ).
tcf(c_659,plain,
j(h(sK0(j(sK1)))) = sK0(j(sK1)),
inference(superposition,[status(thm)],[c_53,c_569]) ).
tcf(c_747,plain,
( sorti1(sK0(j(sK1)))
| ~ sorti2(h(sK0(j(sK1)))) ),
inference(superposition,[status(thm)],[c_659,c_185]) ).
tcf(c_755,plain,
sorti1(sK0(j(sK1))),
inference(global_subsumption_just,[status(thm)],[c_747,c_53,c_61,c_584]) ).
tcf(c_757,plain,
! [X0: $i] :
( ( op2(h(X0),h(sK0(j(sK1)))) = h(op1(X0,sK0(j(sK1)))) )
| ~ sorti1(X0) ),
inference(superposition,[status(thm)],[c_755,c_190]) ).
tcf(c_759,plain,
op2(h(sK0(j(sK1))),h(sK0(j(sK1)))) = sK1,
inference(superposition,[status(thm)],[c_755,c_499]) ).
tcf(c_1021,plain,
! [X0: $i] :
( ( j(h(op1(X0,sK0(j(sK1))))) = op1(X0,sK0(j(sK1))) )
| ~ sorti1(X0) ),
inference(superposition,[status(thm)],[c_755,c_512]) ).
tcf(c_2067,plain,
j(h(op1(sK0(j(sK1)),sK0(j(sK1))))) = op1(sK0(j(sK1)),sK0(j(sK1))),
inference(superposition,[status(thm)],[c_755,c_1021]) ).
tcf(c_2141,plain,
op2(h(sK0(j(sK1))),h(sK0(j(sK1)))) = h(op1(sK0(j(sK1)),sK0(j(sK1)))),
inference(superposition,[status(thm)],[c_755,c_757]) ).
tcf(c_2144,plain,
h(op1(sK0(j(sK1)),sK0(j(sK1)))) = sK1,
inference(light_normalisation,[status(thm)],[c_2141,c_759]) ).
tcf(c_3899,plain,
op1(sK0(j(sK1)),sK0(j(sK1))) = j(sK1),
inference(light_normalisation,[status(thm)],[c_2067,c_2144]) ).
tcf(c_3901,plain,
( sorti1(j(sK1))
| ~ sorti1(sK0(j(sK1))) ),
inference(superposition,[status(thm)],[c_3899,c_49]) ).
tcf(c_3902,plain,
~ sorti1(j(sK1)),
inference(superposition,[status(thm)],[c_3899,c_51]) ).
tcf(c_3903,plain,
~ sorti1(sK0(j(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_3901,c_3902]) ).
tcf(c_3904,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3903,c_755]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG019+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 04:34:51 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 4.24/1.32 % SZS status Started for theBenchmark.p
% 4.24/1.32 % SZS status Theorem for theBenchmark.p
% 4.24/1.32
% 4.24/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.24/1.32
% 4.24/1.32 % ------ iProver source info
% 4.24/1.32
% 4.24/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 4.24/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.24/1.32 % git: non_committed_changes: false
% 4.24/1.32
% 4.24/1.32 % ------ Parsing...
% 4.24/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.24/1.32
% 4.24/1.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.24/1.32
% 4.24/1.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.24/1.32
% 4.24/1.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.24/1.32 % ------ Proving...
% 4.24/1.32 % ------ Problem Properties
% 4.24/1.32
% 4.24/1.32 %
% 4.24/1.32 % clauses 12
% 4.24/1.32 % conjectures 6
% 4.24/1.32 % EPR 1
% 4.24/1.32 % Horn 12
% 4.24/1.32 % unary 1
% 4.24/1.32 % binary 7
% 4.24/1.32 % lits 27
% 4.24/1.32 % lits eq 6
% 4.24/1.32 % fd_pure 0
% 4.24/1.32 % fd_pseudo 0
% 4.24/1.32 % fd_cond 0
% 4.24/1.32 % fd_pseudo_cond 0
% 4.24/1.32 % AC symbols 0
% 4.24/1.32
% 4.24/1.32 % ------ Schedule dynamic 5 is on
% 4.24/1.32
% 4.24/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.24/1.32
% 4.24/1.32
% 4.24/1.32 % ------
% 4.24/1.32 % Current options:
% 4.24/1.32 % ------
% 4.24/1.32
% 4.24/1.32
% 4.24/1.32 %
% 4.24/1.32
% 4.24/1.32 % ------ Proving...
% 4.24/1.32 %
% 4.24/1.32
% 4.24/1.32 % SZS status Theorem for theBenchmark.p
% 4.24/1.32
% 4.24/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.24/1.32
% 4.24/1.32
%------------------------------------------------------------------------------