%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG178+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 : n011.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 12:53:42 PM UTC 2026
% Result : Theorem 2.70s 1.08s
% Output : CNFRefutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 72 ( 23 unt; 0 def)
% Number of atoms : 205 ( 56 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 221 ( 88 ~; 80 |; 27 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 9 ( 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; 2 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 90 !; 2 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> op1(X0,op1(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> op2(X0,op2(X0,X1)) = X1 ) ),
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,
( ! [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(f8,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,[],[f7]) ).
fof(f9,plain,
? [X0] :
( sorti2(X0)
& ? [X1] :
( sorti2(X1)
& op2(X0,op2(X0,X1)) != X1 ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
! [X0] :
( ~ sorti1(X0)
| ! [X1] :
( ~ sorti1(X1)
| op1(X0,op1(X0,X1)) = X1 ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
! [X0] :
( ~ sorti1(X0)
| ! [X1] :
( ~ sorti1(X1)
| sorti1(op1(X0,X1)) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0] :
( ~ sorti2(X0)
| ! [X1] :
( ~ sorti2(X1)
| sorti2(op2(X0,X1)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f13,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,[],[f8]) ).
fof(f14,plain,
( sorti2(sK0)
& sorti2(sK1)
& sK1 != op2(sK0,op2(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
fof(f15,plain,
! [X7] :
( ~ sorti2(X7)
| sorti1(j(X7)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f16,plain,
! [X6] :
( ~ sorti1(X6)
| sorti2(h(X6)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f18,plain,
! [X4] :
( ~ sorti2(X4)
| h(j(X4)) = X4 ),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
! [X2,X3] :
( ~ sorti2(X2)
| ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
sK1 != op2(sK0,op2(sK0,sK1)),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| op1(X0,op1(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f25,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| sorti1(op1(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f26,plain,
! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| sorti2(op2(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i] :
( ( op1(j(X0),j(X1)) = j(op2(X0,X1)) )
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( ( h(j(X0)) = X0 )
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] :
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_55,plain,
op2(sK0,op2(sK0,sK1)) != sK1,
inference(cnf_transformation,[],[f23]) ).
tcf(c_56,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f22]) ).
tcf(c_57,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f21]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( op1(X0,op1(X0,X1)) = X1 )
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_61,plain,
( sorti1(j(sK0))
| ~ sorti2(sK0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_448,plain,
! [X0: $i] :
( ( op1(j(sK1),j(X0)) = j(op2(sK1,X0)) )
| ~ sorti2(X0) ),
inference(superposition,[status(thm)],[c_56,c_50]) ).
tcf(c_449,plain,
h(j(sK1)) = sK1,
inference(superposition,[status(thm)],[c_56,c_51]) ).
tcf(c_454,plain,
! [X0: $i] :
( ( op1(j(sK0),j(X0)) = j(op2(sK0,X0)) )
| ~ sorti2(X0) ),
inference(superposition,[status(thm)],[c_57,c_50]) ).
tcf(c_521,plain,
op1(j(sK1),j(sK0)) = j(op2(sK1,sK0)),
inference(superposition,[status(thm)],[c_57,c_448]) ).
tcf(c_530,plain,
op1(j(sK0),j(sK1)) = j(op2(sK0,sK1)),
inference(superposition,[status(thm)],[c_56,c_454]) ).
tcf(c_618,plain,
! [X0: $i,X1: $i] :
( ( h(j(op2(X0,X1))) = op2(X0,X1) )
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(superposition,[status(thm)],[c_60,c_51]) ).
tcf(c_668,plain,
! [X0: $i,X1: $i] :
( ( op1(X0,op1(X0,j(X1))) = j(X1) )
| ~ sorti2(X1)
| ~ sorti1(X0) ),
inference(superposition,[status(thm)],[c_54,c_58]) ).
tcf(c_775,plain,
( sorti1(j(op2(sK0,sK1)))
| ~ sorti1(j(sK0))
| ~ sorti1(j(sK1)) ),
inference(superposition,[status(thm)],[c_530,c_59]) ).
tcf(c_887,plain,
! [X0: $i] :
( ( h(j(op2(sK0,X0))) = op2(sK0,X0) )
| ~ sorti2(X0) ),
inference(superposition,[status(thm)],[c_57,c_618]) ).
tcf(c_936,plain,
! [X0: $i,X1: $i] :
( ( op1(j(X0),op1(j(X0),j(X1))) = j(X1) )
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(superposition,[status(thm)],[c_54,c_668]) ).
tcf(c_1175,plain,
( sorti1(j(op2(sK0,sK1)))
| ~ sorti1(j(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_775,c_57,c_61,c_775]) ).
tcf(c_1452,plain,
! [X0: $i] :
( ( h(j(op2(sK0,h(X0)))) = op2(sK0,h(X0)) )
| ~ sorti1(X0) ),
inference(superposition,[status(thm)],[c_53,c_887]) ).
tcf(c_1453,plain,
h(j(op2(sK0,sK1))) = op2(sK0,sK1),
inference(superposition,[status(thm)],[c_56,c_887]) ).
tcf(c_1483,plain,
( sorti2(op2(sK0,sK1))
| ~ sorti1(j(op2(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_1453,c_53]) ).
tcf(c_1649,plain,
( sorti2(op2(sK0,sK1))
| ~ sorti1(j(sK1)) ),
inference(superposition,[status(thm)],[c_1175,c_1483]) ).
tcf(c_1656,plain,
! [X0: $i] :
( ( h(j(op2(sK0,h(j(X0))))) = op2(sK0,h(j(X0))) )
| ~ sorti2(X0) ),
inference(superposition,[status(thm)],[c_54,c_1452]) ).
tcf(c_1690,plain,
! [X0: $i] :
( ( h(j(op2(sK0,h(j(h(X0)))))) = op2(sK0,h(j(h(X0)))) )
| ~ sorti1(X0) ),
inference(superposition,[status(thm)],[c_53,c_1656]) ).
tcf(c_1752,plain,
! [X0: $i] :
( ( op1(j(sK1),op1(j(sK1),j(X0))) = j(X0) )
| ~ sorti2(X0) ),
inference(superposition,[status(thm)],[c_56,c_936]) ).
tcf(c_1753,plain,
! [X0: $i] :
( ( op1(j(sK0),op1(j(sK0),j(X0))) = j(X0) )
| ~ sorti2(X0) ),
inference(superposition,[status(thm)],[c_57,c_936]) ).
tcf(c_2018,plain,
op1(j(sK1),op1(j(sK1),j(sK0))) = j(sK0),
inference(superposition,[status(thm)],[c_57,c_1752]) ).
tcf(c_2023,plain,
op1(j(sK1),j(op2(sK1,sK0))) = j(sK0),
inference(light_normalisation,[status(thm)],[c_2018,c_521]) ).
tcf(c_2069,plain,
( sorti1(j(sK0))
| ~ sorti1(j(sK1))
| ~ sorti1(j(op2(sK1,sK0))) ),
inference(superposition,[status(thm)],[c_2023,c_59]) ).
tcf(c_2074,plain,
sorti1(j(sK0)),
inference(global_subsumption_just,[status(thm)],[c_2069,c_57,c_61]) ).
tcf(c_2487,plain,
op1(j(sK0),op1(j(sK0),j(sK1))) = j(sK1),
inference(superposition,[status(thm)],[c_56,c_1753]) ).
tcf(c_2494,plain,
op1(j(sK0),j(op2(sK0,sK1))) = j(sK1),
inference(light_normalisation,[status(thm)],[c_2487,c_530]) ).
tcf(c_2525,plain,
( sorti1(j(sK1))
| ~ sorti1(j(sK0))
| ~ sorti1(j(op2(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_2494,c_59]) ).
tcf(c_2526,plain,
( sorti1(j(sK1))
| ~ sorti1(j(op2(sK0,sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2525,c_2074]) ).
tcf(c_2533,plain,
( sorti1(j(sK1))
| ~ sorti2(op2(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_54,c_2526]) ).
tcf(c_2560,plain,
( sorti1(j(sK1))
| ~ sorti2(sK0)
| ~ sorti2(sK1) ),
inference(superposition,[status(thm)],[c_60,c_2533]) ).
tcf(c_2562,plain,
sorti1(j(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_2560,c_57,c_56]) ).
tcf(c_2563,plain,
sorti2(op2(sK0,sK1)),
inference(backward_subsumption_resolution,[status(thm)],[c_1649,c_2562]) ).
tcf(c_2566,plain,
sorti1(j(op2(sK0,sK1))),
inference(backward_subsumption_resolution,[status(thm)],[c_1175,c_2562]) ).
tcf(c_2632,plain,
op1(j(sK0),j(op2(sK0,sK1))) = j(op2(sK0,op2(sK0,sK1))),
inference(superposition,[status(thm)],[c_2563,c_454]) ).
tcf(c_2639,plain,
j(op2(sK0,op2(sK0,sK1))) = j(sK1),
inference(light_normalisation,[status(thm)],[c_2632,c_2494]) ).
tcf(c_2873,plain,
h(j(op2(sK0,h(j(h(j(op2(sK0,sK1)))))))) = op2(sK0,h(j(h(j(op2(sK0,sK1)))))),
inference(superposition,[status(thm)],[c_2566,c_1690]) ).
tcf(c_2907,plain,
op2(sK0,op2(sK0,sK1)) = sK1,
inference(light_normalisation,[status(thm)],[c_2873,c_449,c_1453,c_2639]) ).
tcf(c_2908,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2907,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG178+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n011.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 04:59:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.70/1.08 % SZS status Started for theBenchmark.p
% 2.70/1.08 % SZS status Theorem for theBenchmark.p
% 2.70/1.08
% 2.70/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.70/1.08
% 2.70/1.08 % ------ iProver source info
% 2.70/1.08
% 2.70/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 2.70/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.70/1.08 % git: non_committed_changes: false
% 2.70/1.08
% 2.70/1.08 % ------ Parsing...
% 2.70/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.70/1.08
% 2.70/1.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.70/1.08
% 2.70/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.70/1.08
% 2.70/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.70/1.08 % ------ Proving...
% 2.70/1.08 % ------ Problem Properties
% 2.70/1.08
% 2.70/1.08 %
% 2.70/1.08 % clauses 12
% 2.70/1.08 % conjectures 6
% 2.70/1.08 % EPR 2
% 2.70/1.08 % Horn 12
% 2.70/1.08 % unary 3
% 2.70/1.08 % binary 4
% 2.70/1.08 % lits 26
% 2.70/1.08 % lits eq 6
% 2.70/1.08 % fd_pure 0
% 2.70/1.08 % fd_pseudo 0
% 2.70/1.08 % fd_cond 0
% 2.70/1.08 % fd_pseudo_cond 0
% 2.70/1.08 % AC symbols 0
% 2.70/1.08
% 2.70/1.08 % ------ Schedule dynamic 5 is on
% 2.70/1.08
% 2.70/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.70/1.08
% 2.70/1.08
% 2.70/1.08 % ------
% 2.70/1.08 % Current options:
% 2.70/1.08 % ------
% 2.70/1.08
% 2.70/1.08
% 2.70/1.08 %
% 2.70/1.08
% 2.70/1.08 % ------ Proving...
% 2.70/1.08 %
% 2.70/1.08
% 2.70/1.08 % SZS status Theorem for theBenchmark.p
% 2.70/1.08
% 2.70/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.70/1.08
% 2.70/1.08
%------------------------------------------------------------------------------