%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG074+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 : n016.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 12:53:21 PM UTC 2026
% Result : Theorem 7.55s 17.84s
% Output : CNFRefutation 7.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 128 ( 49 unt; 0 def)
% Number of atoms : 321 ( 123 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 340 ( 147 ~; 136 |; 35 &)
% ( 0 <=>; 22 =>; 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn 134 !; 4 ?; 70 :)
% 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] :
( ? [X1] :
( op1(op1(X0,X1),X0) != X1
& op1(op1(X0,X1),X1) = X0
& op1(X1,X0) != op1(X0,X1)
& sorti1(X1) )
& sorti1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ? [X0] :
( ? [X1] :
( op2(op2(X0,X1),X0) != X1
& op2(op2(X0,X1),X1) = X0
& op2(X1,X0) != op2(X0,X1)
& sorti2(X1) )
& 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] :
( ~ sorti1(X0)
| ! [X1] :
( ~ sorti1(X1)
| sorti1(op1(X0,X1)) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f8,plain,
! [X0] :
( ~ sorti2(X0)
| ! [X1] :
( ~ sorti2(X1)
| sorti2(op2(X0,X1)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0] :
( ! [X1] :
( op2(op2(X0,X1),X0) = X1
| op2(op2(X0,X1),X1) != X0
| op2(X0,X1) = op2(X1,X0)
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,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(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(flattening,[],[f10]) ).
fof(f12,plain,
( sK1 != op1(op1(sK0,sK1),sK0)
& sK0 = op1(op1(sK0,sK1),sK1)
& op1(sK0,sK1) != op1(sK1,sK0)
& sorti1(sK1)
& sorti1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f3]) ).
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,[],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| sorti1(op1(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| sorti2(op2(X0,X1)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f16,plain,
sK1 != op1(op1(sK0,sK1),sK0),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
sK0 = op1(op1(sK0,sK1),sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
op1(sK0,sK1) != op1(sK1,sK0),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X0,X1] :
( op2(op2(X0,X1),X0) = X1
| op2(op2(X0,X1),X1) != X0
| op2(X0,X1) = op2(X1,X0)
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X7] :
( ~ sorti2(X7)
| sorti1(j(X7)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X6] :
( ~ sorti1(X6)
| sorti2(h(X6)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X5] :
( ~ sorti1(X5)
| j(h(X5)) = X5 ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X4] :
( ~ sorti2(X4)
| h(j(X4)) = X4 ),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
! [X2,X3] :
( ~ sorti2(X2)
| ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| h(op1(X0,X1)) = op2(h(X0),h(X1)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_51,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f20]) ).
tcf(c_52,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f19]) ).
tcf(c_53,plain,
op1(sK0,sK1) != op1(sK1,sK0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_54,plain,
op1(op1(sK0,sK1),sK1) = sK0,
inference(cnf_transformation,[],[f17]) ).
tcf(c_55,plain,
op1(op1(sK0,sK1),sK0) != sK1,
inference(cnf_transformation,[],[f16]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( op2(X0,X1) = op2(X1,X0) )
| ( op2(op2(X0,X1),X0) = X1 )
| ~ sorti2(X1)
| ~ sorti2(X0)
| ( op2(op2(X0,X1),X1) != X0 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_57,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_58,negated_conjecture,
! [X0: $i,X1: $i] :
( ( op1(j(X0),j(X1)) = j(op2(X0,X1)) )
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_59,negated_conjecture,
! [X0: $i] :
( ( h(j(X0)) = X0 )
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_60,negated_conjecture,
! [X0: $i] :
( ( j(h(X0)) = X0 )
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_61,negated_conjecture,
! [X0: $i] :
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_64,plain,
( sorti2(h(sK0))
| ~ sorti1(sK0) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_165,negated_conjecture,
! [X0_iProver_j_1: iProver_j_1] :
( sorti1(j(X0_iProver_j_1))
| ~ sorti2(X0_iProver_j_1) ),
inference(subtyping,[status(esa)],[c_62]) ).
tcf(c_166,negated_conjecture,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( sorti2(h(X0_iProver_sorti1_1))
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(subtyping,[status(esa)],[c_61]) ).
tcf(c_167,negated_conjecture,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( j(h(X0_iProver_sorti1_1)) = X0_iProver_sorti1_1 )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(subtyping,[status(esa)],[c_60]) ).
tcf(c_168,negated_conjecture,
! [X0_iProver_j_1: iProver_j_1] :
( ( h(j(X0_iProver_j_1)) = X0_iProver_j_1 )
| ~ sorti2(X0_iProver_j_1) ),
inference(subtyping,[status(esa)],[c_59]) ).
tcf(c_169,negated_conjecture,
! [X0_iProver_j_1: iProver_j_1,X1_iProver_j_1: iProver_j_1] :
( ( op1(j(X0_iProver_j_1),j(X1_iProver_j_1)) = j(op2(X0_iProver_j_1,X1_iProver_j_1)) )
| ~ sorti2(X1_iProver_j_1)
| ~ sorti2(X0_iProver_j_1) ),
inference(subtyping,[status(esa)],[c_58]) ).
tcf(c_170,negated_conjecture,
! [X0_iProver_sorti1_1: iProver_sorti1_1,X1_iProver_sorti1_1: iProver_sorti1_1] :
( ( op2(h(X0_iProver_sorti1_1),h(X1_iProver_sorti1_1)) = h(op1(X0_iProver_sorti1_1,X1_iProver_sorti1_1)) )
| ~ sorti1(X1_iProver_sorti1_1)
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(subtyping,[status(esa)],[c_57]) ).
tcf(c_171,plain,
! [X0_iProver_j_1: iProver_j_1,X1_iProver_j_1: iProver_j_1] :
( ( op2(X0_iProver_j_1,X1_iProver_j_1) = op2(X1_iProver_j_1,X0_iProver_j_1) )
| ( op2(op2(X0_iProver_j_1,X1_iProver_j_1),X0_iProver_j_1) = X1_iProver_j_1 )
| ~ sorti2(X1_iProver_j_1)
| ~ sorti2(X0_iProver_j_1)
| ( op2(op2(X0_iProver_j_1,X1_iProver_j_1),X1_iProver_j_1) != X0_iProver_j_1 ) ),
inference(subtyping,[status(esa)],[c_56]) ).
tcf(c_172,plain,
op1(op1(sK0,sK1),sK0) != sK1,
inference(subtyping,[status(esa)],[c_55]) ).
tcf(c_173,plain,
op1(op1(sK0,sK1),sK1) = sK0,
inference(subtyping,[status(esa)],[c_54]) ).
tcf(c_174,plain,
op1(sK0,sK1) != op1(sK1,sK0),
inference(subtyping,[status(esa)],[c_53]) ).
tcf(c_175,plain,
sorti1(sK1),
inference(subtyping,[status(esa)],[c_52]) ).
tcf(c_176,plain,
sorti1(sK0),
inference(subtyping,[status(esa)],[c_51]) ).
tcf(c_177,plain,
! [X0_iProver_j_1: iProver_j_1,X1_iProver_j_1: iProver_j_1] :
( sorti2(op2(X0_iProver_j_1,X1_iProver_j_1))
| ~ sorti2(X1_iProver_j_1)
| ~ sorti2(X0_iProver_j_1) ),
inference(subtyping,[status(esa)],[c_50]) ).
tcf(c_178,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1,X1_iProver_sorti1_1: iProver_sorti1_1] :
( sorti1(op1(X0_iProver_sorti1_1,X1_iProver_sorti1_1))
| ~ sorti1(X1_iProver_sorti1_1)
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(subtyping,[status(esa)],[c_49]) ).
tcf(c_421,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( h(j(h(X0_iProver_sorti1_1))) = h(X0_iProver_sorti1_1) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_166,c_168]) ).
tcf(c_423,plain,
j(h(sK0)) = sK0,
inference(superposition,[status(thm)],[c_176,c_167]) ).
tcf(c_424,plain,
j(h(sK1)) = sK1,
inference(superposition,[status(thm)],[c_175,c_167]) ).
tcf(c_425,plain,
! [X0_iProver_j_1: iProver_j_1] :
( ( j(h(j(X0_iProver_j_1))) = j(X0_iProver_j_1) )
| ~ sorti2(X0_iProver_j_1) ),
inference(superposition,[status(thm)],[c_165,c_167]) ).
tcf(c_428,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1,X1_iProver_sorti1_1: iProver_sorti1_1] :
( ( j(h(op1(X0_iProver_sorti1_1,X1_iProver_sorti1_1))) = op1(X0_iProver_sorti1_1,X1_iProver_sorti1_1) )
| ~ sorti1(X1_iProver_sorti1_1)
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_178,c_167]) ).
tcf(c_432,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( op2(h(sK0),h(X0_iProver_sorti1_1)) = h(op1(sK0,X0_iProver_sorti1_1)) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_176,c_170]) ).
tcf(c_433,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( op2(h(sK1),h(X0_iProver_sorti1_1)) = h(op1(sK1,X0_iProver_sorti1_1)) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_175,c_170]) ).
tcf(c_435,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1,X1_iProver_sorti1_1: iProver_sorti1_1,X2_iProver_sorti1_1: iProver_sorti1_1] :
( ( op2(h(op1(X0_iProver_sorti1_1,X1_iProver_sorti1_1)),h(X2_iProver_sorti1_1)) = h(op1(op1(X0_iProver_sorti1_1,X1_iProver_sorti1_1),X2_iProver_sorti1_1)) )
| ~ sorti1(X2_iProver_sorti1_1)
| ~ sorti1(X1_iProver_sorti1_1)
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_178,c_170]) ).
tcf(c_439,plain,
! [X0_iProver_j_1: iProver_j_1,X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( op1(j(h(X0_iProver_sorti1_1)),j(X0_iProver_j_1)) = j(op2(h(X0_iProver_sorti1_1),X0_iProver_j_1)) )
| ~ sorti2(X0_iProver_j_1)
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_166,c_169]) ).
tcf(c_443,plain,
h(j(h(sK0))) = h(sK0),
inference(superposition,[status(thm)],[c_176,c_421]) ).
tcf(c_444,plain,
h(j(h(sK1))) = h(sK1),
inference(superposition,[status(thm)],[c_175,c_421]) ).
tcf(c_445,plain,
! [X0_iProver_j_1: iProver_j_1] :
( ( h(j(h(j(X0_iProver_j_1)))) = h(j(X0_iProver_j_1)) )
| ~ sorti2(X0_iProver_j_1) ),
inference(superposition,[status(thm)],[c_165,c_421]) ).
tcf(c_446,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1,X1_iProver_sorti1_1: iProver_sorti1_1] :
( ( h(j(h(op1(X0_iProver_sorti1_1,X1_iProver_sorti1_1)))) = h(op1(X0_iProver_sorti1_1,X1_iProver_sorti1_1)) )
| ~ sorti1(X1_iProver_sorti1_1)
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_178,c_421]) ).
tcf(c_451,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( j(h(j(h(X0_iProver_sorti1_1)))) = j(h(X0_iProver_sorti1_1)) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_166,c_425]) ).
tcf(c_452,plain,
! [X0_iProver_j_1: iProver_j_1,X1_iProver_j_1: iProver_j_1] :
( ( j(h(j(op2(X0_iProver_j_1,X1_iProver_j_1)))) = j(op2(X0_iProver_j_1,X1_iProver_j_1)) )
| ~ sorti2(X1_iProver_j_1)
| ~ sorti2(X0_iProver_j_1) ),
inference(superposition,[status(thm)],[c_177,c_425]) ).
tcf(c_455,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( j(h(op1(sK0,X0_iProver_sorti1_1))) = op1(sK0,X0_iProver_sorti1_1) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_176,c_428]) ).
tcf(c_456,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( j(h(op1(sK1,X0_iProver_sorti1_1))) = op1(sK1,X0_iProver_sorti1_1) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_175,c_428]) ).
tcf(c_466,plain,
op2(h(sK1),h(sK0)) = h(op1(sK1,sK0)),
inference(superposition,[status(thm)],[c_176,c_433]) ).
tcf(c_473,plain,
op2(h(sK0),h(sK1)) = h(op1(sK0,sK1)),
inference(superposition,[status(thm)],[c_175,c_432]) ).
tcf(c_482,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1,X1_iProver_sorti1_1: iProver_sorti1_1] :
( ( op2(h(op1(sK0,X0_iProver_sorti1_1)),h(X1_iProver_sorti1_1)) = h(op1(op1(sK0,X0_iProver_sorti1_1),X1_iProver_sorti1_1)) )
| ~ sorti1(X1_iProver_sorti1_1)
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_176,c_435]) ).
tcf(c_489,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1,X1_iProver_sorti1_1: iProver_sorti1_1] :
( ( op1(j(h(X1_iProver_sorti1_1)),j(h(X0_iProver_sorti1_1))) = j(op2(h(X1_iProver_sorti1_1),h(X0_iProver_sorti1_1))) )
| ~ sorti1(X1_iProver_sorti1_1)
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_166,c_439]) ).
tcf(c_497,plain,
( sorti2(h(sK1))
| ~ sorti1(j(h(sK1))) ),
inference(superposition,[status(thm)],[c_444,c_166]) ).
tcf(c_498,plain,
( sorti2(h(sK1))
| ~ sorti1(sK1) ),
inference(light_normalisation,[status(thm)],[c_497,c_424]) ).
tcf(c_499,plain,
sorti2(h(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_498,c_175]) ).
tcf(c_502,plain,
( sorti2(h(sK0))
| ~ sorti1(j(h(sK0))) ),
inference(superposition,[status(thm)],[c_443,c_166]) ).
tcf(c_503,plain,
( sorti2(h(sK0))
| ~ sorti1(sK0) ),
inference(light_normalisation,[status(thm)],[c_502,c_423]) ).
tcf(c_504,plain,
sorti2(h(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_503,c_176]) ).
tcf(c_510,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( h(j(h(op1(sK0,X0_iProver_sorti1_1)))) = h(op1(sK0,X0_iProver_sorti1_1)) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_176,c_446]) ).
tcf(c_511,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( h(j(h(op1(sK1,X0_iProver_sorti1_1)))) = h(op1(sK1,X0_iProver_sorti1_1)) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_175,c_446]) ).
tcf(c_512,plain,
! [X0_iProver_j_1: iProver_j_1,X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( h(j(h(op1(j(X0_iProver_j_1),X0_iProver_sorti1_1)))) = h(op1(j(X0_iProver_j_1),X0_iProver_sorti1_1)) )
| ~ sorti2(X0_iProver_j_1)
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_165,c_446]) ).
tcf(c_524,plain,
j(h(j(h(sK1)))) = j(h(sK1)),
inference(superposition,[status(thm)],[c_175,c_451]) ).
tcf(c_525,plain,
! [X0_iProver_j_1: iProver_j_1] :
( ( j(h(j(h(j(X0_iProver_j_1))))) = j(h(j(X0_iProver_j_1))) )
| ~ sorti2(X0_iProver_j_1) ),
inference(superposition,[status(thm)],[c_165,c_451]) ).
tcf(c_526,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1,X1_iProver_sorti1_1: iProver_sorti1_1] :
( ( j(h(j(h(op1(X0_iProver_sorti1_1,X1_iProver_sorti1_1))))) = j(h(op1(X0_iProver_sorti1_1,X1_iProver_sorti1_1))) )
| ~ sorti1(X1_iProver_sorti1_1)
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_178,c_451]) ).
tcf(c_535,plain,
! [X0_iProver_j_1: iProver_j_1,X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( j(h(j(op2(h(X0_iProver_sorti1_1),X0_iProver_j_1)))) = j(op2(h(X0_iProver_sorti1_1),X0_iProver_j_1)) )
| ~ sorti2(X0_iProver_j_1)
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_166,c_452]) ).
tcf(c_539,plain,
j(h(op1(sK1,sK0))) = op1(sK1,sK0),
inference(superposition,[status(thm)],[c_176,c_456]) ).
tcf(c_549,plain,
j(h(op1(sK0,sK1))) = op1(sK0,sK1),
inference(superposition,[status(thm)],[c_175,c_455]) ).
tcf(c_594,plain,
( sorti2(h(op1(sK1,sK0)))
| ~ sorti2(h(sK1))
| ~ sorti2(h(sK0)) ),
inference(superposition,[status(thm)],[c_466,c_177]) ).
tcf(c_621,plain,
( ( op2(h(sK0),h(sK1)) = op2(h(sK1),h(sK0)) )
| ( op2(op2(h(sK0),h(sK1)),h(sK0)) = h(sK1) )
| ~ sorti2(h(sK1))
| ~ sorti2(h(sK0))
| ( op2(h(op1(sK0,sK1)),h(sK1)) != h(sK0) ) ),
inference(superposition,[status(thm)],[c_473,c_171]) ).
tcf(c_622,plain,
( sorti2(h(op1(sK0,sK1)))
| ~ sorti2(h(sK1))
| ~ sorti2(h(sK0)) ),
inference(superposition,[status(thm)],[c_473,c_177]) ).
tcf(c_691,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( op2(h(op1(sK0,sK1)),h(X0_iProver_sorti1_1)) = h(op1(op1(sK0,sK1),X0_iProver_sorti1_1)) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_175,c_482]) ).
tcf(c_739,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( op1(j(h(X0_iProver_sorti1_1)),j(h(sK0))) = j(op2(h(X0_iProver_sorti1_1),h(sK0))) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_176,c_489]) ).
tcf(c_744,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( j(op2(h(X0_iProver_sorti1_1),h(sK0))) = op1(j(h(X0_iProver_sorti1_1)),sK0) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(light_normalisation,[status(thm)],[c_739,c_423]) ).
tcf(c_777,plain,
h(j(h(j(h(sK1))))) = h(j(h(sK1))),
inference(superposition,[status(thm)],[c_499,c_445]) ).
tcf(c_964,plain,
h(j(h(op1(sK1,sK0)))) = h(op1(sK1,sK0)),
inference(superposition,[status(thm)],[c_176,c_511]) ).
tcf(c_978,plain,
h(j(h(op1(sK0,sK1)))) = h(op1(sK0,sK1)),
inference(superposition,[status(thm)],[c_175,c_510]) ).
tcf(c_1020,plain,
j(h(j(h(j(h(sK1)))))) = j(h(j(h(sK1)))),
inference(superposition,[status(thm)],[c_499,c_525]) ).
tcf(c_1027,plain,
! [X0_iProver_j_1: iProver_j_1,X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( j(h(j(h(op1(j(X0_iProver_j_1),X0_iProver_sorti1_1))))) = j(h(op1(j(X0_iProver_j_1),X0_iProver_sorti1_1))) )
| ~ sorti2(X0_iProver_j_1)
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_165,c_526]) ).
tcf(c_1042,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( j(h(j(op2(h(X0_iProver_sorti1_1),h(sK0))))) = j(op2(h(X0_iProver_sorti1_1),h(sK0))) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_504,c_535]) ).
tcf(c_1161,plain,
( sorti1(op1(sK0,sK1))
| ~ sorti2(h(op1(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_549,c_165]) ).
tcf(c_1454,plain,
sorti2(h(op1(sK1,sK0))),
inference(global_subsumption_just,[status(thm)],[c_594,c_51,c_64,c_499,c_594]) ).
tcf(c_1465,plain,
j(h(j(h(j(h(op1(sK1,sK0))))))) = j(h(j(h(op1(sK1,sK0))))),
inference(superposition,[status(thm)],[c_1454,c_525]) ).
tcf(c_1479,plain,
h(j(h(j(h(op1(sK1,sK0)))))) = h(j(h(op1(sK1,sK0)))),
inference(superposition,[status(thm)],[c_1454,c_445]) ).
tcf(c_1484,plain,
j(h(j(h(op1(sK1,sK0))))) = j(h(op1(sK1,sK0))),
inference(superposition,[status(thm)],[c_1454,c_425]) ).
tcf(c_1678,plain,
sorti2(h(op1(sK0,sK1))),
inference(global_subsumption_just,[status(thm)],[c_622,c_51,c_64,c_499,c_622]) ).
tcf(c_1691,plain,
j(h(j(h(j(h(op1(sK0,sK1))))))) = j(h(j(h(op1(sK0,sK1))))),
inference(superposition,[status(thm)],[c_1678,c_525]) ).
tcf(c_1692,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( h(j(h(op1(j(h(op1(sK0,sK1))),X0_iProver_sorti1_1)))) = h(op1(j(h(op1(sK0,sK1))),X0_iProver_sorti1_1)) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_1678,c_512]) ).
tcf(c_1705,plain,
h(j(h(j(h(op1(sK0,sK1)))))) = h(j(h(op1(sK0,sK1)))),
inference(superposition,[status(thm)],[c_1678,c_445]) ).
tcf(c_1710,plain,
j(h(j(h(op1(sK0,sK1))))) = j(h(op1(sK0,sK1))),
inference(superposition,[status(thm)],[c_1678,c_425]) ).
tcf(c_1724,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( h(j(h(op1(op1(sK0,sK1),X0_iProver_sorti1_1)))) = h(op1(op1(sK0,sK1),X0_iProver_sorti1_1)) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(light_normalisation,[status(thm)],[c_1692,c_549]) ).
tcf(c_2307,plain,
op2(h(op1(sK0,sK1)),h(sK0)) = h(op1(op1(sK0,sK1),sK0)),
inference(superposition,[status(thm)],[c_176,c_691]) ).
tcf(c_2308,plain,
op2(h(op1(sK0,sK1)),h(sK1)) = h(op1(op1(sK0,sK1),sK1)),
inference(superposition,[status(thm)],[c_175,c_691]) ).
tcf(c_2311,plain,
op2(h(op1(sK0,sK1)),h(sK1)) = h(sK0),
inference(light_normalisation,[status(thm)],[c_2308,c_173]) ).
tcf(c_3688,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( j(h(j(h(op1(j(h(op1(sK0,sK1))),X0_iProver_sorti1_1))))) = j(h(op1(j(h(op1(sK0,sK1))),X0_iProver_sorti1_1))) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(superposition,[status(thm)],[c_1678,c_1027]) ).
tcf(c_3691,plain,
! [X0_iProver_sorti1_1: iProver_sorti1_1] :
( ( j(h(j(h(op1(op1(sK0,sK1),X0_iProver_sorti1_1))))) = j(h(op1(op1(sK0,sK1),X0_iProver_sorti1_1))) )
| ~ sorti1(X0_iProver_sorti1_1) ),
inference(light_normalisation,[status(thm)],[c_3688,c_549]) ).
tcf(c_4364,plain,
sorti1(op1(sK0,sK1)),
inference(global_subsumption_just,[status(thm)],[c_1161,c_51,c_64,c_499,c_622,c_1161]) ).
tcf(c_4371,plain,
j(h(j(op2(h(op1(sK0,sK1)),h(sK0))))) = j(op2(h(op1(sK0,sK1)),h(sK0))),
inference(superposition,[status(thm)],[c_4364,c_1042]) ).
tcf(c_4388,plain,
j(op2(h(op1(sK0,sK1)),h(sK0))) = op1(j(h(op1(sK0,sK1))),sK0),
inference(superposition,[status(thm)],[c_4364,c_744]) ).
tcf(c_4439,plain,
j(op2(h(op1(sK0,sK1)),h(sK0))) = op1(op1(sK0,sK1),sK0),
inference(light_normalisation,[status(thm)],[c_4388,c_549]) ).
tcf(c_4444,plain,
j(h(op1(op1(sK0,sK1),sK0))) = op1(op1(sK0,sK1),sK0),
inference(light_normalisation,[status(thm)],[c_4371,c_4439]) ).
tcf(c_7799,plain,
h(j(h(op1(op1(sK0,sK1),sK0)))) = h(op1(op1(sK0,sK1),sK0)),
inference(superposition,[status(thm)],[c_176,c_1724]) ).
tcf(c_19607,plain,
j(h(j(h(op1(op1(sK0,sK1),sK0))))) = j(h(op1(op1(sK0,sK1),sK0))),
inference(superposition,[status(thm)],[c_176,c_3691]) ).
tcf(c_60280,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_19607,c_7799,c_4444,c_2311,c_2307,c_1710,c_1705,c_1691,c_1484,c_1479,c_1465,c_1020,c_978,c_964,c_777,c_621,c_549,c_539,c_524,c_504,c_499,c_473,c_466,c_444,c_424,c_174,c_172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG074+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 04:47:13 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 7.55/17.83 % SZS status Started for theBenchmark.p
% 7.55/17.83 ERROR - "ProverProcess:heur/379306:2.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Z3.Error("Sort mismatch at argument #1 for function (declare-fun f_97 (s_0) Bool) supplied sort is s_105")
% 7.55/17.83 Fatal error: exception Z3.Error("Sort mismatch at argument #1 for function (declare-fun f_97 (s_0) Bool) supplied sort is s_105")
% 7.55/17.83 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 6 --comb_sup_mult 32 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground false --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs;Unflattening]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes;DemodLoopTriv;ACNormalisation]" --sup_immed_fw_main "[Subsumption;UnitSubsAndRes;Demod;LightNorm;ACNormalisation]" --sup_immed_triv "[PropSubs]" --sup_indices_passive "[]" --sup_input_bw "[SubsumptionRes]" --sup_input_fw "[SMTSubs;]" --sup_input_triv "[]" --sup_iter_deepening 1 --sup_passive_queue_type priority_queues --sup_passive_queues "[[+min_def_symb;-score;+epr];[-next_state;-conj_dist;+conj_symb]]" --sup_passive_queues_freq "[3;512]" --sup_prop_simpl_given false --sup_prop_simpl_new true --sup_restarts_mult 16 --sup_score sim_d_gen --sup_share_max_num_cl 320 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering arity_rev --sup_to_prop_solver none --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.67" --time_out_real 2.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_96b7v83k/7fh2jh9h 2>> /export/starexec/sandbox/tmp/iprover_out_96b7v83k/7fh2jh9h_error
% 7.55/17.84 % SZS status Theorem for theBenchmark.p
% 7.55/17.84
% 7.55/17.84 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.55/17.84
% 7.55/17.84 % ------ iProver source info
% 7.55/17.84
% 7.55/17.84 % git: date: 2026-07-19 20:42:38 +0200
% 7.55/17.84 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.55/17.84 % git: non_committed_changes: false
% 7.55/17.84
% 7.55/17.84 % ------ Parsing...
% 7.55/17.84 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.55/17.84
% 7.55/17.84 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 7.55/17.84
% 7.55/17.84 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.55/17.84
% 7.55/17.84 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.55/17.84 % ------ Proving...
% 7.55/17.84 % ------ Problem Properties
% 7.55/17.84
% 7.55/17.84 %
% 7.55/17.84 % clauses 14
% 7.55/17.84 % conjectures 6
% 7.55/17.84 % EPR 2
% 7.55/17.84 % Horn 13
% 7.55/17.84 % unary 5
% 7.55/17.84 % binary 4
% 7.55/17.84 % lits 30
% 7.55/17.84 % lits eq 10
% 7.55/17.84 % fd_pure 0
% 7.55/17.84 % fd_pseudo 0
% 7.55/17.84 % fd_cond 0
% 7.55/17.84 % fd_pseudo_cond 0
% 7.55/17.84 % AC symbols 0
% 7.55/17.84
% 7.55/17.84 % ------ Input Options Time Limit: Unbounded
% 7.55/17.84
% 7.55/17.84
% 7.55/17.84 % ------
% 7.55/17.84 % Current options:
% 7.55/17.84 % ------
% 7.55/17.84
% 7.55/17.84
% 7.55/17.84 %
% 7.55/17.84
% 7.55/17.84 % ------ Proving...
% 7.55/17.84 %
% 7.55/17.84
% 7.55/17.84 % SZS status Theorem for theBenchmark.p
% 7.55/17.84
% 7.55/17.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.55/17.84
% 7.55/17.84
%------------------------------------------------------------------------------