%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX185+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 03:32:46 PM UTC 2026
% Result : Theorem 25.83s 6.81s
% Output : CNFRefutation 25.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 46 unt; 0 def)
% Number of atoms : 68 ( 67 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 18 ~; 8 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 113 !; 4 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X0,X1] : proj22(x2(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
fof(f23,axiom,
! [X0,X1,X2,X3] : z(X0,X1) != x2(X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
fof(f25,axiom,
! [X0,X1] : z(X0,X1) != eY,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
fof(f30,axiom,
! [X0,X1] :
( X0 != z(proj1(X0),proj2(X0))
=> assoc(z(X0,X1)) = z(assoc(X0),assoc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
fof(f31,axiom,
! [X0,X1,X2] : assoc(z(z(X1,X2),X0)) = assoc(z(X1,z(X2,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
fof(f32,axiom,
! [X0,X1] : assoc(x2(X0,X1)) = x2(assoc(X0),assoc(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_032) ).
fof(f33,axiom,
! [X0] : append(nil,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_033) ).
fof(f34,axiom,
! [X0,X1,X2] : append(cons(X1,X2),X0) = cons(X1,append(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_034) ).
fof(f38,axiom,
! [X0,X1] : lin(x2(X0,X1)) = append(lin(X0),append(cons(mul,nil),lin(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_038) ).
fof(f39,axiom,
lin(eX) = cons(x,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_039) ).
fof(f41,conjecture,
? [X0,X1] :
~ ( lin(X0) = lin(X1)
=> assoc(X0) = assoc(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_041) ).
fof(f42,negated_conjecture,
~ ? [X0,X1] :
~ ( lin(X0) = lin(X1)
=> assoc(X0) = assoc(X1) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( z(proj1(X0),proj2(X0)) = X0
| assoc(z(X0,X1)) = z(assoc(X0),assoc(X1)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f47,plain,
! [X0,X1] :
( lin(X0) != lin(X1)
| assoc(X0) = assoc(X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f69,plain,
! [X0,X1] : proj22(x2(X0,X1)) = X1,
inference(cnf_transformation,[],[f22]) ).
fof(f70,plain,
! [X2,X3,X0,X1] : z(X0,X1) != x2(X2,X3),
inference(cnf_transformation,[],[f23]) ).
fof(f72,plain,
! [X0,X1] : z(X0,X1) != eY,
inference(cnf_transformation,[],[f25]) ).
fof(f77,plain,
! [X0,X1] :
( z(proj1(X0),proj2(X0)) = X0
| assoc(z(X0,X1)) = z(assoc(X0),assoc(X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f78,plain,
! [X2,X0,X1] : assoc(z(z(X1,X2),X0)) = assoc(z(X1,z(X2,X0))),
inference(cnf_transformation,[],[f31]) ).
fof(f79,plain,
! [X0,X1] : assoc(x2(X0,X1)) = x2(assoc(X0),assoc(X1)),
inference(cnf_transformation,[],[f32]) ).
fof(f80,plain,
! [X0] : append(nil,X0) = X0,
inference(cnf_transformation,[],[f33]) ).
fof(f81,plain,
! [X2,X0,X1] : append(cons(X1,X2),X0) = cons(X1,append(X2,X0)),
inference(cnf_transformation,[],[f34]) ).
fof(f85,plain,
! [X0,X1] : lin(x2(X0,X1)) = append(lin(X0),append(cons(mul,nil),lin(X1))),
inference(cnf_transformation,[],[f38]) ).
fof(f86,plain,
lin(eX) = cons(x,nil),
inference(cnf_transformation,[],[f39]) ).
fof(f88,plain,
! [X0,X1] :
( lin(X0) != lin(X1)
| assoc(X0) = assoc(X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : proj22(x2(X0,X1)) = X1,
inference(cnf_transformation,[],[f69]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : z(X0,X1) != x2(X2,X3),
inference(cnf_transformation,[],[f70]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : z(X0,X1) != eY,
inference(cnf_transformation,[],[f72]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( z(assoc(X0),assoc(X1)) = assoc(z(X0,X1)) )
| ( z(proj1(X0),proj2(X0)) = X0 ) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : assoc(z(z(X0,X1),X2)) = assoc(z(X0,z(X1,X2))),
inference(cnf_transformation,[],[f78]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] : x2(assoc(X0),assoc(X1)) = assoc(x2(X0,X1)),
inference(cnf_transformation,[],[f79]) ).
tcf(c_81,plain,
! [X0: $i] : append(nil,X0) = X0,
inference(cnf_transformation,[],[f80]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] : cons(X0,append(X1,X2)) = append(cons(X0,X1),X2),
inference(cnf_transformation,[],[f81]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] : append(lin(X0),append(cons(mul,nil),lin(X1))) = lin(x2(X0,X1)),
inference(cnf_transformation,[],[f85]) ).
tcf(c_87,plain,
cons(x,nil) = lin(eX),
inference(cnf_transformation,[],[f86]) ).
tcf(c_89,negated_conjecture,
! [X0: $i,X1: $i] :
( ( assoc(X0) = assoc(X1) )
| ( lin(X0) != lin(X1) ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] : append(lin(X0),cons(mul,lin(X1))) = lin(x2(X0,X1)),
inference(demodulation,[status(thm)],[c_86,c_81,c_82]) ).
tcf(c_6247,plain,
! [X0: $i,X1: $i] : proj22(assoc(x2(X0,X1))) = assoc(X1),
inference(superposition,[status(thm)],[c_80,c_70]) ).
tcf(c_6251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : assoc(x2(X0,X1)) != z(X2,X3),
inference(superposition,[status(thm)],[c_80,c_71]) ).
tcf(c_6252,plain,
! [X0: $i] : cons(x,append(nil,X0)) = append(lin(eX),X0),
inference(superposition,[status(thm)],[c_87,c_82]) ).
tcf(c_6304,plain,
! [X0: $i] : append(lin(eX),X0) = cons(x,X0),
inference(light_normalisation,[status(thm)],[c_6252,c_81]) ).
tcf(c_6305,plain,
! [X0: $i] : cons(x,cons(mul,lin(X0))) = lin(x2(eX,X0)),
inference(superposition,[status(thm)],[c_211,c_6304]) ).
tcf(c_6333,plain,
! [X0: $i,X1: $i] :
( ( z(assoc(X0),assoc(X1)) = assoc(z(X0,X1)) )
| ( X0 != eY ) ),
inference(superposition,[status(thm)],[c_78,c_73]) ).
tcf(c_6418,plain,
! [X0: $i,X1: $i] : cons(x,append(cons(mul,lin(X0)),X1)) = append(lin(x2(eX,X0)),X1),
inference(superposition,[status(thm)],[c_6305,c_82]) ).
tcf(c_6679,plain,
! [X0: $i,X1: $i] : cons(x,cons(mul,append(lin(X0),X1))) = append(lin(x2(eX,X0)),X1),
inference(demodulation,[status(thm)],[c_6418,c_82]) ).
tcf(c_6681,plain,
! [X0: $i,X1: $i] : append(lin(x2(eX,X0)),cons(mul,lin(X1))) = cons(x,cons(mul,lin(x2(X0,X1)))),
inference(superposition,[status(thm)],[c_211,c_6679]) ).
tcf(c_6806,plain,
! [X0: $i] : z(assoc(eY),assoc(X0)) = assoc(z(eY,X0)),
inference(equality_resolution,[status(thm)],[c_6333]) ).
tcf(c_6963,plain,
! [X0: $i,X1: $i,X2: $i] : z(assoc(eY),assoc(z(X0,z(X1,X2)))) = assoc(z(eY,z(z(X0,X1),X2))),
inference(superposition,[status(thm)],[c_79,c_6806]) ).
tcf(c_6982,plain,
! [X0: $i,X1: $i,X2: $i] : assoc(x2(X0,X1)) != assoc(z(eY,X2)),
inference(superposition,[status(thm)],[c_6806,c_6251]) ).
tcf(c_6983,plain,
! [X0: $i,X1: $i,X2: $i] : assoc(z(eY,z(z(X0,X1),X2))) = assoc(z(eY,z(X0,z(X1,X2)))),
inference(demodulation,[status(thm)],[c_6963,c_6806]) ).
tcf(c_11229,plain,
! [X0: $i,X1: $i] : lin(x2(x2(eX,X0),X1)) = lin(x2(eX,x2(X0,X1))),
inference(demodulation,[status(thm)],[c_6681,c_211,c_6305]) ).
tcf(c_11239,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( assoc(x2(x2(eX,X0),X1)) = assoc(X2) )
| ( lin(x2(eX,x2(X0,X1))) != lin(X2) ) ),
inference(superposition,[status(thm)],[c_11229,c_89]) ).
tcf(c_11354,plain,
! [X0: $i,X1: $i] : assoc(x2(x2(eX,X0),X1)) = assoc(x2(eX,x2(X0,X1))),
inference(equality_resolution,[status(thm)],[c_11239]) ).
tcf(c_11608,plain,
! [X0: $i,X1: $i] : proj22(assoc(x2(eX,x2(X0,X1)))) = assoc(X1),
inference(superposition,[status(thm)],[c_11354,c_6247]) ).
tcf(c_12128,plain,
! [X0: $i,X1: $i] : assoc(x2(X0,X1)) = assoc(X1),
inference(demodulation,[status(thm)],[c_11608,c_6247]) ).
tcf(c_12199,plain,
! [X0: $i,X1: $i] : assoc(z(eY,X0)) != assoc(X1),
inference(demodulation,[status(thm)],[c_6982,c_12128]) ).
tcf(c_12253,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_6983,c_12199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX185+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 23:35:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 25.83/6.81 % SZS status Started for theBenchmark.p
% 25.83/6.81 % SZS status Theorem for theBenchmark.p
% 25.83/6.81
% 25.83/6.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 25.83/6.81
% 25.83/6.81 % ------ iProver source info
% 25.83/6.81
% 25.83/6.81 % git: date: 2026-07-19 20:42:38 +0200
% 25.83/6.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 25.83/6.81 % git: non_committed_changes: false
% 25.83/6.81
% 25.83/6.81 % ------ Parsing...
% 25.83/6.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 25.83/6.81
% 25.83/6.81 % ------ Preprocessing... sup_sim: 3 sf_s rm: 0 0s sf_e pe_s pe_e %
% 25.83/6.81
% 25.83/6.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 25.83/6.81
% 25.83/6.81 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 25.83/6.81 % ------ Proving...
% 25.83/6.81 % ------ Problem Properties
% 25.83/6.81
% 25.83/6.81 %
% 25.83/6.81 % clauses 41
% 25.83/6.81 % conjectures 1
% 25.83/6.81 % EPR 16
% 25.83/6.81 % Horn 38
% 25.83/6.81 % unary 37
% 25.83/6.81 % binary 3
% 25.83/6.81 % lits 46
% 25.83/6.81 % lits eq 46
% 25.83/6.81 % fd_pure 0
% 25.83/6.81 % fd_pseudo 0
% 25.83/6.81 % fd_cond 0
% 25.83/6.81 % fd_pseudo_cond 0
% 25.83/6.81 % AC symbols 0
% 25.83/6.81
% 25.83/6.81 % ------ Input Options Time Limit: Unbounded
% 25.83/6.81
% 25.83/6.81
% 25.83/6.81 % ------
% 25.83/6.81 % Current options:
% 25.83/6.81 % ------
% 25.83/6.81
% 25.83/6.81
% 25.83/6.81 %
% 25.83/6.81
% 25.83/6.81 % ------ Proving...
% 25.83/6.81 %
% 25.83/6.81
% 25.83/6.81 % SZS status Theorem for theBenchmark.p
% 25.83/6.81
% 25.83/6.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.83/6.82
% 25.83/6.82
%------------------------------------------------------------------------------