%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG040-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n009.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 02:38:17 PM UTC 2026
% Result : Unsatisfiable 1.04s 1.38s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 74 ( 59 unt; 5 def)
% Number of atoms : 230 ( 61 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 77 ( 41 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 104 ( 0 sgn 104 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f9,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f22,axiom,
! [X2,X0,X1] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_symmetry) ).
fof(f23,negated_conjecture,
sum(b,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_c) ).
fof(f24,negated_conjecture,
product(d,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_plus_a) ).
fof(f25,negated_conjecture,
product(b,a,l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_a) ).
fof(f26,negated_conjecture,
product(c,a,n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_plus_a) ).
fof(f27,negated_conjecture,
~ sum(l,n,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
tcf(c_74,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_79,plain,
! [X0: $i] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X2,X5,X4)
| ~ product(X1,X5,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X6,X2,X5)
| ~ product(X6,X1,X4)
| ~ product(X6,X0,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_94,negated_conjecture,
sum(b,c,d),
inference(cnf_transformation,[],[f23]) ).
tcf(c_95,negated_conjecture,
product(d,a,additive_identity),
inference(cnf_transformation,[],[f24]) ).
tcf(c_96,negated_conjecture,
product(b,a,l),
inference(cnf_transformation,[],[f25]) ).
tcf(c_97,negated_conjecture,
product(c,a,n),
inference(cnf_transformation,[],[f26]) ).
tcf(c_98,negated_conjecture,
~ sum(l,n,additive_identity),
inference(cnf_transformation,[],[f27]) ).
tcf(c_110,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_74]) ).
tcf(c_115,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( add(X2,X5) = X4 )
| ( add(X1,X5) != X3 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_81]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_82]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( multiply(X2,X5) = X4 )
| ( multiply(X1,X5) != X3 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_84]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X0,X5) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X1,X3) != X5 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_86]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X1,X0) = X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_93]) ).
tcf(c_140,plain,
add(b,c) = d,
inference(well_definedness,[status(thm)],[c_94]) ).
tcf(c_141,plain,
multiply(d,a) = additive_identity,
inference(well_definedness,[status(thm)],[c_95]) ).
tcf(c_142,plain,
multiply(b,a) = l,
inference(well_definedness,[status(thm)],[c_96]) ).
tcf(c_143,plain,
multiply(c,a) = n,
inference(well_definedness,[status(thm)],[c_97]) ).
tcf(c_144,plain,
add(l,n) != additive_identity,
inference(well_definedness,[status(thm)],[c_98]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(unflattening,[status(thm)],[c_138]) ).
tcf(c_270,plain,
multiply(a,b) = l,
inference(demodulation,[status(thm)],[c_142,c_268]) ).
tcf(c_271,plain,
multiply(a,c) = n,
inference(demodulation,[status(thm)],[c_143,c_268]) ).
tcf(c_272,plain,
multiply(a,d) = additive_identity,
inference(demodulation,[status(thm)],[c_141,c_268]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_120]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_124]) ).
tcf(c_279,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_118]) ).
tcf(c_281,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_128]) ).
tcf(c_330,definition,
iPr_def_10 = multiply(a,d),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_331,definition,
iPr_def_11 = multiply(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_332,definition,
iPr_def_12 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_333,definition,
iPr_def_13 = add(l,n),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_334,definition,
iPr_def_14 = add(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_335,plain,
iPr_def_10 = additive_identity,
inference(demodulation,[status(thm)],[c_272,c_330]) ).
tcf(c_336,plain,
iPr_def_11 = n,
inference(demodulation,[status(thm)],[c_271,c_331]) ).
tcf(c_337,plain,
iPr_def_12 = l,
inference(demodulation,[status(thm)],[c_270,c_332]) ).
tcf(c_338,plain,
iPr_def_13 != additive_identity,
inference(demodulation,[status(thm)],[c_144,c_333]) ).
tcf(c_339,plain,
iPr_def_14 = d,
inference(demodulation,[status(thm)],[c_140,c_334]) ).
tcf(c_415,plain,
iPr_def_10 != iPr_def_13,
inference(light_normalisation,[status(thm)],[c_338,c_335]) ).
tcf(c_416,plain,
! [X0: $i] : add(iPr_def_10,X0) = X0,
inference(light_normalisation,[status(thm)],[c_110,c_335]) ).
tcf(c_418,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_115,c_335]) ).
tcf(c_421,plain,
multiply(a,iPr_def_14) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_330,c_339]) ).
tcf(c_422,plain,
multiply(iPr_def_14,a) = iPr_def_10,
inference(demodulation,[status(thm)],[c_421,c_268]) ).
tcf(c_423,plain,
add(iPr_def_12,iPr_def_11) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_333,c_336,c_337]) ).
tcf(c_424,plain,
add(iPr_def_11,iPr_def_12) = iPr_def_13,
inference(demodulation,[status(thm)],[c_423,c_273]) ).
tcf(c_770,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(iPr_def_10,X1),
inference(superposition,[status(thm)],[c_418,c_279]) ).
tcf(c_771,plain,
! [X0: $i] : add(b,add(c,X0)) = add(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_334,c_279]) ).
tcf(c_826,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_770,c_416]) ).
tcf(c_831,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(superposition,[status(thm)],[c_273,c_826]) ).
tcf(c_1132,plain,
add(iPr_def_14,additive_inverse(b)) = c,
inference(superposition,[status(thm)],[c_771,c_831]) ).
tcf(c_1174,plain,
add(b,c) = iPr_def_14,
inference(superposition,[status(thm)],[c_1132,c_831]) ).
tcf(c_1440,plain,
! [X0: $i] : multiply(a,add(b,X0)) = add(iPr_def_12,multiply(a,X0)),
inference(superposition,[status(thm)],[c_332,c_281]) ).
tcf(c_1765,plain,
add(iPr_def_12,multiply(a,c)) = multiply(a,iPr_def_14),
inference(superposition,[status(thm)],[c_1174,c_1440]) ).
tcf(c_1780,plain,
add(iPr_def_12,multiply(a,c)) = multiply(iPr_def_14,a),
inference(theory_normalisation,[status(thm)],[c_1765,c_277,c_268,c_279,c_273]) ).
tcf(c_1781,plain,
add(iPr_def_12,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1780,c_331,c_422]) ).
tcf(c_1782,plain,
add(iPr_def_11,iPr_def_12) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_1781,c_277,c_268,c_279,c_273]) ).
tcf(c_1795,plain,
iPr_def_10 = iPr_def_13,
inference(demodulation,[status(thm)],[c_424,c_1782]) ).
tcf(c_1796,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1795,c_415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG040-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 % Computer : n009.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Thu Sep 24 07:55:43 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.46 Running first-order theorem proving
% 0.14/0.47 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
% 0.14/0.48
% 0.14/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.48
% 0.14/0.48 % Detected problem language: tptp
% 0.14/0.50 % Proving...
% 1.04/1.38 % SZS status Started for theBenchmark.p
% 1.04/1.38 % SZS status Unsatisfiable for theBenchmark.p
% 1.04/1.38
% 1.04/1.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.04/1.38
% 1.04/1.38 % ------ iProver source info
% 1.04/1.38
% 1.04/1.38 % git: date: 2026-07-19 20:42:38 +0200
% 1.04/1.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.04/1.38 % git: non_committed_changes: false
% 1.04/1.38
% 1.04/1.38 % ------ Parsing...% successful
% 1.04/1.38
% 1.04/1.38
% 1.04/1.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.04/1.38
% 1.04/1.38 % ------ Preprocessing... sup_sim: 19 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.04/1.38
% 1.04/1.38 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.04/1.38
% 1.04/1.38 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.04/1.38 % ------ Proving...
% 1.04/1.38 % ------ Problem Properties
% 1.04/1.38
% 1.04/1.38 %
% 1.04/1.38 % clauses 21
% 1.04/1.38 % conjectures 0
% 1.04/1.38 % EPR 5
% 1.04/1.38 % Horn 20
% 1.04/1.38 % unary 20
% 1.04/1.38 % binary 1
% 1.04/1.38 % lits 22
% 1.04/1.38 % lits eq 22
% 1.04/1.38 % fd_pure 0
% 1.04/1.38 % fd_pseudo 0
% 1.04/1.38 % fd_cond 1
% 1.04/1.38 % fd_pseudo_cond 0
% 1.04/1.38 % AC symbols 2
% 1.04/1.38
% 1.04/1.38 % ------ Schedule dynamic 5 is on
% 1.04/1.38
% 1.04/1.38 % ------ no conjectures: strip conj schedule
% 1.04/1.38
% 1.04/1.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.04/1.38
% 1.04/1.38
% 1.04/1.38 % ------
% 1.04/1.38 % Current options:
% 1.04/1.38 % ------
% 1.04/1.38
% 1.04/1.38
% 1.04/1.38 %
% 1.04/1.38
% 1.04/1.38 % ------ Proving...
% 1.04/1.38 %
% 1.04/1.38
% 1.04/1.38 % SZS status Unsatisfiable for theBenchmark.p
% 1.04/1.38
% 1.04/1.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.04/1.38
% 1.04/1.38
%------------------------------------------------------------------------------